19th European Symposium on Computer Aided Process Engineering, Volume 26: ESCAPE-19: June 14-17, 2009, Cracow, Poland (Computer Aided Chemical Engineering)

COMPUTER-AIDED CHEMICAL ENGINEERING, 26

19th EUROPEAN SYMPOSIUM ON COMPUTER AIDED PROCESS ENGINEERING Edited by

. Jacek Jezowski Rzeszów University of Technology Al. Powsta´nców Warszawy Rzeszów Poland

and

Jan Thullie Faculty of Chemistry The Silesian University of Technology Poland

Amsterdam – Boston – Heidelberg – London – New York – Oxford Paris – San Diego – San Francisco – Singapore – Sydney – Tokyo

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands Linacre House, Jordan Hill, Oxford OX2 8DP, UK First edition 2009 Copyright © 2009 Elsevier B.V. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN (volume): 978-0-444-53433-0 ISBN (CD): 978-0-444-53441-5 ISSN: 1570-7946 For information on all Elsevier publications visit our web site at books.elsevier.com

Printed and bound in Hungary 09 10 11

10 9 8 7 6 5 4 3 2 1

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Preface This book contains papers presented at the 19th European Symposium on Computer Aided Process Engineering ( ESCAPE-19 ) held in Cracow, Poland from 14th to 17th June 2009. Poland has the privilege to host the Conference for the first time but the Symposia have a long history and well-established tradition. The ESCAPE series started in 1992 at Elsinore, Denmark on a strong foundation of 23 events of the CAPE Working Party of European Federation of Chemical Engineering. The first event was organized in Tutzing, Germany, in 1968. The most recent ESCAPE symposia were organized in Garmisch-Partenkirchen, Germany, 2006, Bucharest, Romania, 2007 and Lyon, France, 2008. The series of ESCAPE symposia serves as a forum for engineers, scientists, researchers, managers and students, who are active in research and application of CAPE. Leading scientists from academia and practitioners from industry took part together with young researchers and PhD students. The works presented were often the mile-stone achievements in a steady progress of CAPE. The papers in the ESCAPE-19 Proceedings are organized in the following themes: product and process design, process control and operation, modelling, simulation, optimisation and process integration, new frontiers in CAPE, CAPE in sustainable development and, finally, energy systems and CAPE. About 350 abstracts were submitted to the conference. Out of them 303 authors were invited to submit an extended abstract (6 pages) and 233 were finally selected for oral or poster presentation. In addition to these contributions several plenary and key-note lectures by highly esteemed scientists and practitioners were invited. The review of abstracts and full version manuscripts were carried out by the members of International Scientific Committee and a group of the invited reviewers. We would like to thank all of them. Their effort was crucial in ensuring a high quality of ESCAPE 19 Symposium. This book is the tenth ESCAPE Symposium Proceedings included in the series on ComputerAided Chemical Engineering. We hope that it will serve as a valuable reference document and will contribute to the progress in computer aided process and product engineering.

Jacek JeĪowski Jan Thullie ESCAPE-19 Co-Chairmen

xxiii

International Scientific Committee Conference Co-chairmen Jacek JeĪowski, Rzeszów University of Technology, Poland Jan Thullie, Silesian University of Technology, Poland

Themes Coordinators Product and Process Design Lorenz T. Biegler, Carnegie Mellon University, USA Rafiqul Gani, Technical University of Denmark, Denmark

Process Control and Operation Johan Grievink, Delft University of Technology, The Nederlands Guenter Wozny, Berlin Institute of Technology, Germany

Modelling, Simulation, Optimisation and Process Integration Wolfgang Marquardt, RWTH Aachen University, Germany Natalia Menshutina, Mendeleyev University of Chemical-Technology, Russia Efstratios N. Pistikopoulos, Imperial College London, UK

New Frontiers in CAPE David Bogle, University College London, UK Andrzej Kraslawski, Lappeenranta University of Technology, Finland

CAPE in Sustainable Development Peter Glaviþ, University of Maribor, Slovenia BoĪenna Kawalec-Pietrenko, Technical University of GdaĔsk, Poland

Energy Systems and CAPE JiĜi Klemeš, University of Pannonia, Hungary Sandro Macchietto, Imperial College London, UK Toshko Zhelev, University of Limerick, Ireland

Members Serban Agachi, Babes Boyai University, Romenia Ana Barbosa-Povoa, Instituto Superior Tecnico, Portugal Bertrand Braunschweig, IFP, France Luis Cisternas, Universidad de Antofagasta, Chile Guido Dünnebier, Bayer Technology Services GmbH, Germany

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International Scientific Committee

Sebastian Engell, TU Dortmund, Germany Antonio Espuña, Technical University of Catalonia, Spain Michael Fairweather, University of Leeds, UK Georg Fieg, Hamburg University of Technology, Germany Christodoulos Floudas, Princeton University, USA Dominic Foo, University of Nottingham Malaysia, Malaysia Ferenc Friedler, University of Pannonia, Hungary Ignacio Grossmann, Carnegie Mellon University, USA Andrzej Górak, Technische Universitaet Dortmund, Germany Georges Heyen, Universite de Liege, Belgium Zdzisław Jaworski, Szczecin University of Technology, Poland Xavier Joulia, Université de Toulouse, France Sten Bay Jorgensen, Technical University of Denmark, Denmark Zdravko Kravanja, University of Maribor, Slovenia Milan Kubicek, Institut of Chemical Technology, Prague Thokozani Majozi, University of Pretoria, South Africa Henrique Matos, Instituto Superior Tecnico, Portugal François Marechal, Ecole Polytechnique Fédérale de Lausanne, Switzerland Claudio Oller Nascimento, Polytechnic School of University of Sao Paulo, Brazil Ka Ng, Hong Kong Univ of Science and Technology, China (Hongkong) Zdzisław Pakowski, Technical University of Lodz, Poland Sauro Pierucci, Politecnico di Milano, Italia Valentin Plesu, University Politehnica of Bucharest, Romania Heinz A. Preisig, Norwegian University of Science and Technology, Norway Luis Puigjaner, Universitat Politecnica de Catalunya, Spain Yu Qian, South China University of Technology, China Gintaras Reklaitis, Purdue University, USA Rajagopalan Srinivasan, National University of Singapore, Singapore Gennadiy Statyukha, National Technical University of Ukraine, Ukraine Andrzej Stankiewicz, Delft University of Technology, The Nederlands Natasha Vaklieva-Bancheva, Bulgarian Academy of Sciences, Bulgaria

Additional reviewers Joaquin Acevedo, Tecnologico de Monterrey, Mexico Cristhian Almeida-Rivera, Unilever Food & Health Research Institute, The Nederlands Harvey Arellano-Garcia, Berlin Institute of Technology, Germany Ton Backx, Eindhoven University of Technology, The Nederlands Paul I. Barton, Massachusetts Institute of Technology, USA George M. Bollas, Massachusetts Institute of Technology, USA Peter Bongers, Unilever Food & Health Research Institute, The Nederlands Neima Brauner, Tel-Aviv University, Israel

International Scientific Committee

Heiko Briesen, Max-Planck-Institute for Dynamics of Complex Technical Systems, Germany Jaime Cerdá, Intec, Argentina Paul Dalby, University College London, UK Loïc d'Anterroches, Céondo Ltd, UK Serge Domenech, LGC – INPT – ENSIACET, France Mario Eden, Auburn University, USA Mahmoud El-Halwagi, Texas A&M University, USA Eric Fraga, University College London, UK Duncan Fraser, University of Cape Town, South Africa Anton Friedl, Vienna University of Technology, Austria Mamdouh Gadalla, University Rovira i Virgili, Spain Michael Georgiadis, University of Western Macedonia, Greece Jacques Gouws, University of Pretoria, South Africa Bernhard Gutsche, Cognis Deutschland GmbH & Co. KG, Denmark Andre de Haan, Eindhoven University of Technology, The Nederlands Istvan Heckl, University of Pannonia, Hungary Tibor Holczinger, University of Pannonia, Hungary C.W Hui, Hong Kong Univ of Sci. & Tech., China (Hongkong) Laureano Jiménez, University Rovira i Virgili, Spain Eugeny Y. Kenig, University of Paderborn, Denmark Tony Kiss, AkzoNobel Chemicals, The Nederlands Antonis Kokossis, University of Surrey, UK Hon Loong Lam, University of Pannonia, Hungary Jean-Marc Le Lann, LGC - INPT – Ensiacet, France Patrick Linke, Texas A&M University at Qatar, Qatar Carlos Mendez, Intec, Argentine Alexander Mitsos, RWTH Aachen University, Germany Michael Modigell, RWTH Aachen University, Germany Eugeniusz Molga, Warsaw University of Technology, Poland Iqbal Mujtaba, University Of Bradford, UK Zoltan K. Nagy, Loughborough University, UK Zorka Novak-Pintaric, University of Maribor, Slovenia Nuno Oliveira, University of Coimbra, Portugal Sunwon Park, Kaist, Korea Alexandra Elena Plesu, University Politehnica of Bucharest, Romania Naveed Ramzan, University of Enginering and Technology, Pakistan Susana Relvas, Instituto Superior Tecnico, Portugal Jens-Uwe Repke, Berlin Institute of Technology, Germany Jan Schoeneberger, Berlin Institute of Technology, Germany Panos Seferlis, Aristotle University of Thessaloniki, Greece Mordechai Shacham, Ben-Gurion University of the Negev, Israel Gurkan Sin, Technical University of Denmark, Denmark Kai Sundmacher, Max-Planck-Institute for Dynamics of Complex Technical Systems, Germany Raymond Tan, De La Salle University-Manila, Philippines

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xxvi

International Scientific Committee

Constantinos Theodoropoulos, The University of Manchester, UK Zoltán Varga, University of Pannonia, Hungary Xue Wang, University of Leeds, UK Werner Witt, Brandenburgicshe Technische Universität, Germany John M. Woodley, Technical University of Denmark, Denmark En Sup Yoon, Seoul National University, Korea

xxx

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National Organising Committee Co-chairmen Jacek JeĪowski , Rzeszów University of Technology, Poland Jan Thullie, Silesian University of Technology, Poland

Scientific Secretary Krzysztof Piotrowski, Silesian University of Technology, Poland

Members Jacek Kocurek, Silesian University of Technology, Poland Andrzej Gierczycki, Silesian University of Technology, Poland Łukasz Kurowski, Silesian University of Technology, Poland Janusz Wójcik, Silesian University of Technology, Poland Jerzy Raczek, Silesian University of Technology, Poland Robert Kubica, Silesian University of Technology, Poland Roman Bochenek, Rzeszów University of Technology, Poland Grzegorz Dzido, Silesian University of Technology, Poland Grzegorz Poplewski, Rzeszów University of Technology, Poland Agata KuĞ, Silesian University of Technology, Poland Magdalena Tuszkiewicz, Silesian University of Technology, Poland Marcin Lemanowicz , Silesian University of Technology, Poland

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1

On the appropriate architecture of the water/wastewater allocation problem in process plants Miguel J. Bagajewicza and Debora C. Faria b a b

University of Oklahoma, 100E. Boyd St, Norman 73019, USA, [email protected] University of Oklahoma, 100E. Boyd St, Norman 73019, USA, [email protected]

Abstract We discuss the definition of the water/wastewater allocation problem as it was originally defined by Takama et al (1980), how this concept was modified and simplified through time, as well as additional issues that are still not properly addressed. We review a few attempts where parts of our view were pointed out and we further investigate the impact that proper modeling has on predictions of freshwater consumption and total annual cost. Keywords: water/wastewater allocation problem, recycle, end-of-pipe treatment

1. Introduction Water allocation problems (WAP) have been extensively studied and several approaches to solve it have been presented. A comprehensive review of methods presented up to 2000 is given by Bagajewicz (2000); additional overviews can be found in few books (Mann and Liu, 1999; Sikdar and El-Halwagi, 2001). In general, the methods can be divided into two big classes: those based on mathematical programming, and those based on graphical, heuristic or algorithmic methods. The most promising class is the one based on mathematical programming, originally proposed by Takama et al. (1980). Mathematical programming has become the procedure of choice, especially because of the inability of graphical, heuristic or algorithmic procedures to effectively provide rigorous solutions to multiple contaminant problems. In addition, objective functions like cost, number of connections, etc. are easier to handle using mathematical programming approaches. Although they were not exhaustively detailed, Takama et al. (1980) included a recycle of the water treated by the wastewater treatment. They also used discharge concentration limits that the involved regeneration processes have to comply. This was ignored by Wang and Smith (1994), the work that gave rise to the “water pinch” method, and by several subsequent papers (Doyle and Smith, 1995; Polley and Polley, 2000; Bagajewicz et al., 2000; Hallale, 2002; Koppol and Bagajewicz, 2003; Prakotpol and Srinophakun, 2004; Teles et al., 2008), including the review made by Bagajewicz (2000). All works that have omitted using discharge concentration limits when including regeneration units implicitly used the assumption that there is an end-of-pipe treatment that is able to bring the concentration of the contaminants down to these discharge limits. Among the works that have omitted the existence of discharge concentration limits, some do not consider any regeneration processes and others have included de possibility of having intermediate regeneration processes. In fact, the

2

M.J. Bagajewicz and D.C. Faria

former perform the optimization of the water-using subsystem, the work by Wang and Smith (1994) (water pinch) being among the first. The authors defined three possibilities of reducing freshwater consumption/wastewater (reuse, regeneration reuse and regeneration recycle) and then solve the problem by first allowing only the first possibility, which is reuse. For the second and third wastewater minimization possibility, Wang and Smith (1994) extend their method to allow regeneration-reuse and recycles. Even though they (and others) considered regeneration processes without considering discharge limits, there is no guarantee that the final stream does not need any further treatment. Thus, an implicit end-of-pipe treatment must exist to assure that the final wastewater is discharged with a concentration lower than the maximum allowed by environmental regulations. Although all these methods do not considered discharge limitations, the ones based on mathematical programming can more easily be adapted to include discharge limits. In the graphical approach used by Wang and Smith (1994) this task may not be simple. Although we are not the first to do it, we argue that if end-of-pipe treatment is included in the model, it should also be available as an option of reuse/recycle. In fact, there is no water system without any kind of regeneration process (even those that were classified as “end-of-pipe”). Thus, all water allocation problems must at least include one treatment unit. This conclusion was not made in previous literature. Many authors, however, have considered discharge concentration limits (Takama et al., 1980; Kuo and Smith, 1998; Gunaratnam et al., 2005; Karuppiah and Grossmann, 2006; Alva-Argáez et al., 2007; Ng et al.,2007a,b; Putra and Amminudin, 2008). In reality, the addition of discharge limits constraint normally assumes all the reuse/recycle opportunities without clearly defining or singling out specifically an end-of-pipe treatment. To consider discharge limits and more than one regeneration unit, Kuo and Smith (1998) adapted the method presented by Wang and Smith (1994). They addressed the issue as an interaction among the water-using subsystem, regeneration subsystem and effluent treatment subsystem. The proposed approach can only handle water-using units with fixed mass load. Later, Ng et al. (2007a, b) presented a new graphical procedure to deal with water-using units with fixed flowrates. The intricacies that arise over this issue have not been thoroughly made clear in previous work. In addition, recently developed mathematical programming modeling techniques have not been used to obtain networks with such recycle. Thus, in this article we discuss the consequences of ignoring the existence of at least an end-of-pipe treatment (and consequently the reuse/recycle of the stream treated by it) and the different architectures the WAP problem models can be based on. We also discuss the addition of another subsystem giving raise to a more comprehensive definition of the water allocation problem. The paper is organized as follows: we first present the problem statement and discuss different superstructures. We then discuss previous work and later present the corresponding mathematical model. Finally, several examples are presented to illustrate the differences.

On the Appropriate Architecture of the Water/Wastewater Allocation Problem in Process Plants

3

2. Water System Architecture We define the problem first: Given a set of water using units, a set of freshwater sources with corresponding contaminant concentrations (some usually zero), potential intermediate regeneration processes and a wastewater end-of-pipe treatment unit, one wants to obtain a water/wastewater-reuse/regeneration network that optimizes a given objective with any discharged water (if any) complying with contaminant discharge limits. The above problem statement has different forms depending on the level of detail of the model and the nature of the objective function. In its simplest form, the most popular objective function is the freshwater consumption with an implicit end-of-pipe treatment and no regeneration: This is one of the problems addressed by the now popular technology called “water pinch” (Wang and Smith, 1994) applied to single component cases. The above definition, which has been used by several researchers, implicitly assumes that the end-of-pipe treatment is able to reduce the contaminants concentrations to their discharge limits, and it does not include specifically the possibility of re-using water from the end-of-pipe treatment, although it does not exclude it. Thus, the simplest form of the problem is a water/wastewater reuse system with an assumed end-of-pipe treatment to adjust water to discharge limits (Figure 1). This allows the decomposition of the problem into two parts: Water using Subsystem and End-of-Pipe treatment. Wang and Smith (1994) and several subsequent articles used this assumption.

Figure 1 – Water/wastewater reuse system with end-of-pipe treatment.

Takama et al. (1980) discussed a typical system used in refineries (Figure 2) in which the two subsystems, water-using subsystem and wastewater treating subsystem, are individually optimized regardless of the interaction introduced by the recycle. It shows a recycle of non-treated water and mix it with the freshwater, a scheme that is not necessarily general enough to cover the concept of reuse as we understand it nowadays. In addition, the recycle of treated water is not taken from the discharge stream, possibly indicating that the concentration of pollutants in this stream does not have to be necessarily the same as in the discharge stream. In turn, they suggest the integration of both systems in a total system without define an end-of-pipe treatment. Instead, they handle the regeneration processes that compose the end-of-pipe treatment individually and add discharge limits to the problem. This is what is called “integrated system” or

M.J. Bagajewicz and D.C. Faria

4

“total water system”. Although their model allows connections from any process (waterusing or treatment units) to any other, the solution presented by them did not show any regeneration reuse/recycle. Despite the early appropriate architecture posed by Takama et al. (1980), Wang and Smith (1994), the paper that revived the field did not include the aforementioned recycle from all existing treatments (specifically the end-of pipe treatment in this case).

Treated Water Non-treated Water

Freshwater

Water Using Subsytem

Wastewater Treatment Subsystem

Discharge

Figure 2 – Independently distributed freshwater and wastewater networks (Adapted from Takama et al., 1980).

Later, Kuo and Smith (1998) have pointed out the importance of the interaction of the three subsystems (water-using system, regeneration system and effluent treatment system) as an improvement of the work presented by Wang and Smith (1994). The later had only considered the interaction between water-using and regeneration systems. In reality, the use of the stream treated by the end-of-pipe treatment starts to play an important role not only from the freshwater consumption point of view, but also in the costs of the whole system. Increasing of freshwater costs, declining of water quality in the available freshwater sources and costs ratio between end-of-pipe treatment and intermediate regeneration processes can influence the trade-offs of recycling or not the stream treated by the end-of-pipe treatment. End-of-pipe treatment recycling can also show enormous advantages when retrofit projects are analyzed. For this case an end-ofpipe treatment already exists and therefore eventually no or very small capital cost is required. Not only the possibility of recycling the stream treated by the end-of-pipe treatment may be an alternative to be analyzed, but also different network structures of the wastewater treatment subsystem may be preferred for technical and/or layout issues. We now discuss some of these possibilities: First, consider a water/wastewater reuse system and a centralized as well as sequential wastewater treatment subsystem with a recycle of water that complies with discharge limits. Another possibility is a centralized but distributed wastewater treatment subsystem. In both cases, the centralization is more than geographical: it includes collecting all wastewaters and mixing them in one single stream before treatment. As an alternative, one can envision a centralized and distributed treatment system in the sense that no mixing of all wastewaters takes place and multiple streams feed it. Finally, one can consider a completely decentralized treatment, which is known as integrated

On the Appropriate Architecture of the Water/Wastewater Allocation Problem in Process Plants

5

system (or total water system). We note that allowing flows from any treatment unit in the previous case to be recycled is equivalent to the integrated system. In the limit, the integrated system may become a zero-liquid discharge cycle. These are extensions of the classification proposed by Bagajewicz (2000). Indeed, several researchers have included a regeneration step aiming at reusing the water, but still assuming that the end-of-pipe treatment is present to render a stream with pollutants concentrations below discharge limits. In most cases, this is assumed and not included in the model as no recycle of the stream treated by the end-of-pipe treatment is added. Thus, definitions of the problem are related to the configuration of each subsystem, but also they can be related to its boundaries. Without loss of generality, the evolution of the water allocation problem is presented in Figure 3. This figure shows the different definition of the water allocation problem related to the boundary assumed for the system. Each of the subsystems can exhibit the different options of reuse/recycle previously discussed. An additional structure that has not been investigated yet can generate further trade-offs in the water allocation problem. Although all the definitions of the problem state a set of freshwater sources, the issue of having more than one freshwater quality sources with different costs associated has not been widely studied. In fact, we can define these different freshwater qualities as part of another subsystem: the water pretreatment subsystem. Figure 3c exemplifies the suggested new water allocation problem structure that should be solved to completely include all the possibilities of water integration. As in the wastewater treatment subsystem, both capital and operating cost are associated to the existence and capacity of water treatments that determine the available capacity for each freshwater source. One of the reasons of omitting this subsystem is the fact that such analysis only becomes relevant when cost is analyzed. Otherwise, when freshwater consumption is the target, the source with highest quality (that is, lowest contaminant concentration) is the preferred one and this issue becomes irrelevant. It is also important to note here that the different freshwater sources are not only competing with each other, but more important, they are competing with water reuse and/or recycles from intermediate regeneration processes. In fact, the idea of complete water integration system is to break the boundaries of the subsystems and make use of all available regeneration processes, including the ones available in the water pre-treatment system. We discuss several instances of articles that have discussed some of the aforementioned architectures, explicitly or implicitly, next. We later present the model and we show some examples of grassroots and retrofit cases where the use of an appropriate architecture makes a big difference.

M.J. Bagajewicz and D.C. Faria

6

Figure 3 – Evolution of water allocation problem (a – Optimization of water-using subsystem; b – Integrated system; c – Complete water integration).

3. The Non-linear Model The non-liner model to solve the water allocation problem is given by: Water balance at the water-using units

¦ FWU

w,u

w

+

¦ FUU

u *,u

+

u*

¦ FRU

r ,u

r

=

¦ FUS

u,s

s

+

¦ FUU

u ,u *

u*

+

¦ FUR

u ,r

∀u (1)

r

where FWU w ,u is the flowrate from freshwater source w to the unit u, F U U u *, u is the flowrates between units u* and u, F R U r , u is the flowrate from regeneration process r to unit u, FUS u *, s is the flowrate from unit u to sink s and FU Ru *, r is the flowrate from unit u to regeneration process r. Water balance at the regeneration processes

¦ FUR

u,r

u

+

¦ FRR

r *, r

r*

=

¦ FRU u

r ,u

+

¦ FRR

r ,r*

r*

+

¦ FRS s

r ,s

∀r

(2)

On the Appropriate Architecture of the Water/Wastewater Allocation Problem in Process Plants

7

where FRR r *, r is the flowrate from regeneration process r* to regeneration process r and F R S r , s is the flowrate from regeneration process r to sink s. Contaminant balance at the water-using units

¦ ( CW

w, c

w

(

)

(

)

out FWw ,u ) + ¦ FUU u *,u , c Cuout *, c + ¦ FRU r ,u , c CRr , c + Δ M u , c

(

u*

)

(

r

)

(

out out = ¦ FUU u ,u *, c Cuout , c + ¦ FUS u , s , c Cu , c + ¦ FURu , r , c Cu , c u*

s

r

)

∀u , c

(3)

where C W w , c is concentration of contaminant c in the freshwater source w, Δ M u , c is the mass load of contaminant c extracted in unit u, Cuout,c is the outlet concentration of contaminant c in unit u, and CRrout , c is the outlet concentration of the not treated contaminant c in regeneration r . Maximum inlet concentration at the water-using units

¦ ( CW

w ,c

w

FW w , u ) +

¦ ( FUU

where C u.

) ¦ ( FRU

C uout * ,c +

u*

in, max § ≤ C u,c ¨ ©

in, max u,c

u *, u , c

¦

r ,u , c

r

FUW w , u +

¦

FUU u *, u +

u*

w

¦ r

CR rout ,c

)

· FRU r , u ¸ ¹

(4) ∀u, c

is the maximum allowed concentration of contaminant c at the inlet of unit

Maximum outlet concentration at the water-using units out, max Cuout ∀u , c * ,c ≤ Cu,c

(5)

out, max where C u,c is the maximum allowed concentration of contaminant c at the outlet of unit u.

Capacity of the regeneration processes FRr =

¦ FUR + ¦ FRR u, r

u

r *, r

∀r

(6)

r*

where FRr is capacity of regeneration process r. Contaminant balance at the regeneration processes F R r , c C R rin, c =

¦ ( FU R u

u ,r ,c

) ¦ ( FR R

C uout + ,c

r *, r , c

C R rout *, c

r*

in out CRrout , c = CRr ,c (1 − XCRr ,c ) + CRFr ,c XCRr ,c

∀r, c

)

∀r, c

(7) (8)

where CRrin, c is the concentration of contaminant c at the inlet of regeneration process r,

CRFrout , c is the outlet concentration of contaminant c in regeneration process r and X C R r ,c

is a binary parameter that indicates if contaminant c is treated by regeneration

M.J. Bagajewicz and D.C. Faria

8

process r. We assume that CRFrout , c , the concentration of the treated contaminant is known and constant. Maximum allowed discharge concentration

¦ ( FUS

u , s ,c

) ¦ ( FRS

out Cu,c +

u

r , s ,c

r

out discharge , max § CRr,c ≤ C s,c ¨ ©

)

¦ FUS u

u,s

+

¦ FRS r

r ,s

· ¸ ¹

∀s , c (9)

discharge , max where Cs,c is the maximum allowed concentration at sink s.

Minimum flowrates It is well known that many solutions of the water problem may include small flowrates that are impractical. To avoid these we use the following constraints FWU w,u ≥ FWU wMin ∀w, u ,u YWU w,u

(10)

FUUu,u* ≥ FUUuMin ,u* YUUu ,u* ∀u, u *

(11)

FUSu, s ≥ FUSuMin ∀u, s , s YUSu , s

(12)

FURu ,r ≥ FUR

Min u ,r

FRUr,u ≥ FRU

Min r ,u

YURu,r ∀u, r

YRUr,u ∀r, u

(13) (14)

FRRr , r* ≥ FRRrMin , r * YRRr , r * ∀r , r *

(15)

FRSr , s ≥ FRSrMin ∀r , s , s YRS r , s

(16)

which uses a set of binary variables ( YWUw,u , YUUu,u* , YUS u , s , YURu , r , YRU r ,u , YRRr , r* and YRS r , s ) that are equal to one when the corresponding flowrate is different from zero and zero otherwise. Maximum flowrates To ensure that the connections do not surpass maximum values, we use the following constraints:

FWUw,u ≤ FWUwMax ,u YWUw,u ∀w, u FUUu,u* ≤ FUUuMax ,u* YUUu,u* ∀u, u *

(17) (18)

FUSu,s ≤ FUSuMax ,s YUSu,s ∀u, s

(19)

FURu,r ≤ FURuMax ∀u, r , r YURu , r

(20)

FRUr ,u ≤ FRUrMax ,u YRUr ,u ∀r, u

(21)

On the Appropriate Architecture of the Water/Wastewater Allocation Problem in Process Plants

9

FRRr ,r* ≤ FRRrMax , r * YRRr , r * ∀r, r *

(22)

FRSr ,s ≤ FRSrMax , s YRSr , s ∀r, s

(23)

Objective functions Minimum freshwater consumption: Min

¦¦ FWU w

(24)

w,u

u

Minimum total annual cost: ª Max « OP «¬

º § § ·· ¨¨ ¦¦ α w FWU w, m + ¦ OPN r ¨ ¦ FUN m , r + ¦ FNN r *, r ¸ ¸¸ − af FCI » »¼ r r* © m ¹¹ © w m

(

)

(25)

where OPN r are the operational cost of the regeneration processes, FUNm,r are the flowrates between the water using units and the regeneration process r and FNNr*,r are the flowrates between two regeneration processes. OP is the hours of operation per year. The last term is the annualized capital cost, where FCI is the fixed capital cost and af is any factor that annualizes the capital cost (usually 1/N, where N is the number of years of depreciation). The fixed capital of investment is calculated using the sum of the piping costs and the new regeneration units costs as follows: § YWU w, m ICWU w, m + (YUN m,r ICUN m, r + YNU m ICNU m ) · ¨ w∈W ¸ r∈R FCI = ¨ ¸ YUU m, m* ICUU m, m* + YUSm ICUSm m∈M ¨ + ¸ © m*≠ m, m*∈M ¹ § · 0.7 + ¨ YNN r , r * ICNN r ,r * + YNSr ICNSr + ICN r ( RegCapr ) + YNSr ICNSr ¸ ¨ ¸ r∈R © r *≠ r ; r *∈R ¹

¦

¦

¦

¦

¦ ¦

(26)

All the above equations need to be tailored to the specifics of each system: 1 - In the case of the system of a centralized sequential treatment system with fixed structure, we set FUS u , s to zero and we consider only one treatment with all fixed outlet concentrations, which can be the called end-of-pipe treatment. Thus, equations (7) and (8) are not necessary and CRrout , c can be substitute by

CRFrout , c , which is a parameter. When recycle is not allowed, F R U r , u is also set to zero. 2 - In the case in which the treatment is centralized but distributed, the wastewater treatment system can be individually optimized. In fact, for this system, the water using subsystem could be first optimized and then the treatment subsystem is

M.J. Bagajewicz and D.C. Faria

10

optimized using the output of the water subsystem as input of the treatment subsystem. However a better procedure would be to individually optimize both systems while a connection between them still exist. To achieve that, we introduce a fictitious unit uf. This unit is actually a mixer and have all ΔM u f ,c =0. The connection between the two system is done allowing only the fictitious unit to send water/wastewater to the regeneration processes: FUSu , s = 0 ∀u, s, FURu,r = 0 ∀u ≠ u f , r . In addition, the distributed treatment system has also to be individually optimized and may render concentrations that are smaller than the discharge limits. Thus, we also introduce a fictitious regeneration unit rT with all XCRr , c =0 (no treatment) and we then make T

Max r,s

FRS

= 0 ∀r ≠ rT , s as well as FRUrMax ,u = 0 ∀r ≠ rT , u

. 3 - In the case of decentralized system without regeneration reuse/recycle, we keep the concepts presented for the centralized distributed system, but the fictitious unit is no longer needed. On the other hand, the fictitious regeneration is still needed. In the case of an integrated system, we keep all our equations.

4. Illustrations To illustrate our point of view we first present a single contaminant case, which was originally solved as a water-using unit subsystem problem (no regeneration processes and consequently no discharge limits). With this example we show that freshwater consumption can be reduced if the recycle of the end-of-pipe treatment is allowed. Then a lager multiple contaminant problem is analyzed. This problem was originally solved without discharge limits (but allowing intermediate regeneration processes). With this example we present networks that have different arrangements of the wastewater treatment subsystem and show that the recycle of the stream treated by the end-of-pipe treatment can also reduce costs. In a third example, we return to a case of single contaminant and show the impact of considering the freshwater treatment subsystem. 4.1. Example 1 This is a single contaminant network adapted from Wang and Smith (1994), which was solved by them through pinch analysis. The limiting process data for this problem are shown in Table 1 and it has a freshwater consumption without reuse (conventional network configuration) of 112.5 ton/hr.

On the Appropriate Architecture of the Water/Wastewater Allocation Problem in Process Plants

11

Table 1 - Limiting data for Example 2. Process Number

Mass load of contaminant

Cin (ppm)

Cout (ppm)

1

2 kg/hr

0

100

2

5 kg/hr

50

100

3

30 kg/hr

50

800

4

4 kg/hr

400

800

When the end-o-pipe recycling is not allowed, the freshwater consumption can reach a minimum of 90 ton/hr. With the recycle (assuming an end-of-pipe exit concentration of 5 ppm), the minimum consumption is 20 ton/hr. This could be calculated using the “water-pinch” graphical method. However, here we would like to further analyze cost and thus mathematical programming seems to be more appropriate. Freshwater is assumed to be Įi($/ton)=0.3 and the system operates OP(hours/year)=8600. There is one freshwater source free of contaminants and the end-of-pipe treatment has an outlet concentration of 5 ppm, which is the maximum concentration allowed for disposal. The operating cost of the end of pipe treatment is OPN r ($ / ton ) = 1.0067 and the investment cost is ICN r ($ / ton 0.7 ) = 19,400. The capital costs with connections are presented in Table 2. Table 2 - Capital costs of the connections. Unit 1

Unit 2

Unit 3

Unit 4

End-of-pipe treatment

FW

$39,000

$76,000

$47,000

$92,000

-

Unit 1

-

$150,000

$110,000

$45,000

$83,000

Unit 2

$50,000

-

$134,000

$40,000

$102,500

Unit 3

$180,000

$35,000

-

$42,000

$98,000

Unit 4

$163,000

$130,000

$90,000

-

$124,000

EoPT

$83,000

$102,500

$98,000

$124,000

-

We first analyze the grassroots design case. The network with minimum total annual cost (TAC) without allowing the recycle of the stream treated by the end-of-pipe treatment is presented in Figure 4. This network has a total annual cost of $1,105,352.

Figure 4–Example 1 -End-of-pipe recycling not allowed – Minimum TAC at minimum consumption.

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M.J. Bagajewicz and D.C. Faria

Allowing the option of recycle the stream treated by the end-of-pipe treatment reduces the minimum freshwater consumption to 20 ton/hr. This represents reduction of approximately 78%, with is very significant. Figure 5 shows the minimum TAC network for the grassroots when end-of-pipe recycling is allowed, which costs $826,091.

Figure 5 –Example 1 - End-of-pipe recycling allowed – Minimum TAC at minimum consumption.

4.2. Example 2 We consider the refinery case presented by Koppol et al. (2003). This example has four key contaminants (salts, H2S, Organics and ammonia) and six water-using units. The limiting data of the water-using units are shown in Table 3. This network without reuse (conventional network) consumes 144.8 ton/hr of freshwater. Unlike the original problem, the following discharge limits are included I this problem: 15ppm for salts, 5ppm for H2S, 45ppm for organics and 20ppm for ammonia. It is also considered the existing end-of-pipe treatment is able to reduce the contaminant to these discharge limits (what is the assumption used when the end-ofpipe treatment is not explicitly included in the model) and no concentration limit is imposed at its inlet. Some of the different cases of recycle previously described are discussed in this example: First we analyze the network without the addition of any regeneration processes; Then, the addition of regeneration processes is allowed and the different structures are analyzed (centralized systems and total water system). End-of-pipe treatment recycling and not recycling options are analyzed for all the aforementioned cases.

4.2.1. No additional regeneration process In this case only the water-using units and the conventional end-of-pipe treatment are assumed. The minimum freshwater consumption achieved when end-of-pipe recycling is not allowed is 119.33 ton/hr. The minimum total annual cost (TAC) is found to be $2,291,654, which is also a network that operates at the minimum freshwater consumption. This solution is presented in Figure 6.

On the Appropriate Architecture of the Water/Wastewater Allocation Problem in Process Plants

13

Table 3 – Limiting data of Example 4. Process

1 - CausticTreating

2 - Distillation

3 – Amine Sweetening

4 - Merox-I Sweetening

5 - Hydrotreating

6 – Desalting

Contaminant Salts Organics H2S Ammonia Salts Organics H2S Ammonia Salts Organics H2S Ammonia Salts Organics H2S Ammonia Salts Organics H2S Ammonia Salts Organics H2S Ammonia

Mass Load (kg/hr) 0.18 1.2 0.75 0.1 3.61 100 0.25 0.8 0.6 30 1.5 1 2 60 0.8 1 3.8 45 1.1 2 120 480 1.5 0

Cin,max (ppm) 300 50 5000 1500 10 1 0 0 10 1 0 0 100 200 50 1000 85 200 300 200 1000 1000 150 200

Cout,max (ppm) 500 500 11000 3000 200 4000 500 1000 1000 3500 2000 3500 400 6000 2000 3500 350 1800 6500 1000 9500 6500 450 400

Figure 6 –Example 2.1 -Only end-of-pipe treatment, End-of-pipe recycling not allowedMinimum Consumption

When recycling from end-of-pipe treatment is allowed, the minimum consumption can reach 33.57 ton/hr, which is approximately 72% lower than the earlier solution. The minimum TAC ($2,062,799) for this case is also found at the minimum freshwater consumption. Figure 7 shows the network corresponding to this solution. Note that this solution does not need any additional regeneration processes. However the end-of-pipe

M.J. Bagajewicz and D.C. Faria

14

capacity is significantly increased. Thus, cost analysis may favor the addition of intermediate regeneration process that specifically treat one (or more) contaminant(s) and consequently require lower capacities. This issue is analyzed next.

Figure 7 – Example 2.1 - Only end-of-pipe treatment - End-of-pipe recycling allowed -Minimum Consumption

4.2.2. Additional regeneration processes The example previously presented is now solved for a case in which there are other three regeneration processes available: Reverse osmosis, which reduces salts to 20 ppm; API separator followed by ACA, which reduces organics to 50 ppm; and, Chevron wastewater treatment, which reduces H2S to 5 ppm and ammonia to 30 ppm. First we present solutions for a centralized sequential wastewater treatment system. For both solutions (allowing and not allowing the end-of-pipe recycling) the minimum freshwater consumption is 33.57 ton/hr. Besides minimum freshwater consumption, total annualized cost can be further analyzed as a competitive advantage. Freshwater cost is $0.32/ton and the plant operates 8600 hours/year. The end-of-pipe treatment has a capital cost of $30,000/ton0.7 and an operating cost of $1.80/ton. The costs of the potential additional regeneration processes are presented in Table 4. To cost with connections are presented in Table 5. Here only the costs from the units to the centralized system are considered. The costs with connections between regeneration processes are ignored. The minimum TAC obtained for the case in which the end-of-pipe recycling is allowed is presented in Figure 8. Note that the minimum TAC for this case happens at a freshwater consumption other than the minimum (38.983 ton/h). This network has a total annual cost of $1,351,250 and uses two of the three available additional regeneration processes. Table 4 – Costs of the potential regeneration processes. Regeneration Process API separator followed by ACA Reverse osmosis Chevron wastewater treatment

Capital Cost ($/ton0.7)

Operating Cost ($/ton)

$25,000 $20,100 $16,800

0.12 0.56 1.00

On the Appropriate Architecture of the Water/Wastewater Allocation Problem in Process Plants

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Table 5: Capital costs of the connections. $(x103)

U1

W1

23

50

18

63

16

25

-

-

U1

-

50

110

45

70

42

53

53

U2

50

-

34

40

11

35

51

51

U3

110

34

-

42

60

18

62

62

U4

45

40

42

-

23

34

78

78

U5

70

11

60

23

-

28

58

58

U6

42

35

18

34

28

-

22

22

Centralized System

53

51

62

78

58

22

-

-

EOP

53

51

62

78

58

22

-

-

U2

U3

U4

U5

U6

Centralized System

EOP

Figure 8 –Example 2.2 -centralized sequential scheme when end-of-pipe recycling is not allowed – minimum TAC.

The minimum total annual cost obtained using the centralized sequantial scheme when end-of-pipe recycling is allowed is presented in Figure 9. This network has a total annual cost of $1,292,431 and operates at the minimum freshwater consumption. Note that, allowing the end-of-pipe recylcing, only API separator is needed as additional regeneration process. The centralized distributed system is analyzed next. This scheme corresponds to the one presented in Figure 4. The solution for minimum TAC without recycle of the end-ofpipe treatment is presented in Figure 10. Not that again the minimum TAC for this case does not happen at the minimum freshwater consumption of the system. This network also operates at 38.983 ton/h and has a TAC of $1,330,124. Like the previous case, the suggested network has two regeneration processes. The major difference is due to the distributed system that allows different flowrates to be treated by the different regeneration processes.

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M.J. Bagajewicz and D.C. Faria

Figure 9–Example 2.2 - Centralized sequential scheme -End-of-pipe recycling is allowed.

Figure 10 –Example 2.2 -Centralized distributed scheme -End-of-pipe recycling is not allowed – Minimum TAC.

When end-of-pipe recycling is allowed, the minimum TAC is found at the minimum consumption. This network is the same as the one found when centralized sequential system was analyzed (Figure 9). 4.2.3. Integrated system (or Total water system) Now the integrated system is considered. The optimum solution for both cases, allowing and not allowing the recycle of the stream treated by the end-of-pipe treatment, is able to reach the minimum freshwater consumption of 33.571 ton/hr. The optimum network without end-of-pipe treatment recycling (Figure 11) has a total annual cost of $1,093,018 and a freshwater consumption of 38.876 ton/hr, which is higher than the minimum possible. Once again, forbidding the recycle of the stream treated by the end-of-pipe treatment requires two of the three regeneration processes available. When end-of-pipe recycling is allowed in the total water system scheme, the minimum total annualized cost can reach $1,065,449. This solution (Figure 12) is referred to a network that operates at the minimum freshwater consumption of the system (33.571 ton/hr). Different from the previous cases that handle end-of-pipe treatment recycling, this network has two regeneration processes in which different flowrates are treated.

On the Appropriate Architecture of the Water/Wastewater Allocation Problem in Process Plants

17

Figure 11 –Example 2.3 - End-of-pipe recycling is not allowed – Minimum TAC.

Figure 12 – Example 2.3 - End-of-pipe recycling allowed – Minimum TAC.

4.3. Example 3 In this example we show the simplest form of the suggested complete water integration system. We use a single contaminant problem to illustrate and assume that the water pre-treatment subsystem cannot receive water from the other two subsystems. The limiting data is presented in Table 6. Note that unit two has a maximum outlet concentration of 20ppm and the end-of-pipe treatment has an outlet concentration of 25ppm, which coincides with the discharge limit. We used the same capital and operating cost of the end-of-pipe treatment as well as connection costs of example 1.

M.J. Bagajewicz and D.C. Faria

18

Table 6 - Limiting data for Example 2. Process Number

Mass load of contaminant

Cin (ppm)

Cout (ppm)

1

2 kg/hr

0

100

2

5 kg/hr

20

100

3

30 kg/hr

50

800

4

4 kg/hr

400

800

Two different qualities of freshwater are available at different costs. At the moment we only assume the pre-treatment subsystem as a sequential system that does not necessarily need to treat all freshwater to the highest quality. This scheme is presented in Figure 13.

Figure 13 – Water pre-treatment subsystem.

Note that we also do not consider the possibility of recycling water from the waterusing subsystem and/or wastewater treatment subsystem to the water pre-treatment subsystem. Although these possibilities may offer important advantages, this is not analyzed in this paper and will be detailed investigated in a future work. We assume that the pre-treatment 1 can bring the freshwater down to 10ppm and pretreatment 2 can further treat it down to 0ppm. Pre-treatment 1 has an operating cost of $0.30/ton and a capital cost of $8,500/ton0.7. The operating cost of pre-treatment 2 is $0.50/ton and the capital cost is $10,500/ton0.7. Figure 14 shows the solution found when the complete water integration system scheme is applied and total annual cost is minimized. Recycles from the water using units to the water pre-treatment units is not allowed. Note that both types of freshwater are used and that freshwater treated by only pre-treatment 1 is mixed with the recycle of the end-of-pie treatment before it feeds unit 2. This network has a TAC of $1,258,480.

Figure 14 – Example 3 - Complete water integration system scheme – Recycle of end-of-pipe treatment allowed (WPT: Water pre-treatment process).

On the Appropriate Architecture of the Water/Wastewater Allocation Problem in Process Plants

19

If the same problem is solved considering only freshwater 2 (that is, solved as an integrated system), the minimum TAC found was $1,289,870. This network is presented in Figure 14. The network found in this case only differs from the previous one exactly in the water pre-treatment subsystem. This is an indication of the importance of this issue on the water allocation problem. Moreover, if one looks at this problem from the freshwater consumption point of view, the solution presented in Figure 15 is better than the one in Figure 14. However, in Figure 15 the overall cost of the water pre-treatment system is higher the one in Figure 14. This new trade-off created by the addition of the water pre-treatment subsystem is one of the reasons why the complete water integration system become very important when costs are analyzed.

Figure 15 – Example 3 - Integrated system scheme - Recycle of end-of-pipe treatment allowed (WPT: Water pre-treatment process).

We also investigate the previous cases forbidding the recycle of the end-of-pipe treatment. Figure 16 shows the solution found when the complete water integration system scheme is used. This network has a total annual cost of $1,318,436. For the integrated system scheme case, the optimum network found has a TAC of $1,536,684 and consumes 90ton/h of freshwater. This network has the same structure presented in example 1 (Figure 4).

Figure 16 – Example 3 -Complete water integration system scheme – Recycle of end-of-pipe treatment not allowed (WPT: Water pre-treatment process).

5. Remarks We have discussed some of the different structures used to model the water allocation problem. These structures vary with the different assumption used in each of the subsystems as well as with the recycles that are allowed. We have shown through examples that different structural choices can make significant changes. In essence, we conclude that when the proper architecture is used, i.e. all recycles among the originally proposed subsystems are allowed and the treatment systems are distributed (not sequential), then the boundaries among these subsystems can be erased, reducing the problem to one big superstructure where all connections are allowed. This is the only route to achieve zero liquid discharge cycles.

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References Alva-Argáez, A., Kokossis, A.C. and Smith, R. (2007). A conceptual decomposition of MINLP models for the design of water-using systems. International Journal of Environment and Pollution, 29, 177-105. Bagajewicz, M.J. (2000). A review of recent design procedures for water networks in refineries and process plants. Computer and Chemical Engineering, 24, 2093. Bagajewicz, M. J., Rivas, M. And Savelski, M. J. (2000). A robust method to obtain optimal and sub-optimal design and retrofit solutions of water utilization systems with multiple contaminants. Computer and Chemical Engineering, 24, 1461-1466. Doyle, S. J. and Smith, R. (1997). Targeting water reuse with multiple contaminants. Process Safety and Environmental Protection, 75, 181-189. Guanaratnam, M., Alva-Argáez, A., Kokossis, J., Kim, K. and Smith, R. Automated design of total water system. (2005). Ind. Eng. Chem. Res, 44, 588-599. Hallale N (2002). A new graphical targeting method for water minimization. Adv Env Res, 6, 377–390. Karuppiah, R., Grossmann, I.E. (2006). Global optimization for the synthesis of integrated water systems in chemical processes. Computers and Chemical Engineering, 30, 650-673. Koppol, A. P. R., Bagajewicz, J.M., Dericks, B. J. and Savelski, M. J. (2003). On zero water discharge solutions in process industry. Advances in Environmental Research, 8, 151-171. Mann, J. G. and Liu, Y. A. (1999). Industrial water reuse and wastewater minimization. New York: McGraw Hill. Ng, D.K.S., Foo, D.C.Y. and Tan, R.R. (2007a). Targeting for Total Water Network. 1. Waste Stream Identification. Industrial and Engineering Chemistry Research, 46, 9107-9113. Ng, D.K.S., Foo, D.C.Y. and Tan, R.R. (2007b). Targeting for Total Water Network. 2. Waste Treatment Targeting and Interactions with Water System Elements. Industrial and Engineering Chemistry Research, 46, 9114-9125. Polley, G.T. and Polley,H.L. (2000). Design better water networks. Chemical Engineering Progress, 96, 47. Prakotpol, D. and Srinophakun, T. (2004). GAPinch: genetic algorithm toolbox for water pinch technology. Chemical Engineering and Processing, 43 (2), 203-217. Putra, Z.A., Amminudin, K. (2008). Two-step optimization approach for design of a total water system. Ind. Eng. Chem. Res., 47, 6045-6054. Sikdar and El-Halwagi, (2001). Process Design Tools for the Enviroment. Taylor & Francis. Takama, N., Kuriyama, T., Shiroko, K. and Umeda, T. (1980). Optimal Water Allocation in a Petroleum Refinery. Computers and Chemical Engineering, 4, 251. Teles, J., Castro, P. M. And Novais, A. Q. (2008). LP-based solution strategies for the optimal design of industrial water networks with multiple contaminants. Chemical Engineering Science, 63, 367 – 394. Wang, Y. P. and Smith, R. (1994). Wastewater minimization. Chemical Engineering Science, 49 (7), 981 – 1006.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Perspectives of Application of Computer Aided Process Engineering Tools in Clinical Medicine Eugene J. Kucharz Department of Internal Medicine and Rheumatology,Medical University of Silesia, Katowice, Poland

Introduction Computers are commonly applied in a range of fields of contemporary human activity, including clinical medicine. Effectiveness of computer application depends on a number of factors of technological, social, psychological, financial and other nature, especially related to the specific features of the field of the application. The present study was designed to evaluate the possible and predictable perspectives of application of computers in clinical medicine. The assessment is based on specification of intrinsic features of clinical medicine. These characteristics may limit application or may indicate new areas or forms of further investigations on computer applications to clinical medicine. They also describe differences in characteristic pattern between medical and industrial application of computers. The next step of investigation is classification of areas of computer application in clinical medicine. The classification may be a base for listing potential subjects of research activity, and will facilitate the mutual understanding of physicians and computer experts. It will also reveal educational needs of both sides. Determination of detailed list of needs and opportunities is the best way for mutual recognition of fields of research interest with possible practical applications. Evaluation of medical problems that can be solved with assistance of computer engineering is more that simple application of computer science to clinical practice. It may be beneficial for both sides as well. Medicine recognizes and modifies a very special part of human nature, the human health. Human health is considered as health of individuals as well as health of the population. Better understanding of these problems that are almost perfectly regulated by the evolutiondeveloped complex mechanisms may be a model for technological systems. Creation of such computer tools as the Artificial Neuronal Network is an example of application of nature-imitating systems in the computer technology.

1. The typical characteristics of clinical medicine Clinical medicine is a professional knowledge focusing on prevention, diagnostics and therapy of diseases of humans. There are several specific intrinsic features characterizing clinical medicine. They include: (a) unique nature of every patient, both in terms of unique human nature (psychological) and in terms of biological nature (inherited genetic material, features resulted from influence of the environment), (b) limitation of physician action due to respect of the human nature of the object of the activity, and limitation in the methods used by the physician, (c) lack of adequate data for majority of clinical situations, (d) non-specificity of majority of data referring to clinical situations. a) It is clear that each patient is the unique human being in terms of biological as well as psychological nature. On the hand, diagnostics and therapy are based on probability

22

E.J. Kucharz

modeling that is dynamic collection of data (from patient’s history, physical examination, laboratory tests, imaging investigations) resulting or aiming to classify the individual unique patient within frames of known of medical nosological units, i.e. specific diseases. The higher level of probability that the individual patient is classified to proper nosological unit the better correctness of diagnosis is achieved. It is directly related to proper treatment and determination of prognosis. In general, the system of diagnostics due to natural variability of human beings is less efficient than standardized procedures used in technology. b) The procedures apply in medicine are limited with respect to human being as the person. Their application requires keeping to ethical rules and obeying the law. Application of almost all medical procedures requires the patient’s previous informed consent and the patient has right to refuse the best diagnostic or therapeutic method due to his preferences or moral values. The old medical rule regulating all forms of physician’s activity towards the patient “first do not harm” must be considered as an important principle. In practice, it distinguishes clinical medicine from majority of industrial and technological activities that are as well human-oriented and ethical forms of creativity but deal with inanimate matter. c) A limited number of clinical situations have been investigated according to scientific standards. It applies almost exclusively to evaluation of new drugs, other therapeutic methods, and a few diagnostic tools. In everyday physician practice, most of the patients produce clinical problems that have not been adequately investigated. The most common example is coexistence of two or more disorders in the same patient. Almost all research dealt with a single disease and has been carried out on highly selected groups of patients. Physician has to transfer those “pure” results to significantly more complex clinical practice situations. d) Majority of parameters that are determined by physician have low level of precision. It is resulted from the nature of these parameters (e.g. pain, stress, anxiety, depression, mood cannot me measured with medical equipment) or several parameters that can be measured with technological devices are determined physically (i.e. with hands and senses of physician only) because the more accurate measurement will not provide any applicable results affecting on the physician’s diagnostic or therapeutic decision (e.g. determination of cutaneous elasticity or perspiration, characteristic of cough, color of the skin, properties of the discharge fluids, etc.). There is also other important factor responsible for difficulties in application of computers in clinical medicine. It should be taken into consideration that majority of physicians (especially those who are engaged into clinical practice) have little education in basic sciences, especially in mathematics. Medical education is oriented towards natural sciences (medical biology) and behavioral sciences (psychology). Lack of understanding of problems that are basic for computer applications and sometimes reluctance of physicians towards theoretical problems of sciences may create difficulties in mutual cooperation or at least indicate for the need of further education.

2. Medicine: learning and art. Evidence-based medicine As mentioned above, majority of practical clinical problems that physician are dealing with in everyday practice have not been properly evaluated according to

Perspectives of Application of Computer Aided Process Engineering Tools in Clinical Medicine

23

standards of scientific research. It is caused by a complex of medical problems and a very high number of variables, including the natural diversity of human beings. Of course, the medical knowledge that accumulated through centuries provided several more or less detailed indications and rules for physician’s work but in most of the situations physician have to make an individual synthesis of medical knowledge applicable to the individual patient. The most common example is the patient receiving medication for a few chronic diseases. There is no scientifically proven data that indicate what physician have to do in such situation. The only rational method is deduction based on available medical knowledge and physician’s own experience. In this meaning, medicine is still the art though based on the results of scientific research. One of the problems of contemporary medicine is the avalanche of information. Number of medical publication is huge and constantly increasing. In recent years, a new technique to evaluate the medical information has been elaborated. It is termed “evidence-based medicine”. The main principle of this technique is estimation of the value or strength of medical item of information. The description of a single case has the lowest strength of information while meta-analysis of double-blinded, randomized, multi-centered, prospective studies has the highest available strength of information. Special techniques have been introduced to evaluate from the point of view of the evidence-based medicine the medical handbooks, state-of-art papers, recommendations, guidelines and results of studies on new medications. Application of evidence-based medicine into clinical practice is one of the main aspects of contemporary medicine.

3. Main problems of clinical medicine that may be solved with application of computers Deep detailed analysis of clinical medicine revealed a number of problems that can be solved with computer-assisted systems. These problems should be considered in further studies. In general, these problems are classified into two subgroups: (a) problems related to a high number of data that can be evaluated with computers only, and (b) problems related to the complexity of medical phenomena that need computer-assisted evaluation. The first subgroup include the following problems: investigation of unexpected adverse reaction of the medication that can be detected on the base of national and international registers of therapy, computer-assisted diagnostics and management of some common diseases with application of recommendations or guidelines elaborated by international societies or committees, analysis of a number of so-called anecdotal data referring to so-called orphan diseases, analysis of data detected by some modern devises (e.g. 24 hrs monitoring of heart rhythm disturbances, long-term monitoring of pH changes in esophagus, determination of gastric or intestinal motility, long-term electroencephalography recordings, circadian changes of blood pressure, sleepassociated disturbances – polysommographical studies). The second subgroup of the medical problems includes: multivariable analysis of risk factors of several diseases, analysis of disorders probably caused by coexistence of a few etiological factors, design of new chemical substances (potential medicines) based on computer-assisted structural analysis of biological receptors, design of technologies for production of so-called biological drugs (i.e. produced by living genetically modified organisms or cell cultures), analysis of environmental or geographical factors affecting the development or course of disorders, analysis of genetic, epigenetic or proteomic phenomena related to several disorders (including diseases that are inherited by an assemblage of genes or are caused by impaired post-translational modification of

24

E.J. Kucharz

proteins), so-called personalized medicine i.e. design of therapeutic methods for individual patient on the base of analysis of his/her metabolic pathways or genetic susceptibility to various agents, elaboration of the most effective forms of medical activity with application of the system theory (the Dietrych’s theory), analysis of costeffectiveness aspects of medical procedures, including the quality of life of the patients.

4. Conclusions Clinical practice is always focused on the human being, the individual unique patient. The personality of physician is a potent therapeutic tool, and any other medical personnel cannot substitute physician in his/her discussion with and examination of the patient. In this aspect, any technological product cannot substitute the physician as the person. On the other hand, the excess of knowledge and constantly increasing technological opportunities unambiguously indicate for the need of supporting the physician with technological resources. Moreover, it is easy to imagine that in the nearest future, the physician cannot work properly without computer support. These finding has a profound effect on the direction of research. Specification of problems that can be solved with computers and elucidation of specific characteristics of medical problems as well as their limits (mostly due to human nature of the target of action) are necessary for development of research projects that hoped for significant improvement in efficacy of clinical medicine.

References Kucharz E.J.: Man is the way of medicine. Polskie Archiwum Medycyny WewnĊtrznej, 2006, vol. 116, no 6(12), p. 1229-1243. Kucharz E.J.: Internal medicine: yesterday, today, and tomorrow. I. Origin and development: the historical perspective. European Journal of Internal Medicine, 2003, vol. 14, no. 3, p. 205-208. Kucharz E.J.: Internal medicine: yesterday, today, and tomorrow. II. Definition and development in the 20th century. European Journal of Internal Medicine, 2003, vol. 14, no. 4, p. 272-274. Kucharz E.J.: Internal medicine: yesterday, today, and tomorrow. III. Specialists versus generalists or hospitalists. European Journal of Internal Medicine, 2003, vol. 14, no. 5 p. 344346. Kucharz E.J.: Rheumatology: dreams and reality. Terapia, 2007, vol: 15, no 12 (203), p. 5-6 [in Polish]. Kucharz E.J., Kotulska A., Zmysłowski A.: Application of the methodology of Dietrych in analysis of medical diagnostic and therapeutic procedures. WiadomoĞci Lekarskie, 2006, vol: 49, no 3-4. p. 125-126 [in Polish].

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The Development of an Advanced Systems Synthesis Environment: Integration of MI(NL)P Methods and Tools for Sustainable Applications Zdravko Kravanja University of Maribor, Faculty of Chemistry and Chemical Engineering, P.O. Box 219, 2000 Maribor, Slovenia, [email protected]

But the creative principle resides in mathematics. In a certain sense, therefore, I hold true that pure thought can grasp reality, as the ancients dreamed. Albert Einstein

Abstract The use of the mathematical programming approach to the synthesis of chemical processes and other systems has many advantages: feasibility, optimality, integrality and flexibility of solutions. Since the synthesis activity deals with the generation and selection of design alternatives, it involves discrete/continuous decisions, giving rise to a mixed-integer nonlinear programming (MINLP) class of problems. Although several efficient MINLP solvers have been developed in the last two decades, hardly any academic or professional MINLP synthesizer has been developed so far. The present contribution wishes to shed light on some important issues relating to different challenges that had to and still have to be mastered, and various capabilities which in turn were rewarded by mastering some of the challenges during the development of the advanced systems synthesizer MIPSYN, the successor of the process synthesizer PROSYN (Kravanja and Grossmann, 1994). The primary aim of future research is oriented towards the development of an even more advanced and robust synthesizer shell, capable of solving large-scale sustainable applications in different engineering domains. Keywords: process synthesis, process synthesizer, MIPSYN, synthesizer shell, MINLP.

1. Introduction Our global system is currently facing financial, production, social and environmental crisis. Globalization alone with increasing competition has thus proved to be insufficient for fostering steady economics. On the contrary, globalization based on unsustainable principles can only deepen and prolong the crisis. The community strives for sustainable development in general and sustainable chemical and bio-chemical industries in particular. Sustainable system synthesis in general and process synthesis in particular are for this reason of paramount importance in the area of Process System Engineering (PSE). The synthesis deals with the integration of constitutive elements (e.g. process units), material and energy streams into production plants, and plants into networks. The synthesis can therefore be considered a core innovative activity in developing or reconstructing new chemical and other plants. In the last decades many important achievements were accomplished in the area of synthesis, design and optimization of process and other systems. The methods rely on

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different solution concepts: either on heuristics (intuition, engineering experience), thermodynamics (physical insight) or mathematical programming. Whilst the former heuristic concept is becoming more and more redundant, efficient available optimization techniques, solution algorithms and strategies enable us to solve a wide range of problems arising in chemical engineering (see e.g. Grossmann and Kravanja, 1997; Biegler and Grossmann, 2004). Logic-based modelling representations and optimization techniques (e.g. Grossmann and Biegler, 2004; Sawaya, 2006) can be regarded as one of the most important achievements in the mathematical programming approach to the synthesis of discrete-continuous problems. However, with respect to process synthesis and systems synthesis in general there are many important challenges that still need to be mastered in order for complex problems of today to be solved more efficiently and integrally. This paper presents various challenges and capabilities related to the development of a unique process synthesizer MIPSYN, the successor of the MINLP synthesizer PROSYN (Kravanja and Grossmann, 1994). In addition it aims at shedding light on some important aspects associated to sustainable process synthesis.

2. Mixed-integer process synthesizer MIPSYN: challenges and capabilities 2.1. System synthesis based on the mathematical programming approach A definition of the synthesis activity by A. W. Westerberg (1991) is as follows: synthesis is the automatic generation of design alternatives and the selection of the better ones based on incomplete information. With respect to the cited definition for performing a synthesis in an equation oriented modular environment like MIPSYN, it is necessary to define: i) the superstructure from which design alternatives can be generated, ii) an efficient model formulation, and iii) a solution procedure based on advanced mathematical programming techniques which gives rise to the well-known superstructure approach. The relying solution algorithm should be capable of automatic generation of alternatives and of selecting the best one. The synthesis can be carried out for problems ranging from a simple subsystem synthesis to the synthesis of complex heat-integrated and flexible overall process schemes. It is interesting to note that although several general-purpose MINLP solvers (www.gamsworld.org/minlp/solvers.html), including the logic-based solver LOGMIP (Vecchietti and Grossmann, 1997) were developed in the last two decades, there are hardly any professional or academic discrete-continuous synthesis environments relying on recent techniques. As the development of such a synthesizer is an extremely challenging task and requires interdisciplinary skills of its developers, it provides the users with a set of various advanced capabilities by means of which problems can be solved which could probably not be solved any other way. Challenges in developing solution methods and tools for process synthesis are mostly related to the manifolds nature of the synthesis problems: • There are many complex interactions between subsystems most of which are mostly hidden to the human mind. • Decisions, carried out during the synthesis activity, are discrete and continuous. • All process parameters are uncertain to a certain degree. • Chemical processes are dynamic systems. • Many decisions are rule-based, represented by more or less complex logics. In order to capture these different aspects of problem's nature, different modelling representations, different algorithms and tools have been developed for various

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synthesis applications. Table 1 shows a variety of model complexity ranging from a simple steady state continuous LP process optimization to a flexible dynamical multiperiod entire life-cycle MINLP process synthesis. It is apparent that the numerical and methodological capabilities of our tools are still insufficient for solving complex synthesis problems as shown in the left-bottom corner of Table 1. Thus, very important challenges are associated with our attempts to raise the numerical capabilities of our current solution methods and tools, where the synthesizer MIPSYN is not an exception. Table 1. Variety of model complexity

Types of variables

Certainty variables Continuous, x discrete, y 0-1 logical Y x, y x, Y Uncertain parameter, Ĭ

Equations, Models, Examples Linear Nonlinear Difference Differential Steady state Multiperiod Dynamic Continuous processes Life cycle Batch or cont. processes Nominal LP NLP e.g. e.g. ILP INLP DisLP DisNLP MILP MINLP Mul. MINLP Dyn. MINLP MDisLP MDisNLP Flexible

2.2. Description of the MIPSYN synthesizer Figure 1 shows the flowchart of the synthesizer. Different methods and related components are integrated in this synthesizer's equation-oriented modular environment: i) GAMS with a variety of different NLP and MILP solvers ii) different versions of the OA algorithms, including the modified OA/ER algorithm and a new logic-based OA/ER algorithm, which are supervised by MIPSYN command files, iii) a simple simulator as initializer which is used to provide NLP subproblems feasible or near-feasible starting points, iv) a library of process unit and interconnected nodes models, different simultaneous models for heat integration, mass integration, and a physical property database for the most common chemical component, and v) a hybrid modelling environment with a link to external FORTRAN routines through procedures for solving the implicit part of synthesis models. MIPSYN can be used at different levels of problem abstraction as: • an MINLP solver for more general problems, • process synthesizer for the synthesis of process flowsheets, and as • a synthesizer shell for applications in different domains other than chemical engineering, e.g. the synthesis of mechanical structures. Since the execution of the NLP and MILP steps in OA algorithms are performed through the use of GAMS saving/restart capabilities, MIPSYN can run in automated or interactive modes of operations. The interactive mode is especially important since it enables the user to interfere and assist the optimization steps, which significantly improves the robustness of the MINLP search. Capabilities like initialization of NLP subproblems, calling different NLP and MILP solvers in a sequence with different option files, efficient modelling formulations, different strategies, e.g. multilevel MINLP, a possibility of solving feasibility problems with augmented penalty objective functions, multi-objective optimization, integer-infeasible path optimization, multiperiod optimization, and flexible synthesis in cases of uncertain parameters have been

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implemented thoroughly in the synthesizer. Some of them are briefly discussed in the following sub-chapters.

Figure 1. Integration of methods and tools in the MINLP synthesizer MIPSYN.

2.3. Feasibility, optimality and integrality of a solution Why is the mathematical programming approach to the synthesis so important? It is because of the various important advantages inherently present in the approach. Having the ability of obtaining solutions that are feasible and yet optimal seems to be the main capability. A solution is feasible when it satisfies all the imposed constraints. The analysis steps, in other approaches performed after the solution step, thus become redundant. Being optimal means that the appropriate trade-offs are appropriately established for a given optimality criterion. Also, during the selection procedure only the better design alternatives are generated to compete for the final solution since in practice bad alternatives are hardly ever generated. It should be noted that optimization can be performed only if interactions taking place between subsystems (reaction paths, separations, and auxiliary operations) can be appropriately accounted for. Thus, all the subsystems have to be considered simultaneously, which gives rise to the simultaneous type of optimization based on algorithmic mathematical programming techniques. However, since the subsystems are merged together, their integrated models are harder to solve than when the subsystems are solved sequentially. In many cases such integrated models are even too complex to be solved directly. Special decomposition techniques have to be employed, e.g. the ones based on the Lagrangian suboptimization schemes or multi-level MINLP, in order not to compromise the simultaneity of the solution. Since different subsystems can thus be solved simultaneously considering the various aspects imposed in the constraints and defined in the objective function, the

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obtained solutions are truly integrated. Simultaneous heat integration and the synthesis/optimization of process schemes is such an example where the ultimate effect of the simultaneous approach is not only the expected reduction of utility consumption but surprisingly, an increase of the process overall conversion with reduction of raw material usage (Lang et al, 1988). Thus, appropriately exploring all the interactions between the subsystems, the simultaneous approach is capable of capturing different synergistic effects that are hidden below the surface of the studied systems. Important new insights can be created in this way. There is thus a challenging incentive to apply the simultaneous approach to the synthesis of process schemes. 2.4. Discrete/continuous decision making Besides more usual continuous decisions (operating conditions, sizes, etc.) the synthesis of process schemes and other systems involves many discrete decisions, like selection of different technologies, process units and other constitutive elements, connectivity, selection of standard dimensions, material of constructions, different exclusive operation conditions, etc. The capability of performing discrete decisions simultaneously with the continuous ones enables one to obtain process solutions that are optimal with respect to topology and flowsheet parameters, as well as feasible in logical constraints when logics is modelled through discrete decisions. In the last half century several techniques for solving MINLP problems have been developed, see e.g. a survey by Grossmann and Kravanja (1997), starting with the Generalized Benders Decomposition method by Benders (1962), some of them being very efficient. The Outer-Approximation algorithm (OA) by Duran and Grossmann (1986) and its various extensions can be regarded as the most effective ones for solving complex, highly nonlinear synthesis problems that are characterized by dense row/column matrices. For solving combinatorially more complex problems different multilevel MINLP strategies were developed, e.g. the multilevel tree search by Daichendt and Grossmann (1997) and the multilevel hierarchical MINLP by Kravanja and Grossmann (1997). Besides the reduction of combinatorial complexity, multilevel MINLP strategies allow one to perform hierarchical decomposion at various levels of model aggregation and complexity, starting with larger superstructures and more aggregated models, and progressing toward smaller superstructures, represented with more detailed models. In this way, one can skip expensive modeling of a good number of details in the superstructure. Other very efficient multi-level MINLP strategies which were implemented in the process synthesizer MIPSYN are the Linked Multilevel Hierarchical Strategy (LMHS) and the Reduced Integer Space (RIS) strategy (Kravanja S. et al., 2003). The LMHS strategy is rigorous and can solve convex problems to global optimal solutions. On the other hand, when the RIS strategy is applied for the solution of large combinatorial problems, global optimality cannot be guaranteed, but very good solutions can be obtained. The LMHS strategy was successfully applied to a synthesis problem in mechanics – to a roller steel gate for a hydroelectric power station with 19623 binary variables, whilst the RIS strategy was used to solve the synthesis problem of a heat exchanger network comprising different types of exchangers with 1782 binary variables. Other advanced modelling representation and optimization techniques that are also implemented in MIPSYN are the ones based on logic-based programming by which problems are formulated in a more sophisticated way by global (in)equality constraints, logical disjunctions and logical constraints. The development of logic-based programming also revealed some very important insights into the structure of MINLP

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problems: at the level of non-linear programming (NLP) subproblems, only the existing part of the superstructure is solved, while at the level of mixed-integer linear programming (MILP) linearizations for disjunctions are derived without big-M scalars, which significantly improve the performance of the MINLP techniques, especially of the Outer-Approximation/Equality-Relaxation (OA/ER) algorithm by Kocis and Grossmann (1987) and its extensions. Since NLP subproblems are executed only for existing units, many numerical problems that can be caused by zero conditions are circumvented and NLP subproblems are easier to solve since they are smaller in size. In order to obtain outer approximations for the whole superstructure, the first NLP is solved only for the initial flowsheet while the rest of the units are solved by the Langrangian suboptimization scheme. The main challenge here was related to the development of MILP master problems based on the accumulation of outer approximations derived from solutions of different-size NLPs. Most recently, the alternative generalized disjunctive programming (GDP) formulation, convex hull representations, and the logic-based outer-approximation algorithm for process synthesis problems were proposed (Ropotar and Kravanja, 2008) and implemented in the synthesizer MIPSYN. A special discrete/continuous translation of variables enables modelling and solving process alternatives in a narrowed space of variables, defined by non-zero lower and upper bounds. Initial research indicates that the proposed alternative convex hull representation usually outperforms the conventional one when solving large combinatorial process networks problems. However, in spite of the progress in computational speed, computer architecture and the efficiency of optimization techniques, strategies and computer codes, the solving of large combinatorial problems in general with for instance 1000–20000 of binary variables still remains a major challenge. 2.5. Towards obtaining global or near-global solutions Due to the presence of nonconvexities the OA/ER algorithm does not generally guarantee the globality of solutions. Undesirable effects of noncovexities are twofold: at the level of NLP subproblems the optimizations can get stuck at poor local optima while at the level of MILP master problems part of the feasible region and, hence the global optimum can be cut off. In order to reduce the effects of the nonconvexities involved at NLP subproblems, global NLP solvers like GAMS/OQNLP can be employed, while at the level of the master problem, various structured modifications, rooted in logic-based disjunctive model formulations and non-structured modifications can be applied in MIPSYN. The most important non-structured modifications are: • deactivation of linearizations, • decomposition and deactivation of the objective function linearization, • use of the penalty function, • use of the upper bound on the objective function, and • global convexity test and validation of the outer approximations. In order to handle nonconvexities most efficiently, non-structured modifications were implemented directly in the MIPSYN's MINLP solvers. 2.6. Uncertainty and flexible synthesis The synthesis of large flexible process flowsheets with a significant number of uncertain parameters (say 20 to 100) is still a challenging problem. The main reason is that such problems are usually solved by the discretization of an infinite uncertain space, which causes an enormous increase in the problem’s size and prevents the solving of problems even with a moderate number of uncertain parameters. Since most of the engineering structures we wish to synthesize or optimize in practice have much larger numbers of

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uncertain parameters than we can handle, we are faced with the following two problems: their designs can be either i) nonoptimal if we enlarge their design variables by some ad hoc safety factors in order to make them flexible or ii) infeasible if we optimize them at nominal conditions and the solutions obtained are incapable of tolerating variations of a large number of uncertain parameters. Thus, a capability of performing flexible synthesis enables one to obtain flexible and yet optimal solutions. Different methods and strategies were recently developed and implemented in the synthesizer MIPSYN in order to overcome the two problems. They were developed in order to overcome the following two problems: • Approximate stochastic optimization. In order to a large extent to overcome the problem of nonoptimality an appropriate trade-off between the operating cost and the revenues, on the one side, and the investment cost, on the other side, has to be established by employing the expected objective function. For problems with a large number of uncertain parameters a strategy for the approximate stochastic optimization was developed (Novak-Pintariþ and Kravanja, 2004). Rather than integrating the objective value over ranges of uncertain parameters to obtain the expected objective value, the expected objective function is approximated at a special single point – the central basic point. In this way, the exhaustive calculation at numerous Gaussian quadrature points is avoided and the model is significantly reduced. • A-priori identification of critical points. An approach for the a-priori identification of critical points, either vertex or nonvertex, was developed for the synthesis of flexible flowsheets in order to overcome the problem of infeasibility caused by a large number of uncertain parameters. A set of critical points is determined by merging of critical values of uncertain parameters that are obtained by maximizing the design variables one-by-one, while simultaneously optimizing the economic objective function (Novak-Pintariþ and Kravanja, 2008). The set of critical points is then used to assure the feasibility of the design. An important feature of the approach is that the dimensionality of the model depends only on the number of design variables, which is usually quite modest for the majority of chemical processes. A multi-level MINLP methodology for the approximate stochastic synthesis of process flowsheets with a large number of uncertain parameters was then proposed (NovakPintariþ and Kravanja, 2007). The methodology is a reasonable combination of the above two approaches which significantly reduces a problem’s size. The methodology was applied to the synthesis of a flexible heat-integrated methanol process with 24 uncertain parameters. 2.7. Hybrid modeling and solution environment for disjunctive models In many applications models can be too large and complex to be solved if they are entirely written explicitly in an equation-oriented (EO) environment. Reactivedistillation is a typical example where the distillation model is given by the classical MESH equations (Mass balance, Equilibrium, Summation and Heat balance) while the thermodynamics, kinetics and hydrodynamic behaviour of the system are described by rigorous sub-models. One possible and effective approach is to implement hybrid modelling and a solution environment where only the easiest part of the model (MESH equations) is presented explicitly in the EO environment while the complex part with the rigorous sub-models is modelled implicitly through the use of FORTAN procedures connected to the synthesizer MIPSYN. Since the synthesizer provides the user with many flexible capabilities to interactively assist the course of optimization, e.g.

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initialization of each NLP subproblem, different strategies can be implemented in the MIPSYN in order to converge to feasible and optimal solutions which otherwise could not be obtained (Ropotar et al., 2009). The objective was to optimise the column configuration: optimal feed and catalyst location, optimal operating parameter (e.g. reflux and reboiler duty), optimal design parameter (e.g. column diameter). For a distillation collumn with 50 separation and 10 reactive trays the hybride model typically comprises up to 3000 constraints and 1500 variables, one tenth of them being binary. About 500 equations and almost all variables are part of external procedures. Since NLP subproblems are executed only for selected trays, the course of the MINLP iteration is more robust. However, the main challenge was the development of suitable logics that supervises the execusion of the external FORTRAN routines. Since the model is disjunctive, external funtions are executed only for selected trays. 2.8. Sustainability and multi-objective approach In order to obtain a sustainable solution there are many environmental and other sustainability aspects that have to be imposed as constraints and/or criteria when solving a synthesis problem. Firm and yet simple sustainability principles should be stated and integrated thoroughly in our sophisticated methods and tools, thus upgrading our level of thinking, knowledge and resulted solutions. An example of a guideline for the utilization of resources is that consumption rates of renewable resources must not exceed their regeneration rates, or material brought into the environment must not exceed the carrying capacity of the ecosystem (Voss, 1994). According to Jischa (1998), sustainability can be interpreted by a 3x3x3 sustainability matrix where the three axis show the aspects of justice from fair reward for work to fair distribution of goods, level of strategies ranging from efficiency, consistency to sufficiency, and view of nature from a narrow anthropocentric to eco-centric view. In order to achieve sustainable solutions the scope of the synthesis, as will be discussed later, has to be extended almost to the whole chemical or biochemical supply chain. It should be noted that a two-level MINLP approach for the systematic consideration of the sustainability principles in the synthesis of environmentally benign chemical processes was developed (Kravanja et al., 2005). The approach is based on the generation of a superstructure which contains sustainable structural alternatives for minimal or zero emissions, minimization of energy consumption and exergy loss, and minimal waste and by-product streams resulting from the process. The economic and environmental criteria were identified, for multi-objective optimisation in order to generate sets of Pareto optimal solutions. The approach was illustrated using a wellknown hydrodealkylation (HDA) process. The study indicates that interactions can be very complex and, hence unpredictable, which gives rise to the simultaneous approach.

3. Applications 3.1. Scope of applications Many different case studies were performed by MIPSYN and various OA-based algorithms, solution strategies, prescreening methods, and modeling representations, as mentioned in the previous chapter, have been implemented, all of them indicating that the scope of application can be very extensive, from a simple NLP optimization of process subsystem to a complex and flexible MINLP synthesis of heat-integrated overall process scheme. It should be noted that by using the MIPSYN shell, various case studies and applications were carried out in the area of mechanics ranging from simple NLP

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optimizations, e.g. timber trusses (Šilih et al., 2006) or composite floor systems (Klanšek, 2006, 2008), to complex multilevel MINLP syntheses of mechanical structures where topology, material, standard and rounded dimensions were optimized simultaneously (Kravanja S. et al., 2005), e.g. the synthesis of sliding gates for a hydropower dam (Kravanja S. et al, 2002), steel frames (Klanšek et al., 2007) and steel buildings (Žula et al, 2008). 3.2. Current and future challenging sustainable applications 3.2.1. Process synthesis related to green energy and the biochemical supply chain In order to use MIPSYN for the integration of the whole biochemical supply chain for the production of biogas, MIPSYN is currently upgrading for the syntheses of bioprocesses. The development of library of modules for biochemical process units, including the kinetics of possibly-novel bioreaction paths, is under way. MINLP models will be generated from the library for the synthesis of mass and energy integrated biocommodity networks. Real-world cost functions for biochemical process units will also be defined and used to formulate reliable economic objective functions. 3.2.2. Sustainable feedstock-process-product integration based on prediction models The main vision is to redesign or fundamentally innovate (bio)chemical processes and other systems in order to achieve highly sustainable production and consumption. The main research challenge is to perform product and process design from the molecular level, to the selection of sustainable resource alternatives, to sustainable reaction path and process alternatives, to sustainable product alternatives in a multi-objective and simultaneous design procedure. The development of such a procedure would require employment of the most advanced mathematical programming techniques for the simultaneous structural and parameter optimization. Being integrated with the Molecular modeling and Global life cycle assessment would provide an integrated sustainable framework for the design of new compounds and the synthesis of innovative process solutions. The challenge here is the development of models for different levels of the (bio)chemical supply chain, models that are simple, and yet effective and suitable for the simultaneous selection of: • compound alternatives (Molecular modelling), • sustainable reaction path alternatives, • process flowsheet alternatives, and • prediction of product properties and functionalities. It should be noted that modelling the sustainable reaction path alternatives together with predicting chemical kinetics is the least developed research activity among the proposed ones. Also, according to the vision the synthesis is widening to the selection of molecules and reaction paths in accordance to given designing criteria.

4. Conclusion It is true that we cannot solve environmental and other problems using the same knowledge, the same way of thinking, the same methods and tools as when the problems were created. I believe that solution capabilities of the conventional solution techniques, strategies and concepts are insufficient for solving large-scale complex problems effectively. The scope of process synthesis should be expanded and the capabilities of our methods and tools should be upgraded to enable the identifying of new compounds, new reaction paths, and metabolic networks in order to create new products with desired properties and functionalities, thus fundamentally innovating the chemical industry based on firm sustainability principles. The PSE community is thus

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faced with the greatest challenge ever – with the incentive of developing integrated methods and tools to provide engineers with a powerful tool so that they will be able to shape sustainable development in the chemical industry.

5. Acknowledgements The author is grateful to the Slovenian Ministry of Higher Education, Science and Technology for the financial support.

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Integration of chemical product development, process synthesis, and operation optimization Xiuxi Li, Yun Chen, and Yu Qian* School of Chemical Engineering, South China University of Technology, Guangzhou, 510640, China. [email protected]

Abstract An integrated approach of product development, process design and operation analysis is presented. A kilo-plant was designed and set up as a research platform for fine and specialties chemicals manufacture in kilogram-scale batch process. The investigation emphasizes the issues concerning product synthesis, process operation, and product quality control, as well as process monitoring and operation optimization. It provides a systematic approach of responding to rapid changes in the marketplace demands to new green products. Keywords: integration, kilo-plant, product development, process operation.

1. Introduction The chemical process industry faces very challenging economic and social issues. The globalization of the industry has opened new markets. While potentially this increases market efficiencies, contributes to improve the human being living standard worldwide, it has also resulted in severe competition, reduces the profit margins greatly. Severe market competition needs fast responses from green product innovation, cleaner process development, to production, especially for high value-added fine and specialty chemicals. The whole process from product design, formulation to manufacture can be viewed as a chemical supply chain, including multiple scales from molecular, aggregation, interface, single-phase and multi-phase system, equipment, workshop, enterprise, to market places. The challenges are concerned with the improvement of decision making processes for the creation and operation of the chemical supply chain. It deals with the discovery, design, manufacture and distribution of chemical products in the context of conflicting and multi-attribute goals (Grossmann, 2000, 2004; Charpentier, 2002). Chemical product design and process development usually consist of several stages: products performance analysis, molecular structure and formulation, laboratory test, pilot plant, trial pre-production, and commercial production. Computer aided molecule design (CAMD) approach has been used to simulate possible product structures (Fermeglia, 2003; Qian, 2004). On the macroscale level, the integration of the product design and process design, agile manufacturing, system integration has represented the front and wide prospect of this field too (Bergess and Brennan, 2001). Most fine chemicals and specialty chemicals with high value-added are produced in small volume, even in kilogram scale, but the related manufacture process may still be complicated. A pilot plant is a typical verification tool in the development of a new product/process, which is, however, time-consuming and capital-expensive. To address this requirement, the concept of mini-plant is proposed. In Helsinki University of

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Technology, a mini-plant operates effectively for the NexOctane process development (Wörz, 1995). Hasebe (2004) proposed to uses micro device as the high-efficient and feasible method for industrial scaling up production. A kilo-plant has been assembled and implemented in our lab in the aim of integrated research on product and process development (Qian et al., 2006). It is specifically designed for fine and pharmaceutical chemicals. It is flexible and easily reassembled into different configurations. At the same time, the kilogram-scale makes it inexpensive to build and run than conventional pilot plants. It realizes the concurrent development of chemical products, and shortens the development time.

2. A kilo-plant for integration of product and process development The kilo-plant consists of main features of a complete process system, including reactors, separation units, heating and cooling utilities, instrumentation, control system and recycles. There are two jacketed glass stirred reactors with maximum capacities of 2 and 10 liters, respectively. The temperature range is from -40 up to +200 , while the pressure ranges from 10 mbar to 1.45 bar absolute. The heater/chillers can be controlled with precise temperature profiles for the reaction and crystallization which provide products of high quality. The kilo-plant allows for changes in the configurations of the process flowsheet for investigation of process alternatives. The flowsheet is shown in Figure 1. The kilo-plant provides researchers the knowledge of the process operation based on the real experiment. The main functions realized in the kilo-plant are monitoring, data acquisition, data transfer and computer integrating control. Different processes require different flow sheet and operation units. The kilo-plant is operated in batch mode mostly. Vacuum Pump Pipeline

Condenser 1

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Signal Wire Product Vessels

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Partial Condenser 2 Nitrogen/ Oxygen

0

Heater

Raw Material

Reactor (10 l) Supply Vessels

10l

2l

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Distillation Column Reactor (2 l)

HeatingCooling System

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Fig. 1. Process diagram of the kilo-plant

There are many aspects in product synthesis and operation research, including process design, modeling, optimization, monitoring, control, safety analysis, scheduling. They are intrinsically strong coupling. In consequence, they should be considered in a

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systemic approach rather than in a traditional isolated way. The kilo-plant constitutes the core of the experimental platform towards the integration of product development, process design and operation. As shown in Figure 2, the experimental platform consists of three main layers: 1) In the bottom level, the kilo-plant and a number of process simulators, including ASPEN Plus, Dynamics, Simulink, SuperPro, and the real-time platform G2, to facilitate integrating a variety of process operation tasks. They are used as experimental objects in the platform. 2) In the middle level, a small distributed control system, CENTUM-CS1000, is used. Data acquisition and information transmission are implemented with the application of DataCON, where noise in the process parameters is eliminated. They work together to realize the data exchange among the basic control system and advanced applications. Opening Database Connection (ODBC) and Common Object Request Broker Agent (CORBA) are followed to realize communication among these software systems in the platform. The Standard for exchange of product data (STEP) is used for information integration. 3) Advanced applications involve fault detection and diagnosis, scheduling and optimization, safety evaluation, product quality control, which are illustrated in the top level of the process operation system, as shown in Figure 2. We developed a real-time expert system for the process and equipment operation based on G2 system (Qian et al., 2005). Aspen Plus is used to simulate the process for parameters optimization by comparing with the operation state of the kilo-plant. Fault detection & diagnosis G2

Scheduling and optimization GAMS

Safety evaluation

… ProductQuality control

Process simulation Aspen

Process monitoring Data acquisition and rectification DataCON

Database

Process Control CS-1000 Process simulators Aspen Dynamic, Lab CVI

Process equipments Kilo-plant

Fig. 2. Structure of the experimental platform of process development and operation

To realize remote monitoring control and data interaction, an information interaction platform was established including workstation, remote monitoring custom terminal, network, real time database, distributed database, graph user interface and application tools, which facilitate the use of object oriented data model, simulation, and optimization.

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3. Integration of product and process design Chemical manufacturing processes are to transform raw materials to final products with many different physical and chemical processing steps. With the kilo-plant platform, the practical and key concepts of product engineering technology concerning the product design and process development is developed and examined in a systematic way of three levels. On the microscale level, chemical product engineering investigates the basic models of product quality influenced by active materials with complicated molecular structures, interaction between molecules, and their quantitative relations, such as reaction activity, solubility etc. The theories and methods of computer aided molecular design (CAMD), group contribution method, and group connectivity index models are applied to establish the quantitative structure-activity relation (QSAR). Then, the nonlinear interaction models of component, micro structures, multifunctional and constrain relationship of the product are formulated. The multi-objective nonlinear programming is applied to formulate design modeling and optimization, in order to find the theory and computer model of multiple level structure and compatibility scheme for design of fine chemicals and new materials (Cussler and Wei, 2003). The kilo-plant supports to explore the impact of the adjustment of process parameters on the product quality. Product model can be formulated through relating the performance index to components, micro-structure, and the process operation conditions. On the mesoscale level, the integration of product design and process design make it easier to adjust the product structure and its properties which will accelerate the development process. In the process design and product manufacture, the influence of the operation parameters and processing ways on product micro-structure and properties can be considered. For example, in reaction system, concentration ratio of the raw material and product is influenced by temperature, pressure, and flow rate etc. Different catalysts also affect the reaction selectivity during the process experiment. As to the separation process, the behaviors of the phase equilibria should be clear during the process design. On the macroscale level, product design is also an intriguing area of research (Cussler and Moggridge, 2001), although industry has practiced product design for a long time. The emphasis is on the time of new products to market needs, and the systematic exploration of alternatives for developing new products, which is typically a multidisciplinary task that needs both scientists, engineers of different disciplines and business people. Currently, our effort focuses on the interactive application on the microscale level and mesoscale level. Data can be gained not only from practical operation but also from the commercial software, such as Gaussian, MesoDyn, DPD, CFD(Fluent), and gPROMS. On the kilo-plant, the acquirable process data include those of the size of equipments, the cost of operation, the flow rate, component, the yield and quality of product, temperature, pressure, and decision making data, those of the rate and purity of product, and also control data, those of the preset value of variable and control parameters. These acquirable data provide abundant and useful data for the design of chemical product and the comprehensive studying of process development. Computer-aided tools are applied to monitor the kilo-plant operation and data acquisition. Therefore, the production specifications and operation modes can be adjusted online with the support of the data analysis. It assures the optimal operating conditions not only for the operation units, but also for the whole process.

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4. A case study of integrated development of product and process A case for the production of Nipagin ethyl ester was carried out in the kilo-plant. It is a new anti-mildew and antiseptic agent which has the best inhibiting effect on aflatoxin in food, drink, cosmetics and medicine. It features low cost in production and safety in application. Synthesis of Nipagin ethyl ester is carried out with the kilo-plant to illustrate the application of computer-aided system integration in product quality control in batch process. Nipagin ethyl ester is produced through the reaction of ethanol with Nipagin acid (p-hydroxybenzoate acid). The model of the reaction is developed according to the laboratory analysis results. The 2-liter reactor is chosen for this reaction. Dodecylbenzenesulphonic acid (DBSA) is as catalyst while benzene as water carrying agent. The mole ratio of Nipagin acid to ethanol to catalyze is 1:5:0.06, and acid to water carrying agent 1:0.05, respectively. Nipagin acid dissolved in ethanol is added to the reactor from the top in three times. DBSA, benzene and ethanol are added from raw material tank through peristaltic pump. The pressure in the reactor is maintained at normal atmosphere. As the reaction starts up, the reactor jacket temperature is 85 . The flow of cooling water is adjusted to a temperature of partial condensation. The condensed liquid in the total condenser is composed of water, benzene, and ethanol. During the reaction operation, the samples are taken from the reactor to examine the composition with HPLC in each 30 min. When the reaction runs about 5 hours, the vapour temperature increases greatly, indicating the reaction approaching the end. To adjust the pH value to 7, and the temperature to 40 , then shut down the reactor running. After stewing, crystals appear. The process optimization requires product and process models, to adjust the parameters of the process operation, such as pH value, dynamic temperature trajectory. The operation of the kilo-plant is monitored with 15 sensors of a variety of process variables, such as temperature, pressure, flow rate, pH value, and the rotation speed of stirrer etc. In addition, the instruments for the kilogram scale equipment ensure high frequency data collection and high accuracy parameter measurement and control. In the kilo-plant, the accuracy of temperature measurement is of ±0.1 , while remote data transmission from the installation to the database is conducted in a 0.2s interval for a reliable real time monitoring and dynamic process analysis. In the Nipagin ethyl ester synthesis case, the reaction conversion, reaction dynamics, kinetics analysis, and the process conditions adjustment, control strategy for product design and process design integration are integrated investigated. In terms of the product quality and purity, the process development and the associated operating conditions modifications in the kilo-plant can't be easy realized in the ordinary chemical laboratories.

5. Conclusions Green chemical product design and process development are among the most important research areas of chemical product engineering. The implementation of the kilo-plant experiment platform, modeling, simulation and quantitative analysis of chemical product structures will not only make it more effective to realize flexible operation, but also reflect the dynamic change of the process to adopt an advanced control strategy and system integration method. At the same time, the feasible scheme screened will accelerate the development of the manufacture process for the product. Because it is more convenient to adjust the developing route of the new product, on the other hand,

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the problems likely occurred in the actual industrial production can be tested, discovered and solved a priori. These make the chemical engineering research respond faster to the technical difficulty of the chemical product manufacture and fulfil the market demands for a variety of new green chemical products.

6. Acknowledgements Financial supported from the National Natural Science Foundation of China (No. 20536020, 20876056) are gratefully appreciated.

References Burgess, A. A. and D. J. Brennan (2001). Application of life cycle assessment to chemical processes. Chem. Eng. Sci., 56, 2589-2604. Cussler, E. L. and J. Wei (2003). Chemical product engineering. AIChE J., 49(5), 1072-1075. Cussler, E.L. and G. D. Moggridge (2001). Chemical Product Design, Cambridge Univ. Press. Fermeglia, M., et al. (2003). Molecular modeling and process simulation: Real possibilities and challenges. Chem. Biochem. Eng, 17(1), 19-29. Grossmann, I.E. (2004). Challenges in the new millennium: product discovery and design, enterprise and supply chain optimization, global life cycle assessment. Computers & Chem. Eng., 29, 29-39. Grossmann, I.E. and A.E. Westerberg(2000). Research challenges in process systems engineering. AIChE Journal, 46(9), 1700-1703. Hasebe, S. (2004), Design and operation of micro-chemical plants –bridging the gap beteween nano, micro and macro technologies. in Proc. Intern. Symp. on Proc. Sys. Eng., 89-100. Elsevier. Qian, Y, J.Z. Pan, and L. J. Zhang (2004). Structure- property relationships and models of controlled drug delivery of biodegradable microspheres. Chinese J. Chem Eng, 12(6), 869-876. Qian Y., M J Zheng, X X Li (2005). Implementation of knowledge maintenance modules in an expert system for fault diagnosis of process operation. Expert Sys. with Appl, 28(2), 249-257. Qian, Y., Z.H. Wu and Y. B. Jiang (2006). Integration of chemical product development, process design, and operation based on a kilo-plant, Progress in Natural Science, 16(6), 600-606.

Wörz, O. (1995). Process development via a miniplant. Comp. Chem. Eng., 34, 261268.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Uncertainty, decomposition and feedback in batch production scheduling Sebastian Engell Process Dynamics and Operations Group, Department of Biochemical and Chemical Engineering, TU Dortmund, Emil-Figge-Str. 70, 44227 Dortmund, Germany [email protected]

Abstract In this paper, we consider production scheduling as a control problem under uncertainty. First the similarities and the differences between process control and online scheduling are discussed. A key issue in both contexts is the handling of uncertainty in feedback structures. It is advocated to use explicit models of the uncertainties in the form of scenario trees and to include the existence of feedback by solving two-stage models on rolling horizons. The interaction of planning and scheduling in the presence of uncertainty and feedback is discussed. The proposed model structure is a “telescopic” multiscale model where the layers are coupled by targets for and feedback information about the states of the system. Keywords: Online planning and scheduling, uncertainty models, multi-layer scheduling

1. Introduction Only in rare cases, chemical production plants can be run at full capacity and under the same operating conditions, producing the same product over long periods of time. Usually, the throughput, the operating conditions, and also the products have to be adapted to changing demands, product prices, availability and prices of raw materials etc. The ability to react to these changing conditions and still to maintain a profitable operation is generally called flexibility. Flexibility comes at a price: a lower throughput increases the fixed costs, varying products cause changeover times, off-spec products, and a broad spectrum of products requires a broader set of equipment that is only partly used for each individual product. The more complex and specialized the products are and the smaller the volumes of each individual product, the higher the need for flexibility. The highest degree of flexibility is provided by multi-product plants, usually operated in batch or semi-batch mode. Recently, concepts for increased flexibility with respect to capacity and to the spectrum of products have also been proposed for continuous production, using modularized plants with intensified unit operations. The economics of flexible plants are strongly affected by the efficient use of the available resources and by the ability to meet the demands of the customers with highquality products that are delivered on time. The latter can always be achieved by either keeping a large stock of products or by providing large spare capacity, doing this exceedingly however contradicts the goal of profitable operations. Hence, as discussed in many papers on production planning and scheduling, the management or planning and scheduling of the available resources is a critical, but very complex task. In recent years, remarkable progress has been made in the modeling of planning and scheduling problems by MILPs and their efficient solution (see e.g. Kallrath, 2002, Floudas and Lin, 2004, Castro and Grossmann, 2006, Castro et al. 2006, Ferrer-Nadal et

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al., 2007). Besides classical MILP techniques, other numerical approaches as e.g. evolutionary algorithms (Till et al., 2007, Sand et al., 2008) and automata-based methods (Panek et al., 2008) have also been proposed and demonstrated to be successful for small to medium-sized examples. These important developments provide the basis for the implementation of real production control systems, similar to the use of advanced continuous optimization techniques in RTO and model-predictive control, e.g. reported in (Janak et al., 2006a,b). When designing such systems, besides the representation of the problems at hand as static mixed-integer optimization problems and their solution, the problem formulation in a dynamic context must be addressed. This contribution tries to discuss communalities and differences of process control and online scheduling, in particular the representation of uncertainties, hierarchical decomposition, and rollinghorizon formulations in the context of feedback structures..

2. Process control vs. online scheduling – similarities and differences Both conventional process control and online scheduling are reactive (and partly proactive) activities that have to cope with uncertainties and changes of operating conditions and targets and therefore employ feedback and feed-forward information structures. In (continuous) process control, the focus is on the control of qualitative properties of streams by changing the operating conditions of the plant. The resulting mass flows of raw materials or of products are usually prescribed externally. The challenge is to keep the quality parameters constant or to track time-varying set-points for these parameters, possibly under changing throughputs. The control of the mass flows as well as of the inventories is a less important problem that usually can be taken care of by low-level controls. Feedback control is mainly needed to handle the uncertainties involved, the uncertainty on the dependence of the process outcomes on the degrees of freedom that can be manipulated (inputs) – lack of models or plant-model mismatch – and the existence of external influences that influence the quality parameters and the economics of the process – summarized under the term disturbances. Process control is concerned with meeting the constraints on quality indicators, internal states (e.g. maximum pressures or temperature variations), and flows. Due to the size of plant-wide control problems, often a hierarchical decomposition as shown in Fig. 1 is employed.

Figure 1: Hierarchical process control system and hierarchical planning and scheduling system

The so-called real-time operation (RTO) layer determines the set-points of the lower control layer by a steady-state optimization of the plant performance. The lower level implements these set-points in the presence of dynamic disturbances and deviations of the plant behavior from the model that is used on the RTO layer, to the best extent possible. The RTO layer performs its optimization based on accurate models of the steadystate behavior that are updated using measured data. On the lower level, usually linear MPC controllers or conventional PID controllers are used, and the discrepancy between the assumed linear models and the actual plant behavior is handled by feedback, an as-

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pect that has been extensively discussed in the control literature under the term robust control. Recently, also nonlinear model-based controllers have been used on the lower level. As discussed in (Rolandi and Romagnoli, 2005, Engell, 2007), due to the advances in nonlinear dynamic optimization algorithms, in process control nowadays the option of a fusion of the two layers into one online optimizing feedback control layer is feasible and provides opportunities to improve the dynamic operation of the plant. This avoids several disadvantages of the layered approach, in particular a delayed reaction to disturbances due to the necessity to reach a new steady state before new set-points are computed and mismatch of the optimization criteria on both layers if optimization-based (MPC) control is employed on the lower layer. In contrast to the situation in continuous control, the complexity of the problems does not admit a monolithic single-layer formulation of medium-term planning and scheduling for real-world problems. In continuous process control, feedback is implemented based on measured or estimated values of (all or some) state variables of the process which are qualitative properties of the material along the flow through the plant. Inventory levels are allowed to vary to some extent in order to absorb some variability. In online scheduling, the quality indicators which are of predominant interest in continuous control are considered only in a discretized (abstracted) fashion: a batch production step is terminated successfully or not, in the latter case possibly causing the necessity of additional operations, it delivers certain amounts of products A, B, C, … and it requires certain resources for certain periods of time. The reference trajectories define mass flows of (discrete) products over time, averaged over certain intervals or as impulses at certain points in time (for fixed delivery dates), and the evolution of the inventories. Feedback and feed-forward control manipulate the timing of events – mainly the start times of production steps – and possibly the corresponding amounts of material (batch sizes). The state of the production process in scheduling is defined by the amounts of material stored, by the states of the resources (binary: operational or not, discrete: last operation was A, B, C, or continuous (rarely)) and by the progress of the running operations (discrete or continuous). From the scheduling point of view, the state (in the sense of process control) of the continuous parameters of the material and of the equipment only matters as far as it influences the durations of the operations and the amounts of material delivered upon termination. Consequently, the information obtained from the running processes in a feedback structure should be an accurate prediction of the expected finishing times and of the yields of the running batches. Uncertainties in online scheduling are related to the availability of resources (breakdowns, lack of personnel), uncertain yields or unsuccessful production steps, uncertain durations of operations, and, often most importantly, dynamically changing demands or targets. Both in process control and in online scheduling, the difficulty of the control problem is due to the “inertia” of the processes – the energies and masses stored in the plant in the case of continuous control and the inventories and the irreversible allocations of resources to processing steps in batch plants. The lower this inertia, the faster the production process can be adapted to changing market conditions. Agility roughly is the available range of the degrees of freedom relative to the inertia of the system. The smaller the inertia and the larger the range of the inputs, the faster transitions can be implemented. Translating this into online scheduling, the inertia is determined by the available resources relative to the work in progress and the associated blocking of resources,

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plus the inertia of the procurement of raw materials. The inertia of the plant and of the procurement of raw materials and other resources causes the need for planning on longer horizons. Planning can be understood as the generation of the reference trajectories for the plant and for the procurement of material, similar to the computation of the optimal operating conditions in process control. In the standard approach to plant-wide control shown in Fig. 1, the upper layer performs an infrequent adaptation of the reference values for the low-level control system, and the inertia of the plant that prohibits an abrupt change of the controlled variables is taken care of by the lower layer, inevitably causing a transient period where the variables deviate from the set-points. In continuous plants with frequent product changeovers, the sequences of the changes of the set-points as well as the trajectories between these set-points can be included in the optimization to control the effects of the transient periods better, see e.g. [Marquardt]. Interestingly, in process control the variation of the controlled variables around their set-points has mostly been considered as natural and inevitable, and the idea to constrain quality indicators directly in the control algorithm rather than only reducing the variation around the set-points by optimal tracking is a relatively recent idea (Toumi and Engell, 2004, Rolandi and Romagnoli, 2005). In contrast, in planning and scheduling, targets given to the lower level are often considered as rigid, and the inability to meet these is often assumed to imply the need of a revision of the targets. In online production scheduling, the need for longer-range planning is mostly caused by the interaction with upstream or downstream units (or the respective markets), i.e. the necessary procurement of the raw materials and the request for the delivery of products to customers at fixed times, in contrast to a production from and into large storage tanks. The task of medium-term planning is to synchronize the operations in the various units, to procure the necessary materials in time and to filter the demand variations by deciding how much material is produced to store, to match the temporal spread of the demands and the production orders in campaign production and by adapting the promised delivery dates of the orders according to the available capacities so that the lower level targets are realistic and reliable delivery dates can be promised to the customers. Tightly coupled to this is the planning of the inventories both of raw and of finished materials which increase the flexibility of the overall system in several ways: the available resources can be used more efficiently if the timing of the production leaves room for optimization, unplanned demands can be covered, and breakdowns or other problems do not cause delivery problems. On the other hand, large stocks of material cause cost because of the capital that is not active (an issue that sometimes is overestimated because it is only the interest on this capital that can be saved by lower stock levels) and, more importantly, by products that ultimately cannot be sold or of raw materials that are not used because of lack of demand. The medium-term planning layer itself is confronted with a continuous stream of demands, of information on the actual progress of the production steps and of the actual sales. Moreover, if has to take dynamically varying conditions on the production level in account where the capacities of the units may vary both in a planned fashion and by unplanned shutdown, maintenance etc. Both layers, medium-term planning and scheduling are highly reactive and face considerable uncertainties in their planning data. Similar to the hierarchical decomposition of process control tasks, the hierarchical structure shown in Fig. 1 (right) results. The communication between the layers and the for-

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mulation of the corresponding optimization problems is discussed in more detail in section 4 below. Both in continuous control and in online production scheduling, model abstractions are used on the higher level of the hierarchy. As mentioned above, in control, the abstraction employed usually consists of neglecting the dynamics or the inertia of the plant. This can be seen as an extension of the time horizon to infinity where the small transient periods can be ignored. On the other hand, the models on the upper layer can be more detailed, often rigorous models obtained from first principles, while on the lower layer linear approximations, often obtained from data, are used. In scheduling, abstraction is performed similarly by aggregating demands and production over time (slots, buckets) and by neglecting resources and production steps that are not critical for the actual production outcome. However, the more efficient the production system is the less easy it is to determine bottlenecks a priori and they may shift dynamically depending on the allocation of the jobs. Summarizing, both in process control and in online scheduling, the task of the operational layer is to use the available degrees of freedom to reach the targets set by the upper layer in the presence of uncertainties and model inaccuracies. In both cases, feedback is applied to cope with the uncertainties, including the effects that are not modeled on the upper layer. In both cases, additional operational degrees of freedom are required to counteract the uncertainties and to cope with the aspects that are not included on the higher level: the dynamics of the plant in the case of process control and the unmodelled tasks and resources in the case of scheduling. Only if such additional degrees of freedom are available, a compensation of the effect of the uncertainties is possible. Control systems and online scheduling algorithms have to react to information on the actual situation that arrives iteratively. In model-based control and in model-based scheduling, the decisions are optimized over a forecast horizon in order to take longer term effects due to the inertia of the controlled system into account, but only a subset of “next” decisions or optimized variables have to be fixed and implemented based upon the available information. Moving horizon schemes were first employed in process control but are increasingly used in planning and scheduling, see e.g. (Sand et al., 2000), (Engell et al., 2001), (Kelly and Zygnier, 2008), (Pujgjaner and Lainez, 2008). On the other hand, the use of two-stage formulations to include uncertainties as well as the future reaction of the controller (resp. scheduler) to the realization of the uncertainty into account provides also a suitable non-conservative formulation for robust model-predictive control (Dadhe and Engell, 2008).

3. Uncertainty and feedback in a dynamic scheduling context Uncertainties are a major element in any real-time decision problem where the information about the presence and the future unfolds iteratively. Besides the uncertainty on the future demands, in medium-term planning and in online scheduling, the information on the capacity and the constraints of the plant is to some extent uncertain, due to model abstraction on the higher level and to incomplete knowledge and stochastic events on the lower level. In control problems, it is usually assumed that the reference trajectories are fixed and known over the horizon over which the online optimization problems are solved, but that the plant dynamics are not exactly represented by the model used. The usual approach in model-predictive control to handle these uncertainties is to modify the references and the constraints by the observed difference between the predicted and the ob-

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served outcome of the application of the control moves in order to obtain offset-free control. Due to plant-model mismatch, i.e. the gradients of the plant dynamics and of the constraints with respect to the free inputs are not known exactly, the optimization will usually provide a suboptimal, but feasible operating point (Forbes and Marlin, x). Techniques to modify the gradients based upon measured information have been proposed by (Tatjewski, 2002) and (Gao and Engell, 2005).A second element that introduces feedback in order to counteract the uncertainties is the estimation of the plant state from the available measurements and the update of the optimization problem using the new estimates of the state of the model. 3.1. Representation of uncertainty in scheduling For the handling of the uncertainties in online scheduling, four basic approaches have been proposed: - full event-driven or periodic rescheduling - reactive scheduling - robust scheduling - multi-stage or two-stage stochastic scheduling. The most straightforward approach to handle uncertainties is dynamic rescheduling. Taking into account the real progress of the operations and new information about the production targets, all decisions that can be modified are recomputed iteratively or if major events are encountered, using a fixed nominal model or including model adaptation. This is similar to the approach in model-predictive control when the optimization is iterated over a shifted horizon, the new (observed or estimated) plant state is taken into account and the targets are shifted by the difference of the planned and the real outcomes. The critical aspect of pure rescheduling is the issue of feasibility. There is no guarantee that the process will not run into deadlocks (or very unfavorable situations) because of the discrepancies between the assumed and the real evolution. A key role of humans in the production process is to foresee such situations and to correct the planned actions accordingly. If the computation time required for full rescheduling is too long for a frequent online application, it can be approximated by reactive scheduling. Reactive scheduling modifies nominal schedules as a reaction to the occurrence of unexpected events (see e.g., Cott and Macchietto, 1989; Honkomp et. Al., 1997; Kanakamedala et al. 1994; Mendez and Cerda, 2004; Vin, and Ierapetritou, 2000, Janak et al., 2006a,b). The underlying models themselves usually do not incorporate information about the uncertainties. Reactive scheduling is present in any real production, often performed by the plant managers directly or induced by the process itself –e.g. when the preceding step is finished late, the start-time of the next one is adapted. The analogy to reactive scheduling is the use of nested low-level controllers to implement set-points in process control. Hereby, the effects of disturbances and plant uncertainty are reduced, variability is shifted from the controlled variables to the manipulated inputs. By using carefully chosen regulatory control loops, some of the potential of rigorous optimization can be recovered (Skogestad, 2000, Engell et al., 2005). Robust scheduling and multi-stage scheduling are variants of stochastic scheduling. Here models are employed that take uncertainty explicitly into account. Stochastic models with recourse consider the corrective measures that can be taken after the realization of some uncertain parameters while in robust scheduling, this option is not included.

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In robust scheduling, the parameters of the scheduling problem are considered as uncertain, usually varying in certain intervals, with or without knowledge of the distribution functions of the variation. Scheduling is then performed such that the best value of the cost function is achieved and all constraints are met in the worst possible situation. Jia and Ierapetritou (2004) investigated the use of MILP sensitivity analysis in robust shortterm scheduling under demand uncertainty. Balasubramanian and Grossmann (2003) proposed the use of concepts from fuzzy set theory to describe imprecisions and uncertainty for the minimization of the makespan of flowshop scheduling with uncertain task duration. Lin et al. (2004) and Janak et al. (2007) proposed an efficient MILP optimization methodology for generating schedules that are robust in the sense that the solutions are feasible (with a prescribed infeasibility tolerance) in the presence of uncertainties in the inequality constraints for interval bounds on the parameters and, with a prescribed probability, for probabilistic uncertainties in the inequality constraints, and optimal with respect to the nominal cost function This methodology was applied to short-term scheduling with uncertainties in processing times, demands, and cost coefficients. The problem of robust scheduling – and similarly of min-max formulations in model predictive control – is that the computed solution is feasible for the worst case but may fail to realize the potential of the real plant in all other situations. It corresponds to a pessimistic open-loop approach – all decisions are fixed and computed for the worst possible situation. Note that the concept of iterative optimization on a rolling horizon does not alleviate this problem – the decisions that are implemented are based on pessimistic (worst-case) assumptions and cannot be corrected while in the simple rescheduling approach they are based on average or optimistic assumptions. On the other hand, feasibility is always assured, given that the bounds include all possible situations that are met in the future. In the dynamic context, however, the future decisions can be adapted to the realization of the uncertainties, and this provides significant room for better choices of the decisions that have to be fixed here and now. A multistage stochastic decision problem is characterized by a non-anticipative information structure. The problem description includes stochastic aspects modeled either by continuous probability distributions or by a finite number of scenarios (the latter case is usually considered because it is computationally better tractable). If the uncertainty is modeled by a scenario tree with N stages (see Fig. 2), then the decision process progresses along this scenario tree as well. In stage i, the decision is based on the certain information on the realization of a path in the tree up to this node whereas the future evolution is only known probabilistically, and is represented by the sub-tree that starts at the corresponding node of the tree (Till et al., 2008). To solve multi-stage problems, at each stage the reaction of the algorithm to the information obtained at later stages must be taken into account, leading to a complex nested structure. Therefore multi-stage problems usually are approximated by two-stage problems, as shown in Fig. 2 (right). The decision variables are divided into the first and secondstage vectors x and yȦ, which belong to the sets X and Y, possibly with integrality requirements. The vector x represents “here and now”-decisions which are applied regardless of the future evolution and thus have to be identical for all scenarios. In contrast, the vectors yȦ denote scenario-dependent recourses under the assumption that the respective scenario realizes.

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Figure 2: Multi-stage (left) and two-stage (right) stochastic optimization problems represented by scenario trees

The objective is to minimize the first-stage costs plus the expected second-stage costs calculated using the weighting-vectors c and qȦ. The uncertain parameters are represented by a finite number of realizations (scenarios) Z with corresponding probabilities SZ . The objective is to minimize the first-stage costs plus the expected second-stage costs calculated using the weighting-vectors c and qȦ. In the mixed-linear case, this leads to an optimization problem of the form :

min c T x  ¦ S Z qZT y Z x , yZ

s .t . Ax d b ,TZ x  WZ y Z d hZ ,

(1)

Z 1

x  X , yZ  Y ,Z

^1, ,: `, X  IR

n1'

u IN

n1' '

,Y  IR

n2 '

u IN

n2 ' '

.

The parameters of each realization enter into the matrices TZ, WZ and the vectors hZ, qZ. In Fig. 2b, the first stage comprises the variables associated with stages 0-3 whereas the second stage comprises the variables associated with stages 4-10. The mathematical framework of two-stage stochastic programs provides a modular modeling concept for uncertainty conscious scheduling problems: In principle, any deterministic scheduling model can be extended to a stochastic model provided that the uncertainties affect only the parameters of the formulation. The extension requires the definitions of (1) scenarios for the uncertain parameters along with their probabilities, (2) first stage variables (3) an appropriate objective (e.g. expected value, excess probability). The approximation of a multi-stage problem by a two-stage problem corresponds to an optimistic assumption about the future: It is implicitly assumed that after the first stage decisions have been implemented, all uncertainties are revealed and the subsequent decisions are the optimal ones for the scenario that materializes. In fact, this optimal decision cannot be computed because of the sequential nature of the problem. However, the formulation guarantees that for each optimal first stage decision there is a feasible second-stage vector yZ. for all scenarios Z= 1 ...:The above formulation can be extended to include measures of risk either by adding constraints for risk-aversion or by setting up a two-criteria problem and computing Pareto-optimal solutions. When integer requirements are present in the recourse, the resulting stochastic integer program is often of large scale and cannot be solved easily without incorporating de-

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composition based methods or problem-specific heuristics. Therefore solving stochastic integer programs is sometimes avoided by assuming that all integer decisions are firststage variables. 3.2. Review of scenario-based stochastic formulations of scheduling problems Sand et al. (2000) and (Engell et al. 2001) extended a multi-period model for the medium-term planning of an industrial multi-product batch plant for the production of expandable polystyrene (EPS) to a two-stage model. Interesting features of this example are that the production is strongly coupled, i.e. each batch yields several products and that the final continuous processing stage involves mixing of material from different batches. The model considers uncertainties in demands and in capacities. The objective is to maximize the expected profit including a measure of risk aversion. The first-stage decisions consist only of integer variables and the second-stage decisions consist of integer and continuous variables. Sand et al. (2004) applied the dual decomposition based algorithm of Carøe and Schultz (1999) to solve the resulting stochastic integer programs with approximately 600 continuous variables, 100 integers, and 500 constraints in each of 1024 scenarios. Solutions with a gap of less than 9% were found within 4 h of CPU-time. Their programs are based on discrete-time multi-period models where the stages correspond to the time periods. Vin and Ierapetritou (2001) extended the event based continuous time model of Ierapetritou and Floudas (1998) to a two-stage stochastic program and minimized the expected makespan. They observed that using the stochastic model increased the robustness of the solution. Furthermore, they compared the use of deterministic and stochastic models in the reactive scheduling framework of Vin and Ierapetritou (2000) and found that the reactive scheduling performance was not necessarily improved by using the robust solutions obtained from stochastic models. Bonfill et al. (2004) extended a continuous time batch-slot concept model to a two-stage stochastic program and optimized the weighted sum of the expected profit and a risk term. The first stage comprises all binary and integer decisions of the detailed schedule while the second-stage consists of the remaining continuous decisions as e.g. sales. They observed an improved performance of the stochastic scheduler for a flowshop example. Balasubramanian and Grossmann (2004) modeled integer recourse decisions explicitly in a multi-stage stochastic integer program. Each of the M stages corresponds to a time period and the decisions are assigned corresponding to the stages. An additional stage is added to consider the continuous variables for the amounts sold and lost, the costs, and the revenues after the end of the scheduling horizon. A shrinking-horizon approximation scheme for multi-stage stochastic integer programs was proposed based on the solution of a series of two-stage stochastic programs with continuous secondstage. At stage i, all decisions of stage i to M are taken as the first-stage variables, while the second-stage decisions consist of the continuous recourse decisions of the stage M + 1. The variables that correspond to stage i are fixed, then the procedure is repeated for the remaining stages i+1 to M. Gröwe-Kuska et al.(2005) reported the application of multi-stage programs with mixedinteger recourse for the short-term unit commitment of hydrothermal power systems under uncertainty. The dimension of the multi-stage problems ranges up to 200,000 binary and 250,000 continuous variables. The model was solved by a problem specific scheme based on Lagrangian relaxation that exploits the existence of loose couplings between the units. Two-stage stochastic programming has also been applied in produc-

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tion and supply chain planning (e.g. Ierapetritou et al. 1995, Clay and Grossmann, 1997; Gupta and Maranas, 2003). Goel and Grossmann (2004) applied stochastic programming to the planning of off-shore gas field developments where the uncertainty is partly endogenous, and Tarhan and Grossmann (2008) considered the optimization of investments into production plants under uncertainty modeled as a multistage stochastic program where the uncertainty is gradually removed. Alonso-Ayuso et al. (2005) proposed two and multi-stage programs with mixed-binary recourse for production planning and scheduling problems under uncertainty. Guillen et al. (2006) used two-stage stochastic scheduling models on a shrinking horizon to evaluate the design of supply chains under demand uncertainty. Wu and Ierapetritou (2007) integrated a two-stage stochastic planning model on a moving horizon into a hierarchical planning and scheduling approach. Puigjaner and Lainez (2008) employed a twostage stochastic formulation in supply chain optimization and also related this explicitly to the rolling horizon approach used in model predictive control. Their model integrates the financial situation of the supply chain. In Cui and Engell (2009) the two-stage formulation is applied to the moving horizon medium-term planning problem of the EPS example mentioned above. In order to avoid the blow-up of the problem size with the length of the second stage, the more distant future is represented by only one deterministic scenario with the expected values of the parameters whereas the immediate future is represented by a tree of different scenarios of production capacity and demand evolutions.

Figure 3: Moving horizon two-stage stochastic program in period i

The plant is scheduled under uncertainties ȟ = {ȟ1, ȟ2, . . .  ȟI-1} which are independent discrete random variables with discrete distributions ȥ(ȟi) in a time horizon with I periods as shown in Fig. 3. x1, x2, … xI are the mixed-integer decision variables in each period. The near future within the next I1 periods and represented by f2(g) is modeled by a tree of scenarios in the combined sample space Ȧęȍi of the future demands whereas the more remote future within the following I2-I1 periods is represented by the expected values (EVs) of the stochastic variables (cost contribution f3(g) ). As the inclusion of the more distant future predominantly has the purpose to rule out unrealistic solutions that maximize the benefit over a short horizon at the expense of the long-term performance, and realistic scenarios are difficult to generate for the distant future, this is a reasonable simplification. Both time horizons are rolling in the time coordinate i. In step i , as shown in Fig. 3, a 2SSIP model with the past optimal decisions x1*i 1 , actual decision variables xi, realized uncertainties ȟi-1, additional uncertainties [ i  I1 1 and EVs for the distant future [i  I1i  I2 1 is solved and the first stage optimal solutions x*i are im-

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plemented. Period i is the first stage and period i+1 to period i+I2 constitute the second stage in the 2SSIP setting. The strength of the formulation of scheduling problems as two-stage stochastic decision problems is that it is perfectly adapted to a rolling-horizon approach where the decisions after the first period are re-computed based upon the new information obtained so that in the decision process, a reaction to the future developments is possible. In other words, the feedback that is present in the real decision structure by the update of the decision vector after each period is represented adequately, in a slightly optimistic fashion, because of the assumption that from some point on a clairvoyant scheduler is employed. In contrast, in a robust formulation, the scheduler bases its decisions on the assumption that the worst possible happens in the future and that no corrective action can be taken. The disadvantage of the approach is the high computational cost that is prohibitive in online applications. In particular, the time until a first feasible solution is obtained by an exact algorithm can be very large for large numbers of scenarios In our recent work, hybrid algorithms were developed that employ stage decomposition. (Till et al., 2007, Sand et al., 2008, Tometzki and Engell, 2009). 3.3. Stage decomposition algorithm for the solution of two-stage programs In a stage decomposition appraoch, the variables and the constraints of problem (1) are separated according to the stages into the master-problem (2) and : subproblems (3). Due to the integrality requirements in Y, the implicit function QZ ( x ) is in general nonconvex. :

min x

f1 ( x ) c T x  ¦ S ZQZ ( x ) s .t . Ax d b , x  X , X  IR n1' u IN n1'' ,

QZ ( x )

(2)

Z 1

min yZ

f 2 ,Z ( y Z ) qZT y Z

s .t . W Z yZ d hZ  TZ x , y Z  Y ,Y  IR n2 ' u IN n2 '' . (3)

The main idea of the hybrid algorithm is to use an evolution strategy (ES) (Beyer and Schwefel, 2002) to address the master-problem (2). An ES works on a population of individuals (pool of solution candidates). The ES interprets a certain instantiation of x as an individual and the corresponding f1(x) in (2) as the fitness of the individual. The fitness is evaluated by solving the independent subproblems (3) using a standard MILP solver. Infeasibilities are handled by penalty terms. Computational experiences show that the hybrid algorithm obtaines good feasible solutions for large numbers of scenarios considerably faster than the decomposition algorithm by Caroe and Schultz (1999) and straightforward application of a MILP solver (CPLEX). When CPLEX has found an admissible solution, however, it converges faster to optimal values of the cost function than the hybrid algorithm.

4. Hierarchical decision structures The motivation of hierarchical decision structures is to reduce the complexity of the problem at hand to make it tractable by humans or algorithms and also to maintain transparency of the solutions. While in most problems all decision variables interact in their influence on the overall performance, this interaction can and should be neglected to some extent because of the presence of uncertainty and of feedback. The presence of uncertainty leads to the situation that detailed decisions beyond a certain horizon are obsolete soon after they have been computed, while feedback remedies the propagation of uncertainty. The decomposition in layers corresponds to time-scale decomposition:

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long-term decisions are optimized over a long horizon using simplified (averaged) models, short-term decisions are based upon very detailed models taking into account all available information. The temporal resolution as well as the decisions variables included on each level should reflect the precision of the information that is available as well as the duration of the impact of the decisions. Typically, a hierarchical decomposition for the solution of industrial-size problems will include (at least) the layers of longterm planning, mid-term planning and (short term) scheduling. In long-term planning, decisions on the production capacities, on the distribution of production tasks among sites and on the production volumes are taken using aggregate, and usually predicted, hence relatively uncertain data on market demand, cost structures, raw material prices etc. Usually coarse models of the required and of the available resources are used. The accuracy of long-term planning can be improved by performing detailed planning over the full planning horizon using semi-heuristic algorithms (Plapp et al., 2008), however this requires a large effort and the result can then only be used in “what ... if” investigations. The implications of the decisions on this level concern mostly procurement: ordering of material, addition or reduction of production capacities, long-term staff planning. The precision and the temporal resolution of the data usually is low, a resolution finer than a week will usually by not justified, often planning intervals will be months. The update interval may be (considerably) longer than the resolution, so this is an off-line activity with only weak feedback from the daily operations. The medium-term planning and the scheduling layer correspond to the scope of APS (advanced planning and scheduling) systems (Goebelt et al., 2008, Jaenicke and Seeger, 2008). On these layers, all orders that are considered (customer orders or production to stock) have delivery dates and the assignment of production capacities to the tasks is performed based upon a detailed model of the required resources. The temporal resolution 'M on the medium-term planning layer usually will be days or shifts. Short-term scheduling is the exact temporal assignment of all required resources to production tasks. The temporal resolution will be hours or even minutes. 4.1. Review of hierarchical solution approaches Hierarchical algorithms were first proposed for the solution of large scheduling problems that cannot be solved directly with the goal to obtain a near-optimum schedule over the full horizon. (Bassett et al., 1994/1996) proposed to employ different discretizations of time. On the upper layer, aggregated problems are formulated to allocate production tasks to time slots for which a detailed schedule is computed afterwards one-byone. The automatic aggregation of detailed models was refined in (Wilkinson et al., 1995) with special attention to the couplings between the intervals. Dimitrades st al (1997) applied a non-uniform discretization of the time axis where the initial intervals are modeled on a finer grid than the subsequent ones. In each step, the problem is solved over the full horizon, the initial decisions are frozen and the solution process proceeds in a shrinking horizon fashion until a schedule over the full horizon has been computed. Carryovers from one period to the next are handled by extending the detailed model into the next period until all tasks considered have been finished. The idea that only the immediate future needs to be computed in a detailed fashion goes back to Zentner et al. (1996). Papageorgiou and Pantelides (2000) proposed a hierarchical approach to campaign planning. Harjunkoski and Grossmann (2001) used a bi-level decomposition strategy for the scheduling of a steel plant. The products are grouped into

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blocks, and the sequences within these blocks are determined separately, following by an optimization of the sequence of the blocks. Van den Heever and Grossmann (2003) used a rolling horizon approach and a Lagrangean decomposition strategy for production planning and scheduling of a hydrogen plant. Mendes and Cerda (2003) discussed problem formulations and solution algorithms for dynamic scheduling problems where new data arrives iteratively. A hierarchical decision structure that includes explicit models of uncertainty and a hierarchical decomposition was proposed in (Sand et al., 2000) and (Engell et al., 2001) based on the analysis of the scheduling problem for the EPS plant. This plant presents a typical example were on the one hand side decisions have to be taken on a very fine time scale using detailed models but on the other hand have long-term effects that go beyond the horizon that can be dealt with in detailed scheduling. Moreover, the problem data is uncertain, concerning demands, yields, and capacities. The time horizon needed for the decision on the choice of the recipes and the number of batches exceeds the period over which a detailed schedule can be computed. It was proposed to combine a two-stage stochastic medium-term planning model on a coarse time grid with fixed period lengths with a deterministic short-term scheduling model formulated in continuous time that is solved in an event-driven fashion (see Fig. 4). The upper layer was assumed to provide guidelines (numbers of batches for each recipe that are started in a two-day period and states of the finishing lines (on or off)). Feedback is provided by reporting the batches that have been started or are scheduled to start before the end of the computation period back to the medium-term planning layer. On the upper layer, linearized models are used while for scheduling, nonlinear models of the mixers and a partly heuristic MINLP algorithm are employed (Schulz et al., 1998, Engell et al., 2000).

Figure 4: Two-level online decision structure proposed for the EPS process in (Sand et al., 2000)

In this scheme, the medium-term planning problem with uncertainties in demands and yields was formulated as a two-stage stochastic planning problem using aggregate models (Sand et al., 2000, Sand and Engell, 2004) and the problem was solved using the decomposition strategy by Carøe and Schultz (1999). Stefansson et al (2006) proposed a multi-layer architecture for campaign planning and detailed scheduling in the pharmaceutical industry. They propose a three-layer architecture in which on the upper layer, campaign planning is performed over a horizon of 12 months, on the middle layer, a detailed order allocation is performed over a horizon of three months with the goal to confirm delivery dates, and on the lowest level detailed scheduling is performed based upon confirmed customer orders using a continuous-time model. They assume a one-directional interaction between the layers, i.e. there is no feedback from the lower layers back to the upper ones which implies that all proposed decisions on the upper layers can be implemented on the lower layers.

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Janak et al (2006a,b) applied a temporal decomposition approach to an industrial batch scheduling problem. The decomposition idea is to first determine the time period and the products that are considered in short-term scheduling, and then to solve the scheduling model. The horizon length is maximized under the constraint that the complexity of the resulting problem is bounded, thus enabling reasonable computing times. In the same spirit, Shaik et al. (2008) solve a scheduling problem for a large industrial continuous plant by two-level decomposition. On the upper (medium-term) level, demands are allocated to time slots (sub-horizons), and on the lower level the sequencing of the next operations in the sub-horizon is performed in a rolling horizon fashion. Verderame and Floudas (2008) define a relaxed planning model for large scale problems on the upper layer of a two-level formulation similar to Janak et al. (2006a) where the resources considered are only the bottleneck resources and use this model to generate daily production profiles (targets) for the scheduling layer. Wu and Ierapetritou (2007) proposed a scheme which implements a similar concept as shown in Fig. 4. The planning horizon in their work consists of three stages of different lengths. In the short first stage, the data is assumed to be deterministic and detailed scheduling problems are solved. In the two other stages of increasing lengths that represent the immediate and the remote future, the demands and the production capacity are aggregated. The planning problems are solved using simplified models in which the unmodeled parts of the scheduling problem are represented by a sequence factor that describes how much less products can be obtained due to the additional constraints in the scheduling model compared to the planning model. The planning algorithm determines the amount of product that is required after the first stage, taking into account different scenarios for the future demands with associated probabilities. So the planning model is a two-stage problem with the requested production in the first stage being the here-and-now variables. Depending on whether the scheduling problem is feasible or not, the sequence factor is updated, introducing feedback from the scheduling layer to the planning layer. The results for a case study show the superiority of the approach over pure rolling horizon scheduling approaches with look-ahead of one or two periods, compared to a horizon of 9 periods considered in the planning model, for a situation where the backorder cost is high. The interaction of long-term planning by ERP systems and APS systems is discussed in (Goebelt et al., 2008 and in (Jaenicke and Seeger, 2008) from an industrial point of view. Goebelt et al. assume different models and algorithms on the two layers that are reconciled by overlapping horizons whereas Jaenicke and Seeger propose a top-down refinement approach. (Sousa et al., 2008) discuss a hierarchical multilevel approach to supply chain optimization which is nicely illustrated by an example of active ingredients manufacturing. The proposed approach is to solve a planning problem with aggregated capacities over a cyclic horizon of one year, discretized into 12 planning periods. This provides inputs to the lower scheduling layer, inventory levels of products at locations at the start and at the end of a month, product flows to formulation sites (integrated) per period, product flows to customers (integrated) per period, site opening, allocations of products to manufacturing sites, product supplies to specific customers from specific sites. Based upon this information, schedules are computed at the lower level for each month using detailed recipes and changeover times. On the lower level, the demands are distributed over time whereas on the upper level, they are aggregated to the ends of the months. The inventory levels are considered as constraints whereas the demand satisfac-

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tion is reflected in the cost (penalty terms for late delivery). It is observed that without feedback from the second stage to the first stage, there is a significant mismatch between demands and delivery. In order to solve this problem, capacity correction factors that depend on the number of campaigns planned are introduced on the planning layer and additional constraints are formulated. These measures achieve the goal of reducing the gap between the layers without sacrificing overall production, after some manual adaptations. They increase the inventories computed on the planning level. A direct manipulation of inventory levels did not provide consistently good solutions. 4.2. Considerations on the interaction between medium-term planning and scheduling The relation between hierarchical levels is one of refinement and abstraction. The lower levels include more details on the timing of the production steps and on the resources needed, hence more constraints and more degrees of freedom are present. In the ideal case, these degrees of freedom are sufficient to satisfy the additional constraints that have to be taken into account such that the results of the optimization on the upper layer can be implemented on the lower layer without any violation of constraints. In reality, this will rarely be the case. If, e.g., the production capacity is assumed to be known on a weekly basis on the upper layer and is fully used, it is unrealistic that exactly this amount of products can be produced if more detailed constraints are considered. The simplest way to avoid this situation is to systematically underestimate the capacities when reporting to the higher layer, a strategy that is not uncommon in practice. In general, it cannot be assumed that the implementation of the upper layer decisions is always feasible, hence feedback mechanisms are necessary and it is preferable to provide targets and a cost function that measures the satisfaction of the targets in contrast to restricting the lower layer by hard constraints. Within the horizon under control of the lower layer, as few constraints as possible should be formulated to provide maximum flexibility to the lower layer to cope with unmodelled effects and uncertain parameters and events. The inclusion of explicit descriptions of uncertainty into the models requires a careful design of the decomposition and of the coupling of the layers. Assume e.g. that a solution was obtained on the medium-term planning layer that assigns certain production tasks within the first kM intervals of the planning horizon, taken as first-stage decisions, to the scheduling layer. Then this assignment is based on the assumption of a certain estimated average capacity during the first interval, determined from available information, e.g. on planned maintenance. If the available capacity in the first scheduling interval is higher than this average value, how should the scheduler react? Intuitively, it might be wise to use the higher-than-average capacity in order to account for possible breakdowns in the future. But this would be penalized if the first stage variables from the medium-term planning are used as targets for the scheduler in the respective intervals. In addition, updated information may be available during the scheduling process on the amounts to be produced and on the due dates. Generally speaking, it is not a good idea to fix variables inside the horizon of the lower layer unless these variables really have to be set and are beyond the control of the scheduler. Maximum flexibility should be given to the lower level algorithms to use the information and the degrees of freedom that are available in order to maximize the overall goals in the presence of uncertain parameters, stochastic events and restrictions that are unknown to the upper layer. Conversely, only the information needed to perform the next update on the upper layer should be fed back from the lower layer, e.g. updates on yields, expected capacities, planned resource utilization etc.

S. Engell

58 T0

T0+HS

T0+HS+'M

Online scheduling

T0+ uM'M

X11

iterations 'M

X12

X22 Medium-term

T0+HS+HM 'M

uM'M

planning iteration 1st stage

recourse

Figure 5: Telescopic two-layer moving horizon scheme In Fig. 5, a telescopic two-layer moving horizon scheme is sketched where the mediumterm planning layer employs a two-stage formulation to include uncertain future evolutions. The horizon on the scheduling level is 'S HS = kM.'M, kM • 1 where 'M is the length of the time slots on the medium-term planning layer. On the planning layer, a two-stage formulation is used where the length of the first stage is uM 'M The key idea of the scheme depicted in Fig. 5 is to avoid double planning and to link the layers only via target values or predicted values of the “states” of the system. These are the amounts of materials considered in medium-term planning and scheduling at time t, X(t) and the planned resource utilizations after time t, U(t). From the point of view of the lower layer, a target is required that reflects the look-ahead-capability of the upper layer but does not restrict the decisions of the lower layer more than necessary. From the point of view of the upper layer, the predictions of the materials produced or consumed at the beginning of the medium-term planning horizon and of the resource utilization after this time by the scheduling horizon provide the necessary information about the past and the inertia of the system. Iterative medium-term re-planning is not performed over the full scheduling horizon but only over that part of it that lies in the next planning horizon. At time T0 the scheduling algorithm performs an optimization of the resource allocation over the scheduling horizon of length HS taking the actual data on the available resources and the demands and possibly also scenarios of the future resources and demands into account plus targets for the state X(T0+HS) at the end of the scheduling horizon which is provided by the medium-term planning algorithm (X11 in Fig. 5). The end of the scheduling horizon should coincide with the endpoint of a medium-term planning interval, T0+HS = p0ҏ'M, p0 integer. The scheduling algorithm is iterated either after fixed periods of time or when new data is available with the same end point T0+HS as before and the same target state, until the length of the scheduling horizon is less than or equal to HS-ҏ¨M. At this point, the endpoint is shifted to (p0+1) ¨M and the target is the state at T0+HS+¨M as computed by the medium-term planning algorithm in the previous iteration (X12 in Fig. 5). This is iterated until the endpoint has been shifted by the update interval on the medium-term layer relative to the first endpoint. At this point, the medium-term planning algorithm is run to compute an update of the targets. The planning horizon of the medium-term planning algorithm is shifted by uM ¨M. The horizon that is now considered by the medium-term planning algorithm is ((p0+uM) ¨M, p0+uM¨M+HM] and the decisions between (p0+uM) ¨M and (p0+2uM) ¨M are taken as first-stage variables while the remaining ones are recourse variables. After the computation, the decision variables of the first stage are not given to the scheduler but only the resulting values of the planned materials at times (p0+1+uM) ¨M … (p0+2uM) M (X21 and X22 in Fig. 5). At time T0 + uM ¨M the best possible prediction of the state of the system at the initial time (p0+uM) ¨M is the (expected) value that is computed by the scheduling algorithm for

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X((p0+uM) ¨M) and U((p0+uM) ¨M). Therefore this state is used as the initial condition of the medium-term planning algorithm. This scheme is iterated every uM 'M units of time.

5. Summary and Future Research In this paper, we have discussed the design of medium-term planning and scheduling algorithms from a dynamic systems point of view and drawn parallel between process control and planning and scheduling. In summary, medium-term planning and scheduling are reactive activities where decisions have to be made under uncertainty and in real time. Moving horizon formulations with recourse (two-stage or multi-stage stochastic programs) reflect the dynamic nature, the presence of uncertainty and the potential of reacting to the realization of the uncertainties adequately. In addition, measures of risk can be included in the optimization. A drawback is the computational effort which limits the horizon of the second stage and the number of scenarios. The solution of realworld problems requires a hierarchical decomposition, as advocated by several authors recently. In such a hierarchical decomposition, the coupling of the layers is critical. The task of the lower layer should be formulated such that maximum freedom is left for the adaptation to the constraints and the reaction to uncertainties while the overall goal is properly reflected in the cost function. In a hierarchical decomposition approach, the issue of distributed solutions, in particular on the lower layer arises naturally, as this enables the parallel solution of smaller sub-problems. An initial discussion of the coordination between different layers and different decision makers on these layers can be found in (Kelly and Zygnier, 2008). Distributed decision making for more than very few units however has up to now only rarely been investigated in detail in the literature on batch scheduling and is a promising area for future research. At the interface of scheduling and process control for batch processes, there is a potential for a tighter coupling of the optimization of the batch runs which is a prominent topic in process control (see e.g. Srinivasan et al., 2002a,b) and medium-term planning and scheduling. Depending on the schedule, the optimization goals on the control layer can be modified: if the unit is in high demand, a reduction of the batch time by timeoptimal feeding and cooling policies is indicated whereas in a situation where the schedule is not tight, energy could be saved by a different operation policy or the yield could be increased. In the opposite direction, the scheduling layer could be supported by a precise prediction of the expected batch times and yields before the termination of a batch. Finally, the practical success of any sophisticated solution, in control as in scheduling, depends on a good interface to the operators. Optimal policies must be visualized adequately so that they can be understood by the operators. E.g. for well qualified and responsible operators, not only one single result of an optimization run should be provided but a set of several “best” solutions such that they can trade the loss of optimality with other criteria that are not represented in the optimization and gain confidence in the proposed solutions.

6. References Alonso-Ayuso, A., L. F. Escudero, and M.T. Ortuno (2005). Modeling production planning and scheduling under uncertainty. In S. W. Wallace, and W. T. Ziemba (Eds.), Applications of stochastic programming. MPS-SIAM Series in Optimization, 217–252. Balasubramanian, J., and I.E. Grossmann (2003). Scheduling optimization under uncertainty - An alternative approach. Comp. and Chem. Engg. 27 (4), 469–490.

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Hybrid Molecular QSAR Model for Toxicity Estimation: Application to Ionic Liquids Ángel Irabiena, Aurora Gareaa and Patricia Luisa a Universidad de Cantabria, Ingenieria Quimica y Quimica Inorgánica, Avda de los Castros s/n, Santander, 39005, Spain, E-mail:[email protected] Abstract Ionic Liquids have been suggested as one of the main possibilities to avoid solvent losses in chemical processes, but toxicity needs to be evaluated before technical applications. A quantitative structure-activity relationship (QSAR) based on a hybrid molecular QSAR model has been applied to the modeling of the aquatic ecotoxicity (Vibrio fischeri EC50) of ionic liquids. In this work, the ionic liquids database has a number of 96 data, which has been improved using data from the literature and experimental data following the UNE EN ISO 11348–3 procedure; these data involve nine different cations and seventeen anions, thus, 9x17=153 different combinations can be considered. The range of ecotoxicity covered by the novel QSAR corresponds to: Log EC50 values from –0.23 to 5.00. The modeling has been performed using mechanistic and stochastic considerations, hybrid model. The influence of the anion, cation and substitutions in the ecotoxicity has been estimated to design ionic liquids with lower toxicity, giving the pTS and N(CF3)2 anions and the imidazolium cation the lowest aquatic toxicity (statistically shown). Keywords: Solvents, Green Technology, Molecular Design

1. Introduction The interest in ionic liquids has increased widely in the last years in order to achieve better environmental management of processes and products. Some interesting properties of these compounds, such as their negligible vapour pressure, high thermal stability and attractive properties as solvents, justify paying attention to them. However, it is also important to study the risks associated to their use [1]. Many ionic liquids are soluble in water and toxicity of some ionic liquids has been measured in different aquatic organisms [2-4]: bioluminescent bacteria (e.g. Vibrio fischeri), green alga, cladoceran (e.g. Daphnia magna), fish (e.g. Danio rerio), etc., showing a broad range of toxicity. Because of the large number of ionic liquids, it is necessary to develop estimation procedures in order to estimate the toxicity of specific ionic liquids without measuring it, reducing the material- and time-consumption. Quantitative structure–activity correlations, referred to as QSARs, are models that can be used to estimate the physicochemical and biological properties of molecules from the molecular structure or properties of similar compounds whose activities have already been assessed. In a previous work [4], a novel QSAR was developed in order to estimate the EC50 (Vibrio fischeri) for imidazolium, pyridinium and pyrrolidinium based ionic liquids. In this work, new ionic liquids have been studied to obtain a broader database and model to be used to estimate ionic liquids EC50 (Vibrio fischeri).

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2. Ionic liquids database The studied ILs were based on the cations and anions shown in Figure 1. The database used to develop the QSAR is constituted of a set of log EC50 values (logarithm of 15- or 30-min toxicity to Vibrio fischeri), obtained from experiments and from the literature [3-6]. Experimental data were obtained for some ionic liquids [4,7] by means of the 15min standard bioluminescence inhibition assay according to the UNE EN ISO 11348-3 procedure. Toxicity testing is based on the bioluminescent bacterium Vibrio fischeri using the Microtox Model 500 toxicity analyzer. Those ionic liquids were synthesised as it was shown elsewhere [8].

3. Model development According to group contribution methods, properties of a molecule can be assumed to be the summation of the contributions of its atoms and/or fragments. These methods allow taking into account mechanistic and stochastic considerations, leading to a hybrid model. In this work, the structure of ionic liquids has been based on three main molecular descriptors: anions (Ai), cations (Cj) and substitutions (Sk); these variables have a nonzero value when the group is present in the molecule. A detailed description of the molecular descriptors can be found in Table 1. Some extra descriptors have been included in order to take into account the specific behaviour of some cation-anion combinations to the ecotoxicity; ai, cj, and sk, are the contribution of each group to the toxicity, and the summation is taken over all groups. Subscripts indicate anions (i), cations (j), and substitutions (k). Descriptors with similar contribution have been grouped.

Figure 1. Cations and anions which perform the studied ionic liquids

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The dimensionless ecotoxicity, Y*, between 0 and 1, can be estimated by the novel QSAR as the summation of the contributions of each group:

Y * = ¦ a i ⋅ Ai + ¦ c j ⋅ C j + ¦ s k ⋅ S k i

Y* =

j

(1)

k

log EC 50 _ max − log EC 50 log EC 50 _ max − log EC 50 _ min

(2)

where logEC50_max and logEC50_min are the maximum and minimum values of logEC50 in the database showing the application range of the model, being 5.00 and -0.23, respectively. Table 1. Molecular descriptors of the novel QSAR

Influence of anions (Ai). Value=1 if it exists and 0 if not

Influence of cations (Cj). Value=1 if it exists and 0 if not

Influence of substitutions (Sk).

A1: Cl, BF4, N(CN)2, MetSO4, EtSO4, Br A2: PF6 A3: Cap A4: Ace, For, TfO, 8OSO3, (2-OPhO)2B, N(CF3SO2)2, TFA A5: pTS, N(CF3)2 C1: imidazolium (C<14) C2: imidazolium (C=14) C3: imidazolium (C=16) C4: imidazolium (C=18) C5: specific contribution of imidazolium with N(CF3SO2)2 and specific contribution of butylimidazolium with TFA, Ace, TfO, Cap and For C6: pyridinium C7: Pyrrol, Morp, Piper C8: (dimethylamino)pyridinium, TMG C9: specific contribution of TMG with TFA C10: Melanime C11: Choline S1= C/Cmax (C=number of carbons in R chain; Cmax=18) S2: number of carbons in R1 chain S3: number of short chains (0, 1, 2)

4. Results and discussion The data set has been fitted to the QSAR model by multilinear regression analysis using Polymath 5.0 software, and a good fitting has been achieved, with n=96, r2=0.928, r2adj=0.912, rmsd=0.0062 and variance=0.0046. A comparison between the observed data for the dimensionless ecotoxicity (Y*) of ionic liquids and the prediction based on the novel QSAR has been performed. Figure 2 shows the parity plot. In addition, the distribution of the residuals, defined as the differences (absolute values) between the experimental and estimated Y*, is given in Table 2. 87% of the residuals are lower than 0.1, which shows a good fitting of the model.

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The novel QSAR allows establishing an order in the ecotoxicity, considering the contributions of the anions, cations and substitutions. Figure 3 shows a schematic way to infer the least and most toxic ionic liquids. For example, if an ionic liquid with low ecotoxicity (Vibrio fischeri) is desirable, an useful combination would be an imidazolium based ionic liquid with a short hydrocarbon chain and with the anion pTS or N(CF3)2 (statistically shown). Table 2. Distribution of residuals (absolute values), differences between the observed and calculated dimensionless toxicity.

Range < 0.1 [0.1, 0.15] > 0.15 < 0.2

Nº data 87 6 3 All (96)

% 91 6 3 100

1.2 1

Estimated Y*

0.8 0.6 0.4 0.2 0 -0.2 -0.2

0

0.2

0.4

0.6

0.8

1

1.2

Experimental Y*

Figure 2. Parity plot.

Figure 3. Ecotoxicity order for anions, cations and substitutions.

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There are also specific contributions to take into account, which are produced when a specific anion and cation are put together. About 22% decrease is expected in the toxicity for C5 combinations (see Table 1) and about 58% increase is expected for TMG-TFA combination. In addition, a decrease of about 19%, 46% and 89% in toxicity is produced when the long chain in imidazolium-based ILs has 14, 16 and 18 carbon atoms, respectively. Further work will be focused on the development of new QSARs based on computational chemistry using the state of the art of quantum chemical properties. 5. Conclusions A novel QSAR performed in a previous work and based on a group contribution method has been improved with more kinds of ionic liquids and a broader range of ecotoxicity. This method allows establishing an order of anions and cations based on their contributions to the ecotoxicity in order to be able to design ionic liquids with low ecotoxicity (Vibrio fischeri). The pTS and N(CF3)2 anions and the imidazolium cation showed the lowest toxic effect (statistically shown). Specific behaviour for some combinations cation-anion have been also obtained and a lower toxicity is observed for imidazolium-based ionic liquids with more than 14 carbon atoms in the long chain (R)

6. Acknowledgements This research was funded by the Spanish Ministry of Science and Technology (Project CONSOLIDER CTM2006-00317).

References [1] B. Jastorff, R. Störmann, J. Ranke, K. Mölter, F. Stock, B. Oberheitmann, W. Hoffmann, J. Hoffmann, M. Nuchter, B. Ondruschka, J. Filser. Green Chem. 5 (2003) 136. [2] R.J. Bernot, M.A. Brueseke, M.A. Evans-White, G.A. Lamberti. Environ. Toxicol. and Chem. 24 (2005) 87. [3] J. Ranke, K. Mölter, F. Stock, U. Bottin-Weber, J. Poczobutt, J. Hoffmann, B. Ondruschka, J. Filser, B. Jastorff. Ecotoxicol. Environ. Saf. 58 (2004) 396. [4] P. Luis, I. Ortiz, R. Aldaco, A. Irabien. Ecotoxicol. Environ. Saf. 67 (2007) 423. [5] K.M. Docherty and C.F. Kulpa Jr. Green Chem. 7 (2005) 185. [6] M.T. García, N. Gathergood, P.J. Scammells. Green Chem., 7 (2005) 9. [7] P. Luis, A. Garea, A. Irabien. Proceeding of the EUCHEM 2008 Conference (2008). [8] P. Luis, C.A.M. Afonso, I.M. Coelhoso, J. Crespo, A. Irabien, Proceeding of the 23rd European Symposium on Applied Thermodynamics (2008). ISBN: 2-905267-59-3.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

Prediction of Phase Equilibrium Related Properties by Correlations Based on Similarity of Molecular Structures Neima Brauner a, Mordechai Shacham b+, Roumiana P. Stateva c, and Georgi St. Cholakov d a

Tel-Aviv University, Faculty of Engineering, Tel-Aviv 69978, Israel, e-mail: brauner@ eng.tau.ac.il b Ben-Gurion University of The Negev, Chemical Engineering, P. O. Box 653, BeerSheva 84105 Israel, e:mail: [email protected] c Bulgarian Academy of Sciences, Institute of Chemical Engineering, Sofia 1113 d

Bulgaria, e-mail: [email protected] University of Chemical Technol. and Metallurgy, Department Organic Synthesis and Fuels, Sofia 1756, Bulgaria, e-mail: [email protected]

Abstract We have recently developed several new methods for property prediction to complement the traditional group contribution techniques, asymptotic behavior correlations and Quantitative Structure-Property Relationships (QSPR). These methods include the Quantitative Structure-Structure Property Relationship (QS2PR), the shortcut QS2PR method (SC-QS2PR) and the targeted QSPR method (TQSPR). The main effort has been directed so-far to prediction of constant, pure component properties, while very few attempts of predicting phase equilibrium related properties are documented in the literature. In this paper we report on the use of the QS2PR and SC-QS2PR methods for predicting binary interaction parameters for the Peng-Robinson equation of state, and vapor pressures at various temperatures.

Keywords: Property prediction, Phase equilibria, Molecular structure, QSPR. 1. Introduction. Phase equilibria calculations are of key importance for process and product design. In many cases the required data for these calculations are not available and have to be estimated. Up-to now most published methods, that relate molecular structure and properties have been devoted to constant properties of pure compounds, which are

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necessary but not sufficient for phase equilibria calculations of mixtures at different parameters of state [1]. We have recently developed several new methods for property prediction based on Quantitative Structure-Structure Property Relationship (QS2PR) [2]. These include the short-cut QS2PR method for homologous series [3] and the targeted QSPR method (TQSPR) [4]. With various examples we have demonstrated that they can predict constant properties of pure compounds with high reliability. Hereunder, we present results on the application of our methods for prediction of temperature-dependent properties, and of binary interaction coefficients needed for phase equilibria calculations for mixtures.

2. Prediction of Pure Compound Vapor (Saturation) Pressures with QS2PRs. Vapor (or saturation) pressures of pure components are essential in phase equilibrium calculations for non-ideal systems, for which the vapor-liquid equilibrium ratio K (K-value) for the i -th component, applying the J  M model, is given by:

Ki

J iL f 0 iL Ii

(1)

V

where J iL and f iLo denote the activity coefficient and the standard-state fugacity of the i -th component in the liquid phase and IiV is the fugacity coefficients of the i -th component in the vapor phase. A value for the pure component saturation pressure Pi s is required to calculate f iLo of a pure liquid at a specified temperature and pressure. For ideal systems at low pressures Eq. (1) is reduced to: K i Pi s / P , (2) where P is the total pressure. Hence, for ideal systems the prediction of Pi s is sufficient for phase equilibrium calculations. Several correlations for prediction of vapor pressure are available in the literature (Miller, Riedel, etc.). Most of those correlations require the normal boiling temperature (Tb), the critical temperature (Tc) and pressure (Pc) of the target compound [1]. The prediction of these properties, using either the QS2PR or shortcut QS2PR techniques is straightforward. Pure component vapor pressures are usually available as a function of temperature in an equation of the general form f ( Pi s , T ) 0 . The most commonly used equations (Antoine, Riedel and Wagner) are explicit in Pi s , but the Antoine equation can also be brought into a form that can be explicitly solved for the temperature.

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We have applied the property-property correlation to directly predict the parameters of a particular (say, Antoine) vapor pressure equation of a target compound, when the same parameters are available for the predictive compounds, identified by the QS2PR technique and have found that in general, these parameters do satisfy the property-property correlation. However, this approach has several practical limitations. Firstly, the parameters for the same type of equation must be available for all the predictive compounds and for the same pressure range. Secondly, as these parameters have been obtained by nonlinear regression of data (in case of the Antoine equation), or in some cases ill-conditioned linear regression (Riedel's equation with non-normalized temperatures), the parameters for the target so-obtained may result in deterioration of the vapor pressure predictions. Consequently, a more robust approach was developed. Our approach uses the QS2PR method for predicting the saturation temperature at a specified pressure and it is based on the QS2PR methods proven ability for high precision prediction of the normal boiling point. Accordingly, the temperature Tt at which the vapor pressure of the target compound is Pt should satisfy the property-property correlation (Eq. 3) when the temperatures corresponding to vapor pressure Pt of the predictive compounds (Tp1, Tp2, … Tpm, Tt) are substituted on its r.h.s. Thus, the following set of equations is used:

Tt

E1Tp1  E 2Tp2 E mTpm; f (Pt ,Tp1 ) 0; f (Pt ,Tp2 ) 0; ; f (Pt ,Tpm ) 0

(3)

This is a set of m+1 equations with m+1 unknowns (Tp1, Tp2, … Tpm, Tt), which can be solved by simple substitution if, for example, the Antoine equation is used for representing the vapor pressure curve. If more complex equations (such as the Wagner or Riedel equations) are used, numerical solution of the simultaneous equations is required. Table 1 shows the predicted saturation temperatures of n-hexadecane as a target using the proposed modification of the QS2PR technique. For the predictive compounds n-pentadecane and n–heptadecane the coefficients of the structure-structure correlation obtained by the SROV program are E1 = 0.50848 and E2 = 0.49232. The Antoine equation is used to calculate the saturation temperature of the target n-hexadecane at the chosen pressure P (bar):

Ti s

Bi  Ci Ai  log( P )

(4)

where Ti s is the saturation temperature (K) , and Ai, Bi and Ci are the Antoine equation parameters of component i.

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Table 1. Prediction of saturation temperatures of n-hexadecane Compound1

n-C15 n-C17 n-C16, target n-C16, target Rel. error, %

Coeff. for the S-S correlation 0.50848 0.49232 Calc.3 Pred.

Antoine Equation Parameters2 A B 4.1494 1789.66 3.927 1718.00 4.1731 1845.67

C -111.86 -138.13 -117.05

Saturation Temp. (K) for Pressure (bar) 0.5 0.7 0.9 514.0 527.6 538.5 544.4 559.0 570.5 529.6 543.5 554.5 529.4 543.5 554.7 0.034 0.001 0.028

1

Short notation is used, i.e. n-C15 is n-pentadecane. Reference: NIST chemical data-base. 3 Calculated using n-hexadecane's Antoine equation parameters 2

For the target compound, Ti s is calculated using both the Antoine equation (calculated) and by the property-property correlation (Tt, predicted). Table 2 illustrates the new technique when experimental data for particular pressures are available. Table 2. Prediction of saturation temperatures for butylcyclopentane1 Coefficients Saturation Temp. (K) for Pressure (bar) for the S-S 0.08 0.333 0.8 1.01 correlation methylcyclopentane -0.78156 280.37 312.73 337.48 344.86 ethylcyclopentane 0.65727 306.65 341.73 368.52 376.50 propylcyclopentane 1.1184 330.07 367.20 395.54 403.98 352.15 390.85 420.72 429.75 butylcyclopentane, target Measured.2 butylcyclopentane, target Predicted. 351.57 390.88 420.83 429.74 Relative error, % 0.165 0.007 0.027 0.001 1 Antoine equation coefficients were taken from the NIST chemical data-base. 2 API Research Project 44; TRC, Texas A&M University, College Station, Texas, 1980 Compound

For alkyl-cyclopentanes, Antoine equation parameters are provided in the NIST data-base only for the first three members of the homologous series. Thus, the structure-structure correlation for predicting the properties of butylcyclopentane has to be constructed with methyl-, ethyl- and propyl-cyclopentane as predictive compounds. Still the experimental data for the pressure–temperature relationship are predicted with high precision.

Prediction of Phase Equilibrium Related Properties by Correlations Based on Similarity of Molecular Structures

73

3. Prediction of Binary Interaction Parameters for Equation of State Models. If the equilibrium liquid and vapour phases are both modelled by an equation of state (EoS), then the K-value is expressed as [1]:

Ki

I iL / I iV

(5)

To calculate the fugacity coefficients of the components in the liquid (IiL) and vapor (IiV ) phases usually either the Soave-Redlich-Kwong or Peng-Robinson EoS with mixing rules (e.g. one-fluid van der Waals mixing rule) are employed. In the EoS, the properties of the pure compounds required are the critical temperature (Tc) and pressure (Pc), and the acentric factor (Ȧ). The prediction of these properties by applying the QS2PR or the shortcut QS2PR techniques is straightforward. However, the mixing rules require binary interaction parameters. The binary interaction parameters can be predicted with QS2PR with the modifications illustrated below. The application of EoS to mixtures requires the use of mixing rules for the mixture energy parameter a mix , which accounts for interactions between the species in the mixture, and for the co-volume parameter bmix , which accounts for the excluded volume of the species of the mixture:

a mix

¦¦ x x a i

i

j ij

;

j

bmix

¦xb

i ii

(6)

i

The cross coefficient aij is related to the corresponding pure-component parameters by the following combining rule:

aij

a a 1  k 0.5

ii

jj

ij

(6a)

In order to predict the binary interaction parameter kij for two compounds (i and j), one of the compounds (say i), for which binary parameters with several predictive compounds (j) are available, is selected as a reference compound. The binary interaction parameters of the predictive compounds are then introduced into the property - property correlation (Eq. 3) to obtain the corresponding interaction parameter for the target compound. In Table 3 this method is demonstrated for calculating binary interaction parameters for the Peng-Robinson EoS. The prediction errors obtained are consistent with the experimental error associated with this kind of data.

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Table 3. Prediction of binary interaction parameters for the P-R EoS1,2 Compound Coefficient kij1 Compound ethane Reference ethane n-C4 0.39331 k24 = 0.00464 n-C7 n-C7 1.4425 k27 = 0.01576 n-C5 n-C8e -0.83652 k28 =0.01972 n-C7 n-C4 n-C5 data k25=0.00811 target target n-C5 pred. k25 =0.00806 n-C4 target target Error, % 0.67 1 From the UNISIM process simulation program 2 Short notation is used, i.e. n-C4 is n-butane.

Coefficient Reference 0.29047 0.89464 -0.18909 data

kij* k23 =0.00185 k25 =0.00811 k27 =0.01576 k24 =0.00464

Target, pred.

k24 =0.00482 3.76

4. Conclusions and Future work We have demonstrated above the potential of our new TQSPR methods to predict temperature – dependent properties and interaction parameters for phase equilibria calculations. Our present results (not included because of lack of space) confirm that our methods can be applied for predicting binary interaction parameters for other equation of state (e.g., Soave-Redlich-Kwong) and activity coefficients for non-ideal binary systems. From a methodology point of view, we intend to test also our latest variation of the TQSPR method for members of homologous series [5], which develops linear equations with single descriptors, collinear with the studied property, and maybe applied even when experimental data for even only members of a series are available. Since, data for a few homologues can be found for many compounds, we believe this method has significant potential for various molecules and their mixtures. 5. References [1]. Poling, B.E., Prausnitz, J. M., O’Connel, J. P., Properties of Gases and Liquids, 5th Ed., McGrawHill, New York., 2001. [2]. Shacham, M., Brauner, N., Cholakov, G.St. and Stateva R.P., Property Prediction by Correlations Based on Similarity of Molecular Structures, AIChE J. 50 (2004) 2481-2492. [3]. Cholakov, G.St., Stateva, R.P., Shacham M. and Brauner, N., Identifying Equations that Represent Properties in Homologous Series using Structure-Structure Relations, AIChE J. 53 (2007) 150-159. [4]. Brauner, N., Stateva, R.P., Cholakov, G.St. and Shacham, M., Structurally “Targeted” Quantitative Structure-Property Relationship Method for Property Prediction, Ind. Eng. Chem. Res. 45 (2006 ) 8430-8437. [5]. Cholakov, G.St., Stateva, R.P., Shacham M. and Brauner, N., Estimation of Properties of Homologous Series with Targeted Quantitative Structure−Property Relationships. JCED, 53 (2008) 2510–2520.

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75

Systematic selection of extraction solvents in the aromatics production Dina M.J. Machadoa, Filipe J.M. Nevesb, Fernando P. Mendesb, Paulo P. Araújob, Belmiro P.M. Duartec, Nuno M.C. Oliveiraa a

University of Coimbra, GEPSI-PSE Group, CIEPQPF, Dep. Chemical Engineering, R. Sílvio Lima - Pólo II, 3030-790 Coimbra, Portugal, [email protected] b CUF - Químicos Industriais, S.A., Process Development Dep., Quinta da Indústria, 3860-680 Estarreja, Portugal, c Polytechnic Institute of Coimbra, Chemical and Biological Engineering, R. Pedro Nunes, 3030-190 Coimbra, Portugal, [email protected]

Abstract This paper presents a general approach for the design/selection of single molecular structures with prescribed functionality, based on mathematical programming techniques. The strategy relies on an efficient decomposition of the design problem into two levels, relative to the identification of structurally feasible candidate molecules that satisfy the property constraints, and their ranking regarding a set of performance objectives that include both operational and safety aspects. Group contribution methods and correlations are employed to model a significant fraction of the physical properties used in the problem formulation. The approach introduced is demonstrated by application to an example commonly found in aromatics industry – the design of extraction agents to promote L/L separations.

Keywords: Product design, Mathematical Programming, Group Contribution methods, LL extraction

1. Introduction and motivation This work starts with the axiomatic assumption that a large class of molecular design/selection problems is significantly complex, and can only be partially described by a set of mathematical constraints and objectives. Therefore, the candidate solutions for these problems need to start by satisfying the constraints identified, while simultaneously constituting extreme points of the objectives, or their combinations (in the broader sense). The diversity of the nature of the criteria usually associated with these problems (e.g., performance, safety, environmental, availability, price, chemical and physical interactions with additional existing species, etc.) difficult their realistic formulation as single-objective optimization problems, thus requiring the use of multiobjective optimization techniques, for their meaningful and efficient solution. Additionally, the constraints and objectives not explicitly included in the mathematical formulation of the problem need also to be considered, at least sequentially, in a second phase of the analysis. This implies that the solution of the above mathematical problem should not produce only a unique solution, but instead a set of candidates, together with their ranking according to the individual decision criteria considered, to be further evaluated and compared by the decision maker. Conceptually, this phase falls into the

D.M.J. Machado et al.

76

classic designation of multiattribute decision making (MADM), since the basic goal is to rank feasible alternatives relatively to a set of performance indicators [1].

2. Methodology A molecular design problem can be described by structural constraints g e (n, u , y ) ≤ 0 , property constraints g p (n, u ) ≤ 0 , and operational constraints g o (n, u, x, y ) ≤ 0 and

ho (n, u, x, y ) = 0 , where n represents a set of integer variables, u , y are binary variables, and x are continuous variables A more complete characterization of each category of constraints can be found, e.g., in [2]. Note that g e (.) and g p (.) normally only involve discrete variables. Also, g e (.) corresponds usually to a set of linear constraints, while g p (.) are often posed as bound constraints of nonlinear functions of the discrete variables, g lp ≤ g p (n, u ) ≤ g up . A set of objective indices Φ = {ϕi (n, u , x, y )} is also considered. Frequently, Φ can be partitioned into class subsets, e.g., Φ = Φ p  Φ s , where Φ p denotes the subset of objectives related to the performance of the product, and Φ s represents the subset of objectives related to its safety characteristics. The individual indices ϕi (.) are assumed to be general nonlinear functions, although not necessarily continuously differentiable inside the entire problem domain. These characteristics lead naturally to overall MINLP formulations of the design/selection problem. In order to avoid some of the difficulties and effort associated with their numerical solution, various approaches have been proposed, e.g., the use of global optimization algorithms [3], or decomposition approaches [2]. Here, we consider a sequential approach, structured similarly to [2], in order to significantly reduce the total solution effort required. The methodology includes two major solution levels: 1. The generation of feasible molecular structures that satisfy the property constraints posed as bounds (problem P1). 2. The solution of the optimization problems over the feasible points generated during the solution of P1, or implicitly represented by a set of constraints originating from P1 (problem P2). It is important to note that the solution of problem P1 requires only the enumeration of integer solutions inside a convex domain delimited by linear constraints; therefore, it can efficiently and reliably be obtained with existing MILP solvers. Alternatively, the corresponding constraints can be added directly to P2, without significantly altering the complexity of the solution of this last problem. This corresponds to the generation of feasible points of P1 as required, during the progress of the solution of P2. Therefore, the two solution phases can be applied separately (e.g., when interactively exploring the solution space, or in small/medium size problems), or simultaneously, when solving the complete design problem at once. Various authors have previously considered the mathematical representation of feasible molecular structures [3-5]. Using similar concepts, a possible formulation for problem P1 is:

min n,u , y

¦n v

k k

k ∈K

(1)

Systematic Selection of Extraction Solvents in the Aromatics Production

s.t.

nk =

¦u

m, k

, ∀k ; m s =

m∈M

¦u

¦u

m, k

k ∈K

k ∈K

; m s ≥ 2 + yc ;

y A + yc = 1

≥ ¦ um +1, k , ∀m ∈ M \ {card( M )}

k

k

A

;

k ∈K

j∈J

(3)

¦n

k'

≥ nk (vk − 1) + 2, ∀k

(4)

k '∈K

ªvk ( N G + 1) + N G − pk + 1º ≥ ¦ um +1, k ª vk ( N G + 1) + N G − pk + 1º, ¬ ¼ k ∈K ¬ ¼

m, k

k ∈K

(2)

k ∈K

¦ n (2 − v ) = 2 y

nk = ¦ ykN, j 2 j −1 , ∀k ;

¦u

k

k ∈K

≤ 1, ∀m ;

m, k

¦n

77

(5)

∀m ∈ M \ {card( M )}

¦¦c

k , j,s

j∈J k ∈K

ykN, j − ¦ ¦ (1 − ck , j , s ) ykN, j ≤ ¦ ¦ ck , j , s − 1, ∀s j∈J k ∈K

(6)

j∈ J k ∈ K

g p ( n, u ) ≤ 0

(7)

Note that the objective is only required when solving P1 individually; the solutions are produced in this case as a canonical enumeration of the feasible set, starting from the lower complexity extreme. Here Eq. (2) relates the positional variables in the molecule with the group count, and the molecular size, together with the type of molecule desired (cyclic/acyclic). Eqs. (3) describe the assignment constraints of each functional group at each molecular position, leaving the empty slots at the end. Eqs. (4) include Machietto and Odele valence constraints [6], and the binary decomposition of each group count. Eq. (5) assigns the groups with higher valences to the first molecular positions, and sorts them according to the group of periodic table of the first atom in the group, to originate a canonical molecular representation. Eqs. (6) represent integer cuts, which are added to the formulation after each solution is found, to eliminate them from the feasible set. Their coefficients are determined as ck , j , s = yk , j , s −1 , where yk , j , s −1 is the previously found solution. Table 1 list the nomenclature used in problem formulation. A crucial difference of this methodology with respect to the one described in [2] is the inclusion in P1 of both structural and physical property constraints resulting from linear (or linearized) structure-property relations. This is advantageous, since in these problems a large subset of the physical properties is estimated using group-contributions (GC) methods, with a linear combinatorial part. This approach reduces drastically the number of candidate structures considered, while retaining the simplicity of the enumeration of a convex linearly delimited solution space.

Table 1. Nomenclature.

M ≡ {m :1, , M max } K ≡ {k :1, , K max } J ≡ { j :1, , J max }

S ≡ {s :1, , S max }

- set of molecular positions - set of functional groups - set of bits used to count the functional groups - set of integer cuts generated

D.M.J. Machado et al.

78

vk yA

- valence of group k - assignment of the molecule to acyclic set

yC

- assignment of the molecule to cyclic set

y

N k, j

- assignment of bit j representing group k

pk N ms um , k

- group of the periodic table for the first atom of k - number of groups of the periodic table - size of the molecule - assignment of group k to molecule m

ukmax

- maximum number of groups k allowed in the molecules

nk

- number of groups k assigned - coefficients of the integer cuts

G

cm , k , s

During the solution of P2, a set of feasible molecular configurations are evaluated with respect to the criteria contained in Φ . Due to the diverse nature of the criteria that need to be considered, the following transformations facilitate this task: 1. First, the individual criteria are grouped into classes, e.g., Φ = Φ p  Φ s (as

2.

described previously). The objectives in each class are later combined, producing a cumulative objective index, representative of the entire class. Using the above division, we denote as PIO and SIO the performance index and safety index objectives, respectively, as the combined measure of each candidate molecule relative to the criteria contained in each class. The combination of decision criteria in each class becomes easier if they possess similar scales and orders of variation. To achieve this, the decision maker is required to provide a set of normalizing functions f N ,i (.) for each objective index

ϕi (.) , expressing her/his expectations relative to the scales of variation found in the feasible solutions. These concepts allow the generation of two combined objective indices:

PIO = ¦ wip f Np ,i (ϕi , p (.)) i

¦w

(8)

¦w

(9)

ip

i

and

SIO = ¦ wis f Ns ,i (ϕi , s (.)) i

is

i

where wip and wis are weighting factors specified by the decision maker. This structure can be then be handled more easily with existing multiobjective optimization programming (MOP) algorithms, such as the weighting [7], the constraint method [8], or multiattribute decision methodologies [1]. Grouping the original criteria into distinct combined objectives indices is also possible.

Systematic Selection of Extraction Solvents in the Aromatics Production

79

3. Application example An application example for the selection of a separation agent in the L/L extraction of aniline (ANL), produced by the liquid phase hydrogenation of mono-nitrobenzenze (MNB), was considered. It comprises a fresh feed stream mainly composed by aniline, water, and low fractions of cyclohexylamine (CHA) and cyclohexanol (CHOL). This stream is mixed with the solvent before entering the L/L separator, where two phases are obtained: i. an aqueous phase (above 95% w/w water); ii. an organic phase (with a water content below 5% w/w). The aqueous stream is routed to an effluent treatment plant, and the organic stream is sent to a distillation column where the solvent is recovered as a top product and recycled back to the separator after cooling. Often, the solvent chosen to promote L/L extraction is a substance already present in the process, such as MNB or benzene (BZ). However, various problems are usually associated to these simple choices (e.g., operational, or environmental factors). The systematic choice of a separation agent should verify the following constraints: i. Reduced health impact, good availability, and affordable price; ii. Low (or high) density when compared to aniline, in order to accelerate the separation operation; iii. Nearly insoluble in water; otherwise, the solvent losses in the aqueous stream will be high, thus leading to important economic and environmental drawbacks; iv. It must break the azeotrope formed by water and ciclohexylamine (CHA), since their separation by distillation would be quite inefficient, hindering the commercialization of this product, that requires tight purity specifications; v. It must have a boiling point temperature lower than that of CHA, but sufficiently high to avoid problems in the top condenser. Results The previous methodology was tested to evaluate the relative performance of simple linear hydrocarbons relative of mono- and di-amines. For this purpose, the groups CH3, CH2, CH, C, CNH2, CHNH2, CH2NH2, CH3NH, CH2NH, CHNH, CH3N, and CH2N were considered as candidate blocks in the molecular structure of the agent. Using the previous specifications, a total of 77 different molecular structures were identified, as the solution of P1. These results were obtained using GAMS/CPLEX, requiring a total of 31 seconds of CPU time in a standard Intel Core 2 Quad PC. This amount of time can be significantly reduced, if the order by which the solutions are obtained is not relevant. The PIO index for each alternative was calculated using individual criteria that included the volatility of the agent, its vaporization enthalpy, liquid density and water solubility. The combined SIO index was calculated using its octanol-water partition coefficient, which has been correlated to a number of health and environmental factors, such as the lethal concentration ( LC50 ) and bioconcentration factor (BCF), and the flash temperature of the agent. Figure 1 presents the combined performance of the candidate molecules regarding both indices. From these results, and considering the set of weights used, it is visible that the di-amines provide better solutions, followed by the mono-amine group, and later by the simple hydrocarbons. Afterwards, these results can be generalized by considering additional families of functional groups, and assessing additional characteristics of the molecules identified.

D.M.J. Machado et al.

80 Ϯ

^/K

ϭ͘ϱ

ϭ

Ϭ͘ϱ D



,

Ϭ Ϭ

Ϭ͘ϱ

W/K

ϭ

ϭ͘ϱ

Figure 1 – Performance of candidate molecules regarding PIO/SIO indices (MA – mono-amines; DA – di-amines; HC – saturated hydrocarbons); lower values indicate better solutions.

4. Conclusion and future work A methodology for the efficient molecular structure design/selection of single molecules was presented. Although it shares some common elements with previously proposed approaches, two important aspects (the generation of feasible solutions, and the application of a MDO framework) were introduced to facilitate its realistic application. An application example was presented, where the results produced were able to provide important guidelines for the user, in the task of designing/selecting chemical compounds with prescribed functionality.

References [1] P. Sen, J.B. Yang, Multiple Criteria Decision Support in Engineering Design, Springer Verlag (1998). [2] A.T. Kurananithi, L.E.K. Achenie, R. Gani, Ind. Eng. Chem. Res., 44 (2005) 47854797. [3] N.V. Sahinidis, M. Tawarmalani, M. Yu, AIChE J., 49 (2003) 1761-1775. [4] N. Churi, L.E.K. Achenie, Ind. Eng. Chem. Res., 35 (1996) 3788-3794. [5] V.S. Raman, C.D. Maranas, Computers Chem. Eng., 22 (1998) 747-763. [6] S. Machietto, O. Odele, O. Omatsome, Trans. Inst. Chem. Eng., 68 (1990) 429-433. [7] A.I. Papadopoulos, P. Linke, AIChE J. 52 (2005) 1057-1070. [8] U. Diwekar, Introduction to Applied Optimization, Kluwer Academic Publishers (2003).

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

81

Towards Nanomaterial Design Automation: Hierarchical Computational Architecture Development Jie Xiao, Yinlun Huang Department of Chemical Engineering and Materials Science, Wayne State University, Detroit, MI 48202, USA, E-mail: [email protected]

Abstract Molecular modeling and simulation has been recognized as an effective tool for gaining a comprehensive and insightful understanding of nanomaterial structure-property relationships, which are critical for nanomaterial development. Note that nanomaterial development is a very complicated task involving the design and management of massive runs of simulations and numerous types of subtasks in multiple computational stages. Thus, an effective and efficient nanomaterial development must rely on the appropriate design of a computational architecture as well. In this work, we introduce a generic task-distributed hierarchical computational architecture for nanomaterial design, which can be readily constructed on a usual cluster system. The developed computational architecture, together with the algorithms for hierarchical computations, can facilitate design automation with a high computational efficiency. The efficacy of the architecture will be demonstrated through a case study on nanopaint design, where various fundamental structure-property correlations as well as design guidelines can be fully derived. Keywords: Computational architecture, nanopaint

nanomaterial

design,

hierarchical

computational

1. Introduction Development of nanomaterials has drawn great attention in recent years since this type of materials can demonstrate some superior mechanical and chemical properties and may possess some novel functionalities. It is known that nanomaterial design by experiments alone usually takes a very long development cycle due to design complexity. The existence of vast design parameters can make easily the material development an unmanageable combinatorial problem. The development could be further affected by the availability of experimental resources (Xiao et al., 2009). Molecular modeling and simulation has been recognized as an effective tool for gaining a comprehensive and insightful understanding of nanomaterial structure-property relationships, which are essential for nanomaterial development. Moreover, advanced computing methods can provide great freedom and control over the investigated material parameters and product properties through allowing virtually any number of in silico experiments (Xiao and Huang, 2009). However, computational efficiency has been a major challenge in molecular simulation based nanomaterial design, due to the existence of a huge design space that needs to be thoroughly investigated for achieving design optimality. Over the past years, many efforts have been made to develop algorithms for creating a large-scale parallel computing environment (Ogata et al.,

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82

2001; Xiao et al., 2008). Those methods are very helpful for reducing the computational time of individual in silico experiments. However, nanomaterial development is a much more sophisticated task, involving the design and management of massive runs of simulations and numerous types of subtasks in multiple computational stages. Thus, an effective and efficient nanomaterial development should rely on the appropriate design of a computational architecture as well. In this work, we will introduce a generic task-distributed hierarchical computational architecture for nanomaterial design, which can be readily constructed on a usual cluster system. Using this architecture, a large number of well-structured computational tasks can be efficiently accomplished. Moreover, we will describe a set of molecular modeling and simulation methods for nanopaint material design. By these methods, comprehensive and quantitative correlations among nanopaint formulation, processing condition, nanocoating microstructure, property and performance can be established. A comprehensive study on the design and analysis of an acrylic-melamine-silicate nanoparticle contained nanopaint will demonstrate the methodological efficacy.

2. Hierarchical computational architecture The computational development of nanomaterials involves three major tasks: one for formulating nanomaterial and then generating a virtual sample, one for conducting the needed in silico tests for product performance evaluation, and the other for managing the entire material development task with a final recommendation on the optimal formulation. To execute these tasks effectively, a task-distributed two-layer computing architecture is developed, which is shown in Fig. 1. In this architecture, the upper layer is designed using the master node of a cluster machine, and it is used to manage the Master Node Material analysis, optimal design, task distribution and management S Compute Node 1

F

S Compute Node i

Grid A: Sample development

F

P

S

P

Compute Node i+1

S Compute Node N

Grid B: Sample testing

Legend: S: structure, F: formulation, P: property Figure 1. Task-distributed two-layer hierarchical computing system architecture.

entire material analysis and design process. In this layer, the nanomaterial formulation data (marked by “F” in the figure) are transmitted down to the lower layer to generate samples by the compute nodes (see the block marked by “Grid A” in the figure). Each node there will develop one sample in one design iteration. After they are developed, the samples with their microstructures (marked by “S” in the figure) will be transmitted to the master node in the upper layer. The collected samples will then be sent down to the “Grid B” block in the lower layer for property testing by the assigned compute nodes. The test results (marked by “P” in the figure) will be transmitted up to the master node. After that, the material formulation-product property correlation will be

Towards Nanomaterial Design Automation: Hierarchical Computational Architecture Development

83

analyzed and the most preferable formulation will be identified for that design iteration. Based on a preset design objective, an optimal material design algorithm resided in the master node will decide if the next design iteration is needed or not. If yes, then the algorithm will determine how to modify the formulation and subsequently a new iteration starts; otherwise, the identified material formulation will be considered the design solution. Note that the number of nodes in each grid of the lower layer can be readily determined based on computational needs. If multiple types of property testing are needed, the compute nodes in “Grid B” can be further divided into several sub-grids, each of which will be responsible for a specific type of property testing. This architecture, which can be readily constructed on any cluster computing system, has a potential to improve computational efficiency through a systematic task distribution according to the computational effort required by each individual task.

3. Computational methodology for nanopaint design Nanopaint is a type of thermoset nanocomposite material that contains a certain fraction of organo-modified inorganic nanoparticles in its resin. To successfully develop such a type of material, a deep understanding of the dependence of nanocoating properties on nanopaint formulation is essential. For this purpose, a set of molecular modeling and simulation methods are developed to establish comprehensive and quantitative correlations among nanopaint formulation, processing condition, nanocoating microstructure, property and performance. Note that the nanocoating scratch resistance is the only performance studied in this work. Modeling method for nanopaint A critical need for investigating nanopaint materials is to develop fundamental models, which can describe how to represent the polymer and the nanoparticles in a 3D space and how to establish the physical and chemical interactions between them. Polymer network modeling. The known coarse-grained bead-spring (CGBS) model is used to characterize the polymer network (Kremer and Grest, 1990). In the network, each effective unit (EU, either an effective monomer or a crosslinker molecule) is represented by a polymer bead, while each bond is represented by an anharmonic spring. Any pair of nonbonded polymer beads interacts via a standard Lennard-Jones (LJ) potential. For any two bonded polymer beads, the finite extension nonlinear elastic (FENE) potential needs to be added to quantify the effect of the anharmonic spring. Nanoparticle modeling. In this work, only spherical nanoparticles are investigated. Each nanoparticle is represented by a single ball. The interaction potentials between two nanoparticle balls and between one nanoparticle ball and one polymer bead are evaluated using a modified LJ potential (Vacatello, 2001). Simulation methods for nanocoating development and testing Two off-lattice Monte Carlo based simulation methods are developed: one for sample development where the correlations among the nanopaint formulation, curing condition, and nanocoating microstructure are quantified, and the other for sample testing which allows predicting the nanocoating property using its structural information. Nanocoating development. The nanocoating is developed by following a seven-step procedure, which includes those for: (i) simulation system set-up, (ii) initial configuration generation, (iii) first-stage system relaxation in an NVT ensemble, (iv) crosslinking reaction realization, (v) second-stage system relaxation in an NVT ensemble, (vi) cooling of nanocoating samples, and (vii) third-stage system relaxation in

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84

an NPT ensemble. Through simulation, the microstructure evolution throughout the entire curing process can be predicted. The prepared nanocoating sample needs to undergo a Nanocoating testing. computational tensile test so that its stress-strain behavior can be obtained. An isothermal, uniaxial deformation process at a constant strain rate is simulated. The simulation box is stretched in the x direction through a series of strain increments until the desired maximum strain is reached. Immediately after each strain increment, the system is relaxed for a certain number of MC cycles in an N(lxτ yyτ zz)T ensemble (Yang et al., 1997). The internal stress in the sample at any moment during tensile test can be calculated according to the Virial stress theorem (Chui and Boyce, 1999). Property and performance evaluation The stress-strain behavior of a nanocoating sample can be correlated to its elastic property and further to the scratch resistance performance. The elastic property (stiffness) of a nanocoating is evaluated using Young’s modulus (E), which is quantified as the initial slope of the stress-strain curve. A qualitative correlation between Young’s modulus and the scratch resistance performance is adopted, i.e., an increment of the elastic modulus of a nanocoating is an indication of the improvement of scratch resistance (Misra et al., 2004).

4. Case study The introduced modeling and simulation methods together with the described computing architecture have been successfully employed to study a nanopaint material, which is a mixture of hydroxyl-functional acrylic copolymer, hexamethoxymethylmelamine (HMMM) crosslinker, and spherical silicate nanoparticles. A total of 18 cases are investigated in order to understand the effects of three critical material parameters, i.e., the nanoparticle-polymer interaction strength, the nanoparticle size, and the polymer number average molecular weight. To ensure a reliable prediction, each case has four independent simulation runs and a total of 72 (18×4) samples are prepared and tested. The comparisons are made based on the averaged simulation results. The computational architecture is Computational architecture implementation. implemented on a Beowulf Cluster System (10 Xeon dual processor nodes @ 2.66 GHz). The master node is used to manage and distribute computational tasks for generating and testing all the samples. Since the computational time for generating one nanocoating sample is around three times longer than that for conducting a tensile test, 1st stage 2nd stage 3rd stage Equilibration Equilibration Equilibration Curing Cooling

1.6 1.4 1.2 1

T*

τ*

1.0

0.4

y

0.75

z

2,000 2,000

0.2 0

x

2,000 1,000 5,000 MC cycle

(a)

0.8 0.6

(b)

0

0.01

0.02

ξ

0.03

0.04

(c)

Figure 2. Nanocoating development and testing results: (a) temperature setting for nanocoating formation, (b) nanocoating sample microstructure, and (c) the stress-strain curve.

0.05

Towards Nanomaterial Design Automation: Hierarchical Computational Architecture Development

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seven compute nodes are assigned to Grid A and two compute nodes are assigned to Grid B (see Fig. 1). It turns out that the computations performed using this structure are very efficient. Base case results. A variety of correlations among material formulation, processing condition, structure, property and performance are generated. Due to the space limit, some key results for the base case only are presented here. The base case material has a reduced polymer-nanoparticle interaction strength ( İ pn* ) of 8.0, a reduced nanoparticle radius ( R n * ) of 7.0, and a reduced number average molecular weight ( M n* ) of 8.34. The nanocoating sample is cured to 80% conversion under the processing condition specified in Fig. 2(a). The nanocoating microstructure evolution can be observed throughout the entire sample development and testing processes. Figure 2(b) demonstrates a nanocoating sample microstructure that contains one nanoparticle and 9,896 polymer beads. In the figure, the green and blue beads represent the effective monomers, and the red and pink beads represent the crosslinkers. All the bonds are represented by the rods. The nanoparticle is completely covered by the polymer beads and thus cannot be visually identified. The nanocoating stress-strain behavior obtained from the tensile test simulation is given in Fig. 2(c). Note that the initial slope of the curve gives the reduced Young’s modulus (E*), which is 50.94 in this case. The *

Young’s modulus for a pure polymeric coating ( E p ) is found to be 39.67, which is 22.12% smaller than that for the nanocoating. This indicates that the nanocoating has a much better scratch resistance performance. Design guideline derivation. The effects of ε pn* , R n* , and M n* on the nanocoating scratch resistance and processing efficiency are thoroughly investigated. The results are given in Fig. 3. Note that a higher modulus means a better scratch resistance. More MC cycles in the curing simulation imply a longer curing time and thus more energy needed for curing. It is shown that to improve scratch resistance performance, the 1.4

1.4 1.5 1.3 E /Ep

1

*

1.1

1.3

deterioration

R n*

1.2

*

*

enhancement

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*

*

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E /Ep

*

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16

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3

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5

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7

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N MCC/NpMCC

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N MCC/Np MCC

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0.8

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(a) (b) (c) Figure 3. Modulus and curing time dependence on (a) the polymer-nanoparticle interaction strength, (b) the nanoparticle radius, and (c) the polymer number average molecular weight.

nanomaterial should have a larger ε pn* and M n* , but a smaller R n* . However, such a type of material can lead to more energy consumption, which means a worse processing

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efficiency. Consequently, material designers should be prepared to make appropriate trade-offs between product performance and processing efficiency.

5. Conclusions A critical need for computational design of nanomaterials is to develop methodologies that can effectively reveal the intrinsic relationships among material, processing, and product quality, and to construct an efficient computing system architecture within which the computational methods can be most properly implemented. In this work, a generic task-distributed hierarchical computational architecture is developed for nanomaterial design. This architecture can ensure the high efficiency in accomplishing a large number of computational tasks. Moreover, a set of molecular modeling and simulation methods are introduced for exploring the fundamental knowledge about the nanopaint material. The efficacy of the introduced methodologies has been demonstrated through the design and analysis of an acrylic-melamine-silicate nanoparticle contained nanopaint material. Undoubtedly, more studies on material structure-property correlations are needed in order to draw more comprehensive, quantitative, and reliable conclusions on nanopaint design. Aiming at design automation, an effective optimal material design algorithm is being developed for more intelligent design of in silico experiments. Needless to say, all the correlations and nanopaint design improvement strategies identified through simulations must be validated by experiments.

6. Acknowledgements This work is supported in part by NSF (CMMI 0700178) and the Institute of Manufacturing Research of Wayne State University.

References C. Chui, M.C. Boyce, 1999, Monte Carlo Modeling of Amorphous Polymer Deformation: Evolution of Stress with Strain, Macromolecules, 32, 11, 3795-3808. K. Kremer, G.S. Grest, 1990, Dynamics of Entangled Linear Polymer Melts: A Molecular Dynamics Simulaion, J. Chem. Phys., 92, 8, 5057-5086. R.D.K. Misra, R. Hadal, S.J. Duncan, 2004, Surface Damage Behavior During Scratch Deformation of Mineral Reinforced Polymer Composites, Acta Materialia, 52, 14, 4363-4376. S. Ogata, E. Lidorikis, F. Shimojo, A. Nakano, P. Vashishta, R.K. Kalia, 2001, Hybrid FiniteElement/Molecular-Dynamics/Electronic-Density-Function Approach to Materials Simulations on Parallel Computers, Computer Physics Communications, 138, 2, 143-154. M. Vacatello, 2001, Monte Carlo Simulations of Polymer Melts Filled with Solid Nanoparticles, Macromolecules, 34, 6, 1946-1952. J. Xiao, Y.L. Huang, 2009, Microstructure-Property-Quality-Correlated Paint Design: An LMCBased Approach, AIChE J., 55, 1, 132-149. J. Xiao, Y.L. Huang, C. Manke, 2009, Computational Design of Thermoset Nanocomposites: Methodological Study on Material Development and Testing, AIChE J., submitted. S.P. Xiao, J. Ni, S.W. Wang, 2008, The Bridging Domain Multiscale Method and its High Performance Computing Implementation, J. of Comput. Theor. Nanosci., 5, 7, 1220-1229. L. Yang, D.J. Srolovitz, A.F. Yee, 1997, Extended Ensemble Molecular Dynamics Method for Constant Strain Rate Uniaxial Deformation of Polymer Systems, J. Chem. Phys., 107, 11, 4396-4407.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Vibrational spectra of methane hydrate by Molecular Dynamics Verónica Janeth Landín-Sandovala, Florianne Castillo-Borjaa, Ulises Iván Bravo-Sáncheza, Richart Vázquez-Románb a

Instituto Tecnológico de Aguascalientes, Av. López Mateos 1801 ote. , Aguascalientes 20256, México, [email protected] b Instituto Tecnológico de Celaya, Av. Tecnológico y A.G. Cubas s/n, Celaya 38010, México.

Abstract The interest for the study of methane hydrates owes to the energetic potential that they possess and to the problem that they represent in the petroleum industry due to the obstruction of pipelines. In this work we carried out molecular dynamic simulations to calculate dynamic properties of methane hydrates such as velocity autocorrelation functions. These functions are Fourier transformed to generate the density of vibrational states. The positions of the bands in these spectra are comparable to those predicted for an IR or Raman spectrum. The vibrational spectra of methane hydrate were calculated for different conditions of temperature and pressure and we successfully revealed the different spectral characteristics of the methane hydrate. Keywords: Hydrates, Molecular Dynamics

1. Introduction Hydrates are crystalline substances formed by water molecules and any other substance known as the guest. Under certain specific conditions of temperature and pressure, usually near the freezing point of water with pressures of up to 500 MPa [1], the water molecules form lattices which have cavities on the inside, where the guests are accommodated. Hydrates that have attracted most interest are the natural gas hydrates, specifically methane hydrates, due to the large number of them distributed in different parts of the globe, representing a potential source of energy. Most of the studies about hydrates consist on experiments to determine its kinetics, crystal structure and its composition. However, most of these experiments require certain thermodynamic conditions that complicate the analysis and substantially increase costs. However, techniques such as molecular dynamics (MD) offer an alternative to study this kind of compounds and achieve results comparable to those obtained through an experimental analysis. This is the case for the density of vibrational states obtained from MD simulations, which can be compared with those obtained with Raman and Infrared techniques. For this reason, in this work we obtain the vibrational spectrum of methane hydrate using MD through the Fourier transformed from the autocorrelation function of the velocities of the hydrate. The second purpose of the study is to analyze the effect of pressure and temperature in the vibrational spectrum.

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2. Problem Statement, background MD simulation basically solves the equations of motion so that we can predict the positions, velocities, accelerations and forces of each particle during the time evolution of the system [4]. Usually a simulation of MD requires an initialization stage where several variables are established. These variables include the number of particles, control variables such as pressure, temperature, density or energy, the intermolecular potential, geometry of the region simulation, and so on. Next step considers an equilibration stage where the equations of motion are integrated generating a series of independent trajectories which are but compatible with the external imposed conditions. During this phase of the simulation different properties are obtained from the positions, velocities and molecular forces. This stage ends when the properties averages oscillate within a range of acceptable values. The last stage is production during which static and dynamic properties are calculated. The averages of these properties, obtained during the simulation, can be related to the properties obtained in an experimental laboratory at the macroscopic level. Description of the intermolecular potential The intermolecular potential is a key part in the simulation of MD and should be able to reproduce experimental data of the system in question. In this paper we use the TJE potential [5] for the water molecules and the OPLS-AA [6] to the molecules of methane. Both models consider the molecules totally flexible allowing bending of their angles and stretching of their bonds. For the water molecule, the TJE model uses a LennardJones potential along with a Coulomb potential for interactions oxygen-oxygen. The OH and HH interactions are calculated using only a Coulomb potential. In the case of the methane molecule a Lennard-Jones in addition to a Coulomb potential is used for all interactions. For interactions between water and methane molecules, the LorentzBerthelot rules are used. The intramolecular interactions for both the water and methane molecules are treated as harmonic oscillators. 2.2 Description of the method for obtaining the vibrational spectra In simulations of MD, it is possible to calculate the autocorrelation function of different properties. In this case, we concern with the atomic velocities. The velocity autocorrelation function is represented by the following expression [4]:

ψ (t ) =

1 N

N

¦

v i (t ) • v i (0)

(1)

i =1

where vi(0) is the velocity of a particle i at a given initial time, vi(t) the velocity at a time t and the angle brackets represents an average over the origins of all time intervals elected. From this dynamic property, it is possible to obtain the density of vibrational states f(w) through the Fourier transform of the velocity autocorrelation function [7]: ∞

f ( w) = ³ exp(−iwt )ψ (t ) dt 0

(2)

The Sandey-Tukey algorithm [7] is used to obtain the Fourier transform of the velocity autocorrelation functions.

Vibrational Spectra of Methane Hydrate by Molecular Dynamics

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3. The proposed approach In this work we carried out MD simulations of methane hydrates. Temperature and pressure were controlled using Berendsen's method [4]. The integration of movement equations were carried out using Verlet's velocity algorithm [4]. The OPLS-AA[6] and TJE[5] potentials were used for the calculation of the intermolecular forces. We used the method of reaction field to address the long-range interactions. Periodic boundary conditions, as well as a cutoff radius equal to half of the box simulation were used. During the phases of equilibration and production of the MD simulations, it was necessary to verify whether the structure of hydrate is maintained. This was achieved by calculating the mean square displacement of one atom of oxygen chosen at random. If the value of this function increases in a linear fashion over time, it indicates that monitored the movement of the atom are very long and therefore the structure of hydrate has lost and has become a fluid phase. Case study The choice of the thermodynamic conditions for the case studies was analyzed based on the phase diagram reported by Sloan [1]. The conditions are analyzed within the region where hydrate formation exist. In all cases, it was considered a full occupation of methane within the cavities. The conditions of each case study are reported in Table 1. Table 1. Thermodynamic conditions for obtaining vibrational spectra in the case study

Pressure (MPa) 0.1 3 7 10 2 2 2

Temperature (K) 150 150 150 150 200 250 260

Energy (J/mol) -30015.935989 ± 44.753831 -29945.347961 ± 43.789995 -29918.234719 ± 43.662042 -29723.922538 ± 43.637796 -30688.665628 ± 48.327758 -33856.357456 ± 48.647177 -34303.999946 ± 55.823028

Density (gr/cm3) 1.001846 ± 0.000022 1.001460 ± 0.000021 1.002606 ± 0.000016 1.003020 ± 0.000016 0.985803 ± 0.000016 0.968733 ± 0.000019 0.963441 ± 0.000020

Results & discussions Thermodynamic properties like energy and density were calculated in this work and the results are shown in Table 1. To calculate the vibrational spectra, the first stage was to corroborate the accuracy of the results of the algorithms and subroutines. To confirm these results with the literature, a comparison with the spectra reported in two different studies which used the same way the Fourier transform of the velocities autocorrelation function was carried out [2, 3]. The spectra obtained for the molecule of methane are shown in Figure 1.

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Figure 1. Density of vibrational states of the molecule methane in methane hydrates at 200 K and 2 MPa.

By comparing the area of the spectrum from 1000 to 1700 cm-1 in Figure 1 with the reported by Greathouse et al. at 273 K and 30 MPa [2] and Jiang et al. at 200 K and 2 MPa [3], it is observed that the bands for the vibration of bending angle H-C-H, ν2 and ν4 are the same in the three cases. In the area between 2700 and 3200 cm-1, the band characteristic of the asymmetric stretching of the bond C-H, ν1 and symmetric stretching, ν3, appeared for the three cases. However, the two picks due to the librational motions of methane in all cavities reported in two studies have not been detected in the zone of 0 to 300 cm-1. With the aim of analyzing the effects of temperature on the spectra, 3 simulations were carried out at a pressure of 2 MPa and temperatures of 200, 250 and 260 K. The results are shown in Figure 2. The temperature is a property that affects the stability of the structure of methane hydrate, which is clearly reflected in the spectra. The changes in the intensity and position of the bands were observed mainly for water molecules. The same behavior has been reported by other investigators in the case of the spectrum of pure water [8], confirming that the results of this study are acceptable. In the same way, 4 simulations were carried out at constant temperature of 150 K by varying the pressure. The results obtained are shown in Figure 3. For the pressure range considered, no significant change in the bands for the molecules of the methane hydrate can be observed in Figure 3.

4. Conclusions According to the results obtained, the application of the model TJE [5] and OPLS-AA [6] provides a good approximation considering that the reproduced spectra are similar to those results by using more complex potentials. The main advantage is that the potentials used here speeds up the time of calculation. By comparing the effects of pressure and temperature, it seems that the latter significantly affects the spectrum in both intensity and frequency.

Vibrational Spectra of Methane Hydrate by Molecular Dynamics

Figure 2. Effect of temperature in the spectra of the methane hydrates

Figure 3. Effect of pressure in the spectra of the methane hydrates

5. Acknowledgements Authors acknowledge financial support from CONACYT.

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References [1] E.D. Sloan, (1998), Clathrate hydrates of natural gases, Marcel Dekker, New York. [2] J.A. Greathouse and R.T. Cygan, J. Phys. Chem. B. 110 (2006) 6428. [3] H. Jiang, K.D. Jordan and C.E. Taylor, J. Phys. Chem. B. 111 (2007) 6486. [4] M.P. Allen and D.J. Tildesley, (1987), Computer simulation of liquids, Oxford Press, New York. [5] O. Teleman, B. Jönsson and S. Engström, Mol. Phys. 60 (1987) 193. [6] W.L. Jorgensen, D.S. Maxwell and J. Tirado-Rives, J. Am. Chem. Soc. 118 (1996) 11225. [7] W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannerty, (1992), Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, New York. [8] M. Praprotnik, D. Janezic and J. Mavri, J. Phys. Chem. A. 108 (2004), 11056.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

A Comparison of Deterministic and Stochastic Approaches to Solve the Facility Layout Problem with Toxic Releases Christian O. Diaz,a Richart Vázquez-Román,a Seungho Jung,b M. Sam Mannanb a

Instituto Tecnológico de Celaya, Av. Tecnológico y A,G. Cubas, Celaya, Gto, CP 38010, MEXICO, E-mail: [email protected], [email protected] b Mary Kay O’Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843-3122, U.S.A., Email: [email protected]

Abstract Process units are grouped into facilities and the facility concept is extended to include services and control rooms. Two approaches, deterministic and stochastic, proposed by the authors in previous studies are compared in this work. The stochastic approach considers the random effect of meteorological conditions, reported in databases, on the toxic dispersion. A Monte Carlo method is used to estimate the directional risk distribution for a given release scenario. The deterministic approach is based on the worst scenario where the stochastic meteorological condition is reduced to calm conditions. The problem was formulated as a disjunctive nonlinear optimization model, converted in a MINLP and solved with the GAMS package. The results indicate that the deterministic approach provides more conservative layouts indicating the need of including means to regulate and reduce the risk. Keywords: Layout, Meteorological effect, Monte Carlo, MINLP

1. Introduction The industrial plants layout is an important and very complex problem which has been extensively analyzed. Efficient and systematic strategies are required to significantly improve the production systems. The problem has been typically formulated with the aim of finding the most efficient physical arrangement of the process where new process units are accommodated in a given land where other units might already exist. Several layouts are designed based on heuristics and standards which can be found in different textbooks, e.g. (Mecklenburgh, 1985). Formulations addressing particularities of the layout problems have been presented in other papers. For instance, models were formulated to resolve the one-floor (Barbosa-Póvoa et al., 2001), 2D multi-floor (Patsiatzis and Papageorgiou, 2002), and even 3-D (Westerlund et al., 2007) problems. Two algorithms were presented to find the best routing based on the grid router and the vector router (Schmidt-Traub et al., 1999). Richert and Gruhn (Richert and Gruhn, 1999) presented a heuristic method to find the optimal routing based on a grid of cells. Guirardello and Swaney (Guirardello and Swaney, 2005) disaggregate the plant into modules containing a smaller number of components than the original plant to optimize the layout of these modules to, later on, perform routing between modules. However, a better layout in practice is obtained when there is a balance between several factors such as efficiency, reliability and safety in plant operations, including

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maintenance, with a minimum acceptable hazard and nuisance to the public and efficient and economic use of the space for future expansions and process needs. Safety became an important issue after several accidents such as the BP Texas City, Flixborough and Bhopal disasters, see for instance (Mannan, 2005). When hazard and safety aspects are not considered properly in the layout and if an accident occurs, then the plant owners may get involved in a serious litigious process since criminal laws always deal with aspects of health, safety, environmental protection, etc. Based on our review, just a few papers on plant layout have incorporated safety issues in their models. One of the few papers in the open literature estimates safety distances with the commercial package SAFETI (Matthijsen and Kooi, 2006). The performance of Dow, Mond, Inherent Safety and Safety Weighted Hazard also for inherent safety design has also been studied (Khan and Amyotte, 2004). The first reported approach that incorporated unsafe risk was focus on optional protection devices from a list of safety features and preventive measures through the Mond index (Penteado and Ciric, 1996). The Dow Fire and Explosion Index has been used in a mixed-linear integer programming (MILP) formulation to reduce the financial risk in an ethylene oxide plant layout (Patsiatzis et al., 2004). A number of accidents with fatal consequences in the industry history have been caused by toxic releases in process units. The strategy proposed here aims to reduce this number by providing a better layout for the process units where the accommodation of occupied areas such as control rooms becomes of crucial relevance on the light of toxic releases. Two recent approaches, stochastic and deterministic, to solve the facility layout problem where at least one installed or new facility has at least a toxic release have been developed by the authors of this proposal (Diaz-Ovalle et al., 2008; VázquezRomán et al., 2008) and their comparison is presented in this work.

2. Problem Statement A normal procedure consists on grouping some of the process units where the group remains surrounded by a street. One of the purposes behind this arrangement is the possibility of providing direct access to the process unit for firefighting or maintenance works. The group of units is referred to as a facility. Then, the concept of facility is extended to include control rooms and any other area surrounded by a street. Since purely toxic releases affect lives rather than equipment, then the problem concerns to finding the layout of inhabited facilities. The problem is established as: x For given a set of already existing facilities i  I ; a set of new facilities for siting s  S ; a set of release types r  R ; a subset of existing facilities having a particular release ri (i, r ) , and displacement values, dx ri and dy ri to identify the exact releasing point with respect to the centre of the releasing i-facility; the facilities interconnectivity for both types existing and new facilities; length and depth of each new facility for siting, Lx s and Ly s ; length and depth of each existing facility, Lxi and Ly i , as well as their centre point, ( xi , yi ) ; maximum length, Lx , and depth, Ly , of land; size of the street, st; parameters to calculate the probability of death in each facility that include expected population in the facility, number of slices with parameters to calculate the probability of death in each slice direction and the release frequency factor; cost of pipe per meter, C p ; cost per m2 of land, C L ; fatal injury cost per person in an accident, C pp ; and life time of the layout, t .

A Comparison of Deterministic and Stochastic Approaches to …



95



Determine each new facility center position xi , yi ; the occupied area out of the total land; the final piping, land and risk cost associated with the optimal layout to minimize the total cost. The following section describes the two models, stochastic and deterministic, used in this work. Since the models have been already described in detail elsewhere (DiazOvalle et al., 2008; Vázquez-Román et al., 2008), the section contains only a brief description of them.

x

3. Models Description Any new facility must be placed inside the available land having a street around it to facilitate the fire-fighting and emergency response. For the sake of simplicity, the East is represented by the direction (0,0) to (’,0) and the North by the direction (0,0) to (0,’). A disjunction is proposed to avoid that two facilities could occupy the same physical space. The piping cost depends on the separation distances, estimated by the Euclidian distance, among interconnected facilities. A piping cost factor is included to account for the piping cost. The occupied land is estimated by including all facilities into a rectangular area and a cost factor per m2. In principle, the land has been already paid for; however, the area occupied by the final layout should be minimized not to jeopardize future expansions. Real data compiled in several databases for the meteorological factors are included in the stochastic model. Long term meteorological data is required to get representative distribution functions. The 360º of possible directions are divided in slices which are assumed to have the same injury risk at any point within the same slice and having the same distance from the emission. A risk distribution is produced at each predetermined position within the slice via classical Monte Carlo simulation. Random values are used to select wind direction, wind speed and stability through the fitted distribution functions. Using several simulations, all risk values at each sector and at each position are averaged. A exponential decay function is then used at each direction sector to fit all average values in the sector under analysis. The risk cost depends on the frequency of each release, the expected population in the affected facility, the injury compensation cost, and the expected life for the plant. Details of this approach can be found in (Vázquez-Román et al., 2008). On the other hand, it has been argued that a complete assessment of the safety for a chemical plant must be based on the worst-case scenario. The worst-case scenario for dispersion modelling was defined as the Pasquill-Gifford stability class F but very few tests have been available to ratify this statement (Woodward, 1998). A further analysis by the authors of this proposal has demonstrated that the worst-case scenario occurs during calm weather conditions. Modelling gas dispersion where low wind speed prevails is not an easy task. The difficulty of modelling calm conditions is given by the meandering effect, the large horizontal oscillation of the atmosphere, during the diffusion of chemical species. The meandering effect appears when the differences between wind variations are small and the appearance strongly depends on Coriolis force. In fact, the calm or low speed wind concepts do not correspond to a unique value but it depends on specific modelling conditions. The most typical value used in QRA studies for worst-case scenarios seems to be 2 m/s but the lowest wind speed for toxic releases has been 2.4 m/s for both F and D stability conditions. The deterministic model developed in this approach then eliminates the stochastic effect for the wind. Since calm winds can actually occur in any

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direction then the risk contours become circular around the release point. Details of this approach can be found in (Diaz-Ovalle et al., 2008).

4. Case study One example is considered in this section to compare the results with both stochastic and deterministic approaches and the optimal layout assuming no toxic release. The disjunctions in the model are reformulated via the convex hull method to produce a MINLP model and the case study has been solved in the GAMS modeling system using a PC Intel® Pentium® M processor 2.00 GHz . The example considers two facilities already installed and three, including the Control Room, to be installed. The size of each facility, expected number of inhabited people and the exact position for the installed facilities are indicated in Table 1. The allocation will be in a square land with 1000 m side length. The facility “New A” feeds “Facility A” and gets material from “New B”. Additional information includes 196.8 $/m of interconnecting pipe, 6.0 $/m2 of land and $8,000,000.00 for the injury parameter; the plant life is 45 years, 5 m for the length of street and 0.5 as the frequency factor per accident during the plant life. Spills of chlorine are possible in “Facility A” and “Facility B” where the chlorine ERPG-3 value is 0.057 g/m3. The optimal layouts considering no release and release with the stochastic and deterministic models are shown in Figure 1. Optimal solutions were obtained using DICOPT in GAMS and the relevant results are given in Table 2.

5. Conclusions A comparison of the stochastic and deterministic approaches has been carried out here. The results show a meaningful difference in the optimal layouts. Layouts from the stochastic approach are more compact and hence cheaper than layouts from the deterministic approach. However, the deterministic approach produces safer layouts. The authors believe that the layout design should be regulated by the law though, as any risky activity, the final decision will always depend on the aversive-addictive risk politics of each company.

6. Acknowledgements The authors thank financial support from CONACyT, DGEST and the DHS.

Table 1: Data for facilities in Example 1

Facility A Facility B New A New B Control Room

Lx [m] 200 150 100 300 15

Ly [m] 100 150 300 150 15

People 0 1 0 0 10

(x,y) [m] (105,55) (80,185) -

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Table 2: Results in Example 1

Without toxic release 142,600 941258

Total land [m2] Total cost [$]

Stochastic approach 142,600 898481

a)

Deterministic approach 247249 1529427

b)

c) Figure 1: Layout for the case study: a) Without toxic release, b) Stochastic approach, c) Deterministic approach.

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7. References A. P. Barbosa-Póvoa, Mateus, R. and Novais, A. Q. (2001). "Optimal two-dimensional layout of industrial facilities." International Journal of Production Research, 39(12), 2567-2593. C. O. Diaz-Ovalle, Jung, S., Vázquez-Román, R. and Mannan, M. S. (2008). "An approach to solve the facility layout problem based on the worst scenario." 11th Annual Symposium, Mary Kay O’Connor Process Safety Center, College Station, Tx, October 28-29, pp 2839, ISBN: 978-0-615-25170-7. R. Guirardello and Swaney, E. (2005). "Optimization of process plant layout with pipe routing." Computers & Chemical Engineering, 30(1), 99-114. F. I. Khan and Amyotte, P. R. (2004). "Integrated inherent safety index (I2SI): A tool for inherent safety evaluation." Process Safety Progress, 23(2), 136-148. S. Mannan. (2005). Lees' Loss prevention in the process industries: Hazard identification, assessment and control, 3 Ed., Elsevier Butterworth-Heinemann, USA. A. J. C. M. Matthijsen and Kooi, E. S. (2006). "Safety distances for hydrogen filling stations." Fuel Cells Bulletin, 11, 12-16. J. C. Mecklenburgh. (1985). Process plant layout, John Wiley & Sons, New York. D. I. Patsiatzis, Knight, G. and Papageorgiou, L. G. (2004). "An MILP approach to safe process plant layout." Trans IChemE Part A: Chemical Engineering and Design, 82(A5), 579586. D. I. Patsiatzis and Papageorgiou, L. G. (2002). "Optimal multi-floor process plant layout." Computers & Chemical Engineering, 26(4-5), 575-583. F. D. Penteado and Ciric, A. R. (1996). "An MINLP approach for safe process plant layout." Industrial and Engineering Chemistry Research, 35(4), 1354-1361. H. Richert and Gruhn, G. (1999). "A numeric heuristic system for plant wide pipe routing." Computers & Chemical Engineering, 23, S735-S738. H. Schmidt-Traub, Holtkötter, T., Lederhose, M. and Leuders, P. (1999). "An approach to plant layout optimization." Chemical Engineering & Technology, 22(2), 105-109. R. Vázquez-Román, Lee, J.-H., Jung, S. and Mannan, M. S. (2008). "Designing plant layouts with toxic releases based on wind statistics." IASTED International Conference on Modelling and Simulation, paper 620-018, May 26-28, Quebec, Canada. J. Westerlund, Papageorgiou, L. G. and Westerlund, T. (2007). "A MILP Model for Ndimensional allocation." Computers & Chemical Engineering, 2007.2002.2006. J. L. Woodward. (1998). "Improving the effect of atmospheric stability class for dispersion modeling." Process Safety Progress, 17, 1-8.

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Analysis of chemical routes and processes for production of glycerol ethers Costin Sorin Bildea, Cristian Brunchi, Grigore Bozga University Politehnica of Bucharest, Polizu 1-7, 011061 Bucharest, Romania, E-mail: [email protected]

Abstract The feasibility of glycerol etherification is investigated, considering olefins, alcohols and ethers as co-reactants. Details are presented for the reaction between glycerol and iso-butene. Simultaneous phase and chemical equilibrium calculations show that large glycerol conversion can be obtained at a good selectivity towards the desired di-ether. The behaviour of the reactor-separation-recycle flowsheet is analyzed, demonstrating that the recycle of the mono-ether has a beneficial effect. About 1 m3 of reactor volume is necessary for producing 1 kmol/h of di-ether, while the recycle rates of glycerol and mono-ethers are kept at small values. Keywords: glycerol ethers, phase and chemical equilibrium, process design

1. Introduction A recent European Union directive requires that, by the end of the year 2010, traffic fuels should contain 5.25% of components produced from renewables. Biodiesel, which is a mixture of methyl esters of fatty acids, is produced from vegetable oils by transesterification with methanol. As by-product, 1 mole of glycerol is produced for every 3 moles of methyl esters, which is equivalent to approximately 10 % wt. of the total product. As a result to the increasing availability, the market price of glycerol has dropped rapidly. Therefore, new uses for glycerol need to be found. Although glycerol could be burnt as a fuel, it could also be processed into more valuable components. Di- and tri-ethers of glycerol are compounds soluble in diesel and biodiesel, improving the quality of the fuel [1] . They diminish the emissions of particulate matter, carbon oxide and carbonyl compounds. Moreover, they decrease the cloud point of diesel fuel when combined with biodiesel. Therefore, ethers of glycerol are interesting alternatives to commercial oxygenate additives such as MTBE, ETBE or TAME. In this contribution, we analyze the feasibility of industrial-scale processes for production of glycerol ethers. The reaction can be carried out in homogeneous [2] or heterogeneous [3] [4] catalysis. Calculation of equilibrium conversion shows that relatively high conversions of glycerol can be obtained by etherification with iso-butene and trans-etherification with TAME. Analysis of the reactor-separation-recycle flowsheet where the reaction kinetics is taken into account demonstrates that the reactions are fast enough to allow large di-ether production rates with small recycles of iso-butene, glycerol and mono-ether.

2. Chemistry and thermodynamics Etherification of glycerol with olefins, leading to mono-, di- and tri-ethers, is presented in Figure 1. Etherification with alcohols and trans-etherification take place in a similar way, one mole of water and alcohol, respectively, being additionally formed.

C.S. Bildea et al.

100 H2 C HC H2C

OH

H2C

OH + O OH

OH

HC

OH

H2 C

G

H2C +O

O

R

HC H2 C

ME

O

R +O

OH O

DE

R

H2C

O

R

HC

O

R

H2C

O

R

TE

Figure 1. Etherification of glycerol with olefins. G – glycerol; O – olefin; ME – mono-ether; DE – di-etherl TE – tri-ether. In the following, ME, DE and TE will refer to mono-, di- and tri-tertbutyl ethers of glycerol

Design of an industrial process requires certain information about the chemical reactions and the species involved. Thus, reaction enthalpy is needed to decide about the type of reactor and the necessity of heating or cooling the reaction mixture. The equilibrium conversion limits the performance of the reactor, which in turn determines the configuration of the separation section and the amount of reactants to be recycled. Moreover, the phase equilibrium should be also taken into account. For glycerol, olefins and alcohols, thermodynamic data such as enthalpy and Gibbs free energy of formation, heat capacities, boiling point and heat of vaporization can be obtained from literature. However, the properties of mono-, di- and tri-ethers must be estimated or experimentally determined. In this work, we used the Constantinou - Gani second-order group contribution method to estimate the thermodynamic properties of the tert-butyl ethers of glycerol. A selection of result is presented in Table 1. Table 1. Physical properties of the tert-butyl ethers of glycerol Property

ME

DE

TE

Boiling point / [K]

537.8

513.6

526.2

Critical temperature / [K]

701.0

676.6

691.2

Critical pressure /[bar]

28.16

19.66

13.06

-649.5

-724.6

-787.1

-388.2

-336.5

-269.6

-0.876

-1.302

-1.736

211.7

306.1

398.1

8.00×104

7.35×104

6.62×104

Enthalpy of formation /[kJ/mol] ideal gas, 298.15 K Gibbs free energy / [kJ/mol] ideal gas, 298.15 K Entropy / [kJ/mol/K] ideal gas, 298.15 K Specific molar heat/ [J/mol/K] Ideal gas, 293.15 K Enthalpy of vaporization, J/mol 298.15 K

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101

Chemical and phase equilibrium For the reactions of etherification between glycerol and iso-butene, the enthalpy, free Gibbs energy and equilibrium constant are shown in Table 2. All the reactions are slightly exothermic, while the chemical equilibrium favors the formation of di-tert-butyl ether. Table 2. Enthalpy, free Gibbs energy and equilibrium constants for the etherification reactions Reaction

ǻHr / [kJ/mol]

ǻGr / [kJ/mol]

Ka, 90 °C

G + O → ME

-47.25

9.88

0.038

ME + O → DE

-40.86

0.052

0.98

DE + O → TE

-27.30

15.60

0.0057

When calculating the equilibrium conversion, the occurrence of two liquid phases must be taken into account. This is achieved by solving the following equations describing the simultaneous phase and chemical equilibrium: - component balance equations

N k(0) + ¦ν k , j ⋅ ξ j = N k(1) ⋅ xk(1) + N k(2) ⋅ xk(2)

(1)

j

- phase equilibrium conditions

γ k(1) ⋅ xk(1) = γ k( 2) ⋅ xk( 2)

(2)

- chemical equilibrium conditions (1) (1) (1) (1) (1) (1) xME γ ME xDE γ DE xTE γ K a ,1 = (1) (1) (1) (1) ; K a ,2 = (1) (1) (1) (1) ; K a ,3 = (1) (1) TE(1) (1) (3) xG γ G ⋅ xO γ O xME γ ME ⋅ xO γ O xDE γ DE ⋅ xO γ O

- constraints on mole fractions

¦ x( ) = 1 ; ¦ x( ) = 1 1 k

k

2

k

(4)

k

where N, x, γ and Ka are number of moles, mole fractions, activity coefficients and equilibrium constants. The subscript k = G, O, ME, DE, TE refers to chemical species, while the superscript j=0 and j=1,2 denotes the initial mixture and the two liquid phases, respectively. Figure 2 presents the equilibrium conversion of glycerol and the selectivity of monoand di-ethers formation versus the initial iso-butene / glycerol ratio r, at different temperatures. Because the reactions are slightly exothermic, they are favored by lower temperatures. As expected, the excess of i-butene has a favorable effect on glycerol conversion, while the effect on selectivities is rather small. As the iso-butene and glycerol are immiscible, two liquid phases coexist. Figure 3 presents the ratio between the amounts of these phases versus initial iso-butene / glycerol ratio and temperature. The di-ethers are soluble both in glycerol and in isbutene. For this reason, a single phase exists when the reaction conversion is high. Thus, for a certain temperature, there is a critical value of the ratio r above which the

C.S. Bildea et al.

102

1

1

0.8

0.8

T / [ºC] =

50

0.6

Selectivity

Glycerol conversion

equilibrium mixture consists of a single phase. For a given ratio r, there is a critical temperature below which a single equilibrium phase exists. The regions of the temperature – initial ratio space leading to single- and two-phase equilibrium mixtures are presented in Figure 4.

70

Gly -> Mono-ether Gly -> Di-ether

T / [ºC] = 90 50 70

0.6 0.4

70 50

0.2

0.2

90

0

0

0.4

90

0

1

2

3

4

0

5

1

Initial i-butene / glycerol ratio

2

3

4

5

Initial i-butene / glycerol ratio

Figure 2. Glycerol conversion and reactions selectivity versus initial i-butene / glycerol ratio, at different temperatures.

50 70

10

90

r =4

80

0.8

60

0.6 40

0.4

20

0.2

0

1 0

1

2

3

4

50

5

1

Initial butene / glycerol ratio

60

70

80

90

Glycerol conversion

T / [ºC] =

phase 1 (butene) --------------------------phase 2 (glycerol)

phase 1 (butene) --------------------------phase 2 (glycerol)

1.2

100

100

0 100

Temperature / [ºC]

Figure 3. Ratio between the two liquid phases versus the initial i-butene / glycerol ratio, at different temperatures.

butene ---------------glycerol

5

4 one phase 3 two phases 2 20

30

40

50

60

70

Temperature / [ºC]

Figure 4. Regions in the temperature – initial i-butene / glycerol ratio space leading to one- and two-phase equilibrium mixtures.

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3. Analysis of the reactor-separator-recycle structure Feasibility of a process for glycerol etherification was further analyzed by considering the reactor-separation-recycle flowsheet. Because the equilibrium calculation showed that the reactor-outlet stream contains significant amounts of glycerol, olefin and monoethers while the di-ether is the interesting product, both the reactants and the monoethers are separated and recycled. The behaviour of the plant was investigated after the basic structure of the plantwide control system has been specified [5] . The recommended strategy consists in keeping on flow control the reactor-inlet flow rate of glycerol, while keeping the i-butene / glycerol ratio at a constant value, as shown in Figure 5. i-Butene

i-Butene recycle

0

3

LC

ME recycle FC

3

1

Products Reactor

Glycerol

r

0

2

Separation

4

1

x

3 Glycerol recycle FC

LC

Figure 5. Recycle structure of the flowsheet and plantwide control

The reactor was modeled as a CSTR, with the reaction kinetics taken from reference [2] Perfect separation was assumed. Figure 6 presents the dependence of the production rate F4 versus the reactor inlet flow rate of glycerol, at different reaction temperatures and iso-butene / glycerol ratios r. Because of kinetic effects and contrary to the equilibrium situation, the reaction is favored by higher temperatures. At low production rates, addition of iso-butene improves the di-ether production rate, although the effect is limited. At high production rates, the dependence is non-monotonous showing that an optimal ratio exists.

F 4 / [kmol/h]

6

V= 1 m3 T = 70 C

1.4

4

1.2

5

3

1 0.8 0.6

V= 1 m3 T = 90 C

r= 2

F 4 / [kmol/h]

1.6

1

0.4

r = 2

3 4

4 3

1

2 1

0.2 0

0 1

10

F 1,Gly / [kmolh]

100

1

10

100

F 1,Gly / [kmolh]

Figure 6. Production rate versus reactor-inlet flow rate of glycerol, at different temperatures and iso-butene / glycerol ratios

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104

Figure 7 presents results in a dimensionless form, showing that about 1 m3 of reactor volume is necessary for producing 1 kmol/h of di-ether (F4,DE) while keeping the recycle rates of glycerol and mono-ethers, F3,Gly and F3,ME at low values.

F / F 1,Gly

0.8

F 3,ME / F 1,Gly

F 4,DE / F 1,Gly

15

0.6 0.4

10

F 3,Gly / F 4,DE

5

0.2

F3,ME / F4,DE

20

1

F 3,ME / F 4,DE 0 0.01

0 0.1

1 3

V / F 1,Gly / [h m /kmol]

Figure 7. Dimensionless flow rates versus reactor volume. T = 90 C, r = 4.

4. Conclusions The feasibility of glycerol etherification is investigated, considering olefins, alcohols and ethers as co-reactants. Details are presented for the reaction between glycerol and iso-butene. Large glycerol conversion can be obtained at a good value for the selectivity towards the desired di-ether. Analysis of the reactor-separation-recycle flowsheet shows that recycle of the mono-ether has a beneficial effect. About 1 m3 of reactor volume is necessary for producing 1 kmol/h of di-ether, while keeping the recycle rates of glycerol and mono-ethers at low values. Alternative routes for obtaining derivatives of glycerol by etherification with amylenes, and tert-butanol and trans-etherification with TAME were also investigation. Solution of the simultaneous phase and equilibrium conditions show that using TAME as coreactant can lead to significant values for glycerol conversion. The etherification with tert-butanol is limited by chemical equilibrium. When etherification is performed using amylenes, the equilibrium conversion is large only at low temperatures, which suggest that the process could be limited by kinetic factors.

Acknowledgement The authors kindly acknowledge the National Center for Programms Management - CNMP (Romania) for the financial support through the project PN2 nr. 71-053 / 14.09.2007 “New methods for valorisation of glycerol from biodiesel production” (GLICEVAL).

References [1] R.S. Karinen, A.O.I. Krause, New biocomponents from glycerol, Appl. Catal. A: General, 306, 128, (2006). [2] Behr, A. and L. Obendorf, Development of a process for the acid-catalyzed etherification of glycerine and isobutene forming glycerine tertiary butyl ethers, Eng. Life. Sci. Comm., 2, 185, (2003). [3] Klepáþová, K., D. Mravec, M. Bajus, tert-Butylation of glycerol catalysed by ionexchange resins, Appl. Catal. A:General, 294, 141, (2005). [4] K. Klepáþová, D. Mravec, A. Kaszonyi, M. Bajus, Etherification of glycerol and ethylene glycol by isobutylene, Appl. Catal. A:General, 328, 1, (2007). [5] A. C. Dimian, C. S. Bildea, Chemical Process Design: Computer-Aided Case Studies, Wiley-VCH, 2008

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

Model-based retrofit design and analysis of petrochemical processes Jamal Rashed, Rafiqul Gani CAPEC, Technical University of Denmark, Soltofts plads, 2800 Kgs. Lyngby,Denmark, [email protected]

Abstract This paper presents the development of a systematic methodology that can generate and screen feasible retrofit process alternatives, to produce the same products from the same raw materials and from them, to identify the more sustainable ones. The methodology is organized in three stages: 1. targeted process analysis; 2. reverse process synthesis and design; and 3. final selection and verification. In the first stage, the process flowsheet is analyzed in order to identify the design/operational weak points, indicating potential for improvement and thereby to set design targets that may improve the process. In the next stage, the identification of feasible process options are made based on thermodynamic insights. The process options are generated through an analysis of the physico-chemical properties of the particular mixture present in the system and based on the relationships between properties and separation technique, a list of feasible alternatives for the particular separation task is generated. A reverse approach is used to match the final design details for process options. In the third stage, performance of the identified feasible process alternatives are compared, for final selection, in terms of sustainability metrics. Application of the developed methodology is illustrated through the tert- amyl methyl ether (TAME) production process. Keywords: retrofit, thermodynamic insights, process design, reverse approach

1. Introduction The competition in the chemical market has increased during the past decades. Therefore to be still competitive many of the existing production processes require constant improvements through retrofitting that are available by generation of new alternatives to the process that exhibit improvements on design parameters such as operability, cost, waste reduction and environmental impact. Different methodologies have been used for evaluating the retrofit potential of a chemical process. For example, Rapoport et al. (1994) presented a strategy using heuristic rules for the generation of retrofit options, while Jaksland et al (1995) presented a thermodynamic insights based synthesis method for generating process alternatives applicable to new processes, as well as existing processes. Ciric and Floudas (1989) used algorithmic approaches such as mixed integer nonlinear programming (MINLP). Also, combinations of these methods have been developed, for example, Hostrup (2001) combined thermodynamic and mathematical programming methods. The aim of this paper is to present a methodology plus its associated algorithms for generating and screening of feasible retrofit design alternatives that are particularly suitable for processes in the petrochemical industry.

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2. Methodology The methodology for systematic generation and screening of feasible retrofit alternatives consists of three stages. Stage 1: Target process analysis The purpose of this stage is to analyze the processes to identify design/operational weak points and where (design) targets for improvement could be set. The analysis in this stage employs the indicator based method developed recently by Carvalho et al. (2008). According to this method a set of mass and energy indicators are calculated from information of the process (step 1.1). The calculated indicators give information about costs, benefits and accumulations in the process. They are related with mass and energy paths present in the overall process, thereby making it possible to locate the weak points in the process in terms of mass and energy flows within the process and their influence on the sustainability metrics (step 1.2). This step starts with the necessary process data and information about the process so that the indicators can be calculated. A process simulator is used to generate the steady state process flowsheet stream data, if they are not available. There are five mass indicators and three energy indicators which are defined in the methodology of Carvalho et al. (2008). These are, the material value added (MVA), the energy and waste cost (EWC), the reaction quality (RQ), the accumulation factor (AF), total value added (TVA), the energy accumulation factor (EAF), and the total demand cost (TDC). Stage 2: Reverse process synthesis and design The purpose of this stage is to identify retrofit process options that match the targets for the desired improvement and for each of these process options, to determine the important operational (design) parameters through a reverse design approach. This stage has two main steps. Step 2.1 Process synthesis: In this work, identification and selection of feasible separation techniques are made based on thermodynamic insights (Jaksland et al,. 1995). Jaksland et al. used thermodynamic insights combined with a set of rules related to physio-chemical properties to identify the most appropriate set of separation techniques for a given separation task. The method has been adopted for petrochemical processes and consists of two levels of calculations. In level 1, the mixture to be separated is analyzed, the binary ratio matrices for each property generated, the issues related to the presence of azeotropes and use of mass separating agents are identified, and, based on these, a list of separation tasks is generated. In level 2, appropriate separation techniques are matched (reverse approach) with the separation tasks and sequenced, thereby, generating feasible process (retrofit) flowsheet alternatives. Step2.2 Reverse process design: The purpose of this step is to add design details for the generated flowsheet alternatives from step 2.1. First a target for improvement is identified and then matched with a corresponding maximum (attainable) driving force for specific separation and reaction operations. For example, the driving forces for a separation of a mixture of compounds could be the composition differences in two coexisting phases. Since by definition, an operation is easy and less expensive to operate if the driving force is higher, the use of the identified maximum driving force as the starting point for the design of an operation implies starting from a near optimal solution from which the important process design parameters are back-calculated.

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107

Therefore, the method is called the reverse design approach and does not require simulation and/or optimization to determine the near optimal solutions. The design variables that match the design targets for each unit operation in the process are determined by solving a new class of unit operation models based on the drivingforce that “drives” the operation. First, the driving force needed to convert a given feed stream to the desired product streams, is calculated. Next, the variables (design) through which the calculated driving-force can be matched, are determined. Consider the situation where a given mixture is to be separated by simple distillation to specified product purity requirements. First the maximum attainable driving force for the specified separation task is determined. Then from the known value of the maximum driving force, the important design parameters for the distillation column (such as the reflux ratio, number of stages, feed stage location, etc.) are determined. Note that these variables together with the specified feed mixture and product purity specifications provide sufficient information to completely describe the operation of a distillation column (that is, using a process simulation model, all other variables can be calculated). Driving force based models have been developed for different separation and reaction processes for application in model based retrofit design and analysis of petrochemical processes. Stage 3: Final verification The purpose of this stage is to verify and evaluate the retrofit process alternatives through rigorous simulation and verify this performance in terms of sustainability. This stage involves two main steps: Step 3.1 Simulation of the process with the new design parameters: The purpose of this step is to generate all the data needed to calculate the sustainability metrics. Step 3.2 Evaluate alternatives for sustainability: Use of the sustainability metrics follows the simple rule that the lower the metric the more effective the process. The impact of any retrofit alternative can be summarized in terms of environmental responsibility, economic return and social development. The sustainability metrics are calculated using the steady state data for the process. For environmental impact related metrics, the WAR algorithm is used to calculate the important parameters. This algorithm describes the flow rate and generation of potential environmental impact through a chemical process.

3. Application: TAME case study TAME is manufactured by catalytically reacting isoamylenes, 2-methyl-1-butene and 2methyl-2-butene, with methanol. The process starts with the reaction of isoamylenes with methanol in the reactor followed by reaction-separation in a reactive distillation column. From the top product of the reactive distillation column, methanol is recovered through extractive distillation using water as a solvent. Stage 1: Process Analysis Step 1.1 Identify design/operational weak points: Using the steady state plant data as the reference design (generated through simulation), the mass and energy indicators are calculated using the Sustain-Pro software (Carvalho et al (2008)). From a total of 19 open-paths (paths through which mass and/or energy enter and leave the process) and a total of 27 cycle-paths (paths where mass and energy are trapped within a recycle-loop), 4 open-paths and 3 cycle-paths have been found to be the most sensitive (see Tables 1 and 2). Open-paths O8, O10, O12 and O14, have high –ve values of TVA (Total Value

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Added, which needs to be made zero or positive), have high +ve values of EWC (Energy and Water Costs, which needs to be reduced) and have high –ve values of MVA (which needs to be made zero and/or positive). Cycle-paths (see Table 2) C9, C10 and C19 have high +ve values of EWC and high +ve values of AF (Accumulation Factor, which needs to be reduced). This means that, as a target, the amount of water in the recycle can be reduced (see cycle-path C9), thereby reducing EWC and AF and maybe indirectly, the other open-paths (because of better separation). Open path OP 8 OP 10 OP 12 OP 14

Cycle path C9 C10 C19

Table 1. Calculated MVA, EWC and TVA values of open paths EWC TVA Component Flow-rate MVA (103$/yr) (103$/yr) (Kg/h) (103$/yr) n-pentane 6371.563 -17993.294 68.041 -18061.335 i-pentane 36145.469 -102074.80 367.599 -102442.405 2-pentene 11343.625 -32034.396 126.039 -32160.435 1-pentene 2671.773 -7545.086 28.677 -7573.764 Table 2. Calculated AF and EWC values for cycle path Component Flow-rate (Kg/h) AF H2O 17427.385 11.749 Methanol 7918.953 0.830 Methanol 7361.155 0.729

EWC (103$/yr) 3621.645 730.131 678.282

Step 1.2 Define attainable design targets: In this process, the most critical problem is found in the separation section. Using the reduction of the EWC and the AF as targets for improvement, leads to a re-evaluation of the separation techniques used for the separation tasks in this section. That is, consider the changing of the separation techniques for the separation of the methanol/C5 product mixture as the first alternative to improve the process. Stage 2: Reverse process synthesis and design Step 2.1 Process synthesis: Results from levels 1 and 2 are presented here (briefly). All the calculations related to levels 1 and 2 have been performed through various tools available in ICAS (Gani, 2002). Mixture type: This mixture is a non-ideal mixture with presence of polar associating compounds at moderate pressure and 333 K. Identification of an azoetrope: Methanol forms minimum a low-boiling azeotrope with several of the C5-products. Identification of separation technique: Since two liquid phases are detected when water is added to a mixture of methanol and C5-products, removal of methanol through liquid-liquid extraction with water is an alternative worth investigating. Step 2.2 Reverse process design: The reverse design approach has been used to identify the final design details for the liquid-liquid extraction column and the distillation column for solvent recovery, by first determining the maximum attainable driving forces available for each separation task. The maximum driving force (0.970) and the corresponding solvent to feed ratio (1.0) (see Figure 1) to achieve the desired separation has been determined. Using the identified solvent to feed ratio and simple mass balance calculations, it is possible to determine that the amount of water needed for the extraction operation is 1122 kmol/h. From the maximum driving force based on vapour-liquid equilibrium shown in Figure 2, the design parameters for the distillation column are back-calculated to match

Model-Based Retrofit Design and Analysis of Petrochemical Processes

109

maximum driving force. The parameters for this design are Ns = 29. The equivalent minimum reflux ratio is found to be 1.02 and the feed stage location is found to be 22. The purity of light key component is 0.995. These variables together with the specified feed mixture and product purity specifications provide sufficient information to completely describe the operation of a distillation column (that is, using a process simulation model, all other variables can be calculated). 1.2

water% 30 water% 50 water% 70

Drivingforce

1 0.8 0.6 0.4 0.2 0 0

0.05

0.1

0.15

0.2

Molefractionofmethanolinraffinatephase

Figure 1. Solvent free driving force diagram between methanol with a fixed amount of water (30%, 50%, and 70% from the feed).

0.45 0.4

Drivingforce

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.2 0.4 0.6 Figure 2. Driving force diagram for methanol and water.

0.8

1

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110

Stage 3: Final verification HYSYS has been used to perform rigorous process simulations. Sustainability metrics have been calculated and compared with the reference design (see Table 3). As it can be seen, the new alternative gives an improvement, especially for the energy consumption. The environmental impact factors are calculated using the stream compositions, temperatures and pressures of all input and output streams. No significant differences between the reference design and the new alternative were noted for other process variables and/or specifications (these are not shown in this paper). It is worth pointing out, however, that it has been possible to achieve waste reduction (or more efficient process operation) without disturbing other variables, especially the environmental aspects. Table 3. Comparison of existing process (reference design) and alternative design Indicator

Existing process

New alternative

Total energy primary energy usage rate (GJ/year) Total Net Primary Energy Usage (KJ/Kg) Net water consumed (t/y) Net water consumed per unit mass of product (Kg/Kg)

448 818.5 21.89x106 40

247.1 455.2 11.184x106 20.3

4. Conclusions and future work A systematic methodology for generating and screening retrofit alternatives has been developed and tested with an existing TAME process from the petrochemical industry. Identification of new alternatives is made based on thermodynamic insights. Another application of this methodology, not shown n this paper, considered the styrene production process. Current and future work is looking for additional case studies from the petrochemical industry. This paper shows that adopting CAPE–methods and tools, it is possible to solve interesting industrial problems, systematically, reliably and efficiently.

5. Acknowledgements The authors greatly acknowledge the financial support of the Libyan Petroleum Institute for this project.

References Carvalho, A., Gani, R., and Matos, H. (2008), Design of sustaina processes: Systematic generation & evalution of alternatives, Process Safety and Enviromental Protection, 13, 1 -19. Ciric, A. R., and Floudas, C. A.(1989), A mixed integer nonliner programming model for trofitting heat exchanger networs. Ind. Eng. Chem. Res., 29, 239. Gani, R. 2002, ICAS Documentations, PEC02-15, CAPEC, DTU, Lyngby, Denmark. Hostrup, M., Gani, R., Kravanja, Z., Sorsak, A., and Grossmann, I. (2001), Integration of therdynamic insights and MINLP optimization for the synthesis, design and analysisof processes flowsheet, Comp. Chem. Eng, 25, 73-83. Jaksland , C., Gani, R., and Lien, K., 1995, separation process design and lysis based on thermodynamic insights, Chem Eng Sci, 50, 511-530. Rapoport, H., Lavie, R. and Kehat, E., Comp. Chem. Eng., 18, 743-753 (1994).

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Modelling and experimental validation of emulsification process in continuous rotor-stator units Cristhian Almeida-Rivera,a Peter M.M. Bongersa,b a

Unilever Food and Health Research Institute, Oliver van Noortlaan 120, POBox 114, 3130 AC Vlaardingen, The Netherlands, [email protected] b Chemical Engineering and Chemistry, Eindhoven University of Technology, POBox 513, 5600 MB Eindhoven, [email protected], E-mail

Abstract Despite the wide range of industrial applications of structured emulsions, current approaches towards process design and scale-up are commonly based on trial-and-error experimentation. As this design approach is foreseen to deliver most likely suboptimal process solutions, we propose in this contribution a model-based approach as the way forward to designing manufacturing processes of structured emulsions. In this context, process modelling and simulation techniques are applied to predict production rates and equipment sizing. Moreover, sensitivity analysis of the process model provides insight about potential bottlenecks in the process. Keywords: emulsification, dynamic modelling, rotor-stator

1. Introduction Structured emulsions are a particularly important class of chemically formulated products widely common in the food and beverage, agricultural chemical, consumer products and pharmaceutical industries. Unlike commodity chemicals which are characterized almost exclusively by their composition, structured emulsions have specific end-use properties that are intimately connected with their microstructure. Thus, in contrast to bulk chemicals, structured products are characterized not only by the level of each ingredient (i.e. composition, purity, physical state, temperature, pressure, etc.), but also by the relative spatial arrangement of each ingredient and performance behaviour. All these features are responsible for the exclusive attributes of structured products (e.g. creaminess of an ice-cream, spoonability of a mayonnaise, spreadability of a margarine, etc). As the product and process design problems for such a complex, multiphase, microstructured materials are strongly coupled, the overall design problem involves specification of the chemical formulation and the processing conditions that produce the desired microstructure and physical properties. Reaching a desired microstructure involves not only the close marriage between product composition and processing, but also the development of a process synthesis methodologies embracing both (see e.g. [1]). A model-based approach is a fundamental building block of such synthesis methodology.

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2. System description In this study a continuous rotor-stator unit of the type Fryma-Delmix was considered for the production of an oil-in-water emulsion. As depicted in Figure 1, the Fryma-Delmix process was decomposed into a static mixer, a mixing vessel and a colloid mill. ZDWHU RLO

HPXOVLILHUV

6WDWLFPL[HU

)LQLVKHGSURGXFW

6WLUUHGYHVVHO

&ROORLGPLOO

Figure 1. Schematic representation of the Fryma-Delmix process

According to the process scheme, the ingredients are continuously discharged from the buffer tanks to the static mixer at a given ratio. The resulting premix is fed to the mixing vessel of a given volume, which operates under vacuum conditions and is equipped with a given number of scrappers. From the bottom of the vessel the premix passes through the colloid mill, where most of the emulsification process takes place. The resulting stream is then recirculated to the unit. As soon as the product specifications are met, product is withdrawn from the unit through a 3-way valve. In addition to its emulsification purpose, the colloid mill in this configuration acts as a recirculation pump. The desired product is a structured emulsion with a bounded Sauter mean droplet diameter,

d 32

min

< d32 < d32

max

.

(1)

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3. Model development A mechanistic dynamic model for the continuous process was derived and implemented, with the ultimate goal of assisting the engineer in the choices of equipment sizing, operating conditions and product range. Model assumptions Several assumptions were introduced to the model, without compromising its reliability and representation of the actual process. With the same goal in mind, very simplified models were used to describe the evolution of droplet size (i.e. population balance) and physical properties of the system (e.g. viscosity). The main assumption behind each model building block is that all emulsions will be water continuous. We acknowledged that this assumption might be violated during the startup or shutdown of the process. Moreover, the following assumptions were included: (i) only the change in holdup in the vessel was of importance; (ii) the flow through the piping, static mixer and colloid-mill was approximated to plug-flow; (iii) the mean residence time in the piping was small compared to the vessel and, therefore, neglected; (iv) breakup of oil droplets was the main phenomenon occurring within the boundaries of the system; this assumption was justified by the presence of enough emulsifiers in the product recipe; (v) the droplet size distribution (DSD) was only changed in the static mixer, stirred vessel and colloid mill; (vi) the outflows of the colloid mill and static mixer were mixed in the vessel; thus, the change in DSD of the entire system was described by connecting the components; (vii) the DSD at the outlet of the static mixer was constant; (viii) the change in the DSD in the colloid mill was caused by deformations due to shear; (ix) the DSD in the vessel was a combination of mixing the recirculation flow from the colloid mill and the flow from the static mixer combined with droplet breakup caused by the impeller. Population balance equations Population balances were performed to account for the disappearance and appearance of droplets/particles at each size class in a size distribution. A relevant aspect of these balances is the estimation of the prevailing mechanism (break-up or coalescence) at each size class as a function of droplet diameter, acting forces on the droplet and time domain. Knowing the governing mechanism at a given size class allows us to calculate the rate of production and breakage of droplets. Thus, depending on the droplet mean diameter, stress exerted on it and residence time at a given size class, a droplet is disrupted into a given number of daughter droplets, coalesce with a colliding droplet or remains unchanged in size. The PB equations for a size class of mean volume v is given by the contributions of birth and death terms [2],

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114 v

dn(v, z ) = ³ N (v' , z ) S (v' , z ) B(v, z v')n(v' , z )dv'− S (v, z )n(v, z ) dt v'>v

(2)

where N(v’,z) is the number of daughter droplets at location z produced by breakage from parent droplets of volume v’; B(v,z⏐v’) is the droplet size distribution of daughter droplets of volume v at location z and produced by breakage of parent droplets of volume v’; S(v,z) is the break-up frequency of droplets of volume v at location z and n(v,z) is the number density of droplets of volume v at location z. In this contribution we applied a simplified population balance for each of the building blocks of the model and, furthermore, we used a discretized version of Eqn. 2. The discretization in volume classes was such that vi = 2vi+1. Rheological model equations We described the flow behaviour of the oil-in-water emulsion system using the HershelBulkley model [3]. According to this model, the viscosity of an oil-in-water emulsion is a function of the yield stress IJ0 and shear rate after yield Ȗ. The model expression can be written in the form given by [4],

η (v, z ) =

τ0 γ (v , z )

+ Kγ (v, z ) n −1 for IJ(v,z)> IJ0

(3)

and

η (v, z ) = 0 for

IJ(v,z)< IJ0

(4)

where n is the flow-behaviour index and K is the consistency factor. Additionally, empirical correlations for K and IJ0 for high internal phase emulsions were used for each building block,

τ 0 = f (Φ, d 32 ) and K = f (Φ, d 32 ,η )

(5)

where ĭ denotes the internal phase fraction of the emulsion. Modelling framework for the building blocks The DSD at the exit of the static mixer was described as a log-normal distribution with specified values of mean diameter and variance (100 μm and 0.18, respectively). For the colloid mill model, the breakup mechanism of droplets was divided into sections depending on the droplet diameter: (i) stable droplets, (ii) viscous or inertial breakup; and (iii) breakup behind the gap between rotor and stator. The flow through the colloid mill was estimated accounting for the pressure generated by the rotational action of the mill and the pressure-drop in the unit. Preliminary calculations confirmed that the throughout of the colloid mill decreased with the decreasing d32 values. Whether the governing breakup mechanism is inertial or viscous was determined by comparing the mean droplet size with the Kolmogorov length scale. The maximum stable droplet size for each mechanism was estimated by calculating the critical Webber and capillary

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numbers, for the inertial and viscous mechanisms, respectively. Simulations revealed that the critical diameter in viscous breakup increased as the gap increased, but only until a certain value. The existence of Taylor vortices in the colloid-mill explained this behaviour. Figure 2-left depicts the effect of Taylor vortices in comparison to a baseline case where laminar flow was assumed.

Figure 1. Effect of Taylor vortices (left); experimental validation of the integrated execution of the models: pressure gain as a function of rotor speed at various milling gaps (right)

In the stirred vessel the breakup is confined in a region of approximately 10% of the vessel volume, next to the impeller blades. A simplified CSTR model was used to predict the behaviour of the vessel. Mixing and varying holdup was described in one (large) CSTR and breakup in a small CSTR. Moreover, both CSTRs are interconnected by the flow of material. The critical droplet diameter was estimated by considering the second CSTR as an annulus with a diameter equal to the impeller diameter. Alternatively, the mean droplet size in the vessel could be estimated by empirical correlations involving operational variables, as impeller speed and residence time. The integrated execution of all building blocks was validated against experimental data (discrete points in Figure 2-right). Despite the limited knowledge in some key domain areas and the level of complexity of the PBE and physical properties descriptors, the simulation model was able to successfully predict trends observed during industrial and pilot plant trials.

4. Conclusions Various conclusions can be drawn from the simulation results. Pendent a more exhaustive experimental validation, we conclude that the model is accurate enough for its purpose. Attainable production flowrates were identified as a function of the dispersed phase volume fraction. Additionally, the effect of the impeller in the preemulsion mixing tank was found to be negligible regarding dispersed phase droplet break-up. This fact was explained by the large flows estimated in the recirculation loop as compared to the tank volume and mean residence time. By embracing a model-based approach, important sources of uncertainty have been identified. Namely, the existence of Taylor vortices in the rotor-stator mixing element and their effect on the droplet sizes; the effect of non smooth rotor and stator in the mixing element and the pumping efficiency of the mixing element when it is operated at large milling gaps; among others. CFD-based models, despite being computational expensive, might provide further refinement on the results quality.

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References [1] Ridder, K., Almeida-Rivera, C. P., Bongers, P., Bruin, S. and Flapper, S. D. (2008). Multi-Criteria Decision Making in Product-driven Process Synthesis. Computer-Aided Chemical Engineering, 25,1021-1026 [2] Nere, N. and Ramkrishna, D. (2005). Evolution od drop size distributions in fully developed turbulent pipe flow of a liquid-liquid dispersion by breakage. Industrial and Engineering Chemistry Research, 44,1187-1193 [3] Steffe, J. F. (1996). Rheological Methods in Food Process Engineering. Michigan, Freeman Press [4] Sherwood, J. D. and Durban, D. (1998). Squeeze-flow of a Herschel-Bulkey fluid. Journal of Non-Newtonian Fluid Mechanics, 77,115-121

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Modeling and simulation of a hybrid separation process for the carbon dioxide removal of the oxidative coupling of methane process S. Stünkel1, O. Litzmann, J.-U. Repke, G. Wozny Berlin Centre of Technology, Department of Process Engineering, Chair of Process Dynamics and Operation , 10623 Berlin, Germany, 1 E-mail: [email protected]

Abstract The oxidative coupling of methane (OCM) is a promising alternative for the oil-based production of olefins. The aim is to convert methane-containing natural gas catalytically to ethylene and open up a new feedstock for olefins and further organic synthesis products [1] , [2] . The whole process is designed modular and built up in a miniplant to investigate different new approaches. For realization in a short time period, but in a more efficient way, the entire process is divided into three units: reaction unit, purification unit and separation unit, which are designed simultaneously. Particular requirements for process conditions on the transitions had to be defined and were done by laboratory screenings and literature study. Due to the novel process design strategy, downstream process conditions affect the design specification for the catalyst and the reaction unit. In the article the purification section is discussed particular and a novel hybrid separation process for the CO2 removal is presented. An efficient and modern carbon dioxide separation process of a membrane and an amine unit was developed. The membrane unit has been modeled with Aspen Custom Modeler® (ACM), and was integrated in the Aspen Plus® process simulation. The amine unit was modeled with a rate-based absorption model, including an electrolyte NRTL approach [3] and concentration-based reaction kinetics [4] . The simulation results of the conventional amine process, the single membrane unit and the improved novel hybrid process are presented in this paper. Keywords: hybrid systems, amine, membrane, downstream OCM, gas permeation

1. Introduction Oxidative coupling of methane (OCM) is a novel technology for the conversion of natural gas to ethylene, reaching widespread attraction among various research groups in the last decade. OCM is a surface induced gas phase reaction and their overall yield is still limited up to 30%. Beside new catalysts, a concept for an integrated downstream process is necessary to overcome this limitation [5] . To hit this target in a more efficient way, the downstream process, the reactor and the catalyst are designed simultaneously. This novel strategy causes particular interactions during the design period between the downstream process, the reactor and the catalyst. Various processes for the OCM with integrated downstream concepts were proposed like the OXCO Process, the UCC Process, the ARCO Process, the Suzuki Process, the Turek-Schwittay Process or the Co-Generation Process [7] . All processes have the importance of the product separation under high pressure and the recycling of unreacted

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methane in common, which have major impact to the process economics. Investigation and process synthesis regarding to separation efficiency, energy consumption, operating and investment cost are rare but essential for industrial application of the OCM Process. A roughly process flow diagram of the OCM Process is presented in Figure 1. Recycle of CH , ( CO, C H

O CH Diluton Gas

OCM Reactor

Water Separation

)

Carbon Dioxide Separation

HO

Ethylene Separation

CO

Figure 1: Flowsheet of the OCM Process [5]

2. Process Synthesis in the OCM miniplant The OCM Process has not been applied in the industry yet. Besides general information on the reaction kinetics, the heat and mass transfer efficiency, fundamental studies of the process possibility, catalyst life time, and the effect of recycles and efficiencies of each unit are crucial for process implementation. This can only be gained by investigation of the real process. The miniplant technique is a well known technique in the scope of process synthesis, to obtain fundamental information experimentally. A flow sheet of the generalized miniplant layout is presented in Figure 2. Due to the simultaneous process design and caused by economical reasons, the downstream gives requirements to the reaction unit and the catalyst, especially to the yield, the C2 and CO2 selectivity, the methane conversation rate and dilution concentration.

Figure 2: synthesis Simplified–process flow diagram of and the OCM Process [6] Process simultaneous design construction

For the process synthesis, the whole OCM Process is divided into three general unit operations: the reaction unit, the purification unit and the separation unit (Figure 2). All of them are linked and investigated simultaneously. Therefore a design case for each unit has been defined for the composition, which is presented in table 1. The range of the process and stream conditions for the units is presented in table 2. Those conditions are defined for now by literature study and limited by our laboratory conditions, but have to determined and evaluated.

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Table 1: Defined feed gas concentration in [vol%] for the process section Unit

CH4

O2

C2H4

C2H6

CO2

H2O

Inert gas

Reaction

60 – 70

20

-

-

-

-

20 – 10

Purification

45

-

10

10

25

-

20 -10

Separation

60

-

13

13

-

-

14

Table 2: Process conditions for each unit Unit

Pressure range

Temperature range

Reaction Purification Separation

1 to 5 bar 1 to 35 bar Up to 35 bar

30 to 900 °C 30 to 100 °C Down to -100 °C

3. The downstream process The downstream process of the OCM consists of a phase separation unit, a carbon dioxide removal unit and a product separation unit, as recommended by various authors [7] . Concerning the simultaneous design and construction of the miniplant, the state of the art separation processes are taken as a base and is shown in Figure 2. The purification unit consists of an amine based absorption process for the carbon dioxide separation. The separation unit consists of a cryogenic distillation for the product separation. Due to the high energy consumption of the cryogenic distillation, the pressure is increased up to 35 bar to increase the boiling point of the hydrocarbons. Considering the limitation by the laboratory conditions, the pressure increase is limited too. Regarding the idea of using carbon dioxide as an inert gas for the dilution in the OCM reactor, the carbon dioxide removal step becomes even more important in the downstream process. Therefore, the purification section as the first downstream unit is picked out and the carbon dioxide removal is investigated. The purification unit The specification of this unit is to remove the carbon dioxide from the product stream totally as given in table 1. Such request is not unusual in the process industry, but attracts wide interest nowadays. Different approaches are known for those separation units like: absorption processes, adsorption processes, cryogenic distillation or membrane processes. This processes based on different physical and chemical principles: Absorption: physical or chemical absorption in liquids, caused by the gas solubility in the liquid or in combination with a superimposed chemical reaction. Adsorption: physical or chemical adsorption on a particle surface of the sorbent. Cryogenic separation: caused by the different condensation points of the gas Membranes: selective solubility and diffusion or molecular sieves caused by different molecule dimensions and Knudsen diffusion. The best developed and industrial applied technique is the absorption process with chemical or physical absorption liquids. A modern technique is the membrane separation, which has low selectivity yet and is mainly implemented as stand alone units for biogas or natural gas cleaning. The adsorption is available only for small gas streams and is hard to handle, concerning the sorbent regeneration. The cryogenic separation is applicable in combination with liquefaction and storage of the carbon dioxide. The range of the operation conditions are up to 60 bar for the pressure and from -20 °C to

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20 °C for the temperature, that is uneconomicaly without the combination of liquifaction and storrage. Only the membrane and the absorption techniques can be an opportunity for the OCM miniplant. Absorption processes The absorption technique for the carbon dioxide separation is well developed and industrial available. Physical absorption processes like the UOP Selexol® or the Lurgi Rectisol® Process are known, which is using dimethyl ether and cold methanol respectively. Those physical absorption processes causes high product losses of more than 30 vol%, due to a nearly similar solubility of the product and the carbon dioxide in the liquid. Therefore only chemical solvents like Monoethanolamine (MEA), Diethanolamine (DEA) and Methyldiethanolamine (MDEA) or a mixture of them are applicable for the purpose in the OCM miniplant. Those chemicals are used in amine scrubbing processes like the aMDEA® Process in different concentration ranges [8] . Standalone rigorous simulations for the absorption process of the miniplant were carried out in Aspen Plus®. As detergent 15 wt% MEA and 30 wt% MDEA solution were compared. Table 2 summarizes the basic engineering details for the column design, limited by laboratory conditions. Table 3: Technical and hydrodynamic operation conditions of the absorption process

Packing Column Gas Packing Packing Fheight diameter factor feed section capacity [m] [m] [-] [Pa0,5] kg/h] [m²/m³] 5 0.04 0.8 21 50 450

Maximum Liquid Top liquid load stream pressure [m³/m²h] [kg/h] [bar] 55 70 35

The in-built ELECNRTL model is used, with activity coefficients of the electrolyte NRTL approach for the liquid phase [3] and the Redlich-Kwong equation of state (EoS) for the gas phase is applied. Furthermore, concentration-based reaction kinetics is used and a rigorous rate-based model for absorption in packed columns could apply [4] . The carbon dioxide concentration can reduced to 15 vol% with 25 kW energy demand using MEA solution, whereas with MDEA the carbon dioxide concentration can reduced down to 7 vol% with only 5 kW energy input. This separation efficiency caused obviously by the solvent concentration, but they are corrosion limited [8] . Neither MEA nor MDEA as solvent can remove the carbon dioxide totally in a standalone absorption process for the given conditions. Membrane unit The advantages of a membrane unit are the easy operation and a short start up and shut down time caused by their small size [10] . Those units are very flexible in use, due to the modular design. For vapor/gas membrane separation different kinds of materials are available: Polymeric membranes: rubbery or glassy polymers, with different solubility and diffusion properties for carbon dioxide and hydrocarbons. Molecular sieves: absorption effects, separation by the different molecule dimensions. Glassy and rubbery polymeric membrane preferred for the carbon dioxide separation and hydrocarbon recovery [12] . In the investigated membrane unit a carbon dioxide selective membrane is applied. The membrane unit is modeled with the solubility ® diffusion model in Aspen Custom Modeler as a one dimensional, dense membrane. The Peng-Robinson EoS is used for the fugacity. As further non-ideal effects concentration polarization, the Joule-Thomson effect and pressure loss for low

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Reynolds numbers are considered. The membrane unit is calculated using geometry and permeability data for a GKSS flat sheet membrane module [11] . The carbon dioxide concentration could reduce with a one stage membrane unit of an area of 0.5 m² down to 14 vol %. The product losses in this unit are in the range of 30 vol%, similar to those of the physical absorption and for the purpose in the OCM miniplant not applicable. The two stage membrane process The application of a two stage membrane unit can reduce the product losses, whereas the carbon dioxide reduction is of the same range as for one stage membrane system: down to 14 vol%. The dimension and process conditions of the two stage process are shown in Table 3. Neither with the one stage membrane unit nor with the two stage membrane unit the carbon dioxide can be removed totally. Table 3: Technical requirements of the two stage membrane process

Membrane surface for the 1st Stage 1 m²

Membrane surface for the 2nd stage 0.5 m²

Pressure second stage 6 bar

Product losses 10 vol%

4. Conclusion – The hybrid separation process Facing the required purity of the product stream and the lack of an unlimited absorption column, the use of a membrane section for the pre - separation of carbon dioxide was applied successfully. Table 4: Energy balance of the hybrid process

Compressor power

Cooling power

Heating power

Pumping power

1.5 kW 3.5 kW 5 kW 1 kW This hybrid membrane amine process, Figure 3, can remove the carbon dioxide in the product stream totally. A two stage membrane system shows the lowest hydrocarbon losses and was combined with an absorption column to form a hybrid process. The overall energy consumption is listed in table 4. The ethylene loss could reduced to 10 vol% with an over all energy demand of 11 kW without consuming Figure 3: Hybrid carbon dioxide separation process auxiliary materials. The whole process has to be optimized economically and the simulation results have to be validated in the miniplant by experiments.

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5. Acknowledgements The authors acknowledge the support from the Cluster of Excellence "Unifying Concepts in Catalysis, coordinated by the Berlin Institute of Technology and funded by the German Research Foundation (DFG).

References [1] Kent R. Hall, "A new gas to liquids or gas to ethylene technology", Catalysis today, 2005, 106, 243 [2] Hugill et. al., "Feasibility study on the co-generation of ethylene and electricity through oxidative coupling of methane", Applied Thermal Engineering 25 (2005) 1259–1271 [3] Austgen et. al., "Model of Vapor-Liquid Equilibria for Auqeous Acid GasAlkanolamine Systems Using the Electrolyte-NRTL Equation", Ind. Eng. Chem. Res., 1989, 28, p.P. 1060 – 1073 [4] Aspen Plus Example Library “ Rate-Based Model of the CO2 Capture Process by MEA/MDEA using Aspen Plus” – 2008,Aspen Technolgy Inc. [5] M. Driess et.al., "Unifying Concepts in Catalysis" Evaluation Presentation of the Cluster of Excellence for the German Research Foundation , Bad Honef, 6. Juni 2007 [6] Stuenkel et. al., “Ethylene Production via Oxidative Coupling of Methane (OCM) – Investigation of alternative separation Processes”, 17th International Conference on Process Engineering and Chemical Plant Design, October 2008, Crakow, Poland [7] E.E. Wolf (Ed), Methane Conversion by Oxidative Processes, Fundamental and Engineering Aspects. Van Nostrand Reinhold, New York, 1992 [8] Kohl A. L., Nielsen R., „Gas Purification“, Gulf Pub Co, 5th edition, 1997 [9] Deibele, Dohrn “Miniplant-Technik”, WILEY-VCH Verlag, Weinheim 2006 [10] Brinkmann et al. “Membranverfahren in der Erdgasaufbereitung”, Chemie Ingenieur Technik, 2003, Vol. 75, Iss. 11, pP 1607 – 1611 [11] GKSS-Forschungszentrum Geesthacht in der Helmolz-Gesellschaft, Germany [12] Baker, R.W., Membranes for vapor/gas separation, Membrane Technology and research, Inc, 2006

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Analysis of oxidative coupling of methane in membrane reactors H. R. Godinia,b, H. Arellano-Garcia*b, M. R. Omidkhaha, G. Woznyb a

Chemical Engineering Department, Tarbiat Modares University, 14155-143, Tehran, Iran; [email protected] b Chair of Process Dynamics and Operation, Berlin Instute of Technology, Str. des 17. Juni 135/Sekr., KWT9, D-10623, Berlin, Germany; [email protected]

Abstract In order to increase the efficiency of the Oxidative Coupling of Methane (OCM) process, in this work, a new feeding policy structure for an alternative operation mode of the Packed Bed Membrane Reactor (PBMR) is proposed. In Fixed Bed Reactors (PFR), C2 yield and selectivity still can not fulfill the industrial requirements. Moreover, when the available manipulating parameters (such as oxygen partial pressure or membrane permeability) in a PFR or even in a conventional PBMR are used to improve the selectivity, it leads to a sharp decrease in yield and methane conversion. In this work, a comparison of the OCM process efficiency for these three types of reactors is presented. For this purpose, a mathematical model of each reactor is used. In particular, the effect of oxygen concentration in different structures has been investigated. It can be shown that the efficiency of the OCM process in terms of selectivity and yield performance can be improved by using the proposed PBMR. Moreover, considerable improvement in C2 yield (at some selectivity performances around 5 %) is achieved by using the proposed structure in comparison to the conventional PBMR. Besides, injecting the methane into the shell side of the proposed PBMR structure is deemed to be another possibility of this structure towards the improvement of the process flexibility and efficiency. Based on this, a network of membrane reactors, which includes the proposed and the conventional PBMR structures, is able to improve the economical and industrial considerations in points of selectivity, one-pass yield and methane conversion for OCM process. Keywords: OCM Process, Packed Bed Membrane Reactor (PBMR), Network of Membrane Reactors, Ethylene Selectivity, new reactor concept

1. Introduction Obtaining a high yield and selectivity in the OCM Process still remains a main challenge. During the last two decades the application of membrane reactor to overcome this challenge has been studied widely [Kao, 1997, 2003; Kanno 2001; Tye, 2004]. In this work, OCM kinetic data from [Hinsen; 1983] have been used. According to the OCM kinetic, the competition between the reactions, which produce the desired products (C2 product: ethylene, ethane), with those, which are related to the formation of the undesired product CO2, can be managed using the oxygen concentration as a key factor. Removing the ethylene molecules also can play an important role here. In doing this optimally, it prevents a variety of difficulties in the separation section, process operation and improves the efficiency and economy of the OCM process.

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2. Performance of the different reactor structures Usually, the Plug Flow reactor (PFR structure) is considered as a reference structure in order to evaluate the efficiencies of new type of processes. In the PFR structure, all reactants are entered into the tube side and there is no mass transfer across the tube wall. Figure 1 represents the general sketch of a reactor (including PFR, Conventional Packed Bed Membrane Reactor (CPBMR) and the proposed (PPBMR)) for the OCM process. The set “I” represents the PFR. Shell = strip phase

Ft

Shell impermeable wall Tube wall; D

Catalyst

CH4, O2, N2, CO2 C2 (C2H4, C2H6), H2O

Fs Tube = feed phase

Figure 1- General structure of the reactor for OCM process: Set “I”: PFR; Tube wall diffusivity (D)=0; Tube side Feed (Ft)= N2, CH4, O2; Shell side Feed (Fs)= 0; Set “II”: CPBMR; Tube wall diffusivity (D)=Constant; Tube side Feed (Ft)=N2, CH4; Shell side Feed (Fs)=N2, O2; Set “III”: PPBMR; Tube wall diffusivity (D)= Constant; Tube side Feed (Ft)= N2, CH4, O2; Shell side Feed (Fs)= N2, (possibly CH4)

In the PFR, the concentration profile is reduced sharply due to reaction system, in particular both reactions which produce the C2 (C2H4, C2H6) and C1 (CO, CO2) products. They occur simultaneously without any controlling factor. The tight competition between the parallel reactions producing C2 and C1 products starts just after the reactor entrance due to the considerable reduction in reactants and production of free methyl radical. Based on the availability of the reactants (methane, ethylene and oxygen), the amount of the desired and undesired products will be determined. The ratio of methane to oxygen in each section of the reactor is a key parameter. In order to manipulate the availability of the reactants in different parts of the reactor and also to have the highest possible ratio of methane to oxygen, a membrane reactor could be used, in which oxygen is supplied in a controllable way. Figure 1 with set “II” as its characteristics, represents the CPBMR applied for OCM process. In this structure, oxygen enters into the shell side and gradually permeates through the membrane (porous wall of the tube side) in order to react with methane in the tube side. Here, diffusion and availability of oxygen is controlled by manipulating the oxygen partial pressure in the shell side. Therefore, the selectivity could be improved in comparison to the PFR structure. However, this structure (CPBMR) has still room for improvement because there are still some limitations for the use of the oxygen partial pressure on the shell side as a manipulating variable. This limitation is basically due to this fact that decreasing the oxygen partial pressure increases the selectivity, but simultaneously decreases the conversion (yield) sharply. Moreover, a uniform oxygen supply for the reactions along the reactor is not a policy which is compatible with the sequence of reactions in the OCM process. In these reactions, oxygen accessibility is more harmful for the selectivity at the end of reactor, where some parts of ethylene is converted to CO2. In addition, the shell side gas stream following from the CPBMR, which contains considerable amount of reactants and products, can not be further processed by the same reactor structure. According to this, in this work, a new structure is proposed for the OCM process either as an individual reactor or as a part of a network of reactors. Figure

Analysis of Oxidative Coupling of Methane in Membrane Reactors

125

1 with the characteristics addressed as set “III”, represents the PPBMR applied for OCM process. By this means, oxygen enters into the tube side (same as in the PFR structure). Along the reactor, the reactants and products are removed from the reaction side according to their concentration gradient. These concentrations are optimally controlled in the reaction side in order to increase the process performance in case of yield and selectivity. In this way, oxygen is mainly removed at the first part of reactor and ethylene is separated specially at the end of reactor. This clearly offers the possibility to have a higher oxygen concentration in the feed entrance section, which enhances the absolute yield and also the possibility to remove some components like ethylene from the reaction side for improving the selectivity. Entering a stream of methane into the shell side of this structure is also possible in order to partially supply methane in the tube side, which based on optimal procedure, obviously can improve the yield and the selectivity. Furthermore, the strip phase of the new PPBMR could be simply further processed by another type of reactor. For instance, this structure could be easily connected to a CPBMR structure. In this manner, a network of membrane reactors, in which the OCM yield and selectivity could be simultaneously improved, is viable. Figure 2 shows the most general and advantageous concept for the structure of such a network.

Figure 2- Simultaneous improvement of selectivity and yield using a reactor network: 1-CPBMR: Feeding oxygen as a strip phase into the shell side, feeding methane into the tube side 2-PPBMR: Feeding oxygen and methane into the tube side and removing reactants along the reactor

3. General mathematical model applicable for the different structures In this study, the developed general model is able to simulate the performance of all three types of reactors considered. The main structure of this model consists of the mass, energy and momentum balance equations in the tube and shell sides of the reactor. The dusty gas model was used for calculating the mass transfer and diffusion. The isothermal scenario for heat transfer has been applied. The model also includes relations regarding the dimensional characteristics of the membrane (diffusivity etc), catalysts and reactor. The resulting equation systems are converted to sets of algebraic equations using the three point orthogonal collocation method.

4. Results and discussion The reported results in this section are the individual performance for each reactor structure, which are characterized by selectivity and yield based on the following definitions.

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Selectivity =

2 C C2

Yield =

C CO2 + 2 C C2

2 C C2

(1)

C CH 4

The following parameters are fixed in the simulation: the membrane Į-alumina support with separate layer of Ȗ-alumina with the average pore size diameter of 4 nm and thickness (Ȗ-alumina) 5*10-5m, the reactor length (10 cm), tube diameter (1 cm), and the shell diameter (3 cm). For a comprehensive comparison of the reactor performance under different operating conditions, yield of C2 and CO2 product, selectivity of C2 product, and methane conversion are selected as suitable factors for the evaluation of the different structures. 4.1. Effect of oxygen concentration entering into the different structures The effect of oxygen concentration is evaluated in the three structures. Figure 3 (a) shows that by increasing the oxygen concentration entering into each structure, selectivity is decreased. In figure 3 (b), the results of C2 selectivity for the different reactors have been compared at the same methane conversion. PFR

0.65

Conventional PBMR Proposed PBMR

C2 Selectivity

0.62

0.59

0.56

0.53

0.5 0.0024

0.0028

0.0032

0.0036

0.004

0.0044

Oxygen concentration (mol / liter)

(a) 0.66

Conventional PBMR PFR

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Proposed PBMR

C2 Selectivity

0.62 0.6 0.58 0.56 0.54 0.52 0.5 0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

Methane Conversion

(b) Figure 3- Comparing the efficiency of the three structures in term of selectivity

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Here, the typical operating conditions in the tube side are: T=750°C, PCH4=0.3-0.4 bar, PO2=0.05-0.15 bar, PN2=0.55 bar, Pt=1 bar, gas flow rate= 2 STP cm3/s. In the shell side of PBMR: gas flow rate= 2 STP cm3/s and PO2 for CPBMR= 0.1-0.3 bar and PCH4 for PPBMR= 0-0.3 bar. Another basic parameter, which have been tried to keep constant in each comparison, is the ratio of methane to oxygen. It could be seen that at low oxygen concentration the main function of the PPBMR, which is tuning the oxygen accessibility in the reaction side by applying a removal policy, could be less effective and the difference between PFR and PPBMR performance would be narrowed. Since the removal potential of ceramic membrane is fixed, the efficiency of PBMR is falling in general by increasing the oxygen concentration. In order to give a multi dimensional perspective, a typical set of comparing factors for evaluating the performance of these three structures are quantitatively given in Table 1. Table 1- Different parameters in comparing the three reactors Operating conditions: T=750żC, PCH4/PO2 (CPBMR = 0.7 PPBMR) PN2=0.55 bar, Pt=1 bar, tube gas flow rate= 2 STP cm3/s, shell side gas flow rate= 2 STP cm3/s

Parameter C2 Yield CO2 Yield Methane Conversion C2 Selectivity

Same methane conversion PPBMR PFR CPBMR 0.2027 0.1679 0.1943 0.1200 0.1523 0.1259 0.3226 0.3203 0.3202 0.6282 0.5243 0.6069

Conceptually the PPBMR structure shows a behavior between the PFR and the CPBMR in terms of selectivity. In different structure, the yield of ethylene and CO2 are affected by manipulating the oxygen concentration, but CO2 production is affected more when the availability of its reactants (oxygen and ethylene) are reduced via PPBMR. The oxygen appearance in the kinetic correlations also confirms the observed behaviour. Since the feeding policy in the CPBMR and PPBMR structure are completely different, any comparison in terms of selectivity and yield has to be done carefully. Moreover, for the same methane conversion both versions of PBMR have a better performance than PFR in terms of yield and selectivity. The same is also true when the comparison is performed based on oxygen consumption. Besides, since longer contact time corresponds to higher methane conversion, the effect of contact time is the same as for the methane conversion.

5. Conclusions The results show that a sustainable potential of improvement is expected by using the new proposed structure PBMR in comparison to the other structures. The proposed structure exploits the advantages of PFR and CPBMR. In this manner feeding the oxygen like PFR makes it possible to have a high amount of yield while reducing the accessibility to oxygen especially for the components like ethylene guaranties an acceptable level of selectivity. This is achieved by removing the reactants which is the unique feature of this structure. Also with the potential of the PPBMR structure, now it is possible to construct a network of membrane reactors including PPBMR and CPBMR in order to treat the shell side streams of the each PBMR and have a unique product for whole the process.

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6. Acknowledgements The authors acknowledge support from the Cluster of Excellence "Unifying Concepts in Catalysis" coordinated by the Technische Universität Berlin and funded by the German Research Foundation - Deutsche Forschungsgemeinschaft.

References [1] Kao Y.K., Lei L., Lin Y.S., Catalysis Today 82 (2003) 255–273 [2] Kao Y.K., Lei L., Lin Y.S., Ind. Eng. Chem. Res. 36 (1997) 3583–3593 [3] Kanno T., Jun-ichi H., Masayoshi K., React. Kinet. Cata. Lett. 72 No.2, (2001) 195–200 [4] Tye C. T., Mohamed A. R., Bhatia S., J. Ind. Eng. Chem. 10 No.5, (2004) 834–844 [5] Hinsen W., Bytyn W., Baerns M., Proceeding of the 8th international congress on catalysis; Verlag Chemi: Weinheim, Germany, Vol. 3 (1985) 581-592

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Impact resistance of hetero-phase polymeric materials Blanka Ledvinkova, Martin Klejch, Tomas Gregor, Zdenek Grof, Juraj Kosek Department of Chemical Engineering, Institute of Chemical Technology Prague, Technicka 5, 166 28 Prague 6, Czech Republic, E-mail [email protected]

Abstract Hetero-phase polymeric materials, such as high-impact polystyrene (hiPS) and impact polypropylene (iPP), have many applications because of their excellent impact resistance. The methodology of discrete element method (DEM) is adopted for numerical simulations of hetero-phase polymer particles hitting the solid wall. Systematic mapping from the parametric space of polymer morphologies to the parametric space of impact-resistance properties was carried out. Distribution of rubbery domains in polymeric materials strongly affects their impact resistance. Keywords: hetero-phase polymers, discrete element method, impact resistance.

1. Introduction Many hetero-phase polymeric materials, such as impact polypropylene (iPP) or highimpact polystyrene (hiPS), find many applications due to their excellent impact resistance properties. The reasons for good impact resistance of these materials are well understood, but the quantitative understanding of the mapping between morphology and impact resistance is so far empirical. By the tools of mathematical modeling we identify which morphologies (quantitatively described by morphological descriptors) have the best impact resistance properties with the same content of rubbery phase in the case of iPP and hiPS. Dramatic changes of material structure are observed during the impact of testing hammer on the material. Finite-element based approaches are therefore not suitable for addressing of dramatic structure changes. Thus we adopt the methodology of discrete element method (DEM). Polymer materials are discretized into number of discrete elements with elastic or visco-elastic interactions acting among individual discrete elements (Fig. 1). Several types of discrete elements are employed for different phases present in the material. Also parameters characterizing the force interactions and the deformation causing the break of connection between pair of discrete elements depend on the type of connected discrete elements (i.e., on the polymer phase in hetero-phase structure). agglomerate of discrete elements material force F two interacting discrete elements spherical discrete element Figure 1. Discretization of the continuous phase into discrete elements.

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2. Discrete element method (DEM) DEM discretizes the continuous phase into individual discrete elements or in the case of granular media considers the individual granules as discrete elements. Each discrete element is characterized by the vector of spatial coordinates xi, vector of velocity vi, its characteristic size ri and its type ti, It is advantageous to consider spherical discrete elements of the same size. Other quantities, such as concentration(s) or temperature, can be assigned to each discrete element. DEM is usually used for dynamic simulations. The algorithm of DEM consists of following steps, which are repeated until the end of the simulation is reached. 2.1. List of connections among individual discrete elements Force interactions among discrete elements are considered to be binary or ternary (i.e., acting among two or three elements). Binary connection is created if two elements touch, i.e. if their Euclidean distance u is smaller or equals to equilibrium distance of their centers u0. The relative elongation of the connection is defined as e = (u – u0 )/u0 .

(1)

When the maximum value of the relative elongation is exceeded, i.e., e > emax, the binary connection is broken. As the consequence micro-elements in the distance interval u ∈ (u0, (1+emax)u0) can be connected or disconnected depending on their previous position (i.e., history). Similarly, ternary connection of micro-elements A-V-B is formed, if both binary connections A-V and B-V are created and is disconnected , if one of binary connections is broken or if the difference between the bonding angle Į = ∠ AVB and the equilibrium angle Į0 exceeds the critical value Įmax . 2.2. Calculation of forces

The direction of force acting on the discrete element A corresponds with the direction of the connecting line between centers of elements A and B according to the equation FAB = F(xA – xB) / | xA – xB| .

(2)

The force FBA acting on element B has the same size but the opposite direction, i.e., FBA = – FAB. Many materials have visco-elastic character, therefore the size of the force F is calculated as the combination of two concepts: (i) elastic deformation described by Hook’s law, (ii) viscous flow described by Newton’s equation. In testing the impact resistance simple description of acting forces by Hook’s law is sufficient σ=Ee,

(3)

where σ is the strain, e is the deformation and E is the mechanical modulus. Advanced force interactions described, e.g., by Maxwell or Kelvin visco-elastic model are implemented in our code (Grof et al., 2005a,b; Ledvinkova et al., 2008). 2.3. Equations describing motion of discrete elements The force acting on the i-th discrete element is obtained as the sum of forces of all binary pairs and ternary triplets acting on the i-th element. This resulting force is then introduced into the equations of motion written in the form dxi/dt = vi ,

(4)

mi dvi/dt = ¦j Fij +¦j,k Fijk ,

(5)

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where t is the time, mi is the mass of the i-th element, Fij are binary and Fijk are ternary forces (summed over all elements neighboring to the i-th one). The resulting system of equations is a non-linear system of ordinary differential equations, where six state variables (components of vectors xi and vi) are employed for each discrete element. Initial-value problem of eqs. (4) and (5) accompanied with appropriate initial conditions is solved by the Merson integration method. Due to the evolution of spatial coordinates of individual elements the connectivity of elements is developing in time: some existing connections are broken, new connections are created and the magnitude of the interacting force changes with the distance of micro-elements. Therefore it is necessary to check the connectivity of elements and to evaluate the interaction forces after each integration step. 2 μm

PS – continuous phase PB – particles PS – inclusions in rubbery particles

Figure 2. AFM phase image of high-impact polystyrene (HIPS) with salami-like morphology (PS is polystyrene, PB is polybutadiene).

3. Simulations of impact resistance In the industry the increase of the impact resistance is achieved by the addition of the elastic rubbery phase into „hard“ skeleton of the original polymer. Examples of industrially important hetero-phase polymers are impact polypropylene (iPP) and high impact polystyrene (hiPS). Impact polystyrene contains the continuous polystyrene phase (PS), particles of the polybutadiene phase (PB) and the inclusions of PS and grafted copolymer PB-g-PS. The morphology of hiPS is sometimes given the adjective salamil-like (Fig. 2).

immovable wall glassy polystyrene

polybutadiene rubber velocity v t=0s

t = 1.5x10-5 s

Figure 3. DEM discretization of hiPS particle and particle collision with wall.

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In DEM representation discrete elements of different types are used to represent the structures of hetero-phase polymers (Fig. 3). The mechanical impact resistance is in our simulations tested by the impact of the polymer particle with the immovable wall. The experiment proceeds as follows: the polymer particle is situated in the closeness of the wall and starts to move against the wall with the constant velocity. After the impact the deformed particle is reflected back from the wall. The extent of the damage is evaluated both visually and statistically as the number of disconnected bonds of discrete elements (Fig. 4).

Count of disconnected bonds Poþet rozpojených vazeb of discrete elements

1400 1300 1200 1100 1000 900 800 2

700

4 6

PolomČrof diameter þástic PB PB particles

600

8 10 12 14 5

10

15

20

25

30

35

content of PB PB[%]/ % Zastoupení

Figure 4. Statistically evaluated damage of hiPS particle after its impact in dependence on diameter of PB particles and PB content. Diameter of PB particles has a larger effect on the impact resistance of hiPS than the content of PB phase, as can be seen in Fig. 4. Large PB particles stop the propagation of cracks in the glassy polystyrene phase more effectively than smaller PB particles. With respect to impact resistance it is thus advantageous to produce hiPS with a fraction of larger PB particles. Parametric study of impact resistance of impact polypropylene has been carried out for several different contents of rubbery phase (black elements in Fig. 5) and various distribution of rubbery phase within the hard porous skeleton of the isotactic polypropylene (green elements in Fig. 5). We can observe that the finely dispersed ethylene-propylene copolymer (rubber phase) helps to achieve the best impact resistance of this material. The presence of large compact zones of hard isotactic propylene causes the material to be brittle in our simulated impact resistance test. Statistical evaluation of these simulated tests can be performed similarly as in the case of hiPS material.

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t=0s

wsoft=0.10 v=20m/s t=5×10-5s wsoft=0.37 v=20m/s t=5×10-5s wsoft=0.70 v=20m/s t=5×10-5s

Figure 5. Parametric study of the impact resistance of iPP particle. Black elements are rubber, while green elements represent skeleton of isotactic polypropylene.

4. Conclusions Processes involving dramatic changes in morphology can be simulated by the utilization of discrete element method (DEM). We have applied DEM for the investigation of impact resistance of hiPS particles with salami-like morphology and of iPP particles with various distributions of rubber domains. In both materials we have not only identified morphologies of these polymeric materials with the best impact resistance, but we can also evaluate how sensitive is the impact resistance to the variations in morphology.

5. Acknowledgements The support from GACR 104/07/1127 and MPO FT-TA3/110 is acknowledged.

References Z. Grof, J. Kosek, M. Marek, 2005a, Modeling of morphogenesis of growing polyolefin particles, AIChE J. 51, 2048-2067. Z. Grof, J. Kosek, M. Marek, 2005b, Principles of morphogenesis of polyolefin particles, Ind. Eng. Chem. Res. 44, 2389-2404. B. Ledvinkova, F. Keller, J. Kosek, U. Nieken, 2008, Mathematical modelling of the generation of the secondary porous structure in a monolithic adsorbent, Chem. Eng. J. 140, 578-585.

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Information flow modeling and data mining in high-throughput discovery of functional nanomaterials Yang Yang and Xue Wang* Institute of Particle Science and Engineering, School of Process, Environmental and Materials engineering, University of Leeds, Leeds LS2 9JT,UK, [email protected]

Abstract This contribution describes the information flow modeling and a prototype data mining system designed for the discovery of functional nano-materials using high-throughput experiments. Metal oxide nanoparticles are considered to be one of the most promising photocatalyst materials, but their functionality and efficiency highly depends on the composition, structure as well as the formulation and processing procedures. The aim is to develop a high-throughput hydro-thermal synthesis process which is capable of formulating several hundreds of samples per day. The system is equipped with a robot and various process analytical instruments such as Raman, dynamic light scattering and X-ray diffraction spectroscopy, turbidity, temperature, pressure and flow sensors, as well as off-line characterization instruments. A work flow management system is developed using an e-science tool to manage the large volumes of data that have complicated structures and formats, often with varied sampling intervals. Data is shared between different users and application tools. A data mining system is used for data analysis e.g. in developing quantitative structure activity relationship (QSAR) type of predictive models. Keywords: High throughput, discovery of nano-materials, ceramics, data mining, e-science, QSAR

1. Introduction The ability of industry and academia to accelerate the discovery of new inorganic nanomaterials for applications such as catalysts, optical amplifiers, lithium batteries, dielectrics, healthcare ceramics (sunscreens), etc, is severely limited by the speed at which new compositions can be made and tested for suitable properties. In particular, doped semiconductor nano-materials can show large differences in properties with small changes in particle size or composition, associated with quantum confinement effects. The work described in this paper is part of a project aimed at developing a highthroughput (HT) hydrothermal synthesis robot for rapidly synthesising and characterising doped inorganic nano-particles (<100nm). The work flow is shown in Fig.1. The focus of the paper is on describing the data flow management and data mining system for the project, but firstly a brief introduction of the HT synthesis process is given.

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Robot Design of Experim ent

Synthesis

Clean up

Print/collect

HT performance Analysis

T

Chemometrics & Data mining

Fig. 1 Work flow of HT hydrothermal robot

2. High-throughput hydrothermal flow synthesis robot The HT hydrothermal synthesis robot is equipped with one salt preparation system, one HT reactor, one collection carousel, four centrifuges, four tube racks, one tip rack, one clean-up carousel, one quick turbidity measurement station and one spotting system. A schematic of the HT continuous hydrothermal flow synthesis (CHFS) system1 is shown in Fig 2. For the sc-water feed (F1), a HPLC pump delivers deionised water through an electrical preheater to at least 400ºC under pressure (ca. 220 Bar) to reaction point R. The metal feed (F2) is a salt preparation system containing six Tecan XLP3000 syringe pumps for aspirating and dispensing salt solutions. The auxiliary (AUX) feed (F3) allows up to two modifiers to be added to the premixed metal feed at a conical salts mixing pot (M). At reaction point R, nucleation and grain growth occur. R is essentially a HT reactor system in which supercritical water tube (down flow) mixes with up flowing metal salt mixtures. The particles are then cooled via a heat exchanger (T) and pass though the back-pressure regulator (B), to be collected by the collection system (C). The collection system consists of turbidity detector, carousel and rotation motor. As the turbidity of the sample increases the transmission reduces. So the turbidity detector can set a threshold to decide whether the sample is collected. Once the sample being dispensed into the tube, the cleanup system works. The transmission sensor detects the height of the interface between phases and an aspiration needle is used to remove the aqueous supernatant layer. And then solvent (currently ethanol) will be injected into the tube and a homogenizer will be supplied to re-suspend the nano-particles. After all theses steps, the eligible samples are delivered to automated analyses point (A). Automated analyses include both on-line and off-line analyses such as laser light scattering (LLS), flow cell UV/Vis, x-rays diffraction (XRD), Raman, Zeta potential and selected HT photocatalysis testing. After the HT synthesis and characterisation, it is the HT performance analysis stage. It is clear that the HT synthesis is achieved through automation in all the steps of synthesis, characterisation and analysis. This is different from HT systems that are based on multiple parallel reactors.

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High-pressure section Atmospheric pressure PC

F1: SC-WATER

PC

F2: Metal Feed

PC

F3: AUX Feed

M

R

I

PC

PC

T

B

C

A

PC

PC

PC

Fig 2. Schematic for hydrothermal synthesis of nanoparticles that allows rapid product synthesis and optimisation. R = Reaction point; M = mixing point; I = in-line analyses (high pressure); T = cooling; B = back-pressure regulator; C = collect, centrifugation, cleanup, deliver; A = automated analyses (Raman, Zeta pot., XRD and selected HT photocatalysis testing, etc).

3. Data management and data mining 3.1. Data structure and Data correspondence Data management is setup with Postgresql 8.2 and organized according to three parts: synthesis, storage and analysis. The structure of the synthesis is illustrated in Fig 3. MetalSalts table contains the information about the metal salts for the reaction (cation, anion, supplier, etc). Information about auxiliary modifiers (name, formula, supplier, etc) is recorded in AuxMods table. HFReaction table has the information specific to a single HF reaction (water flow rate, temperature, pressure, etc). One kind of raw

Fig 3 Data structure design for synthesis section showing entities, key attributes and relationships between entities. Yellow tables are the HT process (drying, clean up, reaction…); the blue tables present all the physic things (tubes, materials, equipments…); the green ones are junction tables.

materials may have more than one reactive condition. So HFMetalMixtures and AuxModMixtures tables are used to describe the raw materials for each reaction and modificatory methods added to metal salts for each reaction. Cleanup involves several cycles of centrifuge, measurement, decant, water addition, and dispersing. Washings table contains all cleanup information for a given tube. Every time, HF reaction produces dirty slurry whose information like barcode will be recorded in SampleTube table. Like other junction tables, HF_ST is necessary because HF reaction may produce several slurries. The collaborative project is conducted by two research groups from University of Leeds and University College London (UCL). Experimental work is setup in UCL, while the Leeds group focuses on information modelling, experimental design and data mining.

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So the database in UCL is used for data storage while the database in Leeds is for data analysis. In order to not only keep the data flow but also make the information flow synchronized, the concept “information correspondence bridge” is employed and implemented in an e-Science tool of InforSence.2 InforSense software works as a bridge between server database (Leeds) and client database (UCL), any update by client database can be obtained by server database at the same time and any result obtained and put into the sever database can be published by InforSense and accessed by client point. The data correspondence flow is shown in Fig 4. Malvern LLS 5

Analytical Instruments connected to PC UV/Vis, etc

Configuration and Measurements from other analytical instruments XRD, Raman, Catalytic, XRF, etc

10 Configuration 4 HT Robot

Configuration

1

8 9

2 3

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Labman Control Station

Data

7 6

Process

16

Data Mining

13

Data Station

12

Public

LAN

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Leeds Station

WAN

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Leeds LAN

Website

Fig 4 Information correspondence bridge. Process database controlled by Labman software (flows 1–6). Synthesis and storage data copied into UCL database (flow 7). Analytical data added by PCs running instruments (flows 10, 11). Updated data of UCL database will be captured by Leeds database and data mining support and feedback information will be sent to UCL station through InforSense (flow 13, 14, 15). Revisional experimental design information will be sent to Labman control software (flow 16).

3.2. Data mining system The data mining3 system is divided into four major parts, as represented in Fig 5 (inside the dashed rectangular box): (i) fusion, feature extraction, and interpretation of data from each instrument using chemometrics techniques, (ii) integration of multiple on-line and off-line measurements and multivariate chemometric data analyses, (iii) inductive data mining for causal knowledge discovery

For experimental design

For mechanistic / principle modelling, QSAR

Univariate chemometrics for analysis & interpretation of data from each PAT sensor SEM image anaysis Data integration UV-vis NIR Raman XRD SEM Feed Pro. Off-line data Knowl. …

Inductive data mining for causal knowledge discovery and predictive model development Multivariate multi-scale data analysis: product quaity measures and indices; Process operational envelopes

Causal knowledge and predictive models for process optimisation and control

Fig 5 Data mining system for HT photocatalyst discovery

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and QSAR model development, and (iv) experimental design. Due to space limitation, details of the system’s functions will not be introduced. We briefly describe two examples. The first example is about chemometric analysis of a photocatalyst performance data set. The data is about doped nano-titanias with 17 different ions, prepared at 0.5, 2.5 and 5 mol% dopant ion concentrations4 (Fig. 6). The catalysts were characterised using XRD, and colour. Performance of each catalyst was tested through UV light dye degradation reactions. The objective is obtain knowledge regarding the effects of the type of dopants and amounts of dopants on catalyst performance. The knowledge can then be used to guide the catalyst design. QSAR (quantitative structure – activity relationship) type of models were developed to correlate catalyst composition (dopants) with characterization features (XRD and colour), and between characterization features with dye degradation performance. Using the QSAR models, genetic algorithm was used to find the optimum region of catalysts composition that gives best catalytic performance. Fig. 7(a) shows plot of the first two principal components of XRD data of the catalysts. Red colour represent catalysts that give good performance. Fig. 7(b) shows the optimum region in the PC1-PC2 plot of XRD data which was obtained using genetic algorithm and the the QSAR and PCA models.

Fig 6 Fifty one doped titania nanopowders

(a)

(b)

Fig 7 PCA scatter plot for Original XRD data (a) and the 50th generation XRD data produced by genetic algorithm (b)

4. Final Remarks High throughput strategies are gaining importance in catalyst formulation and discovery. The increased experimental capacity produces large volume of valuable data of varied types and complexity (real-time and off-line data, spectra, images). Data

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management as well as data mining are clearly important in the cycle of HT nanomaterial discovery. Data flow design using an e-Science based data management system is described. A prototype data mining system tailored for HTT nanomaterials formulation and discovery is also introduced. It is also important to use effective design of experiments (DoE). Traditional DoE methods can manage no more than ten factors effectively. A genetic algorithm approach has shown great potential when applied together with QSAR models.

5. Acknowledgements UK Engineering and Physical Sciences Research Council is thanked for providing funding (Grant Reference: EP/D038391). Thanks are also due to Dr J Darr and T Lian in the Chemistry Department of University College London for collaboration on this project. The industrial collaborators are AMR Ltd, Coates Lorilleux Ltd, Faraday: INSIGHT (Chemical throughput), Hydrogen Solar Ltd, Malvern Instruments Ltd, SRI International (inc), Tescom Corporation UK and Thermo Electron Corporation.

6. References 1. Cabanas A, Darr JA, Lester E, Poliakoff M, J Mat Chem, 2001, 11: 561-568. 2. http://www.inforsense.com/. 3. Wang XZ, Data mining and knowledge discovery for process monitoring and control. Springer: London, 1999. 4. Zhang Z, Morgan DJ, Brown S, Clark RJH, Goodall JBM, Weng X, Kellici S, Gong K, Thompson K, Knowles JC, Mordan NJ, JEvans uRG, Carley AF, Bowkerc M, Darr JA, J Mat Chem, In press.

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Model Based Prediction of Crystal Shape Distributions Christian Borcherta, Doraiswami Ramkrishnab, Kai Sundmachera,c a

Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, D-39106, Magdeburg Germany, [email protected] b School of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West Lafayette, IN 47907, USA, [email protected] c Process Systems Engineering, Otto von Guericke University,Universitätsplatz 2, D39106 Magdeburg, Germany, [email protected]

Abstract In classical crystallization as well as in nanoparticle engineering crystal shape is an important property of crystalline products. The emergent properties of bulk material are closely related to the crystal shape. We present a single crystal model describing shape evolution. The model has a hybrid character since the appearance and disappearance of crystal facets is a discrete event in the continuous process of crystal growth. Tight control of not only the single crystal’s shape and size is desirable but with regards to mass production shape and size distribution control is required. A first step in this direction is a model representing the dynamical evolution of the shape distribution of a crystal population. We show that a population balance approach can be used. In the proposed framework the hybrid nature of the single crystal evolution has to be taken care of. We also sketch a numerical scheme with which the proposed model equations can be solved. Keywords: Crystallization, Modeling, Morphology, Population Balance

1. Introduction Crystal shape is a major quality factor for particles being produced as high-added value products in the specialty and pharmaceutical industry. Even though modeling work which can be found in the literature is focused on size and size distributions it is well known that properties of dispersed phase products are strongly linked to their shape. For example, surface structure and binding energies and thus reactivity varies with the crystallographic orientation. Hence, it is important in catalyst engineering to take into consideration that reactivity of crystals depends on their shape, which in turn determines which crystal faces are exposed [1]. New applications in optics and electronics have been afforded by using structured materials build up of small particles. For instance, inorganic nanocrystals have well defined electronic and optical properties [2] which are observable at the single crystal or emerge from their assembly in superstructures. Because the assembling pattern is a strong function of the crystal morphology, the emergent properties of the superstructures are strongly defined by the single crystal shape [3,4]. From the engineering point of view it is therefore an essential task to control and manipulate crystal morphologies. In the literature scientifically well founded concepts have been

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4 h 1

G& i

h2

,∞

h2

h2

3

3

4

2 h 1,∞

1

2

1 h1

a) Morphological transition: octaeder-square-octaeder. In states 2-3 the h2 face is virtual.

b) Morphological transition shown in geometrical state space.

σcrit σ c) Transitions of the morphology are caused by growth rate anisotropies.

Figure 1. Anisotropic crystal growth (a) represented in the state space (b). Growth rates are anisotropic (face specific) (c). discussed which predict growth rates [5,6] and their manipulation using inhibitors and promoters [7,8]. Also experiments have been published in which morphology engineering has successfully been applied using growth inhibitors. For instance, in a recent study Yang showed that the expression of the reactive facets {001} of anatase TiO2 can be increased by growing them in fluorine doped solution [9,10]. The so manipulated crystals have potential applications in solar cells, photonic and optoelectronic devices, sensors and photocatalysis. More examples highlighting the importance of morphology control in nanoengineering can be found in the literature. A good overview give Glotzer & Solomon [11] who present a heuristic conceptual framework for the characterization of complex structured particles among which morphology has been recognized as a key feature. They recognize that shape and size distribution strongly influences the behavior of particles ensembles. In the present paper we propose a modeling approach for shape distribution prediction based on population balances. In Section 2 a quantitative shape model is introduced. It is shown that the geometrical state space has discontinuous properties. The recognition of this feature enables the derivation of rigorous multidimensional population balances capturing the dynamics of shape distributions, see Section 3. We conclude the obtained results in brief in Section 4.

2. Single Crystal Model In the following, convex crystals comprising of n flat faces are considered. Let ni≠nj be the outer unit normal of the i-th face and hi its distance to the crystal center. The crystal polyhedron S is then given by

S = {r : N ⋅ r − h < 0} ,

(1)

where NT=[n1,…,nn] and hT=(h1,…,hn). The vector h is called the geometrical state vector which is a point in the geometrical state space Ω. Even though the crystal shape is fully defined by the geometrical state vector, it is necessary to extract from this information which crystal faces are indeed present on the surface. We can find limits hi,∞(h1,…hi-1,hi+1,hn) at which the i-th face disappears from the crystal surface. Then the plane ni·r = hi,∞ is tangential to S only in an edge or corner. An illustrative 2-D example is shown in Figure 2a: The crystal has two different faces which have the distances h1 and h2 to the crystal center, respectively. In case that h2<√2h1, both faces appear on the crystal surface as in state 1 (and 4). When the h2 faces then grow at a rate which is

Model Based Prediction of Crystal Shape Distributions

143

Figure 2. The distance of the virtual faces hi,∞ (red) depends on the morphology as determined by the real faces. higher than of the h1 faces (G2>√2G1), they will reach the limit h2,∞= √2h1. Then h2 faces disappear from the surface and only virtual h2 faces exist which are tangential tohe remaining shape. In the geometrical state space we can interpret the limit h2,∞ as a point set describing a morphological subspace of Ω. The state space can be divided into three regions, standing for the existence domains of squares (Ω1), octagons (Ω2) and diamonds (Ω3). From the example it is clear that growth processes lead to morphological changes. Growth rates of (real) crystal facets can empirically be modeled using continuous, differentiable functions for instance power laws [12]:

dhi dt

= Gi = k gi Δc gi , Δc = (c − csat (T )) ,

(2)

hi < hi , ∞

where c is the concentration of the crystal substance in solution and csat its saturation concentration. kgi and gi are kinetic parameters which are different on the various faces. That is, the ratio of the growth rates is to some extent controllable by the supersaturation Δc, see Figure 2c. The supersaturation in turn is controllable through the temperature T. Morphological manipulation by supersaturation is limited to naturally occurring growth rate ratios. Such limits can be overcome using additives which can affect the kinetic parameters kgi and gi leading to growth rate ratios – and therefore to morphologies – possibly not achievable through supersaturation control [7,13]. Morphological changes occur when a face disappears, that is, when the trajectory hits a morphological subspace Ωj (hi=hi,∞). Then the virtual face velocity is determined by the remaining real faces:

dhi dt

= hi = hi , ∞

dhi ,∞ ⎛ dh dh dh ⎞ dh ⎜ h1 ,..., hi −1 , hi +1 , hn , 1 ,..., i −1 , i +1 , n ⎟ . dt ⎝ dt dt dt dt ⎠

(3)

The morphology of the remaining shape is determined by h1,…,hi-1,hi+1,hn, and thus describes which real faces dictate the displacement rate of the virtual face. For instance, the distance of the virtual {110} faces (tangential faces) in Figure 2 is determined by the cubic {100} and octahedron {111} faces. The switch between morphologies is not continuous. Further, the virtual face velocity is a linear function of adjoining real faces. Then we can express the virtual face velocity as

dhi dt

= q ij ⋅ G , hi = hi , ∞

(4)

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h1

Cube

dh dt

σmax

h(t)

Ω1 Ω 2 σmin

h(t) σ(t)

Truncated Cube Cubooctahedron

Ω3 Ω4 Ω5

Truncated Octahedron Octahedron

h1

Figure 3. Morphology map.

Figure 4. Morphological subspaces in the cube- octahedron space.

where GT=(G1,…,Gn). The vector qijT=(q1,…,qi-1,0,qi+1,…,qn) is constant and determined by the geometry of the underlying j-th morphology. In case that the i-th face is real in Ωj we can express this as qijT=(0,…,qi=1,…,0). Then we obtain the system of ordinary differential equations with discrete dynamics (hybrid system) on the right hand side

dh = Q j ⋅ G , where dt

⎡q1 j ⎤ ⎢ ⎥ Qj = ⎢ M ⎥ , ⎢q nj ⎥ ⎣ ⎦

(5)

which is called the morphology matrix and is clearly a function of h. A detailed analysis of the subdivision of the state space into morphological subspaces can be found in [14]. Here we consider the example of a rather simple crystal geometry which is for example assumed by potash alum. In Figure 3 a morphological map is shown, which is the result of a geometrical analysis that yields the full set of morphologies as well as geometrical transition conditions and morphological subdomains in the geometrical state space Ω. When the information about the growth rates G are included into the analysis we can also determine which parts of the morphological map are relevant. For instance, if the range of G is bounded by minimum and maximum supersaturations, σmin and σmax, the relevant submap can be obtained (in Figure 3 the part bounded by σmin and σmax). Figure 4 depicts the division of the cubeoctahedron part of Ω into morphological regions Ω1,…,Ω5 in which morphologies from cube to octahedron can be found.

3. Population Balance Equations Within domains Ωj the morphology matrix Qj is constant which means that the velocity field in Ωj is continuously differentiable. Let nj be the number density within Ωj . Presumed that breakage and aggregation of crystals can be neglected the evolution of nj can be described by the following population balance equation [15]:

Model Based Prediction of Crystal Shape Distributions

∂n j ∂t

+ ∇ ⋅ ((Q j ⋅ G )n j ) = −

nj

τ

+ ∑ n& jk ,

145

(6)

j

where τ is the mean residence time n& jk is the flux from a higher dimensional domain Ωk into the lower dimensional domain Ωj as sketched in Figure 4 where the truncated cube (Ω2) strives towards the cube morphology (Ω1). When bj is the outer unit normal of the morphological domain Ωj then the flux from the Ωk to Ωj is given by

n& jk = b jk ⋅ (Q k ⋅ G )nk , h ∈ Ω j , b jk ⋅ (Q k ⋅ G ) > 0 ,

(7)

where the latter condition comes from the fact that the vectors bjk must form an acute angle with the velocity vector (Qj·G) in order to ensure that the flux is directed towards Ωj. In case that the velocity vector (and thus the flux) points from the domain Ωj away, the population nj is not active. We discuss the transfer from lower dimensional domain to higher dimensional ones along the following example. In Figure 4 the octahedral crystals will all vanish instantaneously when the velocity vector points from Ω5 away. Let t1 bet the instant at which b45·(Qj·G)<0, that is, Ω5 and thus n5 becomes inactive (n5=0). The particles which are in Ω5 at t
n ∂n4 ⎫ + ∇ ⋅ ((Q 4 ⋅ G )n4 ) = − 4 + n&43 ⎪ ⎪ ∂t τ ⎬ for t < t1 ∂n5 n5 + ∇ ⋅ ((Q 5 ⋅ G )n5 ) = − + n&54 ⎪ ∂t τ ⎭⎪ ∂n4 n ⎫ . + ∇ ⋅ ((Q 4 ⋅ G )n4 ) = − 4 + n& 43 ⎪ ∂t τ ⎪⎪ + − n4 (t = t1 ,⋅) = n5 (t = t1 ,⋅) ⎬ for t > t1 ⎪ n5 (t = t1+ ,⋅) = 0 ⎪ ⎪⎭

(8)

4. Computational Methods For the solution of the model equations we use a multidimensional moving pivot technique. The fixed pivot technique has been discussed in [16]. We further developed this method for pivots moving through property space. This movement represents crystal growth. We partition the morphological domains Ωj into continuously evolving subdomains Λjk, which make up the unstructured, continuously evolving mesh we solved the model equations with. The particles within a cell Λjk are represented by a pivot at the position hjk which lies in the interior of Λjk . The number of particles existing in Λjk is given by Njk(t). Then the number density of the respective morphological domains can be approximated by ν

nˆ j = ∑i =j1, piv N jk (t )δ (h − h jk ) ,

(9)

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h jk (t 2 )

h jk (t1 )

h j ( k +1) (t 2 )

h j ( k +1) (t1 ) h nuc

h j ( k + 2) (t 2 )

h nuc

h j ( k + 2) (t1 )

h2

h2

h j ( k +3) (t 2 )

h j ( k +3) (t1 ) h1

h1

a)

h j ( k + 4) (t 2 )

b)

c)

Figure 5. Continuously evolving mesh in 2-D from t1 (a) to t2 (b). Unstructured distributed pivots in a 3-D state space (c). where δ is the Dirac delta distribution and νj,piv(t) is the number of pivots within morphological domain Ωj . Clearly, the number of pivots increases. The dynamical equations to be solved after discretization are given by following ODE system:

dh jk dt

= Q jG ,

dN jk dt

=−

N jk

τ

+

∫n

j

dVh .

(10)

Λ jk

This system can be implemented in MATLAB and simulation studies can be performed. Details of the numerical algorithm can be found in [17].

5. Conclusion We have shown that the shape evolution of a single crystal can be modeled using ordinary differential equations with switching right hand sides, represented by morphological matrices Qj. The velocity fields within morphological domains Ωj are continuous. Thus, the dynamics of number densities can be captured using multidimensional population balances. Special initial and boundary conditions are necessary describing the exchange of particles between the domains. The model equations can be solved using a moving-pivot technique.

6. References [1] Ertl, G., et al. (2008). Handbook of Heterogeneous Catalysis, p. 1652. Wiley-VCH. [2] Kelly, K. L. (2003). J. Phys. Chem. B, 107, 668-677. [3] Barnard, A. S. & Curtiss, L. A. (2007). J. Mater. Chem., 17, 3315-3323. [4] Cozzoli, P. D. & Manna, L. (2005). Nature Mater., 4, 801-802. [5] Winn, D. & Doherty, M. F. (2000). AIChE-J., 46, 1348-1367. [6] Boerrigter, SXM, et al. (2004). J. Phys. Chem. A, 108, 5894-5902. [7] Weissbuch, L., et al. (1995). Acta Cryst. B, 51, 115-148. [9] Yang, H. G., et al. (2008). Nature, 453, 638-641. [10] Selloni, A. (2008). Nature Mater., 7, 613-615. [11] Glotzer S. C. & Solomon M. J. (2007). Nature Mater., 6, 557-562. [12] Myerson, A. S. (2002). Industrial Crystallization. Boston: Butterworth-Heinemann. [13] Weissbuch, L., Addadi, M., Leiserowitz, L. (1991). Science, 253, 637-645. [14] Borchert, C. et al. (2008). Proceedings of ISIC17, Maastricht. [15] Ramkrishna, D. (2000). Population Balances. San Diego: Academic Press. [16] Chakraborty, J. & Kumar, S. (2007). Chem. Eng. Sci., 62, 4112-4125. [17] Borchert, C. et al. (2009). Moving pivot technique fo the solution of multidimensional population balances. to appear.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Multi-objective dynamic optimization of fixed bed dryers: simulation and experiments Marcia P. Vega, Mauricio C. Mancini, Luis A. Calçada Departamento de Engenharia Química - Universidade Federal Rural do Rio de Janeiro, BR 465, km7 – CEP: 23890-000 – Seropédica – RJ – Brasil, E-mail: [email protected]

Abstract It is very important a thorough understanding of the drying operation (confident mathematical model) for solving the problems related to the optimization of a dehydration plant, which basic objective is the removal of water up to a certain desired level. Pareto optimization, which improves the performance of dryers for being appropriate to work with conflicting objectives, was implemented through simulation and experimental studies, using a fixed bed alumina drying unit. Keywords: multi-objective optimization, fixed bed, alumina 1. Introduction Chemical processing industries have an important step, named dehydration operation, for conserving energy purposes; tracking a target humidity level and removing of water in the solids up to a certain level, at which microbial spoilage is minimized. Solving the problems related to the operation, design and optimization of the dehydration plants needs a thorough understanding of the drying operation. A review in the drying literature unveils that Pareto optimization has not yet being applied with dynamic mathematical models. The majority of papers in drying area use single objective optimization. Otherwise, there is a growing tendency of maximizing the product quality and diminishing costs simultaneously. The major objective of this paper is applying multicriterion dynamic optimization in fixed bed dryers. Pareto optimization (İconstraint method) is implemented by initializing the optimization algorithm with distinct initial guesses. Finally, experiments were carried out for implementing non inferior solutions in an alumina fixed bed drying unit. 2. Materials and methods Experiments were carried out in a drying unit containing a stainless steal bed, presenting a diameter of 9.8 cm and a height of 15 cm. A PID controller was implemented in order to regulate feed gas temperature by manipulating a resistance. The drying air was supplied by a blower and passed through a

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rotameter. Before reaching the bed, the air passes through a distributor of stainless steal in order to guarantee bed homogeneity. A small part of the particles were utilized for equilibrium isotherm determination in a thermostatic batch. Experimental drying data were employed for determining global mass transfer coefficient, using feed gas temperature Tg and feed gas flow G g . The static method was employed for determining the equilibrium humidity, using over saturated salt solutions. Global heat transfer coefficients of Gupta et al. [1] for fixed bed dryers were employed in the mathematical model. Experiments were carried out in order to identify the global mass transfer coefficient with operational variables ( Tg and G g ), Eq. (1).

ks

-0.27 + 0.0043(T g - 273.15) + 0.016G g (T g - 273.15)

(1)

3. Pareto optimization There are several methods described in the literature about the Pareto set generation [2]. They basically transform the original multi-objective problem into many single objective optimization related problems. The simplest and the most usually applied technique is the İ-constraint approach [3]. In this method, one of the objective functions of the original multi-objective optimization problem is selected to be the single objective function (primordial objective function), while the others are included as constraints. These new constraints are subjected to maximum values previously chosen. Therefore the İ-constraint approach transforms the multi-objective optimization problem, composed by N objective functions, into a single objective optimization problem. 4. Results and discussion A three phase model, describing fixed bed alumina drying, successfully matched experimental data [4]. The differential algebraic system takes into account water vapor condensation by including the psychrometric equations, rendering feasible the presence of a new liquid phase along with solid and gas phases. The set of time varying control inputs (manipulated variables) to the processes are shown in Eq. (2). The end point constraints are imposed on bed height  XL , solid humidity and solid temperature Ts . The final time is fixed and equals 30 minutes, a typical drying time interval. u t

>G g , Tg , XL@

(2)

It is important to mention that the bed height should be as large as possible for maximizing process profitability, but also ensuring the homogeneity of the alumina particles, not allowing the formation of a solid gradient inside the bed dryer. The optimization constraints for feed gas flow, feed gas temperature, fixed bed height and solid temperature are presented in Eq. (3), respectively.

Multi-Objective Dynamic Optimization of Fixed Bed Dryers: Simulation and Experiments

0.5 kg m 2 s  G g  2.7 kg m 2 s ; 327.2 K  T g  390.0 K ; 0.05 m  XL  0.8 m

149

(3)

302.0 K  Ts  373.2 K

The objective functions employed in the Pareto optimization were maximization of XL , Eq. (4), minimization of the humidity error (tracking solid humidity at y sd 0.1 ), Eg. (5) and minimization of Ts , Eq. (6). The optimization utopian points are fixed bed height: F1max 0.8m , humidity error: F2min 0 (humidity of 0.1) and solid temperature: F3min 302.0 K .

F1 >xtf , tf @

>1 1  XL @

F2 >xtf , tf @

> y sd

F3 >xtf , tf @

>TS @

(4)

 y s y sd @

2

(5)

(6)

The use of fixed bed height-feed gas temperature and fixed bed height-feed gas flow manipulated variables are the strategies analyzed in order to maximize fixed bed height, also guarantying a desired alumina humidity level, Fig. 1. The Pareto optimization map indicates that the most appropriate strategy for obtaining humidity (principal) desired value, also maximizing fixed bed height (secondary), is by manipulating fixed bed height and feed gas temperature yielded : XL 0.4 m ; y s 0.09997 ; Tg 375.16 K ; Ts 359.85 K . For solid temperature minimization and alumina humidity level tracking purposes, the approaches using as manipulated variables fixed bed height and feed gas flow or feed gas temperature are shown in Fig. (2). The highest fixed bed was obtained, for an appropriate humidity level, using solid humidity (principal) and solid temperature (secondary) as output variables, also employing fixed bed height and feed gas temperature as input variables ( XL 0.47 m ; y s 0.09982 ; T g 389.99 K ; Ts 371.75 K ). Pareto optimization studies were carried out for design purposes of a fixed bed alumina drying unit. Due to the experimental unit configuration, the optimization problem constraints for feed gas flow, feed gas temperature, solid temperature and fixed bed height are presented in Eq. (7), respectively. 0.5 kg m 2 s  G g  0.76 kg m 2 s; 327.2 K  T g  353.2 K ; 302.2 K  Ts  353.2 K (7) 0.01 m  XL  0.06 m

The building of the drying isotherm of alumina particles, an important correlation for modelling and optimization purposes, employed the static method. It can be observed that experiments carried out at different

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150

temperatures (60 and 80 °C) did not produce a change in the isotherm shape, Fig. (3). These experimental data were employed for estimating the isotherm coefficients a and b, Eq. (8).

F2 (Humidity error)

400 300 200 100 0 -100 0.0 0.2 0.4 0.6 0.8 1.0

F1 (Fixed bed height, m)

F2 (Humidity error)

Figure 1 – Pareto set: 2- Manipulation of T g and XL (principal); š - Manipulation of T g and XL (secondary); - Manipulation of G g and XL (principal); u Manipulation of G g and XL (secondary). 400 300 200 100 0 -100 300 320 340 360 380 400

F3 (Solid temperature, K) Figure 2 – Non inferior solutions; ' - Humidity (principal) through manipulation of XL and T g , – Humidity (secondary) through manipulation of XL and T g ; ’ Humidity (principal) through manipulation of XL and G g ; + - Humidity (secondary) through manipulation of XL and G g .

YS*

a u UR 1  b u UR 2 ; a

0.053; b

0.609

(8)

Fig. (4) shows two strategies, the first is the manipulation of the bed height and the feed gas temperature and the second one is the manipulation of the bed height and the feed gas flow, both seeking bed height maximization and tracking solid humidity at 0.1. The Pareto optimization unveils that the best strategy for obtaining the desired solid humidity (principal) and maximizing bed

Multi-Objective Dynamic Optimization of Fixed Bed Dryers: Simulation and Experiments

151

height (secondary) is through bed height ( XL 0.06 m ) and feed gas temperature ( T g 344.4 K ) manipulation. Next, schemes of bed height and feed gas flow/temperature manipulation are presented, Fig. (5), for achieving a desired solid humidity and minimizing solid temperature. Though analyzing non inferior solutions, it can be observed that the desired solid humidity was obtained, but the height of the bed was not adequate ( XL 0.046 m ), when humidity was the principal objective function and the solid temperature the secondary one, through manipulation of the bed height and the feed gas temperature. 0.3 Temperature = 60 °C Temperature = 80 °C

Ys*

0.2

Isotherm

0.2 0.1 0.1 0.0 0.0

0.2

0.4

0.6

0.8

1.0

RH

F2 (Humidity error)

Figure 3 – Equilibrium isotherm for alumina particles at different temperatures. 100 0 -100 -200 -300 -400 0.00

0.02

0.04

0.06

0.08

F1 (Fixed bed height, m) Figure 4 – Pareto set: 2- Manipulation of T g and XL (principal); ¸ - Manipulation of T g and XL (secondary); - Manipulation of G g and XL (principal); u Manipulation of G g and XL (secondary).

The preferred solution ( XL 0.06 m ; y s 0.1 ; Tg 344.4 K ; Gg 0.76 kg m 2 s ) was implemented for designing the experimental unit. Fig. 6 shows that the alumina drying mathematical model matches exactly the experimental data. As a result, Pareto optimization was an efficient tool for sizing the drying unit and matching a priori established particles properties.

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F2 (Humidity error)

100 0 -100 -200 -300 -400 20

40

60

80

F1 (Solid temperature, °C) Figure 5 – Pareto set; ' - Humidity (principal) through manipulation of XL and T g , – Humidity (secondary) through manipulation of XL and T g ; ’ - Humidity (principal) through manipulation of XL and G g ; + - Humidity (secondary) through manipulation of XL and G g . 0.5

Experimental data Mathematical model

Ys

0.4 0.3 0.2 0.1 0

10

20

30

Time (min) Figure 6 – Experimental implementation of Pareto optimization.

5. Conclusions The height of the fixed bed and the feed gas flow were manipulated for design purposes (solid temperature/solid humidity error/fixed bed height) of alumina drying, through Pareto optimization, in a fixed bed system. Feed gas temperature and fixed bed height as input variables, using solid humidity (principal) and solid temperature (secondary) as output variables, yielded the best strategy for sizing the dryer. The analysis of Pareto optimization in the experimental unit evidenced that the best strategy for obtaining a solid humidity of 0.1 and maximizing bed height (secondary objective function) was through manipulation of the bed height and the feed gas temperature. 6. References [1] V. Gupta, J. Srinivason, Heat and Mass Transfer, Tata Mc Graw Hill Pub., New Delhi, 1982. [2] F-S. Wang, J-W. Sheu, Chem. Eng. Sci. 55 (2000) 3685. [3] H. Madsen, Journal of Hydrology 235 (2000) 276. [4] L.A.Calçada, M.C. Mancini, G. R.S Wildhagen, Drying Technology 24 (2006) 349.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

153

Decomposition Techniques for Multiscale Structured Product Design: Molecular Synthesis Charles C. Solvason, Nishanth G. Chemmangattuvalappil, Mario R. Eden Department of Chemical Engineering, Auburn University, Auburn, AL 36849, USA, [email protected]

Abstract Recent developments in the area of integrated process and product design have shown that products can be designed in terms of their properties without committing to any specific components a priori. Although current techniques make use of group contribution method (GCM) to design molecules, there are many properties, atomic arrangements, and structures that cannot be represented using GCM. One approach to expand the capability of GCM to handle a more diverse range of solutions is to combine property clustering with decomposition techniques in a reverse problem formulation. This approach first utilizes multivariate characterization techniques to describe a set of representative samples, and then uses decomposition techniques such as principal component analysis (PCA) and partial least squares (PLS), to find the underlying latent variable models that describe the molecule’s properties. Keywords: Reverse problem formulation, principal component analysis, multi-scale product design, property clustering, molecular design

1. Introduction One of the most common methods for designing molecules for specific end uses while minimizing computational expense has been group contribution (Gani et al., 2005, Marrero and Gani, 2001). In product design, the associated properties of concern are most often consumer attributes which do not have group contribution parameters (Hill, 2005). One way to address this concern is to map the consumer attribute data from the meta-scale into a set of properties on the macro scale that can be described by group contribution (Solvason et al., 2008a). This step is often performed via chemometrics which defines an empirical relationship through the use of design-of-experiments (DOE) and multivariate-linear-regression (MLR). Any uncertainty in the relationship between the attributes and properties is handled by increasing the size of feasibility regions in the property domain and validating the enumerated candidate molecules in the attribute domain (Solvason et al., 2008b). Often the attribute-property relationship is poorly defined, which limits the effectiveness of this type of approach. To improve this approach it is beneficial to map the attribute information down to a domain subspace which exhibits a stronger attribute-property relationship. The constraints on this new domain are that it must be linear in the constituent space and it must have the ability to be described by a molecular combinatorial technique. A key difference in this method is that the domain subspace is not required to be one of the known properties described by group contribution.

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154 Attribute Targets

Optimization of Property Subspace (P)

PCA Tnxm = Pnxp L pxm

PLS Anxq = Tnxm Bmxq

Target Selection TARGET TARGET ′ Tnxm = Anxq Bqxm

Standardization

(

′TOT Qnxm = X nxn

)

−1

Tnxm

Design Qnxm = Z nxr Qrxm

Figure 1: Method Flowchart

2. Methods The objective of this paper is to enumerate all possible molecules that meet a set of target attributes using a domain subspace mapping function combined with molecular group theory applied to chemometric data. To achieve this objective, a reverse problem formulation is applied where the attributes are mapped down to a domain subspace comprised of properties that have better attribute predictive power than conventional GCM described properties. Several tools, such as characterization and decomposition can be used to find the domain subspace. Molecular combinatorial techniques and property clustering are then applied to find and interpret the solution to the reverse problem formulation. Fig. 1 illustrates the method. 2.1. Characterization Techniques Characterization is a class of tools associated with the determination of not only chemical constituency or molecular structure, but also of larger structural characteristics describing the orientation and alignment of these molecules often called microstructure at the meso-scale. Some examples of characterization techniques include nuclear magnetic resonance (NMR), x-ray diffraction (XRD), and infrared spectroscopy (IR). The techniques are often applied to a training set of molecules defined by an experimental design used to explore the interesting facets of a set of property attributes. The added structural information available from the characterizations can be used to extend the group contribution method to higher orders as well as discern some orientation specific information. The choice of characterization technique for the specific design can be written into a MINLP, minimizing the predicted variance R2predM of the models describing the attribute-property relationships (Solvason et al., 2009c). To significantly reduce experimentation, improve prediction power, and ensure orthogonality of the models decomposition techniques are applied. 2.2. Decomposition Techniques The most common decomposition is principal component analysis (PCA). By definition, PCA uses the variance-covariance structure to compress the property data to principal component data that contains much of the system variability. This result also improves the interpretation of the data structure by consolidating multiple property effects into single, underlying latent variables which are devoid of colinearity. If the original property data are of the same type, then the eigenvalues can be considered measures of the contrasts, or loadings Lpxm of the original variables; and the eigenvectors are referred to as scores Tnxm (Johnson and Wichern, 2007).

′ Pnxp = Tnxm Lmxp

(2)

In most cases the first 2 or 3 principal components can account for 80% to 90% total variance. The remaining components can be removed without much loss of information (Johnson and Wichern, 2007). The relationship between the principal component scores

Decomposition Techniques for Multiscale Structured Product Design: Molecular Synthesis

155

Tnxm and the attribute properties Anxq is then developed using a PLS model of a new DOE factorial design where the scores are varied between there high (+1) and low (-1) levels.

Anxq = Tnxm Bmxq

(3)

Where Bmxq are the regressed coefficients found using PLS. It should be noted that the PLS model uses a separate set of scores and loadings to develop the relationship between Anxq and Tnxm. The overall predicted variance of this model is then estimated using the following: q

R

2 predM

(

=∏ R

2 predj

)

1 q

,

j∈q

(3)

j

2.3. Molecular Design Characterization can be used to extend GCM to handle complex structure and orientation in molecular design. The dissemination of characterization data must follow a set of rules designed to shadow those developed by Marrero and Gani (2001). First, the characterization must be able to completely quantify each individual molecular group used in the design. Second, in some characterizations, progressively larger groups completely contain the information of the smaller groups, but also contain corrections for 2nd order, 3rd order, structural, and orientation effects. This hierarchal nature is handled by specifying that all groups should be combined such that the largest functional group is specified first, then the second largest, and so on. Third, in some situations only partial overlaps may occur, for which the method will fail to specify any corrections to the first order combination at the overlap interface. To minimize this impact, it is specified that the groups be built such that the combinations occur across the C-C bond which carries the smallest amount of information (Marrero and Gani, 2001). Unlike conventional GCM, the molecular group specific variables are case specific. For instance, in many places in literature, typical absorbance wavelengths are published for IR and NMR spectroscopy. In order to convert these spectra to the underlying molecular group scores Trxm a case specific set of loadings Lpxm are needed, which are derived from the original DOE. The full molecule scores Tnxm are then estimated as

Tnxm = Z nxr Trxm

(4)

Where Znxr are the number of structure and orientation specific groups in the molecules being designed. 2.4. Property Clustering Property clustering is a tool used to improve the interpretation of the subspace properties by deconstructing the design problem into a Euclidean vector in the cluster domain and a scalar called the Augmented Property Index AUP. The clusters themselves are conserved surrogate properties described by property operators, which have linear mixing rules, even if the operators themselves are nonlinear. Methods for the application of group contribution method for molecular design have previously been developed using property clustering by Eljack et al. (2007, 2008). To utilize the latent

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variables in the property clustering algorithm, it is important to recognize that the data structure of Eq. 2 follows a linear mixing rule.

Tnxm = Pnxp L pxm

(5)

mix ψ nxm = X nxpψ pxm

(6)

The pure properties ψpxm have the same structure as the loadings Lpxm, thus the loadings can be thought of as the pure values of the principal components. Likewise, the response ψmixnxm data are predicted mixture properties and have the same structure as the score Tnxm data. That means that the mixture fraction Xnxp in the property models is related to the multivariate data in Pnxp. However, there is a concerning difference between the two methods: the mixture fractions sum to 1 across the properties for each sample and the multivariate data Pnxp do not. In order for latent variable models to be utilized in property clustering, it is necessary to standardize the latent variable structure by dividing Xnxp and Tnxm by STnxn. p

S k = ¦ X ik , k ∈ n

(7)

Qnxm = Rnxp L pxm

(8)

i

The new Qnxm matrix now represents standardized scores or mixtures. The loadings matrix Lpxm remains unchanged and the Rnxp matrix now represents fractions of loadings whose cumulative sum is one for each run. Unfortunately, although the components sum to one, they are sometimes negative due to the mean-centering of the multivariate property data prior to PCA. The constraint that the fractions must be between 0 and 1 is removed with no effect on the associated mathematics, only on their interpretation. At this point, the loadings Lpxm are the underlying latent variable domain subspace. Both full molecules and molecular group subspace properties Qnxm or Qrxm can be found by multiplying the latent variables Lpxm by the associated fractions Rnxp or Rrxp. Since the molecular and group subspace property relationships in Eq. 2 and 4 were derived using a decomposition technique, the constraints imposed by decomposition should also be observed for any new molecules or mixtures created.

Qnxm = Z nxr Qrxm

(9)

The molecular design of Eq. 9 is essentially a representation of a linear mixture of the underlying latent variable subspace properties, all of which are linear in nature, essentially a “linear mixture of linear mixtures”. This observation assumes that any nonlinearity in the attribute system is handled by the attribute-latent property relationship and not the molecule-group subspace property relationship (Muteki and MacGregor, 2006).

3. Case Study – Acetaminophen Tablet Design Three attributes that are important to direct compression tablet manufacturing are disintegration time, crushing strength, and ejection force. These attributes have been

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notoriously difficult to analyze based on traditional mixing design because of the complex and highly nonlinear nature of pharmaceutical excipients. In order to better control these attributes, they are mapped down to a domain subspace where they can be approximated as linear combinations of molecular group parameters. The domain subspace was found to be characterized by three properties, P1, P2, and P3 using a training set of 24 excipients (Gabrielsson et al., 2003). To reduce the number of parameters in the subspace, decomposition was performed using PCA. Although the number of parameters could be reduced, it was decided to keep all of them for illustrative purposes. Using PLS models developed from the training set, consumer specific set of targets were mapped to the domain subspace as shown in Table 1. Table 1. Design Targets Subspace Targets

Q1

Q2

Q3

UL LL

2.00 1.00

2.00 0.00

1.00 0.00

The molecular groups identified by the characterization were identified as CH, CH2, OH, CHO, O, CH2-O, CHOH, CH2OH, CHCH2OH, CHCHO, Ocyc, α-pyranose, βpyranose, and cellulose. The group specific subspace properties are shown in Fig. 2. Note the data cluster around the C1 vertex, indicating the first principal component is dominant. Also, the proximity of α-pyranose and alcohols to the target region, indicates that the alcohol groups and their orientations will be important to the design. C2

1

0.5 -CHO P3 -CH2OH C3

P1

-CHCH2OH-CH2-CH--CH2-O-O-

-(α)pyranose-cellulose-

0

-Ocyc-CHOH-

P2 -0.5

0

C1 zero C3 zero

C2 zero Loadings

Training Set -CH2-CHCH2OH-CH2-O-

-CH--OH -O-CHOH-

-CH2OH -CHCHO-(a)pyranose-

-CHO -Ocyc-(b)pyranose-

-cellulose-

0.5

1

-1

1.5

Target Feasibility Region

-(β)pyranose-1.5 2

Figure 2: Molecular Design Property Cluster Diagram

2.5

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158

Using the molecular design procedure outlined in Fig. 1, the molecular groups were combined to build a complete set of molecules as shown in Fig. 2. As expected, αpyranose, and not β-pyranose compounds were identified as candidates, effectively removing the traditional microcrystalline cellulose excipient from consideration. Other candidate excipients are shown in Table 2. Table 2. Design Molecules

Candidate Molecules

Q1

Q2

Q3

CH2OH-CH2OH CH2OH-(α)pyranose-CH2OH CH2OH-CH(OH)-CH2OH CH2OH-CH2-O-CH2OH CH2OH-O-CH2OH CH2OH-CH(CH2OH)-CH2OH OH-CH2-OH OH-(α)pyranose-CH2OH OH-CH(CH2OH)-CH2OH OH-CH2-CH2-CH2-OH

1.22 1.85 1.79 1.75 1.75 1.80 1.17 1.80 1.75 1.75

1.20 1.08 1.07 1.06 1.03 1.45 0.47 0.35 0.72 1.29

0.61 0.90 0.43 0.15 0.14 0.57 0.13 0.42 0.09 0.23

4. Conclusions In summary, the combination of property clustering and principal component analysis offers many insights and advantages for structured product design. In particular CAMD problems are no longer hindered by a lack of structure information in the molecular design. Rather, the uncertainty in predicting large molecular structures has now been removed from the models and replaced solely with the experimenter’s ability to choose appropriate training sets, for which many proven techniques exist. This represents a significant addition to the existing CAMD methodology. Furthermore, the method is universal in nature and can be extended to include other characterization techniques.

References N.G. Chemmangattuvalappil, F.T. Eljack, C.C. Solvason, M.R. Eden (2008), Comp. & Chem.Eng. (In Press). F.T. Eljack, M.R. Eden, V. Kazantzi, M.M. El-Halwagi (2007), AIChE Journal, 53(5), 12321239. F.T. Eljack, M.R. Eden (2008), Comp. & Chem.Eng. 32(12), 3002-3010. J. Gabrielsson, N. Lindberg, M. Palsson, F. Nicklasson, M. Sjostrom, and T. Lundstedt (2003), Drug Development and Industrial Pharmacy, 29(10), 1053-1075. R. Gani, P.M. Harper, M. Hostrup (2005), Ind.Eng.Chem.Res. 44, 7262-7269 R.A. Johnson and D.W. Wichern (2007), Applied Multivariate Statistical Analysis. Pearson Prentice Hall, Upper Saddle River, NJ. M. Hill (2004), AIChE Journal, 50(8), 1656-1661. J. Marrero, R. Gani (2001), Fluid Phase Equilibria, 182-183. K. Muteki and J.F. MacGregor (2006), Chemom. & Intell. Lab. Sys., 85, 186-194 C.C. Solvason, N.G. Chemmangattuvalappil, F.T. Eljack, M.R. Eden (2008a), Ind.Eng.Chem.Res. (In Press). C.C. Solvason, N.G. Chemmangattuvalappil, M.R. Eden (2008b). Comp.&Chem.Eng. (In Press). C.C. Solvason, N.G. Chemmangattuvalappil, M.R. Eden (2009). Comp. Aided Chem. Eng. (In Press).

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Ontological informatics based decision support system for pharmaceutical product development: Milling as a case study Pavan Kumar Akkisetty,a Gintaras V Reklaitis,a Venkat Venkatasubramanian a a

School of Chemical Engineering, Purdue University, West Lafayette IN 47907, USA ,[email protected], [email protected],[email protected]

Abstract The present work focuses on extracting the pharmaceutical product and mathematical model development knowledge from the expert and making it computer interpretable. Present focus is on the milling process case study as the ontological concepts have been discussed in the earlier work. The available knowledge includes the domain knowledge (e.g. milling) as well as data-driven modeling (e.g. statistical, neural nets) knowledge. Our decision support system includes milling ontology and guidelines for mill selection, statistical ontology, and a Java engine to integrate these with the Matlab solver. The support system can be used for not only managing models, but also to build models. As a proof of concept a hybrid neural network – population balance model is being built for the milling process using the support system. Keywords: decision support system, milling, ontology, guidelines, neural network

1. Introduction Pharmaceutical product development is a complex decision making process as it involves the interplay of material properties, equipment characteristics and product quality requirements. As these involve heuristic and mechanistic knowledge, the use of a mathematical model alone to capture such knowledge is not possible. Various decision support systems have been developed in the past few decades to address the problem [1]. However, tool specific knowledge representation has been a major drawback of these systems. Current research work has used the ontological approach to model the information, including operational and mathematical, and guidelines to represent the knowledge that cannot be captured using mathematical models alone. In the previous work [2,3,4] an application independent framework to model information and guidelines using ontology and GLIF (GuideLine Interchangeable Format) has been proposed. Mathematical knowledge modeling has also been addressed in [4] to accommodate physically based models. The present work deals with the mathematical model development knowledge in the data driven domain. The present paper deals with the pharmaceutical milling cast study since the structure of the ontological framework has been presented in the previous work [2,3,4]. In the present work, we demonstrate not only model management but also model development as an application for the framework. A hybrid neural network – population balance model is being developed using the framework. The paper is organized as follows. Section 2 introduces the milling process, section 3 discusses the ontological approach, section 4 explains the current work in mathematical knowledge modeling (MKM), section 5 shows the hybrid model development details and section 6 gives a summary and conclusions.



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2. Pharmaceutical milling Milling is one of the more common, deceptively simple but inherently complex unit operations in use in the process industry in general and the pharmaceutical industry in particular. The particle size distribution produced in milling is the result of a complex interplay between the material properties, the configuration of the milling equipment and mill specific operating parameters, which jointly give rise to specific breakage mechanisms. Consequently, the prediction of breakage behavior becomes difficult in a generalized form. Traditionally the population balance modeling (PBM) approach has been used to model the milling process. Phenomenological or heuristic approaches are the current methods used to predict the breakage mechanism of the process. However, a generalized method of estimation of breakage function based on material properties and mill characteristics has not yet been established. The milling problem at hand is of a twofold nature. The first part consists of modeling the decisions in mill selection while the second part involves predicting the particle size, for given a mill. Certain important decisions such as selection of the mill type based on mill and material properties, scale up factors etc. have been heuristic in nature and are not obtained directly from PBM. Knowledge based tools and data driven (DD) models can be used to overcome these drawbacks. The know-how about the product as well as the DD model development is largely hidden in the expert’s mind and in the development environment’s syntax. Thus, this knowledge is not available for sharing across different platforms and for computer interpretation. Consequently in the current work we address the challenges of modeling the information and knowledge for the milling operation and also handling the mathematical knowledge management of data driven models.

3. Ontological approach: Milling process 3.1 Milling process ontology In P.Suresh et al [4], the operation class is modeled as the subclass of model ontology. In the present work, concepts for milling operations have been created as shown below (Figure 1). An instance for ‘quadro comil’ was created that stores the operating conditions as well as the experimental data.

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Figure 1: Milling process ontology 3.2 Milling process guidelines In the current work, we have developed guidelines for pharmaceutical mill selection based on material properties. Guidelines are built in GLIF as reported in A.Jain et al [2]. The guideline ontology developed by A.Jain et al [2] has been used in this work. These guidelines are developed based on interviews with experts at Eli Lilly& Company, Indianapolis and the Industrial and Physical Pharmacy Department at Purdue University. The following guidelines have been developed in our work: 1) Dry mill or wet mill selection 2) Dry mill selection based on PSD required 3) Wet mill selection based on PSD 4) Media selection for wet mill etc. One of the guidelines is shown below (Figure 2).

4. Mathematical Knowledge Management (MKM) The current work in mathematical knolwedge management is motivated by P.Suresh et al[4]. In the current work, data driven mathematical knowledge that includes statistical and machine learning domains have been handled. The hierarchy of the concepts are shown below (Figure 3). The data driven MKM can be used not only for managing models, but also for model development. As the concepts for various models such as regression (linear, nonlinear etc.), neural networks etc. are available in the system, the user can choose to instantiate one or more model types and develop a model or store the solution obtained from solving multiple models and compare them. Mathml[ 5] is used to store the mathematical representation of the model. The ‘model’ concept has the ‘has mathml’ property that provides the slot to store the mathml [5] representation. In the current work, the neural network ontology is used along with the “differential equation”

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ontology developed by P.Suresh et al[4] to develop a hybrid neural network – population balance model for the milling process.

Figure 2: Milling guideline: selection of dry or wet mill 5. Mathematical Knowledge Management (MKM) The current work in mathematical knolwedge management is motivated by P.Suresh et al[4]. In the current work, data driven mathematical knowledge that includes statistical and machine learning domains have been handled. The hierarchy of the concepts are shown below (Figure 3). The data driven MKM can be used not only for managing models, but also for model development. As the concepts for various models such as regression (linear, nonlinear etc.), neural networks etc. are available in the system, the user can choose to instantiate one or more model types and develop a model or store the solution obtained from solving multiple models and compare them. Mathml[ 5] is used to store the mathematical representation of the model. The ‘model’ concept has the ‘has mathml’ property that provides the slot to store the mathml [5] representation. In the current work, the neural network ontology is used along with the “differential equation” ontology developed by P.Suresh et al[4] to develop a hybrid neural network – population balance model for the milling process.

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Figure 3: Neural network ontology

6. Hybrid neural network – population balance model The neural network model takes material properties, mill characteristics and operating conditions as inputs. Its outputs are the birth and death rates (breakage functions). These are taken as inputs for the PBM. The PBM is solved and the particle size is predicted and sent to the ‘optimization’ routine. This routine minimizes the error between predicted and actual PSDs and computes new weights for the neural network. The updated weights are sent to the neural network and a new PSD is predicted. This continues till the error in PSD prediction is minimized. Depending on the type of mill and material that is being milled, the number of inputs vary from 9-15. Some of the inputs are D10, D50, D90 (of input PSD), material density, tensile strength, mass milled, milling time, volume available for milling, energy input in the mill etc.

Figure 4: Hybrid neural network – population balance model The ‘quadro comil’ that is being modeled currently has 9 inputs. It should be noted that not all weights need to be updated as some of the weights have a constant value. The update of weights is performed in the optimization tool box that implements several routines, such as gradient descent etc. Figure 4 shows the hybrid model that predicts the particle size.

7. Engine The engine for the decision support system is similar that reported in A.Jain et al [2]. Java is used as the engine that interacts with OWL [7] and Matlab. J-Integra [6] is used

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to communicate with Matlab from Java. A graphical interface is envisioned for the user to interact with the decision support.

8. Summary Decision support to model information, heuristic and data driven mathematical knowledge is developed based on ontological informatics. A pharmaceutical milling process is used as a case study to demonstrate the system. A hybrid neural network – population balance model for the milling process is developed using the informatics approach. Future work includes using the framework for developing DD models as well as guidelines for other chemical and pharmaceutical engineering operations.

References [1] V. Venkatasubramanian, C. Zhao, G. Joglekar, A. Jain, L. Hailemariam, P. Suresh, V. Akkisetty, K. Morris, G.V. Reklaitis (2006), “Ontological Informatics Infrastructure for chemical product design and process development”, Computers and Chemical Engineering, CPC 7 Special Issue, 30(10-12), 1482-1496. [2] A. Jain, P. Akkisetty, G. Joglekar, L. Hailemariam, P. Suresh, C. Zhao, K. R. Morris, G. V. Reklaitis, and V. Venkatasubramanian (2008), “Integrated decision support tool for pharmaceutical product development”. ESCAPE 18 [3] L. Hailemariam, P. Suresh, V. Akkisetty, G. Joglekar, S. Hsu, K. Morris, G.V. Reklaitis, P. Basu and V. Venkatasubramanian (2008) “Excipient Interaction Prediction: an application of the Purdue Ontology for Pharmaceutical Engineering (POPE)”, ESCAPE 18 [4] P. Suresh, G. Joglekar, S. Hsu, P. Akkisetty, L. Hailemariam, A.Jain, G. Rekalitis and V. Venkatasubramanian, “OntoMODEL: Ontological Mathematical Modeling Knowledge Mangemenr”, Escape 18 [5] http://www.w3.org/Math/ [6] http://j-integra.intrinsyc.com/ [7] W3C, 2004, Web Ontology Language Overview, W3C Recommendation. Available online at: http://www.w3.org/TR/owl-features/.

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A first-principles model for the freezing step in ice cream manufacture Bogdan Dorneanua , * , Costin S. Bildeab , Johan Grievink a , Peter M. Bongers c a

Delft University of Technology, DelftChemTech, Julianalaan 136, 2628BL, Delft,The Netherlands, [email protected] b University Politehnica of Bucharest, Department of Chemical Engineering, Str. Gh. Polizu 1-7, 011061, Bucharest, Romania c Unilever Food and Health Research Institute, Process and Supply Chain Design, O. van Noortlaan 120, 3133AT, Vlaardingen, The Netherlands

Abstract This contribution deals with the development of a first-principles model for ice cream formation in the freezing unit to support product design and plant operation. Conservation equations for the mass, energy and momentum, considering axial flow assumptions are taken into account. The distributed features of the ice crystals and air bubbles are considered. Information related to the phase equilibrium conditions, the equations of state and the rate equations are added to the model. Some model reduction is already present, regarding the complex laminar fluid flow. The essential uncertainty of the model is in the simplification of the fluid flow, as well as in the structure and parameters of the rate laws. The structure of the model is presented, as well as preliminary computational results. Keywords: ice cream, freezing, modelling, distributed product properties

1. Introduction The commercial scale production of ice cream takes place in a sequence of processing operations, among which the freezing step is crucial for creating a proper product structure [1]. The freezing of the ice cream is performed in a scraped-surface heat exchanger (SSHE) with external deep cooling. The liquid phase mix is pumped along with air into the SSHE and the action of the rotor inside the tube blends the air into the matrix, while the rotating scraper blades continually remove frozen product from the cooled surface and thus maintain a high heat transfer rate. It is within this freezer barrel that much of the product structuring occurs. These product structuring mechanisms include ice crystallization, aeration and fat de-emulsification. The quality of the final product depends to a large degree on the distribution of the air bubbles and ice crystals within the ice cream. Since direct measurement of these variables in a freezer barrel is difficult to achieve, a mathematical modelling approach should be applied to predict these quantities. In a previous model [1] of the ice cream freezing step, the SSHE was modelled in a simplified way. SSHE was considered as a series of well mixed stages. Heat, mass and momentum equations were developed considering the phases as pseudocontinuous. Details regarding the distribution of the air bubbles and ice crystals within the ice cream structure were not taken into account. In other models, the distribution of particles is present only partially. For example only the ice crystals [2] distribution is considered.

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This contribution deals with the development of a first-principles model for ice cream formation to support product design and process operation. The model is a more detailed representation of the process, compared to the one in [1]. Conservation equations for the mass, energy and momentum, considering axial flow assumptions are taken into account. Information related to the phase equilibrium conditions, the equations of state and the rate equations are added to the model. Some model reduction/simplification is present, regarding the complex laminar fluid flow. The distributed features of ice and air phases are modelled using the population balance for particle size. For the other components a pseudo-homogeneous liquid phase is considered, being called the matrix. For the model to be of real help in product design and processing studies, the model must be suitable for use in an inverse mode. This means that target output variables to meet the product quality specifications should be indicated. The feed intake, the processing conditions and equipment design parameters are adjustable to meet the target output variables. Moreover, the model parameters need to be estimated and the model should be validated using experimental data in order to ensure the predictive quality of the model.

2. Physical aspects of the model We will start with presenting the physical aspects of the model. The freezing of ice cream is performed inside the SSHE (Figure 1.a). Ice cream

a NH3

b

NH3

Rotor

Freezer wall Frozen layer (FL)

Scraper blade

Bulk (B)

Scraper blade Rotor

Insulation

Figure 1. Scraped-surface heat exchanger: (a) Section and (b) detail.

The mix is pumped along with air into the SSHE and the action of the rotor inside the tube blends the air into the matrix. The freezing medium in the jacket, typically ammonia, freezes the water into finely dispersed ice crystals that are continuously scraped from the wall and incorporated into the ice cream. The product has a complex microstructure that consists, in semi-frozen state, of ice crystals, air bubbles, partially coalesced fat globules, all in discrete phases, surrounded by an unfrozen continuous matrix of sugars, proteins, salts, polysaccharides and water [3]. Air is distributed in the form of numerous small air bubbles, stabilized by the partially coalesced fat. The effect is a smooth texture of the final product [4]. Ice crystals form another discrete phase in ice cream. The product formulations that lead to numerous, small, discrete ice crystals also lead to enhanced smoothness in texture [3]. Taking into account these aspects, the model considers two types of phases (Figure 1.b): equipment related phases and process related phases. The equipment related phases are: the freezer wall + the rotor and the coolant liquid. On the process side, the model takes into account two categories of

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phases. On one hand the dispersed phases: the ice crystals and the air bubbles; and on the other hand the pseudo-continuous matrix. Moreover, it is assumed that the process side phases are split between two layers (see Figure 1.b). One is a frozen layer (FL) at the wall of the freezer. This frozen layer is an immobile layer of ice which crystallizes instantaneously on the freezer’s wall and is permanently removed by the movements of the scraper blades into the bulk (B) layer, which is the other layer considered. The bulk consists of moving fluid ice cream, in which crystals and bubbles are imbedded. The entire process mixture has a complex non-Newtonian flow which is too demanding for solving. To simplify, we consider that this layer can be modelled as an axial plug flow.

3. Model development The conservation equations are based on three coordinates: axial position associated with axial flow assumptions (with possibility to choose between plug flow and axial dispersed flow), time and sizes of bubbles and crystals. 3.1 Mass conservation equations The equations consider the dispersed phases as size distributed populations, while the matrix is considered as pseudo-continuous system with four components: water, sugar, fat and other components. The mass conservation equations are written for each phase/component and for both the frozen layer and the bulk. For the pseudo-continuous components: k ∂ΩCk ∂ ( Φ C ) + = Ψ Ck ∂t ∂z

Where:

(1)

Ω k = concentration of component k , ª¬ kg / m3 º¼ ; Φ k = mass flux of

k , ª¬ kg / m 2 s º¼ ; Ψ k = rate of change of component k , ª¬ kg / m3 s º¼ ; t = time, [ s ] ; z = axial position, [ m ] ; k = water, sugar, fat, other components; C = FL, B.

component

In case of the dispersed phases the mass conservation equations are written in the following form: j j ∂N Cj ∂uCj ⋅ N Cj ∂rs ,C ⋅ N C + + = BCj + T→j C − DCj − TCj→ j ∂t ∂z ∂s

Where:

(2)

N j = number of particles of component j , with the size s , at instant t and

ª¬ #/ m3 º¼ ; u j = velocity of component j , [ m / s ] ; rs j = growth rate of j component j along the internal coordinate s , [ m / s ] ; B = birth rate of component location z ,

j , ª¬ #/ m3 s º¼ ; D j = death/disappearance rate of component j , ª¬ #/ m3 s º¼ ; T→j C = transfer term of component j to C , ª¬ #/ m3 s º¼ ; TCj→ = transfer term of

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j from C , ª¬ #/ m3 s º¼ ; s = internal coordinate of the particle of component j , [ m ] ; j = ice, air. component

3.2Energy conservation equations The energy conservation equations are written for the equipment related phases and for the two compartments of the process side phases. Several energy generating terms should be taken into account in this case [1]: the mechanical energy, which includes the viscous dissipation and the scraping friction, the refrigeration term, the crystallization energy, as well as the energy of break up. For the process side compartments the energy conservation equation has the following form:

A⋅

∂ ( ΩicC ⋅ hic )

Where: h

∂t ic

= −A⋅

∂ ( u ⋅ ΩicC ⋅ hCic ) ∂z

+ QcC − QbC ± QtC − QrC − QmC + QsC + QvC (3)

= specific enthalpy of the ice cream mix, [ J / kg ] ; Qc = crystallization

[W / m] ; Qb = break-up energy term, [W / m] ; Qr = refrigeration term, [W / m ] ; Qm = melting energy term, [W / m ] ; Qs = scraping friction term, [W / m] ; Qv = viscous dissipation term, [W / m] ; Qt = transfer term from/to C, [W / m] ; A = cross-sectional area of the empty tube, ª¬m2 º¼ ; ic = ice energy term,

cream; C

= B,FL.

It has to be mentioned that some terms presented above vanish when the energy conservation equations are written for each one of the compartments C . 3.3 Momentum conservation equation The momentum conservation equations should cover the evolution of the flow field in relation with the external forces and the pressure gradient, while the ice cream mixture exhibits non-Newtonian viscous behaviour. Rather than solving these complex equations, a strongly simplified equation is written for the whole freezer in the reduced form of the pressure drop equation [1] and an axial velocity flow field. Finally, initial and boundary conditions are added to complete these differential equations. 3.4 Rate equations and equations of state In order to complete the dynamic model of the ice cream freezing step, information related to the constitutive equations for the rates of different processes presented above need to be added, as well as the ice – water – sugar phase equilibrium. There is scarce or inexistent information related to some of these rate equations. In the case of some of the rates (for example the transfer terms from/to C ), there is an essential uncertainty related to the structure of the equations. For others, the structure of the equation is available, but there is nothing regarding the parameters. Before being able to simulate the model, all these information need to be guesstimated. For this reason, a simple-to-complex

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0.15

Flow of particles, Fn / [#/s]

Ice particle fraction, xin / []

approach is considered for refining the model. This approach allows making hypotheses about the missing information regarding the structure and the parameters of the rate equations. Effective, yet simple rate expressions for the formation, growth and agglomeration of ice crystals and air bubbles in size-distributed populations. The rate expressions should be able to describe and explain the observed behaviour of an industrial scale freezer. In this way, a structurally comprehensive model of the ice cream freezing is developed, while the rate sub-models are kept as simple and effective as experimental data will allow for. Another advantage of the simple-to-complex approach is that it allows to check the model equations on consistency and completeness. z = 1.5 m z = 0.9 m z = 0.3 m

0.12 0.09 0.06 0.03

a

z=0m

0 0

20

40

60

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Particle size, s / [ȝm]

100

10000000000

1000000000

100000000

b 10000000 0

0.3

0.6

0.9

1.2

1.5

Axial position, z / [m]

Figure 2. The variation of: (a) the fraction of ice crystals along the freezer for different axial positions and (b) the number of ice crystals along the freezer.

4. Numerical solution aspects From the previous section it can be noticed that the resulting dynamic model of the ice cream freezing step has a modest number of partial differential equations (PDE’s) that need to be solved: 17 PDE’s. However, the discretization of the spatial coordinates considered will cause a multiplicative increase in the number of ordinary differential equations (ODE’s) approximately ~ 17000 ODE’s need to be solved. The model in this form can prove to be quite computationally expensive for repeated, iterative use. Hence some model reduction could prove useful for reducing this effort, especially when the rate equations become rather non-linear. Figure 2 presents the results of solving a simple case of the freezing step model. This simple case considers that the system is in steady-state, and mass conservation equation only for the water and the ice phase. The approximation of the PDE’s is done using the backward difference of derivatives method and using the method of lines. The values for the rate equations parameters are either chosen freely by the user, or determined from conservation constraints. This simple model is able to predict the expected trend in the variation of the number of ice crystals along the freezer.

5. Conclusions and future work A first-principles model of the ice cream freezing step to support the process design and operation is being developed. From the development stage of a first-principles model of the ice cream, model reduction techniques had to be applied in order to reduce the model’s complexity. Although ice cream structure consists of many components, only 6 were considered in the model. moreover, a simplification had to be taken into account when modelling the complex laminar fluid flow: axial flow assumptions. The structure and the parameters for the rate equations need to be determined using experimental

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literature data, together with insights from non-equilibrium thermodynamics. The resulting parameters will not represent the reality in full measure, but the model is able to predict the right “trends”. Parameter estimation and model validation using experimental data is required in order to ensure the predictive quality of the model. In the same time, reduction of the computational effort techniques should be attempted for optimisation applications of the model.

Acknowledgements This research was carried out within the framework of MRTN-CT-2004-512233 (PRISM-Towards Knowledge-Based Processing Systems). The financial support of the European Commission and Unilever R&D, The Netherlands, is gratefully acknowledged. References [1] Bongers, P.M.M., A heat transfer model of a scraped surface heat exchanger for ice cream, Computer-Aided Chemical Engineering 21 (539), Ed. W. Marquardt and C. Pantelides, 2006. [2] Aldazabal, J., Martin-Meizoso, A., Martinez-Esnaola, J.M., Farr, R. Deterministic model for ice cream solidification, Computational Materials Science, 38 (9), 2006. [3] Goff, H.D. Formation and stabilization of structure in ice-cream and related products, Current Opinion in Colloid and Interface Science 7 (432), 2002. [4] Eisner, M.D., Wildmoser, H., Windhab, E.J. Air cell microstructuring in a high viscous ice cream matrix, Colloids and Surfaces A: Physicochem. Eng. Aspects 263 (390), 2005.

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A Framework for Solvent Selection Based on Optimal Separation Process Design and Controllability Properties a

Athanasios I. Papadopoulos, bPanos Seferlis

a

Chemical Process Engineering Research Institute, CERTH, 6th klm Charilaou-Thermi P.O. Box 60361, Thermi-Thessaloniki, 57001, Greece, [email protected] b Department of Mechanical Engineering, Aristotle University of Thessaloniki ,P.O. Box 484, Thessaloniki, 54124, Greece, [email protected]

Abstract This work presents a systematic framework for solvent design based on optimum economic and controllability separation process performance. The proposed framework consists of a solvent screening stage based on conceptual separation process design, where multi-objective solvent design technology is utilized combined with a data mining method in order to rapidly identify major optimum solvent-process design drives. Highly performing solvents identified in the first stage are introduced into rigorous separation process design where detailed process models enable the assessment of the steady state effects of multiple and simultaneous disturbances on the control objectives within an optimized centralized control scheme. In this respect, economically optimum solvents are identified that facilitate the controllability properties of the process in which they are utilized. Keywords: solvent design, process design, static process controllability

1. Introduction Numerous research efforts report on integrated solvent and process design methodologies, as capturing the synergies and interactions between the designed solvents and the processes in which they are utilized leads to process-solvent schemes of optimum economic performance [1-8]. Such methods focus on optimizing process design characteristics, while the performed optimization is combined with a method for the generation of solvent design alternatives, hence the effects of various solvent options in the economic design of the particular process addressed are explored. However, processes are essentially dynamic environments susceptible to variations in operating parameters and exogenous disturbances. Available approaches aiming to design solvent-process schemes of optimum performance often overlook the effects of such variations as is generally assumed that a properly designed control system will eventually compensate for such effects. While a number of methods have been developed to address process design optimality under operating parameter variations, the effects of using alternative solvent options in process design under operating variability that explicitly considers the controllability properties of the overall design have yet to be addressed systematically.

2. Proposed framework This work proposes a systematic framework that enables the selection of solvents based on their economic and static controllability behavior (Figure1). The proposed

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framework implements solvent screening based on a) conceptual economic process performance criteria and b) rigorous process design combined with nonlinear sensitivity analysis that enables the identification of the controllability behavior of the developed solvents. Solvent screening for optimum Solvent screening based on economic process controllability process performance Representative Chart of economic Multi-objective molecules solvent performance solvent synthesis Rigorous process design

Clustering of optimal solvent set Conceptual process design

Chart of economic and controllability solvent performance

Non-linear sensitivity analysis

Figure 1: Proposed framework for solvent selection based on economic and controllability indicators.

2.1. Solvent screening based on economic process design criteria The first stage of the proposed framework employs multi-objective computer aided molecular design (CAMD) technology in order to identify economically optimum solvent candidates [6-7]. The approach does not a priori exclude options that will potentially be useful at the process design stage. In this respect, a variety of objective functions in the form of solvent thermodynamic properties are thoroughly explored, while the optimization results in a comprehensive set of solvents that represents molecules with a broad range of structural, physical and economic characteristics regardless of the process task in which they are to be utilized. Subsequently, the obtained molecules are introduced into conceptual process design through the formation of molecular clusters, thus partitioning the molecular set into smaller compact groups of similar molecules. A representative molecule is selected from each cluster based on the design information already incorporated in each cluster in the form of molecular thermodynamic properties. The representative molecules are introduced into conceptual process design as discrete design options hence the process optimization result represents the economic impact of the solvent in the specific process. The iterative implementation of clustering gradually partitions the original solvent set into clusters of reduced size, hence allowing the development of a tree-like chart that combines structural and physical molecular characteristics with process economic performance. The decisions regarding the development of subsequent clustering paths in the tree-like chart are based on the clustering heuristic probability [6]. This probability combines the statistical clustering information with the representative process economic performance of each cluster in a single index that indicates the clusters containing highly performing molecules. The use of conceptual process models in this stage enables a fast screening of the original solvent set by identifying major integrated solvent-process design drives, hence allowing the efficient extraction of economic solvent performance information within a manageable computational timeframe. As a result, a solvent-process performance chart is generated that identifies clusters potentially containing highly performing solvent molecules.

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2.2. Solvent screening based on economic and process controllability criteria Based on the previous solvent screening stage, representative molecules from clusters containing highly performing solvents are introduced into rigorous separation process design [9], hence enabling the extraction of enhanced solvent economic performance information under realistic processing conditions. Recalculation of the clustering heuristic probability based on the available rigorous assessment of the solvent-process performance provides clear insights regarding the clusters that potentially contain highly performing molecules, hence clusters with low performing molecules are easily identified and rejected with high certainty in this stage. At the same time, the available rigorous process design information for each cluster enables the identification of key control variables for the integrated solvent-process system as well as the assessment of the solvent-process system behavior under multiple and simultaneous process disturbance variations. The controllability assessment relies on the nonlinear sensitivity analysis of the solvent-process system [10-11]. The steady state variation for a selected set of controlled, y, and manipulated, u, variables that is required to optimally alleviate the effect of multiple disturbances from the control objectives is calculated according to the following nonlinear program.

Min f = (y − y sp ) T Wy (y − y sp ) + (u − u ss ) T Wu (u − u ss ) y ,u

,

s.t. rigorous process model y l ≤ y ≤ y u , ul ≤ u ≤ uu

(1)

where ysp and uss are the setpoint for controlled and manipulated variables, respectively. Weights, Wy and Wu, prioritize controlled objectives and manipulated variable utilization. The steady state controllability analysis is independent of the control algorithm and is viewed as a property inherent of solvent selection and process design. The performed sensitivity analysis generates useful insights regarding the imposed control framework and the range of parameter variations within which the solvents demonstrate optimum performance. The steady state disturbance rejection performance is described by a single index with respect to the disturbance magnitude coordinate, zeta.

u * (ȗ ) − u * (0 ) y * (ȗ ) − y * (0) + ¦ w y ,i (ȗ ) i * i ȍSC (ȗ ) = ¦ wu ,i (ȗ ) i * i u i (0 ) y i (0 ) i i 2

2

(2)

In this respect, a final integrated solvent-process performance chart is generated that enables optimum design decisions based on both the rigorous economic and controllability behavior of the solvent-process system.

3. Illustrative example The proposed framework is illustrated through an example that addresses the design of solvents for the separation of a cyclohexane/benzene mixture using extractive distillation. In the first stage, solvents are designed with the aim to maximize the mixture relative volatility and the solute solubility in order to facilitate the separation of the components. At the same time, the solvent heat of vaporization and molecular weight are minimized to facilitate solvent recovery, and molecular structure simplicity, respectively. The designed solvent set consists of 109 molecules that form 6 clusters (Cl) in the first clustering iteration, as shown in Figure 2 together with the number of molecules (Nm) contained in each cluster. Representative molecules from each cluster

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are then introduced into conceptual extractive distillation design hence the obtained information regarding the economic performance of each cluster enables the calculation of the clustering probability (Pc), which indicates the clusters that are likely to contain molecules and could potentially lead to high process performance. Based on the obtained Pc values clusters 2, 3 and 5 go through to the second clustering iteration, while clusters 1, 4 and 6 can be rejected. In the second stage of the proposed framework, the implementation of rigorous extractive distillation design allows the recalculation of the clustering probability (Pr) based on a detailed economic objective function. As shown in Figure 2, the values of Pr verify the selection of clusters 2, 3 and 5 for the second clustering iteration. In this iteration the values of Pr obtained using the rigorous design model clearly indicate that clusters 2 and 3 are likely to include the molecules with the highest process performance. Cl 1 2 3 4 5 6

Nm 1 14 23 34 6 31

Pc 0.00 0.99 0.97 0.92 1.00 0.88

Pr 0.00 0.95 0.94 0.89 1.00 0.85

xd 0.77 0.96 0.8 0.72 0.96 0.91

Æ

Cl 1 2 3 4 5 6

Nm 8 6 6 1 1 21

Pc 0.94 0.99 1.00 0.00 0.00 0.96

Pr 0.51 0.90 1.00 0.00 0.00 0.70

xd 0.96 0.96 0.96 0.77 0.92 0.96

Figure 2: Clustering iterations for identification of cluster containing optimum solvents

The rigorous design results in the form of Pr enable a transparent endorsement of the optimality of these clusters, as opposed to the conceptual design results in the form of Pc implying that clusters 1 and 6 could potentially be considered with 2 and 3 in a third clustering iteration in order to identify the optimally performing molecules. At the same time, the rigorous process design enables the accurate calculation of a key controlled variable such as the mass fraction of cyclohexane in the distillate (xd) and provides insights regarding the clusters containing molecules that reach high operating performance. Hence, the exploitation of rigorous process design information enables the identification of clusters containing potentially optimal molecules based on their economic and operating performance by only incorporating 12 out of 109 molecules into process design calculations. The performed screening reveals the following five molecules that enable generation of optimum solvent –process schemes: (S1: FCH2OC(CH=O)3, S2: (CH=O)3C-O-CH3, S3: Cl-C(CH=O)2-O-CH2-CH=O, S4: (CH=O)2CHO-CH(CH=O)-Cl, S5: (CH=O)2CH-CH(CH=O)-Cl). At this point, the obtained optimum solvent –process schemes are investigated in terms of their static controllability for disturbances in the feed composition and temperature. The controlled variables are cyclohexane purity level at the distillate and cyclohexane recovery. The set of manipulated variables includes reboiler heat duty, reflux flow rate and solvent feed flow rate. Calculation of the controllability index as a function of disturbance magnitude for the five optimum solvent-process systems reveals their steady state effort to compensate for the effects of these disturbances. Clearly, solvents S3 and S4 have superior economic and process controllability performance, as shown in Figure 3a,b, while solvents S2 and S5 indicate solvent options that trade high economic process performance for poor controllability behavior and vice versa.

A Framework for Solvent Selection Based on Optimal Separation Process Design and Controllability Properties 25

a g e m o, x e d ni yt iil b all or t n o C

14

S1

S1 S2 S3 S4 S5

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e ul a v x e d ni yt lii b all or t n o C

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0 34

S5

S4

2

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38

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42

44

Disturbance magnitude coordinate, zeta

Economic objective function value, k$/yr

(a)

(b)

46

Figure 3. (a) Controllability index for solvents S1-S5, (b) economic objective controllability chart.

4. Concluding remarks An integrated solvent-process design framework has been proposed consisting of a solvent screening stage based on conceptual economic process performance criteria that utilizes multi-objective optimization and clustering technologies to identify major solvent-process design drives. Subsequently, the highly performing solvents are introduced into a rigorous process design and non-linear sensitivity analysis stage in order to identify the controllability behavior of the designed solvents under realistic operating conditions. Results obtained from implementation of the proposed framework indicate that useful insights are generated in the form of trade-offs between the economic and controllability process behavior of the designed solvents.

5. Acknowledgements European Commission support is appreciated (INCO-CT-2005-013359).

References [1] Buxton A., Livingston A.G. and E.N. Pistikopoulos (1999), AIChE Journal, 45(4), 817. [2] Hostrup M., Harper P.M. and R. Gani (1999),Comp. Chem. Eng., 23, 1395. [3] Markoulaki E.C. and A.C. Kokossis (2000), Chem. Eng. Sci., 55(13), 2529. [4] Wang Y. and L.E.K. Achenie (2002) Fluid Phase Equilibria, 201, 1. [5] Eden M.R., Jorgensen S.B., Gani R. and M.M. El-Halwagi (2004), Chem. Eng.Proc., 43, 595. [6] Papadopoulos A.I. and P. Linke (2006a), Chem. Eng. Science, 61(19), 6316. [7] Papadopoulos A.I. and P. Linke (2006b), AICHE J., 52(3), 1057. [8] Cheng H.C. and F.S. Wang (2007), Chem. Eng. Sci., 62(16), 4316. [9] Seferlis P. and J. Grievink, Ind. Eng. Chem. Res., 40, 1673-1685, 2001. [10] Seferlis P. and J. Grievink, Comput. Chem. Eng., 25, 177-188, 2001. [11] Seferlis P., and J. Grievink, 326-351, "The Integration of Process Design and Control", P. Seferlis and M. C. Georgiadis (Eds), Elsevier Science B.V., Amsterdam, 2004.

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Design and Optimization of Advanced Materials and Processes for Efficient Hydrogen storage Michael C. Georgiadisa, Efstathios S. Kikkinidesb, Sofoklis S. Makridisb, Konstantinos Kouramasc, Efstratios N. Pistikopoulosc a

Department of Engineering Informatics and Telecommunications, University of Western Macedonia, Kozani 50100, Greece, [email protected] b Department of Engineering and Management of Energy Resources, University of Western Macedonia,Kozani 50100, Greece, [email protected], [email protected] c Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK, [email protected], [email protected]

Abstract This work presents a systematic approach for the optimal design and optimization of metal hydride materials and processes for efficiency hydrogen storage. Techniques for the synthesis and characterization of novel metal hydride materials are presented in a view of designing materials to enhance storage efficiency. A small-scale metal hydride tank has been designed in order to investigate its capacity and efficiency. Then, a dynamic model that have developed previously by the authors provides the basis for investigating systematic optimization and on-line control studies. Optimization results indicate that significant improvement on the storage time can be achieved under tight design and operating constraints. Keywords: Hydrogen Storage, Metal Hydrides, Parametric Model-Based Control

1. Introduction The need for a potential worldwide conversion from fossil fuels to hydrogen requires the elimination of several barriers imposed along the different steps involved in hydrogen technology. Commercially viable hydrogen storage is considered as one of the most crucial and technically challenging barriers to the widespread use of hydrogen as an effective energy carrier. An alternative to the traditional albeit limited hydrogen storage methods is proposed through the use of advanced solid materials as hosting agents for the storage of hydrogen in atomic or molecular form. This type of hydrogen storage is often called “solid” hydrogen storage since hydrogen becomes part of the solid material through some physicochemical bonding. There are at present two fundamental mechanisms known for storing hydrogen in materials in a reversible manner: absorption and adsorption. In absorptive hydrogen storage, hydrogen is absorbed directly into the bulk of the material. In simple crystalline metal hydrides, absorption occurs by the incorporation of atomic hydrogen into interstitial sites in the crystallographic lattice structure. The mathematical modeling of hydrogen storage in metal hydride beds has received considerable attention over the past ten years. Mat and Kaplan (2001) developed a mathematical model to describe hydrogen absorption in a porous lanthanum metal bed. The model takes into account the complex mass and heat transfer and reaction kinetics. Model predictions were found to be in good agreement with experimental data. Aldas, Mat and Kaplan. (2002) presented an integrated model

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of heat and mass transfer, reaction kinetics and fluid dynamics in a hydride bed. Recently, Kikkinides, Georgiadis and Stubos (2006), developed effective heat management strategies and novel cooling design options for hydrogen storage systems in LaNi5 metal hydride reactors by performing systematic simulation and optimization studies.

2. Material Synthesis and Characterisation In this paper, a Ti-Zr-Cr-V-Ni compound has been developed and has been up-scaled for use in a small metal hydride tank. Hydrogen storage efficiency has been investigated for the developed metal hydride tank after a moderate activation procedure. The alloy has been prepared by arc melting under an argon atmosphere of about 1 bar with stoichiometric proportions of high-purity constituent elements (higher than 99.5 %). The XRD profile has been analysed with the Rietveld refinement program Rietica-1.62. A scanning electron microscopy has been used to investigate the microstructure while microchemistry has been studied with electron dispersive X-ray analysis. Hydrogenation experiments have been obtained by using high purity pressed hydrogen, as high as 99.999 %. The small tank has been developed by Cu tube while material quantity ~100 gr has been used by filling the tank’s free space. Figure 1, illustrates the activation and hydrogenation procedure at 25 oC for the as cast powdered sample Zr0.9Ti0.1Cr0.8V0.8Ni0.4. The sample is not a single phase but two phase system, as derives from the Rietveld analysis. The MgZn2 (C14) and MgCu2(C15) coexist at the XRD pattern in amounts of 88.25 % and 12.75 %, respectively. The crystal structure of the C14 Laves phase, preserving its hexagonal structure in space group P63/mmc, has a=b= 0.52300 (2) nm and c=0.88055 (8) nm after refinement while the C15 Laves phase, having the Fd3m space group, refined and revealed that a=b=c=0.72536 (4) nm. It has been proved that both of the samples follows a composite structure where for the Ni doped sample the white region is a Zr – rich (and V-poor) phase and the dark is V-rich (and Zr poor) one. After vacuum the sample container by heating at 100 oC (in boiled water bath) then a hydrogen pressure of about 25 bars at the same temperature has been followed. In figure 2, the charging effect on the metal hydride tank capacity is depicted as a function of time. After an hour 80 % of the total amount of hydrogenation procedure has been reached. After two hours the “solid” hydrogen amount in the metal hydride tank is saturated under 10 bars of applied gas hydrogen. After charging the metal hydride tank, a discharging procedure has been followed by increasing the temperature after time periods.

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o

20

30

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90 26 24 22 20 18 16 14 12 10 8 6 4 2 0

100 80 Temperature vs time

60 Pressure of H2 vs time

40

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90

R

80

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0 0

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Time (min)

Time (min)

Figure. 1. Hydrogenation procedure for charging the as cast bulk sample at 25 oC

R

&KDUJLQJDW &DIWHUFRROLQJDW &XQGHU3+ EDUV 100

Normalized Capacity (%)

10

Pressure of H2 in the container (bar)

Temperature of the sample container (oC)

Experimental procedure for charging at 25 C

Fig. 2. Charging of the metal hydride tank at 25 oC, after the cooling at 0 oC under 10 bars of hydrogen

3. Explicit Parametric Controller Design 3.1. Off-Line control There are two main issues, which must be taken into consideration when establishing optimal control strategies for this system. The first is to ensure that the maximum process storage efficiency is achieved. The second issue is to seek for the best economic performance which can be expressed by the total required storage time since this is proportional to the high compression costs. The optimal control problem can then be mathematically formulated in its general form as follows (ts in the storage time):

min t s ˆ

(1)

u f ,t f , P,d

subject to: ™Detailed model equations provided in Kikkinides et al (2006). ™Constraints on cooling medium availability, pressure drop and bed temperature ™Lower and upper bounds on the design vector d (radial positions of the cooling systems, bed length and radius, etc). Extensive Simulation results indicate that the optimal control structure involves the cooling medium flowrate as the manipulated variable and the outlet temperature of the tank as the state variable. In order to derive an accurate reduced order model suitable for on-line control purposes the profile of U f and T f ( z =1) should be as smooth as possible. In light of this, we choose continuous piecewise linear control profile, which is smoother than piecewise constant control but less complex than polynomial profile, for Uf .

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3.2. Parametric Model-Based Control The benefits of Model Predictive Control (MPC) as an on-line optimization technique, from the view point of cost and efficiency of operartions, have long been recognized in process systems engineering. MPC being an on-line optimisation method, not only provides the maximum output from the controlled process but also takes into account the requirements for satisfaction of physical and operational constraints while simultaneously considering the current state and history of the plant to predict future predictive actions. Nevertheless, its applications is rather restricted considering its profit potential, primarily due to large on-line computational requirements which involve a repetitive solution of of an optimization problem ar regular time intervals. In order to overcome this weakness, the group of Pistikopoulos and co-workers at Imperial College London (Pistikopoulos, Georgiadis, Dua, 2007) explore an advanced technique which can avoid the complicated and repetitive online optimization computations. This technique, the so called explicit multi-parametric MPC, does not reply on numerical optimization but instead it employs novel parametric optimization techniques to solve the on-line optimization problem. Within a MPC based problem, explicit parametric optimization can be applied if the optimization parameters have specified bounds and the optimization objective is to minimize a performance criterion while keeping all the constraints satisfied. Explicit parametric optimization can derive objective functions and optimization variables as functions of the parameters and the regions where these function are valid. Since the controller is produced offline, online optimization only may only need to find the correct controller for the current situation and implement them, hence, enormous online work is cute down. The procedure of implementing explicit controller is described as follows: The optimization problem is solved offline (section 3.1.) and the following values are obtained: (i) performance criterion and u(t) as explicit functions of current and past values of y(t) and/or u(t), (ii) regions where these functions are valid and (iii) optimal look-up table. The Online Implementation involves the following steps (i) Search the look-up table (ii) identify the region and (iii) obtain control from function evaluation. 3.3. Model Indentification Model identification is aimed to a linear input/output ARX model which can approximate the detailed dynamic model derived from gPROMS. The ARX model provides the basis for designing on-line parametric controllers using the Parametric Optimization software (Parametric Optimization Solutions Ltd 2007) On-lines optimization is carried out by using gO:MATLAB linking MATALB (the controller is implemented in MATLAB in the form of parametric optimization functions) and gPROMS to examine how the controller performs. This activity is repeated until a competent controller is gained. Then by using the Parametric Optimization tools originally developed at Imperial College (Parametric Optimization Solutions Ltd 2007), an explicit controlled is designed, which has 780 critical regions and corresponding control laws as depicted in Figure 3.

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3.4. Result of the Online Implementation of Explicit Parametric Controller The profile of the controlled outlet tank temperature, is presented in Fig. 4 in comparison with the open-loop case. Similarly, less fluctuation and lower peak value can be observed. In summary the following conclusion are made: (i) The designed parametric controller produces less aggressive control action in comparison to openloop control action (ii) Open-loop control action operates on upper bound at the end of the storage process (iii) the parametric controller keeps control action away from saturation and thus constraints are never violated . This is due to feedback action and penalising control movement.

 7I]  ZLWKFRQWUROOHU 7I]  ZLWKRXWFRQWUROOHU



7I] 

     

















WLPH

Figure 4. Comparison of the open-loop outlet Figure 3. Figure 16: Critical regions of explicit parametric controller (projection on yt -ut plane)

temperature

T f ( z =1) with the controlled

case

Figure 5 depicts a smoother closed-loop coolant flowrate profile (using the explicit parametric controllers) comparing to the open-loop uncontrolled profile. It is clear that less fluctuations exist and its value is almost constant at 80, (e..g 2.4m/s,) which is desirable for the efficient and robust operation of the storage tank.  8IZLWKFRQWUROOHU 8IZLWKRXWFRQWUROOHU

 

8I

      







 WLPH









Figure 5. Comparison between open-loop and controlled coolant flow rates

In summary the following conclusion are made: (i) the designed parametric controller produces less aggressive control action in comparison to open-loop control action, (ii) open-loop control action operates on upper bound at the end of the storage process and, (iii) the parametric controller keeps control action away from saturation and thus

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constraints are never violated. This is due to feedback action and penalising control movement.

4. Conclusions This work presents a systematic approach for the optimal design and control of materials and processes for efficient hydrogen storage. A pseudobinary Zr-Ti-Cr-Ni-V compound has been developed and fast kinetic of the hydrogenation - dehydrogenation has been observed after crucial activation procedures. Then a systematic parametric programming approach for the optimal design of an explicit parametric controller of a metal hydride storage tank is presented. The approach leads to maximum hydrogen storage efficiency at minimum storage time while ensuring satisfaction of all operating and design constraints.

5. Acknowledgements Financial Support from the European Commission under the DIAMANTE ToK project is gratefully acknowledged (Contract No: MTKI-CT-2005-029544).

References [1] Kikkinides ES, Georgiadis MC, Stubos AK. Int. Journal of Hydrogen Energy 2006, 31(6), 737-751. [2] Mat MD., Kaplan Y. Int. J. Hydrogen Energy, 2001; 26: 957-963. [3] Aldas, K. Mat MD. Kaplan Y. Int. J. Hydrogen Energy, 2002; 27: 1049-1056. [4] Pistikopoulos, E.N. Georgiadis, M.C. Dua, V. (eds.) Multi-Parametric Model-Based Control Volume 2: Theory and Applications; Hardcover - Handbook/Reference Book ISBN-10: 3-527-31692-2 ISBN-13: 978-3-527-31692-2 - Wiley-VCH, Weinheim [5] Parametric Optimization Software (2007). Parametric Optimization Solutions Ltd, London, UK.

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Design and Optimization of Thermally Coupled Extractive Distillation Sequences Roberto Gutierrez-Guerraa, Juan-Gabriel Segovia-Hernándeza, Salvador Hernandeza, Adrian Bonilla-Petricioletb and Hector Hernándeza a

Universidad de Guanajuato, Campus Guanajuato, Departamento de Ingeniería Química, Noria Alta s/n, Guanajuato, Gto., 36050, Mexico, [email protected] b Instituto Tecnologico de Aguascalientes, Ingenieria Quimica, Av. Adolfo López Mateos #1801 Ote. Fracc. Bonagens, A.P. 263, C.P. 20256, Aguascalientes, Ags. Mexico.

Abstract In this paper, design and optimization procedures are developed for a conventional extractive distillation sequence and a thermally coupled extractive distillation scheme. The proposed methodologies detect the optimal values of the design variables in order to guarantee the minimum energy consumption. It was found that the optimum energy consumption can be related to the minimum total annual operating cost, minimum greenhouse gas emissions, higher thermodynamic efficiencies and good theoretical control properties. The methodologies were applied to the study of the separation of several close boiling point mixtures using the two distillation sequences. The results showed that the energy savings predicted in the complex extractive distillation sequence can be achieved along with reductions in greenhouse gas emissions. Keywords: CO2 emissions, extractive thermally coupled distillation, energy savings.

1. Introduction Distillation, which is the workhorse of chemical process industries, is an energyintensive process, and is therefore among the first processes to be addressed to achieve energy savings over the short and long term. Energy consumption in distillation and greenhouse gas emissions (e.g. carbon dioxide) are strongly related. Reducing CO2 emissions is an absolute necessity and an expensive challenge in the chemical process industries, required to meet environmental targets as agreed in the Kyoto Protocol. Therefore, the reduction of CO2 emissions from distillation systems is an important issue, and much effort should be focused on energy savings techniques [1]. Most modifications and research efforts have been aimed principally at increasing heat integration within the distillation unit; some have been made directly to the heating device systems, while others have been performed on the main distillation columns. In particular, the use of columns with thermal coupling has received considerable attention in recent years, with a special development reported for the case of separation problems of ternary mixtures. Thermally coupled distillation systems (TCDS) are obtained through the implementation of interconnecting streams (one in the vapor phase and the other one in the liquid phase) between two columns; each interconnection replaces one condenser or one reboiler from one of the columns, thus providing potential savings in capital investment. Furthermore, through proper selection of the flow values for the

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interconnecting streams of TCDS, one can obtain significant energy savings (and, consequently, reductions in CO2 emissions) with respect to the energy consumption of conventional distillation sequences. There is a considerable amount of literature analyzing the relative advantages of TCDS for ternary separations [2]. These studies have shown that those thermally coupled distillation schemes are capable of typically achieving 30% energy savings over conventional schemes. Azeotropic and low-relative volatility mixtures are commonly encountered in the finechemical and specialty industries, and many chemical processes depend on efficient and economical methods for their separation. These mixtures can be separated in a distillation column by altering the relative volatilities or shifting the azeotropic point to a more favorable position. Extractive distillation is defined as distillation in the presence of a miscible, high boiling, relatively non-volatile component, the solvent, which forms no azeotrope with the other components in the mixture. The method is used for mixtures having a low value of relative volatility, nearing unity. Such mixtures can not be separated by simple distillation, because the volatility of the two components in the mixture is nearly the same, causing them to evaporate at nearly the same temperature at a similar rate, making normal distillation impractical. The method of extractive distillation uses a separation solvent, which is generally nonvolatile, has a high boiling point and is miscible with the mixture, but does not form an azeotropic mixture. The solvent interacts differently with the components of the mixture thereby causing their relative volatilities to change. This enables the new three-part mixture to be separated by normal distillation. The original component with the greatest volatility separates out as the top product. The bottom product consists of a mixture of the solvent and the other component, which can again be separated easily because the solvent does not form an azeotrope with it. The bottom product can be separated by any of the methods available. It is important to select a suitable separation solvent for this type of distillation. The solvent must alter the relative volatility by a wide enough margin for a successful result. The quantity, cost and availability of the solvent should be considered. The solvent should be easily separable from the bottom product, and should not react chemically with the components or the mixture, or cause corrosion in the equipment. Extractive distillation is widely used in several different processes: i) recovery of aromas or fragances; ii) separation of aqueous alcohol solutions; iii) mixtures which exhibit an azeotrope and iv) separation of hydrocarbons with close boiling points [3]. In this paper we study the purification of several mixtures (only feasible the separations with extractive distillation) using the thermally coupled extractive distillation scheme with side rectifier (TCEDS-SR; Figure 1). Design, optimization and control properties were obtained for the examined complex configurations. The results show that the thermally coupled configuration is a better option than the conventional extractive distillation sequence (Figure 2) in terms of energy savings (reductions in greenhouse gas emissions) and capital investment.

2. Design of Complex Distillation Schemes To overcome the complexity of the simultaneous solution of the tray arrangement and energy consumption within a formal optimization algorithm, we decoupled the design problem in two stages: (i) tray configuration; (ii) optimal energy consumption. The first stage of our approach begins with the development of preliminary designs for the complex systems starting from the design aspects of conventional distillation columns.

Design and Optimization of Thermally Coupled Extractive Distillation Sequences

Figure 1. Conventional extractive distillation sequence (DS).

191

Figure 2. Thermally coupled extractive Distillation sequence (TCEDS-SR).

The design of the TCEDS-SR column is obtained by using a thermal link in the vapor phase in the conventional direct sequence (DS), which eliminates the reboiler in the second column of the conventional scheme, and the tray section (named section 4) is moved to the bottom of the first column of the conventional scheme (Figures 1 and 2). After the tray arrangement for the TCEDS-SR sequence has been obtained, an optimization procedure is used to minimize the heat duty supplied to the reboiler of the complex scheme, taking into account the constraints imposed by the required purity of the three product streams. Next, the degrees of freedom that remain after design specifications and tray arrangement are used to obtain the operating conditions that provide minimum energy consumption. Two degrees of freedom remain for the complex sequence. They are the side stream flow and the extractant stream stage. The optimization strategy can be summarized as follows: (a) A base design for the complex scheme is obtained. (b) Values for the extractant stream stage and interconnecting flow are assumed. (c) A rigorous model for the simulation of the complex scheme with the proposed tray arrangement is solved. In this study, Aspen Plus OneTM was used for this purpose. If product compositions are obtained, then the design is kept; otherwise, appropriate adjustments must be made. (d) One value of side stream flow is changed, going back to step (c) until a local minimum in energy consumption for the assumed value of the side stream stage is detected. (e) The value of extractant stream stage is modified, going back to step (c) until the energy consumption is minimum (optimization criterion). This result implies that an optimum value has been detected for the design of the complex scheme.

3. Case of Study To compare the behavior of the sequences, three ternary mixtures were considered (Table 1). The number of ideal stages, the feed stage and the initial extractant stage in the thermally coupled extractive distillation sequence were set after the optimization of the structure of the conventional direct sequence was carried out. These parameters enabled a successful separation. The UNIQUAC model was used to predict thermodynamic properties. Different extractant/feed (E/F) ratios were investigated. The design pressure for each separation was chosen to ensure the use of cooling water in the condensers. Purities of 99 % in mole in the products were assumed.

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192 Table 1. Mixtures analyzed.

Mixture

Feed Components

Extractant

M1

Feed Component Flows (kmol/h) Tetrahydrofuran/Water 40.82/4.53

M2

Acetone/Methanol

45.35/45.35

Dimethyl sulfoxide

M3

n-Heptane/Toluene

90.72/90.72

Aniline

1,2-Propanediol

4. Results The resulting designs and their performance with respect to energy consumption, CO2 emissions [1], thermodynamic efficiency [4] and total annual cost (TAC) are discussed. Typical optimization curves for the DS and TCEDS-SR (case M2) are shown in Figures 3a and 3b, respectively, where the optimal value for the extractant stage can be determined for the DS, and for the case of the TCEDS-SR both values of the extractant stage and interconnecting flowrate can be detected in order to guarantee minimum energy consumptions. The optimization curves show an interesting effect of the search variables on energy consumption. The design is sensitive, in terms of its energy consumption, to changes in interconnecting flowrates and extractant stage. An implication of this observation has to do with operational considerations (the presence of recycle can contribute in a well dynamic behavior).

a) DS b) TCEDS-SR Figure 2. Search for the minimum energy consumption of the designs.

Tray arrangements and some important design variables for that sequence after the optimization task are given in Tables 2. The results of the rigorous optimization are collected in Table 3 for the extractive distillation configurations, indicating the effect of solvent feed ratio (E/F) on energy consumption, economic evaluation, second law efficiency and CO2

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Table 2. Design variables for TCEDS-SR (M1; E/F=2.0).

Pressure (atm) Stages Feed Stage Extractant Stage Interconnection Stage FV (kmol/h)

Main Column 1.14 33 17 3 24 4.98

Side Rectifier 1.14 17

Table 3. Results for different extractant/feed ratios, case M1.

Sequence

DS TCEDS-SR Sequence

DS TCEDS-SR Sequence

DS TCEDS-SR Sequence

DS TCEDS-SR Sequence

DS TCEDS-SR

Energy Consumption (kW) 2264.11 1719.49 Energy Consumption (kW) 2463.47 1823.18 Energy Consumption (kW) 2711.0 1943.06 Energy Consumption (kW) 2968.30 2088.39 Energy Consumption (kW) 3228.83 2243.70

E/F = 2.0 TAC ($/yr)

η

CO2 Emissions (Ton/h)

827,624.71 656,333.29 E/F = 2.5 TAC ($/yr)

48.40 32.08

0.62 0.47

η

CO2 Emissions (Ton/h)

887,466.55 686,478.34 E/F = 3.0 TAC ($/yr)

27.95 37.58

0.68 0.50

η

CO2 Emissions (Ton/h)

962,586.56 721,606.88 E/F = 3.5 TAC ($/yr)

30.20 42.15

0.74 0.53

η

CO2 Emissions (Ton/h)

1,040,571.40 764,676.89 E/F = 4.0 TAC ($/yr)

31.95 45.62

0.81 0.57

η

CO2 emissions (Ton/h)

1,119,517.07 810,951.68

33.39 48.41

0.89 0.62

For all cases of study, the results can be summarized as follows: (i) reducing solvent feed ratio of the complex extractive distillation systems causes a reduction of energy savings in comparison with the conventional distillation sequence, and consequently the

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total annual cost will be increased; (ii) the energy savings achieved by complex extractive schemes are in the range between 20 and 30% in contrast to the conventional arrangement; (iii) the second law efficiency (η) of the TCEDS-SR is higher than that of the corresponding conventional extractive distillation option; (iv) the reduction in global CO2 emissions, in TCDES-SR, is considerable: in the range between 24 and 30%. The inefficiency of conventional sequences (associated with CO2 emissions) has been reported as a consequence of remixing [2]. Therefore, proper optimization of the thermally coupled extractive sequence should avoid such a remixing problem. The methodology proposed generates designs where the effect of the remixing is eliminated. In general, the results show that the optimization of the thermal link causes significant energy savings, TAC savings and reduction in CO2 emissions, and improves the values of second law efficiencies (especially at high values of E/F). Those results also were observed in other cases of study.

5. Conclusions The design and optimization of a thermally coupled extractive distillation sequence with side rectifier were studied and compared to those of a conventional extractive distillation sequence. A general energy-efficient design procedure has been used that accounts for CO2 emissions from the TCEDS-SR. The approach optimizes all process conditions in order to achieve energy savings and reductions in CO2 emissions. Examples have shown that the design procedure can provide all of the operating parameters needed. Some trends were observed: TCEDS-SR presented energy savings (and TAC savings) between 20 and 30% over conventional schemes. The complex scheme presents a reduction in carbon dioxide emissions. The results imply that the proposed extractive thermally coupled distillation sequence can achieve significant energy savings that can be translated into reductions of CO2 emissions.

6. Acknowledgements We acknowledge the financial support provided by Universidad de Guanajuato, CONACyT and CONCyTEG (Mexico).

References [1] Gadalla, M.A., Olujic, Z., Jansens, P.J., Jobson, M., Smith, R., Environ. Sci. Technol., 2005, 39, 6860. [2] Triantafyllou, C., Smith, R., Trans IChemE Part A., 1992, 70, 118. [3] Abushwireb, F., Elakrami. H., Emtir, M., In the Proceedings of European Symposium on Computer Aided Process Engineering-17 (ESCAPE), 2007, 243. [4] Seader, J. D., Henley E., Separation Process Principles, 1998, USA: John Wiley and Sons.

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Evaluation and Application of the Extended TBP Curves in Processing and Refining of Heavy Oil Fractions José F. Cuadros,a Rubens Maciel Filho,a Maria R.W. Maciel,a Cesar Benedito Batistella,a Lilian C. Medinab a

School of Chemical Engineering, State University of Campinas, UNICAMP, P.O. Box 6066, 13083-970, Campinas – SP, Brazil, [email protected] b Petrobras Research Center, CENPES, 21949-900, Rio de Janeiro- RJ, Brazil

Abstract Oil reserves in Brazil are characterized by heavy and ultra heavy petroleum. This type of oil is relatively difficult to process. In fact, it is necessary to upgrade such kind of oil in order to increase productivity of light fractions, mainly diesel. An important step in the definition and set up of suitable process to deal with this is the oil characterization. This is made with the aid of the True Boiling Point (TBP) curve through ASTM standard test methods until 565ºC and it extension obtained from molecular distillation for heavy oil and residues. In this work, it is proposed a refining evaluation making use of the extended TBP curves. The conceptual process was implemented in Hysys Process Simulator through a novel procedure for the generation of pseudocomponents for characterizing the feeding of distillation columns. It was developed a simulation methodology in order to evaluate the petroleum residues extended TBP curves in the process separation after the FCC (Fluid Catalytic Cracking) reactor, for producing liquefied petroleum gas, gasoline and diesel. Keywords: Heavy Oil, FCC, extended TBP curves, Molecular Distillation

1. Introduction According to the standard ASTM D 4175-08, crude oil or crude petroleum is a mixture of natural materials, generally in liquid state, consisting predominantly of hydrocarbons and organic sulphurated derivatives, nitrogenated and / or oxygenated compounds. The petroleum refining is constituted of different stages where it is converted in light fractions. The simplest form for separating its basic compound is through distillation of the sample, which is used to separate the raw oil in fractions, according to the different boiling points of these fractions. In order to increase the productivity of light fractions from heavy oil fraction, molecular distillation process, which uses high vacuum and low temperatures as separating agents was used, making possible the characterization of the heavy oil fractions. The analytical data results for two types of petroleum heavy oil residues obtained from molecular distillation (extended TBP curves), Alpha 565ºC+, 33.0 ºAPI and Gamma 545ºC+, 16.8 ºAPI (Alpha and Gamma petroleum’s names are unreal), were evaluated in a recovery section of an industrial catalytic cracking unit able to work with heavy oil. These results were compared with industrial data running with

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conventional oil mixture. It is shown that to deal with heavy oils, it is necessary to have different process arrangements in order to match, both, refinery demands and quality.

2. Steady State Simulation of the Process The first units in an oil refinery are the atmospheric and vacuum towers. The vacuum gas oil and the vacuum residue of the vacuum distillation unit, or a mixture among these streams with other gas oils produced in other unities in the separation process are fed in the catalytic cracking unit, where the conversion in light products is carried out by the use of catalysts. The focus of this work is on the recovery section of an industrial catalytic cracking unit able to work with heavy oil, it is composed by: fractionator, gas recovery and treatment sections. Figure 1 presents a general scheme of Catalityc Cracking unit [2]. The simulation is built up in a plant constituted by four recycles and the validation of this process was made with industrial data obtained from REPLAN (PETROBRAS Paulinia refinery) and published in [3].

Figure 1. Catalityc Cracking Process

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3. Extended TBP curves evaluation The fractionator load is composed of downstream overheated gases from the FCC reactor; containing mainly heavy and light hydrocarbons. It caracterization was made through FCC unit products analyses through ASTM standards and their mixture using a mass balance, obtaining 50 compounds (32 pseudocomponents and 18 pure compounds) in the Hysys Oil Manager environment.The thermodynamic model used was Peng Robinson. Next, the extended TBP curves for two cases were evaluated in the process separation after FCC reactor. In [1], different types of atmosferic and vacuum Brazilian heavy oil residues were distillated above 545ºC by means of a high vacuum distillation called molecular distillation until approximately 700°C (atmospheric equivalent temperature- AET), giving as result the extended TBP curves. From this work, the extended TBP data of two types of petroleum heavy oil vacuum residues, Alpha 565ºC+, 33.0 ºAPI and Gamma 545°C+, 16.8 ºAPI were considered. The introduction of extended TBP curves in the recovery section, was made by means of definition of pseudocomponents by means of Peng Robinson model and using the default correlations of the HYSYS oil characterization environment to calculate the physical properties. The light compounds were obtained from PETROX data base (process simulator property of PETROBRAS , Petróleo Brasileiro S.A) and integrated with the distillation test. To verify the validity of the pseudocomponent calculations carried out in HYSYS, two curve properties were compared: density curve and the TBP curve, with a methodology for characterization of heavy oil fractions published by [4]. This methodology requires the tbp distillation curve and density petreoleum fraction to create the pseudocomponents by means of the integral method. Comparisons between this methodology and HYSYS curve properties calculations gives very good match. From the evaluation of the extended TBP curve for petroleum Gamma, 58 components were obtained. Of this, 45 are pseudocomponents in a temperature range (normal boiling point ) from 22ºC to 1019ºC. For petroleum Alpha, 59 components were obtained, of which 46 are pseudocomponents in a temperature range from 11ºC to 1056ºC. Pseudocomponents densities are between 0.7- 1.2 g*cm-3.

3.1 Simulation Results The simulation results (flow rate and product temperatures), of the extended TBP curves evaluation were compared with the results based on industrial data. The evaluated products were: Fuel gases, liquefied petroleum gas (LPG), naphtha, light cycle oil (LCO) and clarified oil (CO). In Table 1, the feed conditions of petroleum residues characterized through extended TBP curves are presented. These feed conditions are the

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same values of temperature, pressure and flow rate in the simulation based on industrial data. Table 1- Feed conditions for tested residue petroleum

Variable Vapor fraction Temperature (K) Pressure (kPa) Molar Flow Rate (kgmol/h) Mass Flow Rate (kg/h)

Petroleum residue Gamma vapour fase liquid fase 0. 770 0. 229 803.15 200

Petroleum residue Alpha vapour fase liquid fase 0. 972 0. 028 803.15 200

3642

3642

1.34*106

7.91*105

Figure 2 presents the comparisons between the flow rates of FCC process products obtained in the simulation based on industrial data (standard simulation) and the simulation obtained based on extended TBP curves of the petroleum residues. Figure 3 presents the comparisons between the temperature of FCC products obtained in the simulation based on industrial data and the simulation obtained based on petroleum heavy residues extended TBP curves. In this figure, is observed that higher temperatures are necessary to separate each fraction of the feed stream petroleum residue Gamma compared with the petroleum residue Alpha and the standard based on industrial data. This can appear because the petroleum residue Gamma specific gravity (16.9 API), is lower compared with the specific gravity of the petroleum residue Alpha (33.0 API). It affect the petroleum fractionation process and products formation, as can be seen in figure 2. Configuration of the four recycles in the separation process also determine the simulation convergence as well as products formation.

4. Discussion and conclusions Results presented in Table 1 show that the evaluation of the extended TBP curves in the separation unit after FCC depends on the conditions of design of this unit, since values of distilled above 550°C do not vaporize, affecting significantly the fractionator operation and the operation of the process as a whole, due to the fact that the fraction that remains in the liquid state of the feed affects the vapor flow rate.

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Figure 2. Comparison between product flow rates of streams of FCC separation process

From Figure 2 and 3, it may be concluded that the evaluation of the extended TBP curves of petroleum residues should be carried out in another section of the FCC process different from the separation unit after FCC reactor, since this one does not distill the residue feed with boiling point above 550ºC, so that this fraction will be present in the bottom of the fractionators. The unit that could cracking this fraction is the riser of the FCC unit . In general, this one cracks the high molecular weight charge in light fractions which would be processed in the fractionation column. This one could convert the distilled above 565°C, called ultra heavy gasoil, in light fractions than could be fractionated in the separation unit after FCC.

Figure 3. Comparison between product temperatures of streams of FCC separation process

The characterization of the fractionator feed stream in pseudocomponents is very important because the larger number of pseudocomponents reduces the possibility of mistakes in the extended TBP curve characterization.

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200

5. Acknowledgement The authors would like to acknowledge the financial support from PETROBRAS.

CNPq and

References [1] P. Sbaite., C. B. Batistella., A .Winter., C. J .Vasconcelos., M. R.Wolf., R . Maciel., A. Gomes., L . Medina and R. Kunert., Petroleum Science and Technology., 24(2006)265. [2] E. Abadie., Catalytic Cracking, Petrobras, Rio do Janeiro (RJ),1997. [3] P. Pedrosa, Simulation and optimization of the fragmentation and products recuperation section in the fluid catalytic cracking unit, MS.c. Dissertation, University of Campinas, Campinas (SP), 1994. [4] J. Miquel and F. Castells., Hydrocarbon Processing.,73 (1994) 99.

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Integrated Design of Solvent-Based Extractive Separation Processes Including Experimental Validation P Lek-utaiwana,b, B Suphanita, N Mongkolsirib, R Ganic a

ChEPS, Dept of Chem Eng , King Mongkut’s Univ of Tech Thonburi, Bangkok, Thailand; bSCG Chemicals, Rayong, Thailand c CAPEC, Dept of Chem & Biochem Eng, DTU, DK-2800 Lyngby, Denmark

Abstract In this paper, emphasis is given on an industrial case study involving the purification of ethylbenzene through solvent-based extractive distillation – the design of experiments, the collection of data and the validation of the performance of the selected solvent as well as the optimal design of the separation process, are covered. Well-known methods and tools from CAPE, such as, selection of solvents through CAMD (Computer-Aided Molecular Design), design of the extractive distillation columns through driving force based technique for optimal process synthesis/design, and, process simulation, have been used. The objective of the experimental work has been to validate the estimated performance of the selected solvents as well as to clarify the uncertainties in the final design. Using the collected experimental data, it has been possible to perform a sensitivity analysis and through it, verify the solvent selection, process design as well as a cost analysis to make the final evaluation of the new design. The paper presents the new, combined analysis, the evaluation and validation of the process design. Keywords: Separation, Solvent selection, Ethylbenzene-xylene separation, Driving force.

Extractive

distillation,

CAMD,

1. Background Predictive property models like UNIFAC and UNIFAC-Do provide useful alternatives for estimation of properties related to process synthesis, design and analysis involving organic chemical systems whenever data is scarce. The final design, however, needs to be verified through experimental data before the design is commissioned industrially. In an earlier work, Lek-utaiwan et al. [1] proposed several design alternatives together with a sensitivity analysis for an industrial problem involving the separation of ethylbenzene (EB) from C8-aromatics (PX) through solvent-based extractive distillation. The solvent selection method [2, 3] and the driving force based design of extractive distillation [4] are both very much dependent on a number of physicochemical properties, including UNIFAC (two versions) based phase equilibrium estimations. Analysis of the predictions with two different versions of the UNIFACmodels (as available in ASPEN PLUS®) indicated uncertainties in the calculated properties. Therefore, a sensitivity analysis was performed to identify the important variables whose uncertainties in their estimated values needed to be established before the proposed process design could be commissioned. The uncertainties were mainly related to the predicted activity coefficients for the chemicals involved in the liquid phase of the vapor-liquid equilibrium system. This property affects the solvent selection criteria (and therefore, its performance) as well as the calculation of the driving force for the design of the extractive distillation systems. Therefore, a series of experiments

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were designed to clarify the uncertainties in design and determine the final process design.

2. Design of Experiments Two steps were considered: In the first step, experiments were designed to test the relative volatility enhancement at various solvent to hydrocarbon ratios – this issue effects the solvent selection as well as the design of the extractive distillation process. In the second step, the best solvents from the first step were selected to verify the vaporliquid phase equilibrium data, so that the driving force used in the design of extractive distillation could be evaluated. It was decided to investigate in detail, three solvents that were found to be the candidates with the highest possibility to succeed. Also, the time, cost and availability of samples restricted this study to these three candidates. Another restriction was the temperature of operation that had to be less than 453 K. The three solvents, whose names cannot be given because of reasons of confidentiality, are AAD1 (because according to the UNIFAC-Do model, it is the best), AE2 (because the calculated driving forces predicted through the two UNIFAC models were very different), and AK2 (because of their differences in the predicted relative volatility enhancements). The solvent AAD1 is an aromatic aldehyde, AE2 is an aliphatic ester and AK2 is an aliphatic ketone.

3. Material and apparatus For all three selected solvents, the solutes - ethylbenzene (EB) and p-xylene were obtained from Fluka and Merck as a high purity grade chemical. The chromatographic analyses showed a purity of 99.86%wt for EB, 99.98%wt for PX, 99.72%wt for AAD1, 99.88%wt for AE2 and 98.54%wt for AK2. All compounds were used without any additional purification. The apparatus used for the experiments is the atmospheric vapor-liquid equilibrium apparatus with recirculation of liquid and vapour, from Fischer (Model-602) is shown in Figure 1.Temperature of the system was kept constant by regulating the supplied heating. Samples were taken from the condensed vapor and liquid, and, analyzed with the Agilent Technology 6890 series gas chromatograph equipped with a flame ionization detector (FID) and a 30 m × 0.32 mm × 1 μm capillary column. The equipment operates at atmospheric pressure and a maximum temperature of upto 453 K. The temperature sensors for both liquid and vapor phases were calibrated using the ASTM E644-02 method.

Figure 1: Experimental set-up of Fisher VLE apparatus (Model 602)

Integrated Design of Solvent-Based Extractive Separation Processes Including Experimental Validation

203

First the apparatus was tested and calibrated by measuring the VLE data for a system involving n-Hexane and n-Heptane and comparing with known data [5]. After adjustments of the experimental set-up, it was possible to match the known data almost exactly (see Fig. 2). VLE data of n-Hexane and n-Heptane system 110 xC6-test yC6-test

100

xC6-literature

Temp (C)

yC6-literature 90

80

70

60 0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

xC6

Figure 2: VLE data of n-Hexane and n-Heptane system used for equipment calibration.

4. Measured data collection and analysis As mentioned above, two sets of experiments were performed to clarify the effectiveness of the selected solvents and to validate the estimated driving forces of the key components, and thereby, the process design. 4.1 Relative volatility verification Solvent to feed mole ratio (S/F ratio) was the parameter varied in the experiments in the first step. Data was measured for the following values of this parameter: 1.0, 2.5 and 5. The measured data for the three solvents were collected, plotted (see Fig. 3) and compared. The measured data for AAD1, as shown in Fig. 3, does not indicate any difference in the performance, confirming thereby, the predictions with the two UNIFAC models (both predicted similar performance). With respect to solvent AE2, the original UNIFAC VLE model predicted a positive relative volatility enhancement but not UNIFAC-Do. The measured data confirmed the predictions of the original UNIFAC VLE model for this solvent. 1.15

Relative Volatility EB/PX

AAD1

AE2

AK2

No-Solvent

1.10

1.05 1.0

2.5 S:F (mole ratio)

5.0

Figure 3: Measured relative volatility enhancements of EB/PX with three different solvents

P. Lek-utaiwan et al.

204

4.2 Driving force verification Since AAD1 was found to be the best solvent from relative volatility enhancement, the measured data for only this solvent for the driving force analysis is highlighted in this section. Calculation of the driving force for VLE systems for any component i (of the chemical system) requires measured (or predicted) data of the liquid and vapour compositions in equilibrium for component i. Isobaric VLE data were therefore collected for three binary systems: EB-PX, AAD1-EB and AAD1-PX. were tested in the experiments. The known pure component boiling point temperatures (at atmospheric pressure) were also analyzed to ensure accuracy of the measured end-points of the VLE phase diagrams. The measured accuracy of the end-points was found to be within 99.44% of the known data. Thermodynamic consistency of the measured data was checked with the Gibbs-Duhem for isobaric case [6, 7, 8, 9], given as; Δh (1) x1d ln γ 1 + x2 ln γ 2 + m2 dT = 0 RT Where x1 = mole fraction of Ethylbenzene in liquid phase x2 = mole fraction of the solvent in liquid phase γ1 = mole fraction of Ethylbenzene in liquid phase γ2 = mole fraction of the solvent in liquid phase Δhm = the molar enthalpy of mixing, which can be estimated with a UNIFAC model. Txy diagram of EB-AAD1

activity coefficient of EB in EB-AAD1 0.600

180.0

Exp

xEB yEB 170.0

NRTL

ln(activity coefficient),EB

UNQ-xEB UNQ-yEB

Temp (C)

NRTL-xEB 160.0

NRTL-yEB

150.0

140.0

130.0 0.000

UNQ

0.500

0.400

0.300

0.200

0.100

0.200

0.400

0.600

0.800

0.000 0.0

1.000

0.2

0.4

(a)

0.8

1.0

(b)

7[\GLDJUDPRI3;$$' 

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(c) (d) Figure 4: Comparison of experimental and calculated (UNIQUAC and NRTL models) of VLE data and activity coefficient plots of EB-AAD1 [(a) and (b)] and PX-AAD1 [(c) and (d) systems.

Integrated Design of Solvent-Based Extractive Separation Processes Including Experimental Validation

205

Measured data that did not match the Gibbs-Duhem condition by the area test method of Herington to within 10% were considered inconsistent and were rejected. Only the remaining good VLE data were then used to regress the model parameters for the widely used correlative thermodynamic property prediction models that enable handling the strongly non ideal system of polar and non-polar component mixture, i.e. UNIQUAC and NRTL [8]. The suitable thermodynamic model was selected from VLE data curve fitting and the residue sum of square errors of three predicted parameters in consideration i.e., temperature, vapor phase composition and activity coefficient, which in this case, UNIQUAC was apparently observed to be the better fitted model as seen in figure 4. Hence, the experimental driving force curve could be generated by the UNIQUAC model with the full set of binary interaction parameters of EB-PX, EBAAD1 and PX-AAD1 as shown by the plots on figure 5. Again, based upon the driving forces comparison, the original UNIFAC VLE model appears to give the more accurate values while UNIFAC-Do gives significantly larger values. Therefore, the process design based on this version of the UNIFAC model is more reliable for the systems studied in this work. 'ULYLQJIRUFHFXUYHRI(%3;V\VWHPZLWK$$'DVDVROYHQW  ')([ ')81' ')81 ')QRVROYHQW



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Figure 5 : Driving force curves in comparison between exp-data with and without solvent, UNIFAC and UNIFAC-Do predictions

4.3 Process design analysis Compared to the experimental data, however, it appears that the driving force is overpredicted with the original UNIFAC VLE model. This means that the driving force available for separation is actually smaller than what was previously assumed. For these new driving forces, the extractive distillation columns were designed with the driving force approach [4] and rigorously simulated with ASPEN PLUS®. Using the simulated data, the costs (investment and energy consumption) were calculated for four values of driving force (Df = 0.015; = 0.025, = 0.035 and = 0.062). The first value corresponds to zero-solvent addition and second to fourth values correspond to three different effects of solvent addition found by the experiments and the predictions by the original UNIFAC VLE model and UNIFAC-do model. These results are listed in Table 1. It can be noted that compared to conventional distillation, the extractive distillation reduced energy consumption by 19% when adding solvent at the S/F ratio = 5, which is now validated with experimentally measured VLE data. In this case, it can be noted that experimental

P. Lek-utaiwan et al.

206

verification actually points to a higher cost for energy and investment (since the actual driving force is smaller than those predicted earlier). Table 1 Economic parameters of the promising solvent represent in term of Dy Economic Parameters Investment (MUSD) Relatively reduction (%) Energy cost (USD/hr) Relatively reduction (%)

Df = 0.015 (No solvent) 8.9 Base 3,700 Base

Df = 0.025 (Exp.) 7.5 16 3,000 19

Df = 0.035 Df = 0.062 (UNIFAC) (UNIFAC-Do) 6.0 3.3 33 63 2,300 1,500 38 59

5. Conclusion Integrated process design for solvent-based separation processes in general and extractive distillation in particular, has been highlighted. The model-based design alternatives previously proposed [1] have been validated and analyzed and a final (experimentally verified) process design has been presented. It has been seen that as the actual driving force is smaller than the model-based prediction, the actual cost has increased (compared to the previous design), but significant reductions in employing solvent based designs are still possible to obtain. Also, although the final quantitative values needed to be adjusted, the model-based results, at least, gave qualitatively the correct results. That is, the best solvent-based design did not change. The results and analysis presented in this paper show that CAPE methods and tools can be used for design decisions and preliminary design with experiment resources used only for the final verification step, thereby, saving time as well as funding and man-power resources.

References [1] P Lek-utaiwan, B Suphanit, N Mongkolsiri, R Gani, 2008, Computer Aided Chemical Engineering, Volume 25, 121-126 [2] R. Gani, 2006, ICAS-Program Package, CAPEC Report, DTU, Lyngby, Denmark [3] AT Karunanithi, LEK Achenie, R Gani, 2006, Chem. Eng. Sci. 61, 1247-1260. [4] R Gani and Bek-Pedersen, 2000, AIChE Journal, 46, 1271-1274 [5] Jan,D.S., H.Y.Shiau and F.N.Tsai, J.Chem.Eng.Data, 39, 438 (1994) [6] K.-D. Kassmann*and II. KNAPP, Fluid Phase Equilibria, 33 (1987) 125-136 [7] Younghun Kim, Chem. Eng. Report Series, No. 48, Espoo2005, Lab. of Chem. Eng. and Plant Design, Dep. of Chem. Tech., Helsinki Univ. of Tech., Finland, [8] J.M. Smith, H.C. Van Ness and M.M. Abbott, Intro. to Chem. Eng. Thermo., 6th Edition, The McGraw-Hill Companies, Inc., New York, 2001 [9] Dimistrios P. Tassios, Applied Chem. Eng. Thermo., The Springle-Virlag Companies, Inc., USA, 1993 [10] Mark A. Gess, Ronald P. Danner and Manoj Nagvekar, Thermo., Aanlysis of VaporLiquid Equilibria: Rec. Models and a Standard Data Bases

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

207

Liquid solutions evaporation accompanied with mass transfer resistance in liquid phase Janusz Dziak, Jacek Kapłon, Lechosław Królikowski, Wojciech Ludwig, Wojciech SawiĔski Wrocław University of Technology, Norwida 4/6, 50-373 Wrocław, [email protected]

Abstract Mass transfer resistance in liquid phase during evaporation of liquid solutions in thinlayer evaporator may substantially influence on the results of the process of distillation. Theoretical approach, which is commonly used in designing practice, leads in such cases to wrong estimation of heat transfer area, necessary for obtaining anticipated purity of the products or even worse, it could give results of distillation that are unrealistic taking into account the composition of distillate. The authors of the paper performed an extensive experimental work on distillation of solutions possessing components with substantially different volatility. They applied a thin-layer evaporator of static type and the evaporator equipped with blades that mixed evaporated liquid. The results of work lead the authors to conclusion that the mass transfer resistance in liquid phase depends on properties of evaporated liquid, its composition as well as the construction of the evaporator and the process conditions. Keywords: Thin-layer evaporation, mass transfer

1. Introduction Thin-layer evaporation of liquids is often applied in food , pharmaceutical and chemical industries, especially in cases of evaporation of heat sensitive materials. This kind of process is also a scope of interest for many scientists. One can find in the literature mathematical models of hydrodynamics of thin- layer flow over a vertical wall [1], [2],[3]. There are many studies on heat transfer in liquid thin-layer presented in the literature. The examples are [4] and [5]. On the other hand there are a few works that deal with simultaneous heat and mass transfer during thin-layer evaporation of liquid solutions and the influence of this processes on each other [6],[7],[8]. The processes of heat and mass transfer, considered in those articles, proceed in thin-layer evaporator of static type, without action of mixer blades inside liquid phase. Thin-film evaporation of liquid solutions possessing components that considerably differ in volatility may lead to creation of significant composition gradient at the vicinity of the phase border in liquid. Concentrations of distillate obtained in the process of thin-layer distillation in such cases are not the same as the results calculated from the theory presented by Billet [9], which is commonly applied in thin-film evaporator designing practice. This theory does not take into account the possibility of mass transfer resistance during process of vaporization. Gröpp and Schlünder [8] presented theory describing process of vaporization from thin-layer liquid solution in case of existence of mass transfer resistance in liquid phase. That theory enables calculation of mass transfer coefficient in liquid, knowing distillation results and conditions in which the process of vaporization was proceeded. The results of thin-film evaporation of liquid solutions: isopropanol-

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208

water and water propylene glycol are presented in this paper. Isopropanol-water system is characterized by low viscosity and water-ethylene glycol system possesses much higher viscosity. Both systems contain one component which is much more volatile than the other. The results of isopropanol-water solution distillation were obtained in thinlayer evaporator of static type and the results of water-propylene glycol solutions distillation were obtained in thin-layer evaporator equipped with a mixer, which mixed the liquid during its evaporation.

2. Theories of liquid solution thin-film evaporation 2.1. Billet theory Billet [9] presented the way of calculation of the results of distillation in a thin-layer evaporator. The base for this theory is mass balance of more volatile component in differential element of liquid and vapor. This theory does not take into account the possibility of mass transfer resistance existence in liquid phase. From the mass balance the equation (1) can be developed, which allow to calculate the residual liquid flow from the evaporator L•W (mol/s), knowing the values of feed flow L•S and concentrations of the liquid at the inlet and the outlet of the evaporator xS mol/mol xW. To proceed the calculations one needs to know the vapor-liquid equilibrium data [y* =f (x)].

ln

xS L• S dx = ³ ∗ • L W xW y − x

(1)

The average value of distillate concentration could be found from the overall mass balance: xD =

L• S ⋅ x S − L•W ⋅ xW D

(2)

where: D- distillate flowrate, mol/s

2.2. Gröpp and Schlünder theory of simultaneous heat and mass transfer during

thin-layer distillation of two-component solutions The process of liquid solution evaporation in thin-layer evaporator is more complex than evaporation of one component liquid. It is connected with the fact of mass transfer resistance arise in some conditions of two-component liquid thin-layer evaporation. Gröpp and Schlünder [8] presented equation (3) that allow calculation of mass transfer coefficient in liquid phase ȕL during distillation in thin-layer evaporator.

ln

y Aph − x A

y Aph − x Aph

=−

vL

βL

(3)

vL in this equation denotes linear velocity in the direction of interface in liquid phase, which is obtained from equation (4).

vL =

q

ρL ⋅ r

(4)

Liquid Solutions Evaporation Accompanied with Mass Transfer Resistance in Liquid Phase

209

where: q- heat load of the evaporator surface, W/m2; r- liquid heat of vaporization, J/kg, ρL-liquid

density, kg/m3

Knowing the values of liquid heat of vaporization (r), heat load (q) and liquid density (ρL)one can calculate the value of vL from equation (4). After that, knowing the value of vL and the values of concentrations in liquid and vapor on the interface boundary yAph, xAph, as well as the average concentration in liquid phase xA, one can determine the value of mass transfer coefficient β L from relationship (3).

3. Experimental Scheme of installation applied in an experimental work is presented in Fig. 1. As it was stated in chapter 1 two kind of evaporators were used in experiments: one of static type and the second equipped with mixer. The main dimensions of both evaporators are presented in table 1. Table 1. Main dimensions of thin-layer evaporators used in experiments Static type thin-layer evaporator 0.56 0.04 0.07

Heated height h, m Evaporator diameter d, m Heat transfer area A, m2

Thin-layer evaporator equipped with mixer 0.266 0.06 0.05

ENG

TI

CND

TI

VC C.W.

V4 VC

VC

T.L.E. PI H.L.

TI

CND

VC

C.W. VC

V3

FI

CND C.W.

V1 V2

P1

Fig.1. Scheme of installation for heat and mass transfer examination in thin-layer evaporator. CND-condenser, C.W.-cooling water, H.L.- heating liquid, P1- pump, V1- feed tank, V2- residue tank, V3- distillate tank, V4- feed sample receiver, VC- to vacuum, T.L.E.- thin-layer evaporator, FI- flow indication, PI- pressure indication, TI- temperature indication

Intensity of heated surface sprinkle by liquid was calculated from relation (5): m’=m•/O

(5)

where: m•- average mass flowrate of liquid, kg/s; O- evaporator perimeter, m

Heat load of evaporator heated surface was determined from equation (6): q=Q•/A

(6)

J. Dziak et al.

210

where: Q•- heat exchanged in the evaporator, A-heat exchange surface area of the evaporator

The concentrations of examined liquids were determined by measuring density for isopropanol-water system and refractive index for water-propylene glycol system. The vapor-liquid equilibrium data was taken from the literature [10]. Table.2. Ranges of changeability of magnitudes applied in experiments Magnitude Isopropanol-water system water-propylene glycol system External pressure, Pa 3332 1,013⋅105 2 (82oC) Relative volatility= 47 (74oC) Pmore volatile /Pless volatile (t,oC) Feed concentration-XF, mol/mol 0.0678-0.133 0.1788- 0.2475 Sprinkle intensity-m’, kg/(ms) 0.0531-0.213 6.839Â10-3- 9.9882Â10-2 Heat load-q, W/m2 8087.9-32809.5 7216.8- 19752 878.4-921.4 989.2-1008.4 Liquid density-ρ, kg/m3 0.3106-0.3449 3.4- 4.8 Liquid viscosity-η, mPa⋅s Mixer revolutions, rev./min. 200-800

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ŶсϮϬϬƌĞǀͬ͘ŵŝŶ͕͘Ƌсϭϰ͘ϮŬtͬŵϮ ŶсϰϬϬƌĞǀͬ͘ŵŝŶ͕ͬƋсϭϰ͘ϮŬtͬŵϮ ŶсϲϬϬƌĞǀͬ͘ŵŝŶ͕͘Ƌсϭϰ͘ϮŬtͬŵϮ ŶсϴϬϬƌĞǀͬ͘ŵŝŶ͕͘Ƌсϭϰ͘ϮŬtͬŵϮ ŶсϮϬϬƌĞǀͬ͘ŵŝŶ͕͘Ƌсϵ͘ϲϴŬtͬŵϮ ŶсϰϬϬƌĞǀͬ͘ŵŝŶ͕͘Ƌсϵ͘ϲϴŬtͬŵϮ ŶсϲϬϬƌĞǀͬ͘ŵŝŶ͕͘Ƌсϵ͘ϲϴŬtͬŵϮ ŶсϴϬϬƌĞǀͬ͘ŵŝŶ͕͘Ƌсϵ͘ϲϴŬtͬŵϮ ŶсϮϬϬƌĞǀͬ͘ŵŝŶ͕͘Ƌсϭϳ͘ϭŬtͬŵϮ ŶсϰϬϬƌĞǀͬ͘ŵŝŶ͕͘Ƌсϭϳ͘ϭŬtͬŵϮ ŶсϲϬϬƌĞǀͬ͘ŵŝŶ͕͘Ƌсϭϳ͘ϭŬtͬŵϮ

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a/

Ϭ͘ϭϱ Ϭ͘Ϯ y>͘Ăǀ͕͘ŵŽůͬŵŽů

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Fig. 2. Results of distillation of isopropanol-water (static type thin-layer evaporator a/) and waterpropylene glycol (wiped-film thin-layer evaporator b/) solutions, carried out in thin-film evaporator. Dependence between more volatile component concentration in distillate and its average concentration in evaporated liquid. Solid line represents the results obtained from Billet theory. Points represent experimental data.

ďĞƚĂ͕ŵͬƐ

3.00E-04 2.50E-04

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Fig.3. Individual mass transfer coefficient dependence on process variables. a/ Static type thinlayer evaporator. Isopropanol-water system. b/Wiped thin-layer evaporator. Water-propylene glycol system

Liquid Solutions Evaporation Accompanied with Mass Transfer Resistance in Liquid Phase

211

5. Conclusions Taking into consideration the results of calculations and experimental works, which results are presented above one can conclude as follows: • theoretically calculated compositions of distillate for distillation in a thin-film evaporator are not in line with experimental results, in case of evaporation of liquid solutions containing components that differ significantly by volatility • mass transfer resistances in liquid phase exists during liquid solutions evaporation in thin-film evaporator • One can diminish mass transfer resistances in liquid phase using wiped film thinlayer evaporator and applying intensive mixing of liquid phase • Calculations of the results of thin-film distillation of the solutions containing components that substantially differ by volatility, carried out in thin-layer evaporator, should take into account the conditions at which the process of distillation takes place as well as physical properties of the liquid

References [1] Ludwig W., Dziak J., Królikowski L., Kapłon J., Tuta J., Modeling of hydrodynamics of thin-layer evaporator with grawitational liquid flow using CFD methods, Chemical and Process Engineering, 29,215-220, 2008 [2] Chen F.C., Gao Z., An analysis of black liquor falling film evaporation, Internationa Journal of Heat and Mass Transfer, 47, 16577-1671, 2004 [3] El Haj Assad M., Lampinen M. J., Mathematical modeling of falling liquid film evaporation process, International Journal of Refrigeration, 25, 985-991, 2002 [4] Alhusseini A. A., Tuzla K., Chen J.C., Falling film evaporation of single component liquids, Int. J.Heat Mass Transfer, 41, 12, 1623-1632, 1998 [5] Chun K.R., Seban R.A., Heat transfer to evaporating liquid films, Journal of Heat Transfer,93, 391-396, 1971 [6] Krupiczka R., Rotkegel A., Ziobrowski Z., The influence of mass transfer on the heat-transfer coefficients Turing the film boiling of multicomponent mixtures, Chemical Engineering and Processing, 43, 949-954, 2004 [7] Leuthner S., Harun Maun A., Fiedler S., Auracher H., Heat and mass transfer in wavy falling films of binary mixtures, International Journal of Thermal Science, 38, 937943, 1999 [8] Gröpp U., Schlünder E.S., The influence of liquid-side mass transfer on heat transfer and selectivity during surface and nucleate boiling of liquid mixtures in a falling film, Chemical Engineering and Processing, 20,no.2, 103, 1986 [9] Billet R., Trennwirkung im Dünnschichtverdampfer mit extrem kurzer produktverweilzeit, Chemie Ing. Techn., 1, 9, 1974 [10] J.,Onken U., „Vapour-Liquid Equilibrium Data Collection. Aqueous-Organic Systems” DECHEMA (1977)

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

Mineral Processing Flow Sheet Design Through A Group Contribution Method Gonzalo I. Herreraa, Edelmira D. Gálvezb,c, Luis A. Cisternasa,c a

Dept. Chem. Eng., Universidad de Antofagasta, Antofagasta, Chile. Centro de Investigación Científico Tecnológico para la Minería, Antofagasta, Chile c Dept. Metallurgical Eng., Universidad Católica del Norte, Antofagasta, Chile b

Abstract d’Anterroches and Gani [1] have introduced the concept of process-group contributions for process flowsheet property estimation and process flowsheet synthesis and design. This concept has been highlighted through a flowsheet property model for distillation operations. In this work a group contribution model have been development for flowsheet properties for flotation circuit. The model was adjusted based on simulated values for a set of flotation circuits. This model will be the base for the development of a systematic strategy for computer aided mineral flow-sheet design, where modelling, synthesis and design are integrated tasks. Keywords: process group contribution, process synthesis, flotation circuit. 1. Introduction Flotation is a practical method to separate valuable minerals based on differences in surface properties of the particles from milled mineral mixtures. Also new applications as the separation of individual plastics of equal density in waste streams containing a mixture of plastics have appeared. In froth flotation, various types of equipment exist which promote particles-bubbles encounter which contribute to controlling the balance between high recovery of the desired metal, and a high grade value of the metal in the product outflow. Past

213

214

G.I. Herrera et al.

experience has shown single step separation is inefficient, and the inclusion of several complementary and supportive steps are required. Taking into account the large volume of material to be treated and its associated costs, choices related to the configuration of the separation system are critical. Modelling and simulation of a mineral process flowsheet usually involve identifying the structure of the flowsheet, deriving model equations to represent each operation, and solving the resulting total model equations according to one of various available simulation strategies. The flowsheet synthesis problem determines the type of operations and their sequence needed to achieve the extraction of valuable components from the raw materials. The flowsheet design problem determines the optimal values for the conditions of operation and related variables for the synthesized flowsheet. It can be noted that the flowsheet modelling, synthesis and design problems are related since for generation and screening of flowsheet alternatives (synthesis/design), some form of flowsheet models are needed. Also, flowsheet models are needed for verification of the synthesis/design problem solution. In mineral process synthesis three types of approaches exist: a) the methods that employ heuristics or are knowledge based [2]; b) the methods that employ mathematical or optimization techniques [3-4], and c) the methods that employ physical insights [5]. A review of methods for conceptual flotation circuit design has been recently published [6]. d’Anterroches and Gani [1] have introduced the concept of process-group contributions for process flowsheet property estimation and process flowsheet synthesis and design, and they presented a property model for distillation operations. The objective of this work is to develop a group contribution model for flowsheet properties applied to flotation circuit. 2. Group Contribution Model Development The generation of the group contribution method was carried out in two steps: 1) data generation of flotation circuit properties and 2) model development and model adjustment. 2.1. Data generation The supposition that the flotation process corresponds to a first order reaction is broadly used. If a group of solid particles transported in a pulp collide with bubbles within certain defined volume, the valuable (hydrophobic) mineral will adhere to upward bubbles, becoming separated from the gangue. This phenomenon can be considered as a simple mechanism where flotation is a pseudoreaction between the solid particles (A) and the bubbles (B) where A+BĺAB. If the concentration of bubbles is constant, then the flotation kinetic can be represented as a first order pseudoreaction. Then, the mineral flotation can be modeled considering that a mineral is formed of different classes or pseudospecies that have the same floatability. It means floatability represents

Mineral Processing Flow Sheet Design through a Group Contribution Method

215

the propensity of the particles to be floated according to its composition and size given certain flotation environment conditions (pH, Eh, reagent type, concentration), in such a way the most valuable particle, i.e., the most completely liberated valuable particle, has the greater floatability value in an intermediate particle size. Then, in figure 1, the following equations can be written:

Ci

Ti Fi

(1)

Wi

(1  Ti ) Fi

(2)

Where Ti is the ratio of flow of concentrate and feed of class specie i. The ratio may be obtained from plant data, values from pilot plants, or theoretical or empirical models. For example, for a bank of N cells,

Ti

1

1 (1  kiW ) N

(3)

Where ki is the first order kinetic constant of class specie i, and W the retention time in one cell. In order to adjust a group contribution model, recovery values for different flotation circuits were generated by the simulation of several flotation circuit. Figure 2 shows a superstructure that represents a total of twenty four flotation circuits: two circuits with two flotation stages, four circuits with three flotation stages and eighteen circuits with four flotation stages. Each flotation stage was simulated using the equation 2, for multiple hypothetical classes of minerals. Each hypothetical mineral was generated with random values for the kinetic constant, cell retention time, and N=1, 3, 5 and 7 in equation 3.

2.2. Model adjustment To generate the group contribution model two types of contribution were considered. First, it was considered each flotation stage can be characterized by the ratio of flow of concentrate and feed, Ti . Then the interconnections among flotation stages were considered, represented by the product of the ratios of concentrate/feed or tail/feed and concentrate/feed or tail/feed as it is the case: Ti Ti , Ti (1  Ti ) , or (1  Ti ) (1  Ti ) . Then the model for recuperation of one pseudospecie has the following form: R D  ¦ E i N i Ti  ¦¦ J i , j N i , j / i , j i

i

(3)

j

Where D , Ei and J i , j are adjusted parameters, and Ti and / i , j are process-group contributions. The adjusted parameters were fitted to simulated recovery values for mineral class with low recovery (0 to 10%), medium recovery (10 to 60%)

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and high recovery (60 to 100%). The D values were -3.5542, -5.9192, and 2.5507 for low, medium and high recoveries. The values for Ei are given in table 1 and some J i , j values in table 2. Good results have been obtained in the prediction of recovery (see figure 3).

Figure 1. Flotation Stage

Figure 2. Superstructure of flotation circuit

Table 1. Values for Ei groups. Flotation stage groups

Recovery

TR

TC

TCC

TS

Low

1.8913

1.9870

-3.2947

0.0348

Medium

2.0104

2.3000

-5.1205

-1.0106

High

1.3011

1.2367

-1.0042

-1.3571

3. Example

To explain the use of the equation 3, let us consider the flotation circuit shown in figure 4, where a mineral conformed by two pseudospecies, one with high recovery and another with low recovery, is fed. The equation 3 for this case corresponds to:

R D  ETR TR  ETC TC  J TRTC TRTC  2J TR (1TC )TR (1  TC ) 

J (1T

R )(1TC

)

(1  TR )(1  TC )

(4)

Mineral Processing Flow Sheet Design through a Group Contribution Method

Table 2. Some values of J i , j Flotation stages groups, / i , j

J i, j

217

values

I

j

low

medium

High

TR 1  TR TC TCC TR 1  TR

TC TS TS TS 1  TC 1  TC

0.4251

2.6465

1.2645

0.7060

1.3288

0.6314

-0.3160

0.8209

2.6079

-0.2917

1.1177

3.4985

1.8040

3.1885

1.1269

3.0154

6.0501

2.5505

1.0 0.9 0.8

Recuperation Group contribution

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Recuperation (Simulation)

Figure 3. Recuperation values: Group contribution versus simulated values

Figure 4. Flotation circuit for the example.

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218

For values of T R 0 .9 0 6 and TC 0 .7 1 6 for the high recovery speudospecie, the calculated valor of R, in equation 4, corresponds at 0.867, while the mass balance value of R corresponds at 0.873. On the other hand, for the low recovery speudospecie, with values of T R 0 .0 7 and TC 0 .0 5 , R correspond at 0.009 and 0.007 for equation 4 and mass balance respectively. 4. Conclusion and future work

A group contribution model was presented for the recovery estimates in flotation circuits. For the analyzed circuits the method gives acceptable results for process synthesis purpose. Works to include circuits with more flotation stages, development of an approach for the selection of T values, and an approach for the determination of the maximum number of flotation stages are under way. 5. Acknowledgements

We thank the CONICYT for financing and support of the work reported in this manuscript (FONDECYT 1060342). The authors want to thank to Rafiqul Gani for his valuable contribution to this work. 6. References [1] d’Anterroches L., R. Gani, 2005, Group contribution based process flowsheet synthesis, design and modelling, Fluid Phase Equilibria 228–229 , 141–146 [2] Connolly, A.F., R.G.H. Prince, 2000, Performance improvement in minerals beneficiation circuits by retrofitting ,Separation and Purification Technology 19, 77–83 [3] Guria C, Verma M, Gupta SK, Mehrotra, 2005, Simultaneous Optimization of The Performance of Flotation Circuits And Their Simplification Using The Jumping Gene Adaptations of Genetic Algorithm, International Journal of Mineral Processing, 77 (3): 165-185. [4] Cisternas LA, Mendez DA, Galvez ED, Jorquera R., 2006, A MILP model for design of flotation circuits with bank/column and regrind/no regrind selection, International Journal of Mineral Processing, 79 (4), 253-263. [5] Gálvez E.D., 1998, A shortcut procedure for the design of mineral separation circuits, Minerals Engineering, 11 ( 2), 113-123. [6] Mendez D.A., Gálvez E.D., Cisternas LA, 2008, State of the art in the conceptual design of flotation circuits, Int. J. Miner. Process. In press, doi:10.1016/j.minpro.2008.09.009

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Modeling of separation process in a chromatographic column packed with porous adsorbents Georg Fieg a, Yan-Ming Gao b, Xing Luo a,b a

Institute of Process and Plant Engineering, Hamburg University of Technology, D21071 Hamburg, Germany, [email protected] b Institute of Thermal Engineering, University of Shanghai for Science and Technology, 200093 Shanghai, China, [email protected]

Abstract The adsorption-desorption process in a chromatographic column is simulated by using a numerical method. There are several process parameters which can affect the breakthrough curves, such as adsorption and desorption rates and mass transfer coefficient between the main solution flow and the particles. Moreover, for the chromatographic columns packed with porous adsorbents, the diffusivity of adsorbates in the porous adsorbents would play an important role. To design an effective separating process, it is necessary to analyse the effects of these parameters on the breakthrough curves. The numerical results were compared with the experimental data and good agreements between them were obtained. Keywords: separation, chromatography, porous adsorbent particles, trans-resveratrol

1. Introduction Chromatography is widely used in separation and purification processes. For a given set of adsorbent and solution, the breakthrough curves of different adsorbates might differ with each other, therefore it is possible to separate them from the mixture and get the products with high purity. There are a set of factors and process parameters which can affect the breakthrough curves significantly. Moreover, for the chromatographic columns packed with porous adsorbents, the diffusivity of the solution in the porous adsorbents would play an important role. To design an effective separating process, it is necessary to analyse the effects of these process parameters on breakthrough curves. A numerical method was developed to simulate the adsorption/desorption process. By matching the numerical results with the experimental data, the equivalent pore diffusivity of the solution can be estimated.

2. Mathematical model Consider a liquid solution flowing steadily through a chromatographic column filled with spherical porous particles. Because the interior diffusion is usually the governing part in the whole mass transport process, the adsorption and desorption could be considered in an equilibrium state, and therefore the adsorption isotherm can be used in the model. In the present work based on former activities [1, 2], the Langmuir isotherm is adopted. It is assumed that the solution flows uniformly through the column packed with spherical porous particles. The ratio of the particle diameter to the column diameter is very small, so that the axial dispersion in the main flow can be neglected. It is

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220

assumed that the spherical porous adsorbents are homogeneous, and the diffusion in the stagnant liquid in pores is equivalent to the diffusion in a spherical liquid body with an equivalent diffusivity, which might depend on the molecular diffusivity, internal porosity, pore tortuosity and concentration and should be determined experimentally or according to data from literature. The assumptions are summarized as follows: (1) The chromatographic process is isothermal. (2) The velocity of the main solution flow in the column is constant. It is uniformly distributed (plug flow). (3) Local equilibrium between the pore surface and the fluid exits and can be expressed by the Langmuir isotherm. (4) The solid matrix in the column consists of porous particles which have a spherical shape. (5) The diffusion in the pores can be modeled by an equivalent diffusivity. According to these assumptions, the mathematical model can be expressed as follows:

ε

∂c ∂c +u = βσ (cp,s − c) ∂τ ∂x

(1)

in which c is the species concentration ( kmol/m 3solution ) of the solution flow, u the superficial velocity (with respect to the empty column), ε the external porosity, σ the ratio of the total external area of the particles to the effective column volume ( m 2particles /m 3column ), and β the mass transfer coefficient between the main solution flow and the external surface. cp,s denotes the species concentrations of the stagnant fluid at the particle surface,

cp,s = cp

(2)

r =R

where R is the particle radius. The mass transfer in the stagnant fluid within the pores of the particles is caused by diffusion and is described by an equivalent diffusivity Dp,eq as:

εp

∂cp ∂τ

+ (1 − ε p )

∂c · ∂q 1 ∂ § ¨¨ Dp,eq r 2 p ¸¸ = 2 ∂r ¹ ∂τ r ∂r ©

(3)

in which ε p is the internal porosity of the particles. It is assumed that the adsorbate concentration in the pores q ( kmol/m 3solid ) follows the Langmuir isotherm,

q=

acp 1 + bcp

(4)

The initial and boundary conditions are as follows:

τ =0:

c = cp = 0

(5)

Modeling of Separation Process in a Chromatographic Column Packed with Porous Adsorbents

­c , 0 < τ ≤ τ 0 c=® 0 ¯0, τ > τ 0

x=0:

∂c p

r =0:

∂r

r =R:

Deq

(6)

=0

∂cp ∂r

221

(7)

= β ( c − cp )

(8)

If the mass transfer coefficient β is very large, then, Eq. (1) reduces to:

ε

∂cp ∂c ∂c +u = −σDeq ∂τ ∂x ∂r

(9) r=R

The boundary condition at the particle surface becomes:

r =R:

c = cp

(10)

The above governing equation system is non-linear and is solved with a finite difference method. Before the discretization, the following dimensionless variables and parameters are introduced:

x=

cp a cp c x u V ,τ = τ= τ, c= , cp = , q = L Vc εL c0 c0 1 + b cp

St m =

B=

βσL u

=

uε p R 2 ε pVR 2 βσVc βR , Pe p = = , Bi m = = B ⋅ St m Pe p  Dp εDp L Vc Dp εV

1− εp ε , a= a , b = c0b ε pσR εp

in which Vc is the effective volume of the column, c0 the injection concentration and β the film mass transfer coefficient. The dimensionless governing equation system is written as follows:

∂c ∂c + = St m (cp,s − c ) ∂τ ∂x H ( cp )

∂cp ∂τ

=

1 1 ∂ Pe p r 2 ∂r

(11)

§ 2 ∂cp ¨¨ r © ∂r

· ¸¸ ¹

(12)

τ =0:

c = cp = 0

(13)

x =0:

­1, 0 < τ ≤ V0 / Vc c =® ¯0, τ > V0 / Vc

(14)

G. Fieg et al.

222

r =0:

r=R:

∂cp

=0

(15)

= Bi m (c − cp )

(16)

∂q a = 1+ ∂cp (1 + b cp ) 2

(17)

∂r ∂cp ∂r

in which

H ( cp ) = 1 +

The above equation system is solved numerical by integrating Eq. (11) along its characteristic line s = τ + x .

3. Numerical simulation The numerical simulation was carried out using experimental data of chromatography for separation of trans-resveratrol from mixtures [3]. The length and inner diameter of the chromatographic column is 400mm and 20mm, respectively, resulting an effective column volume of 125ml. The hexane-acetone mixture was used as the solvent and the volumetric compositions of three test are 7:10, 8:10 and 9:10, respectively. The concentration of trans-resveratrol of the injection is 1.087 mg/ml, and the injection volume is 5 ml. The porous silica gel 60 (Merck KGaA) was filled in the column as the adsorbent. The measured breakthrough curves and the numerical simulation results are shown in Fig. 1. By matching the numerically calculated breakthrough curves with experimental data, it is found that the film mass transfer coefficient between the mobile phase and the particle surface tends to a very large value, therefore in the further analysis it is assumed that the film mass transfer coefficient β → ∞ . Since the parameter B = ε /(ε pσR) does

Fig. 1. Comparison of the numerical simulation with experimental data.

Modeling of Separation Process in a Chromatographic Column Packed with Porous Adsorbents

223

Table 1. Parameters used in the numerical simulations

Hexane-acetone (v/v)

7 :10

8 :10

9:10

Pep

0.253

0.157

0.077

Stm

’

’

’

B

0.8

0.8

0.8

a

2.785

1.495

3.298

a /b

0.023

0.285

0.745

not depend on the solvent, therefore, it should be a constant for the three tests. The matching by numerical calculation yields B = 0.8 for the porous particles. The parameters used in the numerical simulations are given in Table 1. It shows that the hexane/acetone composition has significant effect on the breakthrough curve of transresveratrol.

4. Conclusions A mathematic model is developed for the simulation of the adsorption/desorption of trans-resveratrol in a chromatographic column filled with porous silica gel and is solved numerically. The model take the porous diffusion of the adsorbate into account. Because the specific surface area of the porous particles is very large, the film mass transfer resistance between the mobile phase and the particle surface can be neglected. The model take the porous diffusion of the adsorbate into account, which depends on the molecular diffusivity, internal porosity, pore tortuosity and concentration and can be estimated by comparison of the breakthrough curve with numerical simulations.

5. Acknowledgements The authors would like to thank Dipl.-Ing. Matthias Johannink who has made the experiments in the present research work.

References [1] B. Niemeyer and X. Luo, A diffusion model for desorption of hazardous components from solids, Proceedings of the International Colloquium on Modelling of Material Processing, May 28-29, 1999, Riga, Lithuania. [2] X. Luo and B. Niemeyer, Modelling and Simulation of Transient Transport Processes Using Axial Dispersion Model, Scientific Computing in Chemical Engineering II, Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties, F. Keil, W. Mackens and H. Voß (Eds.), Springer-Verlag, Berlin, 167-174, 1999. [3] G. Fieg, N. Rümmeli, D. Sperling and M. Johannink, Experimentelle Untersuchungen der Extraktion von Resveratrol aus Wurzeln Polygonum Cuspidatum, ProcessNetJahrestagungen, Karlsruhe, 2008.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

225

Process and Equipment Design Optimising Product properties and attributes Peter M.M. Bongersa,b a

Unilever Research and Development, Oliver van Noortlaan 120, POBox 114, 3130 AC Vlaardingen, The Netherlands, [email protected] b Chemical Engineering and Chemistry, Eindhoven University of Technology, POBox 513, 5600 MB Eindhoven, [email protected]

Abstract Classically, when products have been developed at the bench, process engineers will search for equipment to manufacture the product at large scale. More than often, this search is constraint to the existing equipment base, or a catalog search for standard equipment. It is then not surprising, that the product manufactured at large scale, either deviates significantly from the intended product, and/or the incurred costs to manufacture the product are much higher than anticipated because the equipment has not been designed for this product, or product range. This paper describes the combined design of an extruder equipment and the operating conditions to process ice cream with desired product attributes. Keywords: process synthesis, structured products, process development, equipment design, ice cream freezing process 1. Introduction 1.1. Classical ice cream freezing process Freezing of ice cream is performed in a scraped surface heat exchanger, where rotating scraper blades continually remove frozen product from the cooled surface. In this operation mode a high heat transfer rate is maintained. It is within the scraped surface heat exchanger that much of the product structuring occurs. These product structuring mechanisms include ice crystallisation, aeration and fat de-emulsification. Then, the ice cream product is formed and sequentially hardened in a hardening tunnel, where cold air is blown over the product. In this hardening tunnel, the remaining water is frozen. As the product is quiescently frozen, the air cells and ice crystals grow, reducing the product quality. An alternative is to replace the hardening tunnel by a single screw extruder, in which further freezing and mixing occurs, preventing air cell and ice crystal to grow and, subsequently, increasing the product quality. The quality of the final product depends to a large degree on how these structuring processes have been carried out.

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226

1.2. Design problem To optimise the freezing process for a given product formulation or to maintain a desired product quality on scale-up, it is necessary to know the local conditions inside the heat exchanger and how these change with operating conditions. Since direct measurement of temperature and shear conditions in a single screw extruder barrel is difficult to achieve, a mathematical modelling approach has been applied in this work to predict these variables. However, consumers do not buy ice cream on their bulk properties, but on how they perceive the products. Hence, there is a need to extend process models with sensory attributes. Figure 1 shows how the process model can be extended into a model chain from raw materials, equipment and operational conditions through sensory attributes to consumer liking. operational conditions

raw materials

process function

external disturbances

physical attributes

consumer liking

sensory attributes

property function

pressure temperature air/crystal sizes

consumer function

smoothness iciness creaminess

Figure 1 Process, property and consumer function for ice cream

In the design phase there is the need to evaluate concepts without ‘large’ and expensive consumer trials. For this purpose sensory attributes measured by a trained QDA panel, are used to determine consumer benefits. 2. Equipment and process design To design the equipment and operating conditions for an ice cream with desired attributes we need to 1. obtain a dynamic model of the process function 2. obtain a model for the property function 3. combine the models 4. determine the optimal geometry and operating conditions

Process and Equipment Design Optimising Product Properties and Attributes

227

2.1. Process model At this level the strategy is to describe the process mathematically using the most simple model that fulfils the purpose. Additionally, the process model relies on the observation that model predictions can be viewed as a chain of phenomena, in which a rough description of all phenomena provides better predictions than a detailed description of only one phenomenon. The model has been described by Bongers [1].

Figure 2 Equipment overview

2.2. Property model Also the property model [2] (Bongers, 2008b) should be as simple as possible, but not too simplistic. This statement means that for each of the sensory parameters we need to determine the ‘simplest’ relation. On the data set three types of describing functions will be determined: constant, linear regression or neural network to describe the nonlinearities. The neurons weight all inputs and provide an output via the activation

function. The complexity of the neural networks used will be determined by the number of nodes in the hidden layer (2,3,5 or 7). The activation applied in this application is a hyperbolic function. The selection of the models to use will be done by trading-off the prediction error against the number of parameters used, i.e. the AIC [3].

P.M.M. Bongers

228

2.3. Integrated model Both models are integrated in Matlab/Simulink [4], and control loops are added to stabilise the process. time Clock

To Workspace1

Torque

display

Torque

Torque Sensor Range

CoolTemp Coolant Temperature PI [TTIME TorqueSetpointIn

] Torque Controller

Rate Limiter

CoolTemp actuator

[TIME PressureSetpointIn ] PI

Rate Limiter 1

Pressure Controller

Speed actuator RPMout

Extruder

Rotor Speed Pressure Sensor Range Pin Inlet Pressure

Figure 3 Integrated model schematic

2.4. Determine the optimal geometry and operating conditions Determination of the optimal geometry and operating conditions is cast in a non-linear, bounded, optimisation problem. As the aim is to maximise product quality the maximisation criterion is the weighted sum of creaminess and extrusion temperature. The production rate has been fixed by the manufacturing end. Operating conditions that can be chosen are the rotational speed and torque of the screw, both being limited by equipment constraints. Furthermore, as cooling is applied by evaporating ammonia, the minimum ammonia evaporation pressure is also fixed by the manufacturing end. Key equipment parameters that can be varied are shown in figure 4.

θ BARREL

H

SCREW wc

Db

wf

•Extrusion temperature •Creaminess

ef Sp

•Pitch angle •Number of thread starts •Channel depth •Barrel length •Barrel diameter

Optimisation function: •MATLAB: “fconstr”

Figure 4 Schematic representation of the optimisation problem

It must be noted that also these equipment parameters are bounded. For example only an integer number of threadstarts are allowed, as well as the barrel diameter has to be a number that can be manufactured ‘easily’.

Process and Equipment Design Optimising Product Properties and Attributes

229

2.5. Results The outcome of the optimisation routine was, to some extent, counter intuitive. Whereas all existing extruders in the polymer industry have a large L/D and are running at high speeds, this extruder has a very small L/D and is running at very low speeds. This difference can be explained by the fact that polymer screws are mainly used for heating the product, whereas in this application we want to freeze the product. To minimise heating by viscous dissipation, the rotational speed needs to be low and in order to achieve the throughput, the annulus for product flow needs to be of a large diameter. Another key difference is the pitch angle, which was determined at approximately 42°, which is significantly higher than the usual 11° for solids conveying. The large pitch angle can be explained by the fact that ice cream at very low temperatures still behaves like a liquids if it is continuously stirred. All the above differences resulted in a novel design of an ice cream extruder, as it has been patented [5]. 3. Equipment Based on the model based design, an actual full scale machine was designed, built, installed and commissioned (shown in figure 5).

Figure 5 Actual prototype

The actual prototype was performing within the accuracies specified by the model. 4. Conclusions and recommendations A model based equipment and process design has been shown in which both the product properties as well as the attributes (creaminess) have been optimised. A feasible set of equipment parameters have been calculated. These have been implemented and validated on both pilot plant and factory scale. The results are filed in patent WO 00172697 [5]. It is recommended to extend these models to incorporate different processing steps and more ice cream groups.

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230

References [1] Bongers, P.M.M. (2008a) Model of the Product Properties for Process Synthesis. Proc. 18th European Symposium on Computer Aided Process Engineering [2] Bongers, P.M.M., I. Campbell (2008b) A Heat Transfer Model of an Ice Cream Single Screw Extruder. Proc. 18th European Symposium on Computer Aided Process Engineering [3] Akaike, H (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (6): 716–723. [4] SIMULINK (1992) - A Program for Simulating Dynamic Systems, The Mathworks Inc., Natick, MA, USA. [5] Bakker, B.H. P.M.M. Bongers, W. Wang-Nolan (2000). Process And Apparatus For Production Of A Frozen Food Product. Patent No: Wo2000072697a1

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

231

Product Driven Process Synthesis Methodology Peter M.M. Bongersa,b, Cristhian Almeida-Riverab Chemical Engineering and Chemistry, Eindhoven University of Technology, POBox a 513, 5600 MB Eindhoven, [email protected] Unilever Food and Health Research Institute, Oliver van Noortlaan 120, POBox 114, b 3130 AC Vlaardingen, The Netherlands, [email protected]

Abstract In the last ten years much more processes are being reported to be designed through a process synthesis approach. It has been recognized during those years that (i) processes for structured products are more difficult to design through process synthesis; (ii) process synthesis is disconnected from product development. In a response to those shortfalls a number of authors have described that the gaps need to be filled, however no methodology extension has been proposed. In this work, we will present extensions to the conceptual process synthesis methodology to include (structured) product design. The whole design methodology spans from how the new product can enlighten the consumer, financial and supply chain boundary conditions, through an optimal flowsheet able to produce the desired product cost effectively. A real case study will be used to illustrate the applicability and scope of the proposed methodology Keywords: process synthesis, structured products, product development

1. Introduction All leading fast moving consumer goods companies are rapidly transforming from general manufacturing hubs of loosely connected products to companies delivering health, wellness and nutrition. Manufacturing in a responsible and sustainable way products within those strategic areas imposes technical challenges to work on and requires the development of R&D capabilities. These challenges and capabilities have the clear aim of delivering a product with all associated benefits at a short time to market and at a reduced manufacturing expenditure. Finding and creating business opportunities to be brought successfully to the market [1] is the response of leading companies to the rapidly changing environment, characterized by slim profit margins and fierce competitiveness. A key activity in this innovation process is the actual creation of the conversion or manufacturing system. This creative activity, referred to as process synthesis (PS), accounts for a cost of 2% of the total design costs and allows fixing 80% of the combined capital and operational costs [2]. In contrast to its relevance, PS is normally carried out by copying existing processes or scaling-up lab scale non-optimized protocols. Our challenge is addressing the PS problem from a systems engineering perspective and proposing a structured approach.

232

P.M.M. Bongers and C. Almeida-Rivera

Process Synthesis takes place in all conceptual process engineering steps within the innovation process and includes the selection of desired process unit operations, their interconnections and a preliminary design and cost estimation of the major units with key dimensions and operating conditions. Although the definition of PS might suggest a straight-forward and viable activity, the synthesis is complicated by the nontrivial tasks of: (i) identifying and sequencing the physical and chemical tasks to achieve specific transformations; (ii) selecting feasible types of unit operations to perform these tasks; (iii) finding ranges of operating conditions per unit operation; (iv) establishing connectivity between units with respect to mass and energy streams; (v) selecting suitable equipment options and dimensioning; and (vi) control the process operations. Moreover, the synthesis activity increases in complexity due to the combinatorial explosion of potential options. The number of possible combinations can easily run into many thousands [2]. The PS methodology is regarded in this context as a way to beat the problem complexity.

2. A Product-driven Process Synthesis (PDPS) Approach in Foods It is now well-established by industry and academia that chemical industry focus has shifted from a process-centered orientation to a product-centered one [3]. During the last decades we have experienced how the commodity chemical business is gradually releasing its dominating role towards higher-added value products, such as specialty chemicals and consumer products. This trend is further reflected in the increasing number of scientific publications addressing product and process design [3-8], textbooks [9] and undergraduate/graduate courses in chemical process design [10;11]. Stretching the boundaries of the synthesis activity towards products has brought challenges for the chemical and process engineers. Those refreshing problems need the development of novel methods and tools, involving areas like the fundamental understanding of the product-process interactions, multi-level modelling of consumer products, property models for products with internal micro-structure, prediction of consumer liking and its dependence on ingredients and processes, etc. Despite the maturity of most process synthesis approaches for chemical products, they fall short when it comes to extending its scope and applicability to food products. This drawback of current approaches is derived from the intrinsic differences between bulk chemicals and food products, and include for the case of structure food products [12]: (i) food products are typically structured products where the performance is determined by the internal microstructure of the product; (ii) unit operations are quite different, involving less reaction and separation tasks and more mixing and preservation; (iii) food processes are generally multi product processes, where a same production line can accommodate the manufacturing of different products with different properties; and (iv) cleaning is an essential and non-negotiable task within the operational policy. Thus, in contrast to bulk chemicals, structured products are characterized not only by the level of each ingredient (i.e. composition, purity, physical state, temperature, pressure, etc.), but also by the relative spatial arrangement of each ingredient and

Product Driven Process Synthesis Methodology

233

performance behaviour. All these features are responsible for the exclusive attributes of structured products (e.g. creaminess of an ice-cream, spoonability of a mayonnaise, spreadability of a margarine, etc).

Figure 1. Lamellar structured hair conditioner[3] (left); confocal micrograph of a full-fat O/W emulsion (center); microscope photograph of an ice-cream matrix (right)

Aiming at a more structured approach towards the synthesis of product and processes in the food and drink sector, we proposed a methodology termed product-driven process synthesis (PDPS). This approach exploits the synergy of combining product and process synthesis workstreams and is based on the systems engineering strategy. Thus, it is supported by decomposing the problem into a hierarchy of design levels of increasing refinement (Table 1), where complex and emerging decisions are made to proceed from one level to another.

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234

Table 1. Description of each level of the PDPS approach Level Generic description -2

Framing level. We embed the design into the overall project. Description of the background of the project and the business context, overall supply chain considerations (product portfolio, demand profiles, regional spread, …)

-1

Consumer wants. We obtain the consumer wants (consumer likings, focus groups, interviews) in qualitative descriptions and translate them into quantifiable product attributes.

0

Product attributes. We map the quantifiable product attributes onto the product properties, which are measurable.

1

Input-output level. We make a complete specification of the output. We choose inputs (ingredients) and the descriptors of the output (microstructure, flavour profile and microbiological status). We determine performance parameters such as quality, economic potential, hygienic considerations, flexibility, pumpability, availability...

2

Task network. We define the fundamental tasks needed to go from input to output, taken from a cluster of tasks and its subgroup. Furthermore, tasks that require a certain sequence or that belong together without any doubt are grouped, to reduce the number of sequencing possibilities. Then, a network is made from the selected tasks and clusters.

3

Mechanism and operational window. We select mechanism and principles that can be used to perform a task. This step includes the driving forces and kinetics. Furthermore, the operational window of the problem (time, P, pH, shear, T, etc.) is defined.

4

Multi product integration. The outcomes of steps 1 – 3 for the different products are compared to look for overlap and possibilities to combine the production.

5

Equipment selection and design. The operating units are selected. Integration possibilities (e.g. by combining tasks with the same driving force that are close together in task network) and controllability should be considered. The operational window from step 3 is compared to the operating boundaries of the unit. Then, the final design of the units (only of the key dimension) and final flowchart are made.

6

Multi product-equipment integration. We optimise the interaction of the various unit operations in the flowsheet (plant-wide control). Multi-stage scheduling of the multiple products is applied, fed by the run-strategy based on the product demand and portfolio.

Moreover, each level in the PDPS methodology features the same, uniform sequence of activities (scope and knowledge → generate alternatives → analyze performance of alternatives → evaluate and select → report), which have been derived from the pioneering work of Douglas [2], Siirola [13] and further extended by Bermingham [14], Almeida-Rivera et al. [15], Meeuse et al. [16;17], Stappen [17] and recent internal Unilever work. The input of the PDPS methodology is a complete and comprehensive specification of the desired product(s), raw materials along with any other requirements the process needs to fulfil (e.g. the capacity requirements, cost requirements, hygiene standards, etc). Moreover, the methodology is fed by consumer preference studies and business

Product Driven Process Synthesis Methodology

235

relevance involving the desired product. The output of a process synthesis exercise is a flowsheet structure, along with unit interconnections, operating conditions and key dimensions of key equipment units. Additionally, controllability, reliability and flexibility of the proposed process are accounted for within the methodology. Recent efforts in the development of PDPS methodologies have been focusing on broadening the design scope to consumer preferences, product attributes, process variables and supply chain considerations [18;19]. The applicability and scope of the proposed methodology has been demonstrated using industrial cases as examples. These case studies include the synthesis of a novel freezing equipment for the production of ice-cream, a novel process for the production of ice-cream premix and a novel process for the production of low-fat starch-free mayonnaise.

3. Conclusions In this contribution we present our approach towards product-driven process synthesis. The proposed methodology is composed of 9 levels of increasing degree of complexity and where complex and emerging decisions are made to proceed from one level to another. The whole design methodology spans from how the new product can enlighten the consumer, financial and supply chain boundary conditions, through an optimal flowsheet able to produce the desired product cost effectively. The applicability and scope of this methodology has been demonstrated using industrial cases as examples. A model-based strategy was implemented at various levels of the methodology, stressing the relevance of modelling towards more time- and cost-effective process synthesis.

References [1] Verloop, J. (2004). Insight in Innovation - Managing Innovation by Understanding the Laws of Innovation. Amsterdam, Elsevier [2] Douglas, J. (1988). Conceptual design of chemical process. USA, McGraw-Hill [3] Hill, M. (2004). Product and Process Design for Structured Products. AIChE Journal, 50(8),1656-1661 [4] Gani, R. (2004). Chemical product design: challenges and opportunities. Computers and Chemical Engineering, 28,2441-2457 [5] Edwards, M. F. (2006). Product engineering: Some challenges for Chemical Engineers. Transactions of the Institute of Chemical Engineers - Part A, 84(A4),255-260 [6] Norton, I., Fryer, P. and Moore, S. (2006). Product/Process Integration in food Manufacture: Engineering Sustained Health. AIChE Journal, 52(5),1632-1640 [7] Wibowo, C. and Ng, K. M. (2002). Product-Centered Processing: Manufacture of Chemical-Based Consumer Products. AIChE Journal, 48(6),1212-1230 [8] Wibowo, C. and Ng, K. M. (2001). Product-Oriented Process Synthesis and Development: Creams and Pastes. AIChE Journal, 47(12),2746-2767 [9] Cussler, E. L. and Moggridge, G. D. (2001). Chemical Product Design. New York, Cambridge Series in Chemical Engineering [10] Moggridge, G. D. and Cussler, E. L. (2000). An Introduction to Chemical Product Design. Transactions of the Institute of Chemical Engineers - Part A, 78,5-11 [11] Cussler, E. L. and Wei, J. (2003). Chemical Product Engineering. AIChE Journal, 49(5),1072-1075

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P.M.M. Bongers and C. Almeida-Rivera [12] Meeuse, F. M. (2005). Process Synthesis Applied to the Food Industry. Proceedings of the European Symposium of Computer Aided Process Engineering - 15, Barcelona [13] Siirola, J. J. (1996). Strategic process synthesis: advances in the hierarchical approach. Computers and Chemical Engineering, 20(SS),S1637-S1643 [14] Bermingham, S. (2003). A design procedure and predictive models for solution crystallisation processes. PhD thesis, Delft University of Technology [15] Almeida-Rivera, C. P., Swinkels, P. L. J. and Grievink, J. (2004). Designing reactive distillation processes: present and future. Computers and Chemical Engineering, 28(10),1997-2020 [16] Meeuse, F. M., Grievink, J., Verheijen, P. J. T. and Stappen-vander, M. L. M. (1999). Conceptual design of processes for structured products. Fifth conference on Foundations of Computer Aided Process Design, Breckenridge, USA [17] Stappen-vander, M. L. M. (2005). Process Synthesis Methodology for Structured (Food) Products. NPT Procestechnologie, 6,22-24 [18] Almeida-Rivera, C. P., Jain, P., Bruin, S. and Bongers, P. (2007). Integrated product and process design approach for the rationalization of food products. Computer-Aided Chemical Engineering, 28,449-454 [19] Ridder, K., Almeida-Rivera, C. P., Bongers, P., Bruin, S. and Flapper, S. D. (2008). Multi-Criteria Decision Making in Product-driven Process Synthesis. Computer-Aided Chemical Engineering, 25,1021-1026

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

237

Property based product design using combined property clustering and GC+ techniques Nishanth G. Chemmangattuvalappil, Charles C. Solvason, Mario R.Eden Department of Chemical Engineering, Auburn University, Auburn, AL 36849 USA

Abstract Property integration techniques have enabled a systematic procedure for the identification of suitable molecules to meet certain process performance. Algorithms exist for identifying molecules with a given set of properties by combining property clustering and group contribution methods (GCM). Yet, there are situations when the property contributions of some of the molecular groups of interest are unavailable in literature. To address this limitation, an algorithm has been developed to include the property contributions predicted by combined GCM and connectivity index (GC+) method into the cluster space. Keywords: Property clustering, Molecular design, GC+ method

1. Introduction The integrated property clustering and group contribution (GC) techniques provided tools to design molecules corresponding to optimum process performance [1]. However the property contributions of all the candidate molecular groups may not be available in the literature. Recently, techniques have been developed to predict the property contributions of molecular groups using zero order and first order connectivity indices (CI) [2]. So, there should be an algorithm to include the property contributions of the CI groups into the clustering framework. As the complexity of the target molecule increases, the higher orders of molecular groups will have significant effects in their final properties. So, the methodology should account for the effects of higher order molecular groups on properties before committing to any molecular structure.

2. Combined GC-CI Method for Pure Component Property Estimation In GCM, the property function f(Y) of a compound is estimated as the sum of property contributions of all the molecular groups present in the structure [3]:

§ · § · § · f (Y ) = ¨ ¦ N i C i ¸ + ¨ ¦ N s C s ¸ + ¨ ¦ N t C t ¸ © i ¹ © s ¹ © t ¹

(1)

Ni, Ns and Nt are the numbers of first, second and third order groups and Ci, Cs, Ct are their respective property contributions. If the contributions of any group are unavailable, a connectivity index (CI) based expression can be used [2]:

(

)

( )

f (Y * ) = ¦ (ai Ai ) + b v χ 0 + 2c v χ 1 + d i

(2)

Here ȞȤ0 and ȞȤ1 are the zero and first order CIs, Ai is the number of atom i, ai is the estimated contribution of atom i, while b, c and d are adjustable parameters. The values of adjustable parameters are available in literature [2].

N.G. Chemmangattuvalappil et al.

238

3. Molecular Design using Property Clustering Methods for the application of GCM for molecular design have been developed using property clustering [1,4]. If Pjg is the contribution of property j from group g, ng is the total number of that group in the molecule, molecular property operator ȥMj, normalized molecular property operator ȍM, Augmented property index AUP and molecular property cluster CMj are defined as: Ng

ψ ( Pj ) = ¦ ng Pjg M j

(3)

g =1

ȍ

M j

=

ȥ j (P ji ) ȥ ref j (P ji )

NP

A UP = ¦ ȍ

M j

C

j =1

M j

=

ȍ Mj AUP

(4)

For the groups whose property contributions are not available, the property operator is defined by Eq. 2. Note that there will be different values for the same group corresponding to different bonds it can make with other groups.

ψ jk ( Pj ) = ¦ (a m,i Am,i ) + b( v χ 0 )m + 2c( v χ 1 )mk

(5)

i

3.1. Visual Solution The standard algorithm for molecular design using molecular property clusters [1] has been extended to include CI groups as explained below: 1. The property targets must be converted to property clusters using the Eqs. 3 and 4 and form a target region on a ternary diagram (simplex) according to the algorithm developed by El-Halwagi et al. [4]. The feasibility region boundaries can be represented by six unique points as shown in fig. 1. 2.

Generate the first order molecular property operators. For non-GC groups, identify the possible types of atoms that can form bonds with it and estimate the possible zero order and first order CI values. Generate the molecular property operators based on CI. Separate operators have to be calculated for different types of bonds. Form a locus of points in the simplex with CI groups. Calculate AUP and molecular cluster values of all the groups and plot all the molecular groups on the simplex.

3.

Mix different molecular groups according to the procedure developed by Eljack et al. [3,4]. When mixing a CI group with a GC group, the number of hydrogen atoms bonded with the GC group will define the corresponding group in the CI locus. The CI group corresponding to the same number of hydrogen atoms in the GC group must be chosen for mixing. In the example shown in figure 1, the designer wants to mix a CH2CO group with a CHF2 group. The heat of vaporization value of CHF2 group is not available in literature. So, according to the GC+ method, the cluster values for CHF2 groups which form bonds with carbon atoms with different numbers of hydrogen are estimated and plotted on the simplex. As the carbon atom in CH2CO has two hydrogen atoms bonded to it, the cluster corresponding to (CHF2)-C (with two H atoms) is to be selected from the locus of CHF2 groups.

4.

Formulations with zero free bonds, AUP value inside the AUP range of the sink and cluster location inside the feasibility region are possible solutions.

Property Based Product Design Using Combined Property Clustering and GC + Techniques 239 2 M1: O=S(CH3COH) M2: O=S(CH3COCH2)CH2CH3 M3: O=S(CH)(CH 0.1 2)5(CH3) M4: O=S(CH)(CH2)2(OH) (CH3)2 M5: O=S(CH 0.2 2CO)CH20.8

C2 0.1

0.2

CH-CH

0.7

0.3

CH2-CH

0.6

O

2C

0.6 0.5

0.7

CH

0.5

g10.6 : SO g2: aC g3: aCH g4: CH3 g5: CH2 0.4 g6: CH g7: CH3CO 0.3 g8: CH2CO

0.4

0.8

0.4

C-CH

0.7

0.3

0.9

0.6

0.4

C.I. Locus for CHF2 group 0.7

(Ω (Ω

m in 1 m ax 1

, Ω m2 in , Ω 3m ax0.8) (Ω 1m in , Ω m2 ax , Ω 3m ax ) (Ω 1m in , Ω m2 ax , Ω 3m in )

0.8 0

m in )(Ω 1m ax , Ω m2 in , Ω 3m in ) (Ω 1m ax , Ω m2 in , Ω 3m ax ) , Ω m2 ax , Ω0.9 3

Figure 1: CI+GC group mixing example

CI group locus

0.9

0.2

0.1

C3

C1 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 2: Metal degreaser problem

3.2. Algebraic Approach The visual solution mentioned before has the following drawbacks 1. Only three properties can be considered at a time. 2. The property operators in visual solution are formed based only on first order groups and by CI groups. So, the applicability of this method is limited only for the design of simple monofunctional molecules. 3. Generating a complete solution set can be a tedious process. The algebraic approach is developed to solve the problems in which the above drawbacks are significant. Here, the first step is to represent the property target as a function of molecular groups from GCM models [5,6]. The bounds on each property are:

Pijlow er ≤ Pij ≤ Pijupper j= 1,2,…….Nj ; i=1,2,…

(6)

Ω min ≤ Ωij ≤ Ω max j j

(7)

Here, ȍij is the property of molecule i. It can be represented in terms of first order groups as follows Ng

Ω ijf = ¦ n g Ω jg 1

(8)

g =1

Where, ȍjg1 is the normalized property operator of first order group, g. For any missing first order group and/or property contribution, the value of ȍij obtained through CI method has to be used. But, since there are many possible ȍij values for each missing group based on the bonded atoms, it is not a straight forward choice. Since the objective of this work is to narrow down the search space of possible compounds, it will be more logical to select the least value of the possible ȍij’s. This will generate more number of feasible solutions and ensure that no correct solution left undetected. Again, since the change in bond indices will not create a significant impact on the property contribution of the complete group, this assumption will not produce a large number of infeasible solutions. So, the molecular operator for the property contribution of the CI group is given by Eq. 9 and the corrected first order property contribution is given by Eq. 10.

N.G. Chemmangattuvalappil et al.

240

Ω CI = Min(Ω jgm )

(9)

Ng

Ω ijf =

¦n Ω g

Nm

jg1

g =1

+

¦n

m

Ω CI

(10)

m =1

Where ȍjg1 is the normalized property operator of first order group g, nm is the number of missing groups and ȍCI is its minimum contribution. Let the number of first order groups given in the set (ngk: ngn) form the second order group s. Ș is the number of occurrences of one specific first order group in a selected second order group. Suppose, some of the second order groups are completely overlapped by a bigger second order group and some of the former groups are not overlapped. In that case, if (ngk: ngn) has subsets of smaller second order groups (ngl: ngm) with some of the first order components of (ngk: ngn) then, the normalized property operator for the second order group contribution ȍijs is: Ns Ns ª n ·º § n gk n gn · §n n · §n ¸¸Ω jg 2 + ¦ « Min ¨¨ gl : gm ¸¸ − Min ¨¨ gk : gn ¸¸»Ω ∗jg 2 Ω ijs = ¦ Min ¨¨ : s =1 s =1 ¬ © ηk ηn ¹ © ηl ηm ¹ © η k η n ¹¼

(11)

Here ȍjg2 and ȍ*jg2 are the property contributions of the group s and the smaller unoverlapped second order group respectively. If t is the index for third order groups, the normalized property operator for molecule i is:

Ω ij = Ω ijf + Ω ijs + Ω ijt

(12)

A few structural constraints must also be satisfied along with the property constraints. The number of each group should be non-negative. The minimum number of molecular fragments forming a ring must be three and for the design of aromatic compounds, there must be multiples of six aromatic carbon atoms. The constraints must be imposed considering the fused ring compounds too along with poly ring compounds. For instance, if the maximum numbers of aromatic carbon atoms are 16, then the value of Ȉnac can be 6, 10, 12, 13, 14, and 16. The values other than multiples of six correspond to possible fused ring compounds. n

g

≥ 0

¦

n gr ≥ 3 or 0

¦n

ac

= 0,6,12.....

(13)

Where ngr is the number of groups forming ring compounds and nac is the number of aromatic carbon atoms. The Free Bond Number (FBN) is the number of valance electrons in each molecular string [3] and is represented mathematically in Eq. 14:

§ FBN = n g FBN g − 2¨ ¨ g =1 © Ng

¦

FBN = 0

Ng

¦n g =1

g

· − 1¸ − 2 N r ¸ ¹

(14)

(15)

Where, Nr is the number of rings (including aromatic groups) in the final molecule and FBNg is the number of free bonds in each group. The molecule’s FBN should be zero to insure complete molecular structure with no charge/no free bonds in the final molecule.

Property Based Product Design Using Combined Property Clustering and GC + Techniques 241

4. Case Study - Identification of Alternative Metal Degreasing Solvent A case study on a metal degreasing process has been revisited [7]. Here, we are designing the molecules that satisfy the property targets shown in table 1 identified during the process design stage. The groups being considered for designing the molecule are shown in fig. 2. The ǻhv value of the SO group is not available in literature. To estimate the ǻhv value, the CI method can be used. The SO group can form bonds with two other groups as it has two free bonds in the structure. The possible values for ǻhv for the SO group with all possible substituents are estimated and given in table 2. 4.1. Visual Solution The target properties, their bounds, property operators, their reference values, and the normalized property operator are given in Table 1. Table 1. Property targets and operators Property Hv (kJ/mol) Tb (K) Tm (K)

ȥj Hv-hv0 exp(Tb/tb0) exp(Tm/tm0)

GC+ expression Ȉnghv1+f(Y*) Ȉngtb1 Ȉngtm1

Ȍjref 20 4 4

LB 50 480 280

UB 100 540 350

ȍmin 1.53 2.16 1.67

ȍmax 3.53 2.83 2.68

The property targets are converted into corresponding cluster values and the boundaries of the feasibility region is determined. These points are plotted on a simplex to obtain the feasibility region corresponding to the target properties. Now, the property contributions of the groups of interest are obtained and converted into normalized property operators. But, the property contribution of the SO group for heat of vaporization is not available in literature. To use the CI method to calculate the value of Hv, the values of zero and first order connectivity indices of SO group corresponding to potential bonds are estimated. Here, the SO group has two valence electrons in its structure and two bonds are possible from an SO group. In this case study, there are 4 different types of carbon atoms (with 3, 2 and 1 hydrogen and aromatic C) that can potentially form bonds with the SO group. The estimated values are shown in Tables 2. Now, Eq. 5 is used to estimate contribution of the SO group for heat of vaporization for the different possible bonds which are given in Table 2. So, there are 10 property operators for the SO group. The operators are normalized and the clusters for all groups are calculated as shown in figure 2. Note that all cluster locations of the SO groups are close and it is possible to form a locus of SO groups. The reason for such a close range of values is because the major contribution to the property is from the zero order CI which depends only on the atoms. The GC groups are scattered in the different locations of the simplex. Now, the cluster values of different combinations of molecular groups are plotted on the simplex by satisfying the FBN constraint defined in Eq. (15). While mixing SO groups with other groups make sure that the SO group corresponding to the proper valence delta is used. For instance, if one CH2CO and one CH3 are combined with the SO group, the SO group corresponding to carbon atoms with three hydrogen and two hydrogen are to be used. The molecular group formulations which fall inside the feasibility region and satisfy the AUP constraint of the sink are potential solutions. A part of the final solution is shown in Figure 2. 4.2. Algebraic Solution Here, the first step is to estimate the maximum possible number of each group. For the hv value of the SO group, the lowest among the estimated values is being considered,

N.G. Chemmangattuvalappil et al.

242

which is 16.68 kJ/mol. Now, Eq.6 is used to generate the inequality expressions corresponding to each property. All first order groups are maximized subject to the structural constraints in Eqs. 11 and 12: SO: 1 aC: 1 aCH: 5 CH3: 6 CH2: 8 CH: 4 OH: 1 CH3CO:1 CH2CO:2 Higher order groups possible from these first order groups are listed in table 3. All possible combinations of first order groups are generated and the property contributions from higher order groups have been estimated using Eq. 11. The molecular property operators are generated subject to the constraints in Eqs. 13-15 and AUP values for each combination are calculated. The combinations whose AUP values are within the limits are potential solutions. The property values of those combinations are back calculated to confirm they are real solutions. A part of the final solution is shown in table 4. Table 2: CI group property data 0

Group

Ȥ

C3 C3 C3 C2 C3 C1 C3aC C2C2 C2 C1 C2aC C1C1 C1aC aCaC

1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02

Ȥ

1

0.56 0.47 0.43 0.33 0.40 0.38 0.31 0.35 0.30 0.21

Table 3: 2nd order groups

hv

(CH3)2CH

17.72 17.26 17.06 16.58 16.94 16.80 16.46 16.68 16.40 16.28

CH(CH3)CH(CH3) CH3COCH2 CH3COCH CHOH CH3COCHnOH CHm(OH)CHn

Table 4: Part of solution

Final solution (CH3CO)CH2(SO)CH3 CH3CH2(SO)CH2COCH3 CH3CO(SO)CH3 CH3(SO)CH(CH3)COCH3 CH3(SO)CH(OH)CH3 CH3(CH2CO)SOCH(CH3)2 (CH3)2SO(CH2)3CH3 CH3(CH2)2SO(CH2)2CH3 CH3(CH2CO)SOCH2CH3

5. Conclusions In this work, a modified algorithm has been developed for molecular design using GC+ technique when the property contributions of some of the candidate groups are not available in literature. The expressions for molecular property operators developed in our previous paper have been modified using the third order groups to make the design more accurate. The future work need to be focused on incorporating more structural information during molecular design.

6. References [1] F.T. Eljack, M.R. Eden, V. Kazantzi, M.M. El-Halwagi (2007), AIChE Journal, 53(5), 1232-1239. [2] R. Gani, P.M. Harper, M. Hostrup (2005) Ind.Eng.Chem.Res. 44, 7262-7269 [3] J. Marrero, R. Gani (2001), Fluid Phase Equilibria, 183/184, 183-208. [4] M.D. Shelley, M.M. El-Halwagi (2000) Computers & Chemical Engineering, 24, 20812091. [5] N.G. Chemmangattuvalappil, C.C. Solvason, F.T. Eljack, M.R. Eden (2008), Computers & Chemical Engineering (in press) [6] F. T. Eljack, C.C. Solvason and M.R. Eden (2007), Computer Aided Chemical Engineering 24, T2-326 [7] M.R. Eden, S.B. Jorgensen, R. Gani, M.M. El-Halwagi (2004), Chemical Engineering & Processing, 43, 595-608.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

243

Reaction networks – A rapid screening method Anna Besler, Andreas Harwardt, Wolfgang Marquardt a a

AVT – Process Systems Engineering, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany, [email protected]

Abstract Innovative and sustainable processes for the conversion of whole plants into fuels are developed in the cluster of excellence “Tailor-Made Fuels from Biomass” (TMFB) at RWTH Aachen University. In order to guarantee an efficient production a large number of process alternatives needs to be evaluated systematically at an early design stage, including both preliminary research results and literature knowledge. In order to review potential chemical synthesis routes, a rapid screening method is developed to detect and to classify all combinations of reaction steps using mixed integer programming. Based on these results promising reaction pathways as well as bottlenecks can be identified and a first insight in possible process chains can be gained. This paper introduces the scope and the methodology of the approach and illustrates both on an appropriate example. Keywords: reaction network, process synthesis, biofuels, MILP

1. Motivation Renewable raw materials are attaining an increasing interest in the production of transportation fuels. The TMFB project takes an interdisciplinary research approach towards new synthetic fuels. These fuels will be blends of a few well-defined oxygenated components with tailored properties for novel low temperature combustion engines. In contrast to other approaches selective bio- and chemo-catalysis is applied to preserve the synthesis power of nature [1]. In this approach various types of feedstock are converted into platform chemicals followed by bio- and chemo-catalysis into different fuel components. Since new concepts for the re-functionalization of biomass are required, a variety of reaction pathways and associated process alternatives can be applied to produce novel target fuel molecules. Even though process engineering is challenging within the novel field of biorenewables, a systematic evaluation of possible combinations is absolutely necessary: the economic performance of the production process from raw materials to fuel components strongly depends on the fundamental decisions regarding the reaction pathways. In order to identify a coarse process structure, possible reaction pathways can be evaluated by means of a flux analysis which is based on a reaction network including all potential reactions from starting materials to target molecules. By applying well established methods of metabolic pathway analysis, all possible reaction pathways can be identified systematically and ranked subsequently by multiple criteria.

2. Introduction Metabolic pathway analysis summarizes different concepts which are used to understand biochemical processes in particular organisms [2, 3]. Flux-balance models for metabolic networks help to design experiments for the identification of the exact metabolism, to distinguish between different operating states or to locate possibilities

244

A. Besler et al.

for metabolic engineering. Among others, the mathematical method of extreme pathways is one of the most promising concepts [4]. Here the metabolic network is modeled by nodes (metabolites) and connections (reactions) such that material flows can be traced by formulating stationary flux balances for each node taking the stoichiometric coefficients of the reactions into account. Since this results in an underdetermined system of linear equations, efficient linear programming (LP) strategies can be applied to find the optimal flux distribution [5]. The application of optimization strategies requires the choice of an objective function reflecting a specific target such as the maximization of yield of the target component. Alternate optima – i.e. optimal solutions with the same objective function value but different flow scenarios – are possible and need to be detected to explore the solution space completely. This set of extreme point solutions can be generated using mixed-integer programming algorithms [6]. All other flux distributions can then be represented by linear combinations of these extreme point solutions.

3. Methodology In order to get a first insight into central questions of process design, reaction networks can be set up and evaluated according to the concepts of metabolic pathway analysis. After a basic flux model of a reaction network is built, all alternative reactions pathways are identified by MILP strategies and can then be evaluated by additional criteria. In most cases the decision to realize a process in a certain configuration is taken by reasons of the economic potential and the selection of options is constrained by aspects of process safety and environmental compatibility, minimization of energy consumption and of waste fabrication as well as the operability and control of the operation. Even though these questions cannot be answered in detail, important indicators about advantages and disadvantages of a specific reaction pathway can already be spotted by a systematic flow analysis and a subsequent evaluation closing the gap between laboratory chemistry and process engineering. Besides the optimization of yield, the composition of the reactor effluent is automatically calculated for each reaction step and for the final product. This is especially important because the product purification and design of an adequate separation sequence are essential factors for the energy efficiency of the process. In addition first decisions about the handling of high volume by-products can be taken: they can either be recycled or sold. As mass balances are provided for all components in the network, main reactants can be identified and a suitable supply strategy can be developed. In general, all indicators that depend on the fluxes through the network can be estimated easily, for example material costs. In the following the fundamentals of the reaction networks approach are described and the extension by additional evaluation criteria is shown by particular examples. Basic model The reaction network comprises nodes representing every substance linked by arcs representing reactions. Flux analysis requires mole balances for each node which are summarized in matrix form for the entire network,

Ax = b ,

(1)

where A is the matrix of stoichiometric coefficients. The rows of matrix A represent the substances and the columns relate to the reactions. The stoichiometric coefficient is positive, if a substance is formed and it is negative, if the component is consumed by a certain reaction. x refers to the molar flux through the network while b balances the

Reaction Networks – A Rapid Screening Method

245

product and by-product formation for each node. If the yield of a target molecule should be maximized, a linear programming problem can be formulated as

max bt arg et x,b

s.t. Ax = b

(2)

x, b ≥ 0 The problem is reformulated in canonical form as suggested by S. Lee et al. [6], implemented in GAMS and solved by the proposed MILP algorithm. The obtained set of extreme point solutions represents all possible combinations of reaction steps between starting and target molecule. The identification of all alternative reaction pathways based on the basic model serves as backbone for the approach of reaction networks. Even though the routes have the same value of the objective function (in this case the same yield), they differ for example in the consumption of additional reactants, in the formation of byproducts and in the number of reaction steps. Based on this few information, a first classification can be done. Depending on specific questions, additional criteria can be introduced for further discrimination. Additional criteria Several evaluation criteria can be easily coupled to the basic model as soon as the different flux distributions are known. In the following paragraphs some relevant examples are selected to illustrate this option. As maximizing the product yield is one of the major objectives of process design, it is especially important to include known limitations in the procedure. Yield constraints can be modeled such that only a limited fraction of the incoming flows can be converted by a certain reaction

xj ≤η j

¦ν

k

x k ∀j ,

(3)

k ,k ≠ j

where Ș is the molar yield of a reaction j and k is the set of fluxes entering or leaving a node. Another important aspect in the process of decision-making is the production cost for the individual reaction pathway. While investment and operating costs are difficult to estimate at this stage, material costs can be calculated by

C = cT x ,

(4)

if the molar flows are known. Capital C stands for the total material costs of the reaction pathway and c includes the cost data for reactants and catalysts. This cost estimation enables a comparison between the different reaction pathways, but absolute costs should be considered carefully as they scale with the required amount and especially catalyst costs change rapidly. The toxicity of the utilized substances and catalysts can be chosen as another classification category. The use of toxic materials should be avoided for environmental and safety reasons. Besides special storage, handling and waste disposal regulations for the use of hazardous substances would increase production costs. In order to evaluate the toxicity, all substances are categorized based on their health, environmental and safety aspects [7]. In this paper, the classification system is based on the risk- and

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safety-phrases, which are officially coded classifications standardized in the EU, and which can be found in the material and safety data sheet of the substance. The toxicity of the entire reaction path can then be described by

T = tT y

(5)

x ≤ My

(6)

where T is the toxicity of the reaction pathway, t stores the toxicity scores of the particular reaction and y is a binary variable that indicates, if a certain reaction is active. The binary variable y is forced to one for active reactions by Eq. (6), while M is a sufficiently large parameter. Alternatively, an average value for the toxicity of a reaction pathway can be calculated or solutions with carcinogenic and mutagenic substances can be avoided by a penalty function.

4. Case study In this case study the application of the procedure and the interpretation of results is demonstrated by an example of the TMFB cluster. A reaction network towards fuel components is set up with itaconic acid as a starting molecule, which is selected as one of the platform chemicals produced from biomass [8]. The reaction network is built based on chemists’ knowledge supported by a detailed literature research. In general, reactions increasing the hydrogen to carbon and decreasing the oxygen to carbon ratio are included in the network. Finally, the reaction network consists of 116 reactions and 80 substances. According to its physical and chemical combustion properties 3Methyltetrahydrofuran (MTHF) is selected as target molecule. In the analysis of the basic model 19 different reaction pathways producing MTHF can be detected maximizing the MTHF yield. Six of these reaction routes require additional main reactants like methanol or ethanol, which must either be produced by an integrated biorefinery or supplied by an external source. As this demands additional efforts, these solutions are deferred for now. The results of the evaluation by some additional criteria are illustrated in Fig. 1 for the remaining solutions.

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Hydrogen consumption [mol/mol]

10 Cost index Low: Filled symbol High: Empty symbol 13 9

8

7 4 11

2

12 6

6

8

10

53

1

4 0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Yield [mol/mol]

Figure 1: Evaluation of reaction routes concerning yields, hydrogen use and catalyst costs

The maximal yields are shown on the abcissae. If no information about the yield can be found in the literature, a value of 97% is assumed accounting for separation and purification losses. The highest MTHF yields that can be reached under these assumptions account to approximately 90%. However, the definition of an upper yield is a distinct disadvantage for routes with a large number of reaction steps. If these solutions show great promise for an overall evaluation, a possible improvement of the performance by an integration of multiple reactions in one reactor should be considered. Besides, reaction pathways with lower yields in terms of the target molecules can also be suitable for the fuel production: high volume by-product can either be sold, recycled sold or used in subsidiary reactions and perhaps the product mixture can utilized as fuel blend without further separation. The hydrogen consumption is automatically balanced in the model. Depending on the pathway 5-9 moles of hydrogen are required to produce one mole of fuel. Hence, the provision of a sustainable hydrogen source becomes one of the major challenges in biofuel production. The formation of byproducts instead of MTHF explains the correlation of hydrogen usage and product yield. In this case study prices for catalysts are used as a first cost estimation. It turns out that all routes can be classified into high or low cost solutions, which are marked by the filling of the symbol in the diagram. Based on this analysis a set of high yield and low cost routes with a moderate hydrogen usage can be selected as promising candidates. Obviously, research should primarily focus on a completion of information about these solutions and on further improvement of the reaction steps. Besides a detailed process design can be performed to get a first insight in the process chain and to identify core unit operations. But alternative reaction pathways should also be kept in mind. They can become interesting by eliminating the main bottlenecks: the yield of a key reaction could be increased and an expensive catalyst could be replaced by a cheaper variant or recycled efficiently.

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In summary, out of 116 reactions 19 reaction pathways can be identified in this case study. The set of candidate solutions can be refined by discarding solutions with additional main reactants and by a classification in terms of yields, hydrogen need and catalyst costs. Low cost and high yield solutions are regarded as the most promising ones, but based on this analysis research can be well-directed to reduce catalyst costs or increase the yield of key reactions and turn these routes into competitive alternatives.

5. Summary and Conclusions In this contribution a rapid screening method for reaction networks, which is based on concepts of metabolic pathway analysis, is presented. After finding all alternative reaction pathways by a MILP algorithm, the solutions are evaluated according to multiple criteria in order to identify promising routes as well as bottlenecks. Thus, key questions of process engineering can be answered. Once the reaction network is built, it can be applied to advanced problem formulations for example the inclusion of separation tasks, energy analysis or the production of fuel blends. Besides, this approach can be integrated as the first stage of a framework for process synthesis: after generating all possible alternatives, the number of relevant solutions is reduced by further evaluation with an increasing level of detail until an optimal design is obtained for the best route.

6. Acknowledgements This work was performed as part of the Cluster of Excellence "Tailor-Made Fuels from Biomass", which is funded by the Excellence Initiative by the German federal and state governments to promote science and research at German universities.

References [1] RWTH Aachen University: Tailor-Made Fuels from Biomass – Excellence RWTH Aachen University establishes a Fuel Design Center, NatureJobs, 2007 [2] C. Schilling, S. Schuster, B. Palsson and R. Heinrich: Basic Concepts and Scientific Applications in the Post-genomic Era. Biotechnol. Prog., 5 (1999), 296-303 [3] S. Schuster, D. Fell and T. Dandekar, Nat. Biotechnol: Metabolic Pathway Analysis: A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. 18 (2000),267-268 [4] K. Klamt and J. Stelling: Two approaches for metabolic pathway analysis?, Trends in Biotechnology. Trends in Biotechnology, 21 (2003), 64-69 [5] C. Schilling and B. Palsson: The underlying pathway structure of biochemical reaction networks. Proc. Natl. Acad. Sci, 95 (1998), 4193-4198 [6] S. Lee, C. Phalakornkule, M. Domach and I. Grossmann: Recursive MILP model for finding all the alternate optima in LP models for metabolic networks. Computers and Chemical Engineering, 24 (2000), 711-716 [7] H. Sugiyama, U. Fischer and K. Hungerbühler: Decision Framework for Chemical Process Design Including Different Stages of Environmental, Health and Safety Assessment. AIChE Journal, 54(4) 2008,1037-1050 [8] A. Corma, S. Iborra and A. Velty: Chemical Routes for the Transformation of Biomass into Chemicals. Chem. Rev., 107 (2007), 2411-2502

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249

The Virtual Product-Process Design Laboratory as a Tool for Product Development Elisa Conte1, Ricardo Morales-Rodriguez1, Rafiqul Gani1 1

CAPEC-Dep. of Chem. and Biochem. Eng., Tech. Univ. of Denmark, DK-2800 Lyngby, Denmark

Abstract The objective of this paper is to present a virtual laboratory for chemical productprocess design (virtual PPD-lab) where users can test their design ideas on model-based computer-aided tools before performing experiments to validate the designed product. Design alternatives for products and processes matching a priori defined targets can be generated and verified through the PPD-lab. The significance of this virtual laboratory is that the experimental effort in the development of new products and processes can be drastically reduced and attention can be focused on few alternatives; as a consequence, time and resources can be spared. This paper highlights a new feature of the virtual PPD-lab which handles the design of mixtures. Through a case study dealing with a coating formulation, the application of this new feature is illustrated. Keywords: Product Design, Process Design, Formulation Design, Paint/Coating Design

1. Overview of the Virtual Laboratory In design of chemical products and the processes that can manufacture them, one first tries to find a candidate product that exhibits a certain desirable or targeted behavior and then tries to find a process that can manufacture it with the specified qualities. The candidate may be a single chemical, a mixture, or a formulation of active ingredients and additives. The common practice to develop these products is experiment-based trial and error approach, supplemented sometimes with model-based computer-aided tools to speed-up some of the steps. The virtual PPD-lab (Figure 1) is an innovative and more effective approach to product and process design. It contains methods and tools to allow the modeling and simulation of the needed experimental scenarios. For this to work the ‘in-house’ models need to be reliable and efficient and the architecture of the software needs to include the work-flows related to different product-process design problems. Also, interfaces for efficient data-flow between different tools need to be defined. The architecture has to be flexible to allow changes in work-flow, addition of new models and of new data for future extension of the application range. The product-process design problem is solved through the reverse approach1 that includes a stage to define the design target, and a stage to identify the alternatives that match the target. This approach is based on the idea that all processes depend on some key properties of the products and on the effect of these properties on the process performance, that is, in the first stage the targets for the product performance are set and the process model is solved with property parameters as the unknown variables. In the second stage, any appropriate property model can be used, including database search, in order to identify a list of product alternatives matching the targets.

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Problem Definition

Start

Selection of the compounds (database & property model)

Modelbased verification of product behavior (using MoT)

Product Design

Selectioncalculation of primary properties

Selectioncalculation of functional properties

Perform product behavior (Process model)

Are the perform. criteria matching the desired targets?

Further develop. of selected productprocess

Process Design Stop

Product-Process Modeling tool

Start Production/Use

Figure 1. Virtual PPD-lab, user interface.

With this reverse approach it is possible to design products tailormade to suit the process demands by solution of integrated product and process models. Resident models, methods and templates From the virtual PPD-lab it is possible to access ICAS2, an Integrated Computer Aided System consisting of a number of toolboxes that help to efficiently solve a wide range of problems. Some ICAS toolboxes can be launched as standalone applications for the virtual PPD-lab, such as CAPEC DataBase, the Computer Aided Molecular Design tool (ProCAMD), the Property Prediction tool (PropPred), and the Modeling Tool (MoT). These toolboxes can easily be updated with newer and more reliable models3. To guide users in solving specific product and process design problems, templates defining workand data-flow for different types of design problems have been developed for the PPDlab. According to the templates, the product and process design problems are decomposed in several sub-problems, as it is evident from the user interface shown in Figure 1: the first important task is to define the problem; then the substances involved in the design problem have to be selected; afterwards, the user has to choose the property and the process model from model libraries; models are then solved and, finally, a model-based verification of the design product/process is performed. If the product/process matches the targets, further development of the identified product/process is considered. Currently, two design templates are already available: design of polymeric microcapsules for the controlled release of active ingredients, and, design of pesticide formulations for plant uptake. A third template, which guides the user to design solvent mixtures for formulated products, has been recently added and is presented in this paper. Mixture Design feature Many chemicals-based products of everyday life such as sun lotions, shower creams, paints and insect repellents, are consumer-oriented products, since they have to meet the consumer needs in order to be commercially successful. The consumer needs are

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usually manifold and formulations of several chemicals are needed in order to meet all these needs. Solvents, polymers, preservatives, emulsifiers, pigments, and many more chemicals can be present in one formulations, thus, they are very complex products to design; they usually contain a large amount of solvents (single solvents are rare), which have the function of binding all the chemicals together and conferring important end-properties to the product. A tool for designing solvent mixtures in formulations, therefore, has become a template in the virtual PPD-lab environment. It is based on a new algorithm called MixD that has been developed for designing mixtures of solvents, but that can, in principle, be employed for the design of mixture of any kind of chemicals. Currently, MixD considers only binary mixtures, but it can be easily extended to multicomponent mixtures. The reverse approach is applied in the following way: given the mixture target properties, identify the chemicals which could be mixed in order to match the design target and then determine the mixture composition minimizing the cost. The MixD algorithm starts by Problem identifying a set of feasible binary definition pairs of chemicals, then, it reduces the number of feasible candidates through five levels of screening, as LEVEL 1 highlighted in the flowchart of Linear Figure 2. The first important Constraints Rule 1.1 requirement of the methodology is Rule 1.2 to define the problem, that is, to translate the product performance Composition criteria into product properties. The Cost performance criteria are the end-use properties of the product, which LEVEL 2 correspond to the user needs. A Non-Linear Constraints knowledge-based system helps the Rule 2 developer in relating the user-needs to chemical properties on which the LEVEL 3 design constraints can be applied, Stability Check and, also in defining the targets. Rule 3 The screening of the mixtures starts (Level 1) applying the linear LEVEL 4 constraints for the target properties; Product linear models are based on linear Verification mixing rules. According to Rule Rule 4 1.1, any binary mixture is rejected if the pure component property values LEVEL 5 of both compounds in the mixture Optimal are either greater/lower than the Search upper-/lower-bounds of the targets, Rule 5 respectively. Then, the composition range for each feasible mixture is Optimal mixture Composition Cost calculated as shown in Eq. 1, where xi,1LB and xi,1UB are calculated as shown in Eq. 2. Figure 2. Flow-diagram of the method.

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(

)

(

)

x1 = max xi ,1 ,... , x1 = min xi ,1 ,... LB

LB

Pi ,2 − Pi ,mix

UB

UB

xi ,1 = LB

Pi ,2 − Pi ,1

UB

Pi ,2 − Pi ,mix

(1)

LB

, xi ,1 = UB

Pi ,2 − Pi ,1

(2)

Pi is one of the target properties, Pi,1 and Pi,2 are the pure properties of the chemicals involved in the binary mixture and Pi,mixUB and Pi,mixLB are the constraints values on Pi (UB-Upper Bound, LB-Lower Bound). According to Rule 1.2, the binary pairs, which do not have a composition (within 0-1) that satisfies the targets, are rejected. At this point, for each binary mixture, the composition corresponding to the lowest cost is chosen (either x1LB or x1UB). The second level of the design is based on non-linear constraints; non-linear models, which employ rigorous mixing rules to account for excess properties, are now used to further screen the feasible mixtures from Level 1 (Rule 2). The mixtures designed up to this point satisfy all the constraints on the target properties. At Level 3, their phase stability is verified (Rule 3). Information about the stability of a liquid mixture can be obtained from the Gibbs energy of mixing (ǻG/RT), and from its first and second derivatives. A new routine for the calculation of the immiscibility gap of partially miscible mixtures with negative ǻG/RT in the entire composition range, has been developed and tested on various binary mixtures, containing linear, branched and cyclic, aliphatic and aromatic hydrocarbons, and water. The routine employs the tangent plane condition4,5 and a new numerical solution method. The compositions defining the immiscibility gap have to show two properties: 1) same value of the first derivative of the function ǻG/RT; 2) the straight line connecting the corresponding points on the ǻG/RT function is the lowest tangent on the ǻG/RT curve touching these points. The single phase mixtures matching the target criteria have been found, and product verification would be the logical next step. Linear property models give good predictions for the properties of mixtures with negligible excess properties of mixing; with large excess properties of mixing it is necessary to calculate the mixture properties values with rigorous models accounting for excess properties, and to verify if the mixture properties still match the targets. Level 4 of the methodology consists of verification, related calculations and analysis. Finally, at Level 5 the optimal is found applying Rule 5: a performance index (PI) is fixed and the optimal solution is identified by ordering the feasible mixtures in terms of PI (usually, the cost). If multiple PI need to be considered, optimal solutions for different PI are ranked and weighted to identify the best common solution. Note that at this stage a short list of feasible candidates is available and it is a simple task to order the feasible candidates according to specific PI/PIs to find the optimal selection.

2. Case Study: Coating Formulation A coating is a formulation constituted by four different kinds of chemicals. The pigments, solid particles responsible for the particular coloration of the paint, are the Active ingredients (AIs); the binder is usually a polymer with the function of binding the pigments together; a mixture of solvents is responsible for the structural properties of the final product; finally, additives (usually less than 2% in volume) are added in order to enhance the end-use properties of the formulation, and they can have different functions (dispersant, emulsifiers, wetting agents).

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A paint should have good spreadability to be easily applicable on surfaces; it has to dry in a reasonable time but not too fast for not to be inhaled by the painter; it has to have a low toxicity for the same reason; in addition, it needs to have a competitive price. These performance criteria are achieved through the addition of a solvent mixture, while the additives can further enhance the product performance but not shape it completely. Problem statement and methodology results The formulation taken into consideration is a white paint. Titanium dioxide (TiO2) is a well known pigment used in paints6; poly(3-hydroxylalkanoates)6 are water insoluble polyesters which can dissolve pigments like titanium dioxide (TiO2) and iriodin®, and they are often used in paints. Poly(3-hydroxylalkanoates) are suitable candidate for the binder to use in this formulation. A mixture of solvents for the formulation matching the performance criteria stated above needs to be designed. The first and most important step of the design is to translate the target performance criteria into target chemical properties. The following properties have been considered: spreadability is related to density, viscosity and surface tension; the drying time is associated with the evaporation time T90, which is the time for the 90% (by weight) of the solvent mixture to evaporate; toxicity is controlled with the parameter LC50, the aqueous concentration causing 50% mortality in a fathead minnow population after 96 hours. In addition, the solvent mixture should be able to dissolve the binder. Since the binder is water insoluble, it is reasonable to assume that it will be soluble in solvents which dislike water, thus, in order to ensure the polymer solubility, in this design problem only solvents that are not miscible with water will be considered. Besides, the mixture solubility parameter should be close to that of the polymer (įpolymer = 15.67 MPa½), since when two substances have close values of the solubility parameters, they are also mutually soluble7. For modeling all the target properties linear mixing rules are sufficient, except the evaporation time model8, which is based on UNIFAC method. The stability of all binary mixtures composed of a solvent from the database and water has been checked. All solvents showing miscibility with water have been excluded from the database. It is worth noting, however, that two solvents which are immiscibile with water may not also form a single liquid phase. Therefore, the stability check of Level 3 (see Figure 2) is necessary. All the mixtures have been found to be one phase in all the composition range; only one mixture, ethylbenzene-dichloromethane, has miscibility problems in a certain composition range (xet.benz.=0.00÷0.71), but the mixture is one phase in the designed composition, which is 0.90 (with respect to ethylbenzene). Mixtures designed up to Level 3 have been verified in terms of their viscosity and surface tension using more rigorous models based on UNIFAC9,10. The property values calculated in this way have been found to be close to the ones calculated with the linear models; the RSME (Root Square Mean Error) for viscosity is 0.03, while for surface tension is 0.79; all the mixtures designed up to this point still match the design constraints, except for the mixture toluene-butyrolactone (xtol.=0.96) and ethylbenzeneethylacetate (xet.benz.=0.87), which have been rejected. The feasible single phase solvent mixtures after the verification step are listed in Table 1; they have been ordered in terms of increasing cost, the PI chosen for this case study. The estimated values of the mixture properties are also reported in the Table. The mixture diethylen glycol monoethyl ether (DEGEE)-toluene is the optimal solution since it is the cheapest mixture. The necessity of additives can now be analyzed. In the case of a paint, it would be good to enhance the spreadability on surfaces.

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Table 1. Mixtures matching the target properties and their estimated property values; į [MPa½], ȝ [cP], Ȗ [mN/m], ȡ [g/cm3], LC50 [mol/m3], T90 [s], Cost [$/kg]. Mixtures DEGEE - toluene toluene - cyclohexanone toluene - ethylbenzene ethylbenzene - heptane ethylbenzene - butyl acetate ethylbenzene - hexane ethylbenzene - butanone ethylbenzene - dichloromethane ethylbenzene - isopropylacetone

x1

į

ȝ

Ȗ

ȡ

LC50

T90

Cost

0.05 0.95 0.56 0.62 0.87 0.77 0.80 0.90 0.72

18.35 18.24 18.03 17.67 17.42 17.92 18.09 18.11 17.54

0.71 0.63 0.60 0.67 0.60 0.60 0.60 0.600 0.62

28.63 28.80 28.41 26.93 26.50 27.18 27.56 28.19 26.50

0.87 0.86 0.86 0.87 0.84 0.87 0.85 0.89 0.84

0.40 0.40 0.40 0.40 0.46 0.69 1.02 0.62 0.84

256.1 256.4 345.8 448.0 436.1 403.8 427.2 449.7 418.2

1.35 1.37 2.49 3.51 3.70 3.72 3.72 3.85 3.91

The additive sodium dioctyl sulfosuccinate is a wetting agent, that also promotes the solubilization and the dispersion of the pigment solid particles; it is water insoluble and has a solubility parameter close to mixture one, so it is a suitable candidate.

3. Conclusions and Future Work The virtual PPD-lab has been introduced and the use of the resident models, methods and tools has been illustrated. A systematic methodology developed for mixture design has been highlighted. A useful feature of the mixture design feature is that it can be employed for the design of formulations, and a case study for paint formulation has been highlighted. Current work is to consider new design problems, for other formulations, through which the methodology can be further tested and validated. Future work is to develop models and design tools for the mixing (process) operation and to enlarge the number of products which can be tested and designed through the PPD-lab.

4. References [1] Gani, R., 2004, Computer-aided methods and tools for chemical product design, Chem, Eng. Res. Des., 82(11), 1494-1504. [2] ICAS Documentation, 2003, Internal report, CAPEC, KT-DTU, Lyngby, Denmark. [3] Conte, E., Martinho, A., Matos, H. A., Gani, R., 2008, Combined group-contribution and atom connectivity index-based methods for estimation of surface tension and viscosity, Ind. Eng. Chem. Res., 47(20), 7940-7954. [4] Baker, L. E., Pierce, A. C., Luks, K. D., 1982, Gibbs energy analysis of phase equilibria, Soc. Pet. Eng. J. AIME, 22(5), 731-738. [5] Michelsen, M. L., 1982, The isothermal flash problem. Part I. Stability, Fluid Phase Equilibr., 9, 1-19. [6] Van der Walle, G. A. M., Buisman, G. J.H., Weusthuis, R. A., E. Gerrit, 1999, Development of environmentally friendly coatings and paints using medium-chain-length poly(3-hydroxyalkanoates) as the polymer binder, Int. J. Biol. Macromol., 25, 123–128. [7] Hancock, B. C., York, P., Rowe, R. C., 1997, The use of solubility parameters in pharmaceutical dosage form design, Int. J. Pharm., 148, 1-21. [8] Klein, J. A., Wu, D. T., Gani, R., 1992, Computer aided mixture design with specified property constraints, Comp. and Chem. Eng., 16(5), 229-236. [9] Suarez, J.T, Torres-Marchal, C., Rasmussen, P., 1989, Prediction of surface tensions of nonelectrolyte solutions, Chem. Eng. Sci., 44(3), 782-786. [10] Cao, W., Knudsen, K., Fredenslund, A., Rasmussen, P., 1993, Group-contribution viscosity predictions of liquid mixtures using UNIFAC-VLE parameters, Ind. Eng. Chem. Res., 32, 2088-2092.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

255

Anomaly detection in batch chemical processes Isaac Monroy,a Gerard Escudero,b Moisès Graellsa a

Chemical Engineering Department (DEQ), bSoftware Department (LSI) EUETIB, Universitat Politècnica de Catalunya (UPC), Comte d´Urgell 187, Barcelona 08036, Spain, [isaac.monroy, gerard.escudero, moises.graells]@upc.edu

Abstract Fault detection and diagnosis systems (FDDS) are efficient ways for preventing accidents and helpful for supporting plant operators’ decision-making. In this direction, a new anomaly detection system (AD) has been posed through a fault detection and diagnosis system. The objective is to be able to detect faults that have never happened before by using training information obtained from processes history (known faults). The methodology consists of two steps: a first fault detection stage (binary classification problem) and a subsequent diagnosis stage (multi-class problem) addressed under a multi-label (ML) approach. The FDDS has been implemented using Support Vector Machines (SVM). The problem addressed is the monitoring and diagnosis of transient operation modes, for which the FDDS has been tested in a pilot plant heat exchange system operating batch wise. Results are discussed and promising measures of diagnosis performance (F1 index) are finally reported. Keywords: Anomaly detection, Fault Detection and Diagnosis, SVM

1. Introduction Anomaly or novelty detection (AD) is a one-class classification problem of growing interest in Statistics and Machine Learning [1,2]. The related Chemical Engineering problem is detecting operation faults which have never been reported, thus not included in process history data. Anomaly detection has been addressed using artificial neural networks [3]. More recently, soft margin SVM has shown to discriminate nominal and anomalous operation states, or classes, using pre-acquired learning information [5]. One-class SVM using unsupervised learning has been applied for detecting anomalies because of its unlabeled classification capability. This method identifies and classifies outliers among positive examples (one single class) classifying them as negative, only requiring pre-existing knowledge [4]. A new anomaly detection method is presented in this work that encompasses techniques for fault detection and diagnosis and uses both kind of classification, binary classification as detection technique and multiclass classification as diagnosis technique. SVM was used as the data-kernel-based learning algorithm for incorporating these AD tool to the Fault Detection and Diagnosis System (FDDS). The detection and diagnosis performance is measured using the normalized F1 index [6,7]. This performance is improved by a final feature extension step [8].

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2. Case study A simple pilot plant case study is addressed (Fig. 1). A heat exchange system melting a batch of ice illustrates a recipe for producing a certain amount of product. The base case is the heat exchange between a water stream at room temperature and a bath with water and ice. Hence, a bath temperature above +1ºC is easily established as the recipe final condition. Process variables (operation time, stream flow rates and temperatures -both, inlet and outlet) were measured at one second intervals. Fig 2 shows the process variables behavior through the time in the base case. Experiments were run simulating 4 different faults: external heating of the cold water (Fault or Class 1), failure of the cold stream inlet temperature monitoring (C2), failure of the cold stream flow monitoring (C3) and the simultaneous heating of the bath and failure of the cold stream inlet temperature monitoring (C4). Experiments for normal and abnormal conditions were run and the logged information was arranged in training and test sets. Information representation consisted on 5 data matrices, 4 of faults and one of base case (class 0) whose columns represent the attributes or process variables (7) and the rows the values of these variables through the time. The original sample set is composed of random samples containing the 5 classes. This set is divided into two sets of the same magnitude, which correspond to the training and testing sets. Fig 1. Batch wise heat exchange system as case study

Fig 2. Process variables behavior through the time in the batch heat exchange system.

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3. Methodology The FDDS has been implemented using a ML&SVM approach [8]. Preliminary studies determined the best diagnosis performance was obtained using a linear kernel. Next, feature extension allows improving the FDDS performance by including new attributes that enhance the characterization of process dynamics. These new attributes are the standard deviations and linear trends (slopes) of the data within a time window of 20s. Hence, the original sample sets (training and test) containing 5 classes information were used for demonstrating the right diagnosis of the harassed faults in the experiments. The AD method is developed using only 4 classes for building the classification model (3 faults and the class 0) because the fourth class will be taken as a new fault never registered before. This methodology is showed in Table 1. The novel fault has to be first detected by a binary classification system. The training set is composed of the 4 classes’ information, labelling the data of the 3 faults as if only one happened in a positive class, and class 0 (normal operation) in a negative class, while the test set is composed of new fault’s information (fault 4), labelling the data as positive class (fault). If the detection performance after applying SVM is high, a process abnormal behaviour will be identified and therefore the presence of a fault. The second step consists of applying a multi-class and multilabel diagnosis procedure. Training set data are the same than in first step but labeled according to their class and test set information is the same than in first step but labeled as negative class or class 0 like process information without the presence of any fault. If test set is diagnosed as class 0, means that it won’t happen any of the faults registered in the diagnosis system, but a new fault will be produced because it has been detected as fault before by the detection system. The results obtained after applying this method are presented and discussed in the next section. Table 1. Anomaly detection methodology supported by fault detection and diagnosis systems. Training set Class

Test set Information

Label

Class

Information

Label

Normal (positive) C0 (base)

-1

Novel

C4 (fault 4)

+1

Anomalous (negative)

C1 (fault 1)

+1

C2 (fault 2)

+1

C3 (fault 3)

+1

Training set

Test set

Class information

Label

Class information

Label

C0

-1

C4

-1 as C0

C1

+1 as C1

C2

+1 as C2

C3

+1 as C3

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4. Results and Discussion Fault diagnosis performance is obtained after applying SVM with linear kernel to the sets with the 5 class data information, not only for the original attributes (7) but also for the extended features added to the original attributes such as the standard deviations and slopes (14) and all the features gathered (21). Both original training and test sets are formed by 2275 samples (455 per class). Table 2 shows the results obtained. Table 2. F1 index of the FDS using linear kernel for the original attributes and the features created F1 Index (%) Features

Class0

Class1

Class2

Class3

Class4

Mean1

Mean2

Original attributes

99.8

100

64.4

99.7

90.1

84.5

88.6

Orig+Std. dev.

99.4

100

81.5

99.7

98.5

93.7

94.9

Orig+Slopes

81.0

100

37.6

99.7

98.8

81.7

84.0

Orig-Std dev-Slopes

99.4

100

96.0

99.7

93.6

97.0

97.3

Faults are diagnosed with good performance and additional improved diagnosis is got with feature extension, especially using standard deviations and slopes as extended features (Table 2). A training set composed of 2264 samples and 4 classes (566 samples per class) is used for assessing the performance of the anomaly detection methodology. These classes correspond to the class 0 and 3 faults. Test set changes according to the fault to detecting and diagnosing. Test sets employed for assessing the AD system using SVM with linear kernel are: • Test set containing samples of the class 0 (2264 samples) • Test set containing samples of the class or fault 1 (565 samples) • Test set containing samples of the class or fault 2 (1428 samples) • Test set containing samples of the class or fault 3 (568 samples) • Test set containing samples of a new class or fault not registered in the FDDS training model (fault 4 data, 910 samples). Table 3. F1 index for the fault detection system using a training set with class 0-3 information and a test set with information of only one class. One-class classification system. F1 index (%) Test set data

Class0

Fault

Mean1

Mean2

Class 0 data

100

0

0

0

Class 1 data

0

99.8

99.8

99.8

Class 2 data

0

99.9

99.9

99.9

Class 3 data

0

100

100

100

Class 4 data

0

100

100

100

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Table 4. F1 index for the fault diagnosis system using a training set with class 0-3 information and a test set with information of only one class. Multi-class classification system. F1 index (%) Test set data

Class0

Class1

Class2

Class3

Mean1

Mean2

Class 0 data

100

0

0

0

0

0

Class 1 data

0

100

0

0

100

0

Class 2 data

0

0

99.4

0

99.4

0

Class 3 data

99.7

0

0

100

100

0

Class 0-3 data

99.4

100

99.4

100

99.8

99.8

Class 4 data, labeled as class0

100

0

0

0

0

0

Table 3 and 4 show the results for all these cases which assess the AD system. New fault’s detection and diagnosis is presented in the last row of both tables, where a test set with new class information is used. The results of the 4 first classes (0-3) confirm the good performance of the FDDS. Regarding to class 4 containing information of a new class not included in the detection and diagnosis models, it is firstly detected as fault with the detection model and it is diagnosed as class 0 with the diagnosis model not belonging to any of the other faults, thus this class is confirmed to be a new fault and a new AD system is established by this way.

5. Conclusions A new anomaly detection (AD) procedure has been incorporated to a fault detection and diagnosis system (FDDS), which was implemented using SVM with linear kernel and a multilabel (ML) approach. The FDDS performance has been increased by means of feature extension (including standard deviations and linear trends) to almost 100%. The new AD system was established by assessing the detection model with a test set with a new fault data predicted as fault and then evaluating the diagnosis model with the same test set data predicted as class 0 or normal case so as to diagnose the process information as a novel fault. This is proved because it had been firstly detected as fault with the detection system. A lab batch wise heat exchange system was used as case study in this work and a new fault was detected and diagnosed at 100% so the new AD system efficiency was demonstrated. The application of this new system to any continuous and batch process could develop promising results in fault diagnosis.

6. Acknowledgements Financial support from Generalitat de Catalunya through the FI fellowship program is fully appreciated. Support from the Spanish Ministry of Education through project no. DPI 2006-05673 is also acknowledged.

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References [1] J.B.D. Cabrera, C. Gutiérrez & R.K. Mehra, 2008, Ensemble methods for anomaly detection and distributed intrusion detection in Mobile Ad-Hoc Networks, Information fusion, 9, 96-119 [2] A.L.I. Oliveira, F.R.G. Costa & C.O.S. Filho, 2008, Novelty detection with constructive probabilistic neural networks, Neurocomputing, 71, 1046-1053. [3] A. Arranz, A. Cruz, M.A. Sanz-Bobi, P. Ruíz & J. Coutiño, 2008, DADICC: Intelligent system for anomaly detection in a combined cycle gas turbine plant, Expert Systems with Applications, 34, 2267-2277. [4] T. Shon & J. Moon, 2007, A hybrid machine learning approach to network anomaly detection, Information Sciences 177, 3799-3821. [5] C.M. Rocco S. & E. Zio, 2007, A support vector machine integrated system for the classification of operation anomalies in nuclear components and systems, Reliability Engineering and System Safety, 92, 593-600. [6] I. Yélamos, M. Graells, L. Puigjaner & G. Escudero, 2007, Simultaneous fault diagnosis in chemical plants using a MultiLabel approach, AIChE Journal, 53, 11, 28712884. [7] C.J. Van Rijsbergen (1979). Information Retrieval. 2nd edition, London, Butterworths. [8] I. Monroy, M. Graells & G. Escudero, 2008, ESCAPE 18.

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Data-driven generation of multi-modal control programs for continuous-discrete processes Mariano De Paula, Ernesto Martínez INGAR (CONICET-UTN), Avellaneda 3657, S3002 GJC Santa Fe, Argentina {marianodepaula, ecmarti}@santafe-conicet.gov.ar, E-mail

Abstract Multi-modal control is an increasingly used design tool for supervisory control of complex systems by resorting to sequences of modes each one comprising of a feedback law and stopping condition. In this paper, the problem of developing multi-modal control programs from a given mode alphabet using data is addressed. By viewing the control space as a set of tokenized instructions rather than as real-valued signals, reinforcement learning algorithms becomes applicable to develop optimal control strategies for continuous-discrete processes using a Lebesgue-sampled finite state machine. A case study related to capacity management of a buffer tank in a petrochemical plant is presented. Keywords: Hybrid systems, supervisory control, reinforcement learning, switchedmode dynamic optimization, discrete-event systems.

1. Introduction There has been a lot of interest in modelling and control of hybrid dynamical systems in recent years, motivated by a growing number of chemical plants involving tight interaction between continuous variables and discrete events/decisions (Engell, et al., 2000). A multi-modal system is a system whose dynamics switches among finitely many possibilities to achieve a desired goal or behavior. These switches can be in response to an occurrence of a specific event or a controlled decision (Mehta and Egerstedt, 2006). Optimal control of multi-modal dynamic systems is of paramount importance for designing a supervisory control structure (Koutsoukos, et al., 2000). In this context, a mode V is specified as a triple N• [• T), where N• is a control law (closed-loop control policy) seeking to achieve a given sub-goal or to deploy a certain behavior, [• is the interrupt function mapping process observations to the set {0,1} and T is the time interval over which the mode is active. The key issue in the design of a supervisory control system is to find the optimal concatenation of modes in a finitelength mode string S based on the rewards observed after each mode transition occurs.

2. Multi-modal control programs Suppose the state x of a dynamic system follows: dx dt

f ( x, u (t ), z (t )) , x  X

ƒn , u U

ƒm

(1)

where z(t) is a time-varying measurable disturbance which evolves arbitrarily as dz dt

g ( z, t ) , z  Z

ƒd

(2)

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If at a given time W, where the state is x(W) and disturbance z(W), the system receives the input string S ^N1,[1),…,Nq,[q)} and the following state transition results W1

Wq

W0

W q 1

G (V , x(W 0 ), z (W 0 )) x(W 0 )  ³ f ( x(t ), u (t ), z (t )dt  ... 

³

f ( x(t ), u (t ), z (t )dt (3)

If the length of the mode sequence Sis bounded, only a a finite set of states are reachable. Hence, by resorting to control programs with maximum length N a quantization of the system state results. Based on this multi-modal quantization a ~ Q Lebesgue-sampled finite state machine ( X N , 6 ,G , ~ x0 , ~ z 0 ) , where Q stands for the ~ value function (Sutton and Barto, 1998) and the state transition G is defined as follows ~ ~ (4) x k 1 G ( ~ xk , ~ z k , V k ) G (V , x(W 0 ), z (W 0 )), k 0,1,2,.... , x0 x(W 0 ), z 0 z (W 0 ), Q

The discrete state space X N is given by the set of all states that are reachable from F 0 ( x 0 , z 0 ) using a sequence of modes V  6 of length less than or equal to N. The issue of concern here is finding a sequence of control-interrupt pairs that maximizes a Q given reward for such state transitions. Based on the multi-modal quantization X N of the state space and the transition dynamics of the Lebesgue-sampled FSA, reinforcement learning (Sutton and Barto, 1998) can be used to learn the Q-values for a given reward function. It is worth noting that both state exploration and disturbance Q scenarios are required to discover which is the best mode V  for each pair F  X N .

 : {F~0 , G ( F~0 , V )} ; step ( F~0 ) :=0; ~ step G ( F~0 , V ) :=1, V  6 k:=1 ; index for counting visits to state-disturbance pairs F  

Qk ( F~, V ) : const , F , V  6 repeat k=k+1

( F~ ) : rand ( F  step( F )  N ) V : rand (6 ) ~ F~ ' : G ( F~, V ) if F~ ' then step( F~ ' ) step( F~ )  1  :  ‰ F~ ' Q ( F~ ' , V ) : const , F , V  6 k

end if

Qk 1 ( F~ ' , V ) : Qk ( F~ ' , V )  D k [ U ( F~ ' , V )  J min V '6 [ Q k 1 ( F~ ' , V ' )  Q k 1 ( F~ , V )] until mod(k , L) 0 and Qk ( F~, V )  Qk  L ( F~, V )  H , F , V  6 X NQ



Fig. 1. Q-learning algorithm for multi-modal control programs

Data-Driven Generation of Multi-Modal Control Programs

263

Q In the Q-learning algorithm of Fig. 1, the quantized state-disturbance space X N is assumed to be unknown initially and we thus begin learning/exploring from selected x0 , ~ z 0 ) and simulating transitions toward all the states states/disturbances pairs F~0 ( ~ which are reachable using the first mode of all control programs V  6 . At each iteration of the learning process, a state-disturbance pair is randomly is chosen from the set of known states-disturbance pairs and a control mode from the set 6 is applied to x ' ; U ( F~ ' , V ) is the reward obtained for the transition observe a state transition to ~ observed once the execution of mode Vis finished.

In the algorithm, the function step( ~ x ) represents the length of the shortest control x 0 . As a result, only program used so far to reach the state ~ x ' from the initial state ~ states that are reachable from ~ x 0 using mode strings of length less than or equal to N are explored, i.e. ~ x '  F~ ' X NQ is guaranteed. As the transition to the next state ~x ' is observed it is necessary to determine if it is in the neighborhood of a previously visited state-disturbance pair F~ . If not the pair F~ is added to the known state spacedisturbance, the coresponding number of steps is increased by 1 and a new entry to Qtable is added. It is worth noting than when F~ ' is in the the neighborhood of a previously visited state the Q-values of all states-disturbances pairs in the neighborhood are updated. Exploration of the state-disturbance space and updates of the Q-table (value function) continues in this manner until the Q-table is stationary. Stopping conditions are imposed so as to guarantee that sufficiently many state-disturbance pairs are visited and all control programs V  6 are tried enough times for the Q-table to converge.

3. Case study 3.1. Problem statement Buffer tanks are frequently used in the process industry to alleviate the impact downstream of significant variability in flowrate, concentration and temperature of important process streams (Tani, et al., 1996; Crisafulli and Peirce, 1999). The most common example is typically found in the petrochemical industry where there exists a material decoupling point between a reaction section (upstream) and a distillation train (downstream) which cannot handle abrupt variations in its inflow rate Fin. Also, buffer tanks play a key role in hybrid chemical plants such as the Solvay PVC production line (Melas, 2003) To dampen upstream flow rate variations a buffer tank is used as shown in Fig. 2. One important component of the desired tank operation is that its outflow rate Fout must be changed smoothly despite significant variations in its inflow rate. To do so the tank capacity must be managed properly by allowing the tank level to vary within its minimum and maximum limits. Also, the outflow rate Fout is constrained by minimum and maximum values that must be enforced due to throughput limitations downstream in the separation train. It is worth noting that in hybrid chemical plants the main role of the buffer tank is handling intermitent inflow rates which prevents resorting to averaging level control techniques (McDonald, et al., 1986). Also, for this type of processes the inflow rate pattern is the result of significant deviations from periodic or optimal schedules due to resouce sharing, e.g. utilities (Simeonova, 2008).

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How does multi-modal control fit in the problem of capacity management of a buffer tank? Let’s take a quick look to what an expert operator normally does. Firstly, the operator always try to use the inflow variability to his/her advantage. For example, the operator seeks to accumulate when Fin is going up and to do so the level must be low enough to accommodate the inflow upsurge in this way. Secondly, the operator stops seeking a sub-goal (accumulate or drain-off inventory) when is not practical to do so or a constraint becomes active, e.g. a maximum/minimum outflow rate. Finally, the operator always resorts to a sequence of behaviors (modes) that are somehow derived from anticipating the long-term impact on the tank situation of alternative courses of actions. Implicitly stated in the latter remark is the fact that the inflow rate, despite it may exhibit quite unsystematic variations, still follows an underlying pattern or regularity which allows enough room for learning a multi-modal control program. 3.2. Tank operation data and control modes As a very simple example of the application of the algorithm in Fig. 1, let’s assume the buffer tank has a maximum height of 1 m which is equal to its diameter. The inflow rate variability is modeled here as the time-series generated using the well-known MackeyGlass differential delay equation using random initial values

dFin dt

0.2 Fin (t  30)



1  Fin (t  30)



10

 0.9 Fin (t ) [m3/h]

(5)

Time series generated using Eq. (5) are very sensitive to initial conditions while exhibiting a non-periodic/non-convergent pattern as can be seen from portions of the series shown in Fig. 3. This type of inflow variability may look far from real but it will serve as an extreme benchmark for developing multi-modal control programs using the algorithm of Fig. 1. Modes are designed so as to achieve either the sub-goal “accumulate” (A1, A2 and A3) or the sub-goal “drain-off” (D1, D2 and D3) using different control strategies. Control laws refer to the amount of change in the outflow rate. Modes A3 and D3 are based on a constant outflow rate; mode A1(D1) is based on 1% decrease (increase) in the outflow rate whereas mode A2(D2) is based on 3% decrease (increase) in the outflow rate. Stopping conditions are defined either on the infeasibility of achieving the corresponding sub-goal or when outflow rate constraints become active. Stopping conditions includes minimum (25%) and maximum (75%) safety levels and maximum number of time steps for the behavior to be achieved.

Fig. 2. Buffer tank

Data-Driven Generation of Multi-Modal Control Programs

265

Inflow rate [m3/h]

1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

100

200

300

Time [min]

400

500

Fig. 3. Inflow rate variability pattern

3.3. Results In Fig. 4, results obtained using the multi-modal control system are shown. There are certain strings of modes that are repeated which allows devising a supervisory control logic. Despite significant variations in the inflow rate the learned control programmed succesfully managed the tank capacity.

Fig. 4. Control program for the disturbance scenario in Fig. 3

4. Final remarks A novel algorithm for automatic generation of a multi-modal control program using simulations and reinforcement learning has been presented. The application of the methodology to a buffer tank decoupling the reaction section from the product separation train in a petrochemical plant has been discussed. The greatest advantage of the proposed methodology is that if the inflow rate pattern change the Q-table will also change and the optimal control program will be modified accordingly.

M. De Paula and E. Martínez

266 Tank level [m]

1 0.9 0.8 0.7 0.6 0.5 0.4 0

100

200

300

Time [min]

400

500

Fig. 5. Tank level dynamics using the control program

5. Acknowledgements The authors thanks to the ANPCyT of Argentina which partially supports the work presented here through project PICT 1099/06.

References S. Crisafulli and R. Peirce, 1999, Surge tank control in a cane raw sugar factory, J. Process Control 9, 33-39. K. McDonald, T. McAvoy, and A. Tits, 1986, Optimal averaging level control, AiChE J., 32, 75– 86. S. Engell, S. Kowalewski, C. Schulz and O. Stursberg, 2000, Continuous-Discrete Interactions in Chemical Processing Plants, Proceedings of the IEEE 88, 1050-1068. X. Koutsoukos, P. Antsaklis, J. Stiver and M. Lemmon, 2000, Supervisory Control of Hybrid Systems, Proceedings of the IEEE 88, 1026-1049 T. Mehta and M. Egerstedt, 2006, An optimal control approach to mode generation in hybrid systems, Nonlinear Analysis 65, 963–983. S. Melas, 2003, Pvc line predictive inventory control: a production rate optimization for a hybrid system, Solvay-Group report, 1–34. I. Simeonova, 2008, On-line periodic scheduling of hybrid chemical plants with parallel production lines and shared resources, PhD Thesis, Université Catholique de Louvain, Center for Process Systems Engineering and Applied Mechanics, Belgium. R. Sutton and A. Barto, 1998, Reinforcement learning:An Introduction, The MIT Press, Cambridge, MA. T. Tani, S. Murakoshi, M. Umano, 1996, Neuro-fuzzy hybrid control system of tank level in pretroleum plant, IEEE Trans. Fuzzy Syst., 4, 360-368.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

267

DICA enhanced SVM classification approach to fault diagnosis for chemical processes Isaac Monroy,a Raul Benitez,b Gerard Escudero,c Moisès Graellsa a

Chemical Engineering Department (DEQ), bAutomatic Control Department (ESAII), Software Department (LSI) EUETIB, Universitat Politècnica de Catalunya (UPC), Comte d´Urgell 187, Barcelona 08036, Spain, [isaac.monroy, raul.benitez, gerard.escudero, moises.graells]@upc.edu

c

Abstract A new methodology combining a new feature extraction method and a classification algorithm is proposed in this paper for diagnosing faults in chemical processes. These techniques are Dynamic Independent Component Analysis (DICA) and Support Vector Machines (SVM). DICA is an extension of conventional Independent Component Analysis (ICA) dealing with multivariate dynamic data while SVM is a powerful tool for data classification. This methodology was applied to fault diagnosis in the simulation benchmark of the Tennessee Eastman (TE) plant. The approach compares the diagnosis performance obtained when applying ICA and DICA with SVM. In order to verify the fault diagnosis performance improvement with these techniques, the results are compared with the SVM performance when no feature extraction is used. Keywords: ICA, DICA, SVM, Fault diagnosis.

1. Introduction As a result of the inherent dynamic and nonlinear characteristics of chemical processes and their increasing complexity, on-line monitoring and fault diagnosis are gaining importance for plant safety, process economy, reliable maintenance and product quality. Thus, statistical process control (SPC) has been used to monitor individual process signals to detect trends, outliers and other anomalies. However, these procedures have revealed limited use with high-dimensional multivariate data that are strongly crosscorrelated. The need to monitor such multivariate processes has led to the development of many process monitoring schemes that use standard statistical methods such as principal component analysis (PCA) and partial least squares (PLS). [1] Despite their extended applications, these methods do not explicitly take into account possible time correlations in the observations or deviations from Gaussianity of the latent variables. However, in most cases state variables are driven by uncontrollable disturbances and random noise which make they present both auto and crosscorrelation. In order to address this problem taking into account serial correlations in the data, Dynamic Principal Component Analysis (DPCA) was proposed [2]. This approach constitutes a process monitoring method that uses an augmenting matrix with timelagged variables and has been shown to be valid in different practical applications [3,4]. Recently, Independent Component Analysis (ICA) has been developed as a statistical technique that extracts statistically independent components from multivariate observed

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data. By using higher order statistical properties of the data, ICA provides a better identification of the underlying factors in the data than standard PCA techniques [5,6,7]. PCA finds a set of uncorrelated signals, whereas ICA finds a set of independent source signals. The extension of DPCA to ICA led to a new method called dynamic independent component analysis (DICA) which applies ICA to the augmenting matrix with timelagged variables[3,8] for developing dynamic models and improving the monitoring performance. This method is able to extract the major dynamic features or source signals from the process and to find statistically independent components from autoand cross-correlated inputs. This paper addresses fault diagnosis by combining ICA and DICA with Support Vector Machines (SVM). Both ICA and DICA are used for process monitoring and feature extraction in order to provide an enhanced representation of process information and SVM is used for fault detection and diagnosis as a classification algorithm. The methodology is explained in the next section.

2. Methodology ICA is a technique that extracts independent components in complete statistical sense from mixed signals. A generic ICA model can be written as:

§ x1 (k ) · ¨ ¸ ¨ x 2 (k ) ¸ ¨: ¸= ¨ ¸ ¨ x (k ) ¸ © d ¹

§ s1 (k ) · ¨ ¸ ¨ s 2 (k ) ¸ A¨ ¸ : ¨ ¸ ¨ s (k ) ¸ © m ¹

(Eq. 1)

where [x1(k), x2(k), …, xd(k)], is a set of d variables observations at each time or sample index k, A is an unknown mixing matrix and s is the independent component data matrix. It can be assumed that they are generated as a linear mixture of m (”d) unknown independent components. When k samples are available, the preceding relationship can be written as:

X = AS

being X ∈ R d ×n , S ∈ R m×n

(Eq. 2)

where m is the number of independent components, d the number of process variables and n the number of samples. ICA is extended to the modeling and monitoring of dynamic systems by augmenting each observation vector with the previous l observations, and stacks the data matrix in the following manner:

ª xkT « T x X (l ) = « k +1 « : « T ¬« xk + p

xkT−1 xkT : xkT+ p −1

xkT− l º » ... xkT− l +1 » : : » » ... xkT+ p − l ¼» ...

T

(Eq 3)

where xkT is the d-dimensional observation row vector at time k, (p+1) is the number of samples and l is the number of lagged measurements, so the matrix dimension per class

DICA Enhanced SVM Classification Approach to Fault Diagnosis for Chemical Processes

269

is d(l+1)×n. The rows of these matrices represent features. By performing ICA on the data matrix in Eq 3, a dynamic ICA (DICA) model is extracted directly from the data. Once DICA has been applied and the matrices A and S have been obtained, SVM is employed as classification algorithm, using as information sets the inverse of the independent component matrix (S) separating the data according the class they belong to. On this way, the inputs of SVM will be sets containing matrices of n×m size per class, where n is the number of samples per class and m [”d(l+1)] is the number of independent components or extracted features.

3. Case study The hybrid ICA/DICA with SVM technique has been computationally implemented in MATLAB by using the free packages FastICA[9] and SVM-light[10]. The resulting fault diagnosis system (FDS) is then applied to the Tennessee Eastman process [11] as case study. This benchmark consists of 52 process variables (attributes) and 20 faults (classes) to be diagnosed. Simulation runs of 50 hours with the fault produced at 2 h and a sampling time of 3 minutes have been carried out for obtaining source data sets. Training and test sets are composed of S matrices after applying ICA and DICA to matrices of 200 and 100 samples per class (25 to 35 h of simulation for training set and 35 to 40h for test set), considering 21 classes. A time-window of two samples has been considered for DICA. The results are presented in the next section.

4. Results and Discussions First the waveforms of faults standardized with class 0 allow determining the difference that exists among them and the opportunities to reduce some attributes, as well as allow distinguishing each fault applying ICA or DICA. Figure 1 shows the waveforms for the faults 1, 2, 7, 12 and 16 and reveals little differences among the faults and mainly seen in few attributes.

Figure1. Waveforms of faults 1,2,7,12 and 16 standardized with class 0 using the training samples

270

I. Monroy et al.

Figure 2 shows the plots obtained after applying ICA and DICA to data matrices containing faults 3,4,5 and 15 standardized with class 0 and extracting 3 IC (plot in 3D).

Figure 2. Projections after applying ICA (above) and DICA (below) for some faults standardized with class 0.

A better separation among classes is obtained with ICA as it can be seen in Figure 2. Finally, the results obtained applying SVM to the original data sets and to the IC matrices after ICA and DICA are presented in Table 1, which shows that SVM

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271

classification performance is better when using the IC matrix obtained from ICA. However, preliminary results indicate that the bigger the training set for applying DICA, the better performance is obtained and a trade-off should be investigated regarding the time-window size influence in the results but preliminary results indicate that performance decreases for time windows or lags larger than 2. Table 1. Fault diagnosis performance comparison for the ICA and DICA application before SVM F1 INDEX (%) Class

SVM

ICA+SVM

DICA+SVM

1

100

100

97.6

2

100

100

99.0

3

6.2

8.3

8.6

4

10.4

70.1

18.9

5

6.1

15.6

7.9

6

100

100

100

7

100

100

100

8

9.2

13.3

11.9

9

8.2

6.3

7.9

10

6.6

9.7

8.1

11

7.7

8.9

9.0

12

7.6

8.0

9.0

13

13.8

11.5

10.6

14

7.9

7.5

8.2

15

6.4

9.4

9.2

16

9.7

7.9

9.4

17

100

100

100

18

9.9

99.5

85.5

19

9.1

8.7

8.9

20

44.0

97.6

82.9

Mean

33.1

44.1

39.6

5. Conclusions A novel statistical process monitoring framework using ICA and DICA with SVM was proposed in order to monitor a process with auto and cross correlated variables and improve the fault diagnosis performance. Since the goal of ICA is to find a linear representation of non-Gaussian data with components statistically independents, DICA

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applying ICA to an augmenting matrix with time-lagged variables could remove the major dynamics from the process. SVM are trained and the IC matrices are used as their inputs to identify and diagnose faults. The best fault diagnosis performance is obtained using only ICA+SVM with the conditions used in this paper (time-widow of 2 samples for DICA). The approach is applied to diagnose the TE faults. ICA and DICA-SVM based method is worth investigation for diagnosing faults.

6. Acknowledgements Financial support from Generalitat de Catalunya through the FI fellowship program is fully appreciated. Support from the Spanish Ministry of Education through project no. DPI 2006-05673 is also acknowledged.

7. References [1] P Nomikos and J.F Macgregor. Monitoring batch processes using multiway PCA. AIChE Journal, 40, 8 (1994). [2] W-F Ku, R-H Storer and C Georgakis. Disturbance detection and isolation by DPCA. Chemometrics and intelligent laboratory systems. Vol 30(1995). [3] J Lee, C Yoo and I Lee. Statistical monitoring of dynamic processes based on dynamic independent component analysis. Chemical Engineering Science 59 (2004). [4] J Chen and K Liu. On-line batch process monitoring using dynamic PCA and dynamic PLS models. Chemical Engineering Science 57 (2002). [5] R.F Li and X.Z Wang. Dimension reduction of process dynamic trends using independent component analysis. Computers and Chemical Engineering 26 (2002). [6] L Jiang and S Wang. Fault diagnosis based on Independent Component Analysis and Fisher Discriminant Analysis. Proceedings of the third Conference on Machine learning and cybernetics, Shanghai 26-29 (2004). [7] J Lee, S.J Qin and I Lee. Fault Detection and Diagnosis Based on Modified Independent Component Analysis. AIChE Journal, 52, 10 (2006). [8] A Chen, Z Song and P Li. Soft Sensor Modeling based on DICA-SVR. Lectures notes in computer science. Vol 3644 (2005). [9] Laboratory of Computer and Information Science. Helsinki University of Technology. [10] Thorsten Joachims. Department of Computer Science. Cornell University. http://svmlight.joachims.org [11] J.J Downs and E.F Vogel. A plant-wide industrial process control problem. Computers and Chemical Engineering, 17, 3 (1993).

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

273

Inferential estimation of kerosene dry point in refineries with varying crudes Chang Zhoua, Qiyue Liua, Dexian Huanga,c, Jie Zhangb a

Department of Automation, Tsinghua University, Beijing 100084, China. School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle upon Tyne NE1 7RU, UK, E-mail: [email protected] c TNList, Beijing 100084, China b

Abstract A bootstrap aggregated model approach to the estimation of kerosene dry point in refineries with varying crudes is proposed in this paper. Using on-line measurements of process variables, the feed crude oil is classified into one of the three types: with more light component, with more middle component, and with more heavy component. Bootstrap aggregated neural networks are used in developing the on-line crude oil classifier. Historical process operation data are classified into these three groups. A bootstrap aggregated partial least square (PLS) regression model is developed for each data group corresponding to each type of feed crude oil. During on-line operation, the feed crude oil type is first estimated from on-line process measurements and then the corresponding bootstrap aggregated PLS model is invoked. The overall inferential estimation performance of the bootstrap aggregated PLS estimator integrated with feed crude oil classifier is significantly enhanced. Keywords: Bootstrap aggregated model, Data-driven models, Inferential estimation, Crude distillation

1. Introduction Crude oil distillation is a primary process in petro-chemical industry and its operation determines the resource usage efficiency and economic benefits of refineries. In order to properly control refinery operations, it is essential that product quality measurements are available. Since most of the quality indexes can hardly be measured in real-time, various soft-sensor methods have been proposed to estimate these indexes using measurable process variables and have been successfully applied in practice [1, 2]. However, soft-sensing in crude oil distillation with feedstock changes remains a difficult problem because the relationship between the easy to measure process variables and the difficult to measure quality variables varies with the type of crude oil used. Many refineries are operated with mixed sources of crude oil. One possible solution is to develop an inferential estimation model for each type of crude oil. However, this will require many models and, furthermore, crude oil from the same supplier may also vary in the hydrocarbon content. In order to address this problem, this paper proposes a multi-model inferential estimation strategy integrated with crude oil classification for the estimation of kerosene dry point in refineries with varying crudes. Using on-line measurements of process variables, the feed crude oil is classified into one of the three types: with more light component, with more middle component, and with more heavy component. Historical process operation data are classified into these three groups. A bootstrap aggregated partial least square (PLS) regression model is developed for each data group corresponding to each type of feed crude oil. Each model

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has a favourable predictive ability upon the same type of oil but low predictive accuracy upon other types. During on-line operation, the feed crude oil type is first estimated from on-line process measurements and then the corresponding PLS model is invoked. In the crude oil classifier development, bootstrap aggregated neural networks are used. The inputs to the crude oil classifier are the ratios between product and feed rates. Since the relationship between the classifier inputs and output is nonlinear, a nonlinear model has to be developed using process operational data. Through bootstrap re-sampling of the training datasets, multiple neural network models are developed based on bootstrap re-sampled datasets. A bootstrap aggregated neural network shows better accuracy and generalization capability than a single neural network which can be trapped in a local minimum or over-fit the training data during network training. The overall inferential estimation performance of the bootstrap aggregated PLS estimator integrated with feed crude oil classifier gives much better performance than various single PLS estimators. The paper is organised as follows. Section 2 presents a simulated atmospheric distillation column in a refinery with varying feed crude oil. On-line crude oil type classification is presented in Section 3. Section 4 presents inferential estimation of kerosene dry point using bootstrap aggregated PLS models integrated with on-line crude oil classification. Some concluding remarks are given in Section 5.

2. A simulated atmospheric distillation column in a refinery with varying feed crude oil The techniques developed in this paper are tested on a simulated refinery with varying feed crude oil. The simulation is carried out in the HYSYS environment. Fig. 1 shows a schematic diagram of an atmospheric distillation column which is one of the major units used in refineries. Three kinds of crude oil are used as varying feed: light, middle and heavy, each of which is produced by setting different assay values to make different hypothetical components that compose the crude oil. A MATLAB programme is used to change the operation condition in a random way to approximate the real industrial process and get a large number of process data automatically. Also, the product flows are carefully set to ensure that product quality constraints are met.

Fig. 1 A HYSYS flow diagram of an atmospheric distillation column

3. Crude oil classification using bootstrap aggregated neural networks Using on-line measurements of process variables, the feed crude oil is classified into one of the three types: with more light component, with more middle component, and

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with more heavy component. Fig. 2 shows the relationship between feed crude types and the ratios between products and feed. Fig. 2 indicates that the three ratios could be used in classifying the feed crude oil.

Fig. 2 Relationship between feed crude types and the ratios between products and feed

A linear classifier was first developed and the classification accuracy on the testing data is given in Table 1. It can be seen that the classification accuracy is not very high for the middle and heavy oil. This is due to the fact that the two classes are not linearly separable as indicated in Fig. 2. Thus a nonlinear classifier needs to be developed. Bootstrap aggregated neural networks are used in developing a crude oil classifier. Fig. 3 shows a bootstrap aggregated neural network where several neural networks are developed to model the same relationship and are combined together. The individual networks are developed on data sets obtained from bootstrap re-sampling of the original training data [3]. Earlier studies show that an advantage of stacked neural networks is that they can not only give better generalisation performance than single neural networks, but also provide model prediction confidence measures [4]. The aggregated neural network output is given by: n

f ( X ) = ¦ w i fi ( X )

(1)

i =1

where f(X) is the aggregated neural network predictor, fi(X) is the ith neural network, wi is the aggregating weight for combining the ith neural network, n is the number of neural networks, and X is a vector of neural network inputs. For the purpose of comparison, a single neural network based classifier is also developed. Table 1 shows the classification accuracy of different classifier. It can be seen that bootstrap aggregated neural network classifier gives the best classification accuracy while the linear classifier gives the worst performance. In order to demonstrate the robustness of bootstrap aggregated neural networks, five different netwrok combination schemes listed in Table 2 were studied. The experiments were repeated 20 times with different bootstrap resamples generated. Fig. 4 shows the

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classification accuracy and their 95% confidence bounds. Fig. 4 clearly indicates that bootstrap aggregated neural networks give much accurate and reliable (with narrower confidence bounds) classifications.

x

y

™

Fig. 3 A bootstrap aggregated neural network Table 1. Classification accuracy on testing data

Light

Middle

Heavy

All

Linear

100%

88.22%

97.81%

95.34%

Single network

100%

89.04%

99.18%

96.07%

Aggregated network

100%

90.96%

98.63%

96.53%

Table 2. Network combination schemes

1

Single neural network

2

Median of 20 neural networks

3

Median of 10 neural networks with better performance on training data

4

Average of 20 neural networks

5

Average of 10 neural networks with better performance on training data

4. Inferential estimation with bootstrap aggregated PLS models Three PLS inferential estimation models, corresponding to the three types of crude oil, were developed. PLS is a powerful modelling technique for situations where the predictors are correlated [5]. The prediction performance of a PLS or PCR (principal component regression) model on unseen data is highly influenced by the number of latent variables or principal components retained in the model. Bootstrap aggregated PCR or PLS models have been shown to be an effective way to obtain robust PCR or PLS models [6].

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In the bootstrap aggregated PLS model, 20 re-sampled datasets are produced through bootstrap re-sampling of the training datasets. And 20 different PLS model are developed based on the re-sampled data sets. As the industrial process condition is always changing (i.e. the varying crude), it is hoped that one or more of the models based on the re-sampled datasets is able to reflect the currents condition better than the original training datasets. Training data 99

98

98

97

97

Classification accuracy (%)

Clasification accuracy (%)

㨍 㻴 ᡌ 䌁 ᢌ

Testing data

99

96

95

㨍 㻴 ᡌ 䌁 ᢌ

94

93

92

96

95

94

93

92

91

91

90

90

89

1

2

3

4

㿤䕕䗗䕢䕊᪎ⰿ⻎

5

Network combination schemes

89

1

2

3

4

㿤䕕䗗䕢䕊᪎ⰿ⻎

5

Network combination schemes

Fig. 4 Classification accuracies and their 95% confidence bounds

The inferential estimation model uses the following 16 measured process variables as its inputs: top stage temperature, diesel temperature, AGO temperature, kerosene temperature, preheat crude flow rate, reflux temperature, feed temperature, five product and feed flow rate ratios, reflux ratio, and three middle draw heat ratios. Simulated data were obtained using the HYSIS simulation described in Section 2. For building each of the PLS models corresponding to the three types of feed crude oil, the training data set contains 50 sample and the testing data set contains 400 samples. The reason for using a small training data set is from a practical consideration that the laboratory analysis data for kerosene dry point is usually limited. Table 3 shows the root mean squared errors (RMSE) of the developed models on the testing data, using both single PLS and bootstrap aggregated PLS. In Table 2, models I to III are developed using light oil data, middle oil data, and heavy oil data respectively. The results reveal that bootstrap aggregated PLS performs better on the whole, especially when a model is used on other types of crude oil (e.g. model II used on Light dataset). Thus the bootstrap aggregated PLS model will not give significantly large errors when the crude oil is occasionally misclassified.

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5. Conclusions A bootstrap aggregated PLS model inferential estimation approach integrated with online crude classification is developed for kerosene dry point estimation. Bootstrap aggregated neural networks are used to on-line classify the feed crude oil into three types using the ratios between on-line measured product and feed rates. It is shown that bootstrap aggregated neural network gives better classification accuracy than a single neural network. A bootstrap aggregated PLS inferential estimation model is developed for each type of crude oil. The results demonstrate that the bootstrap aggregated PLS model inferential estimation approach gives better performance than a single estimation model. Table 3. RMSE on testing data

Models

I

II

III

single

multiple

single

multiple

single

multiple

Light

2.38 

2.28 

93.40 

12.91 

89.89 

15.82 

Middle

45.49 

31.08 

2.44 

2.47 

268.04  89.15 

Heavy

187.63  41.32 

230.16  59.95 

2.38 

All

111.48  53.47 

143.41  42.24 

163.23  63.90 

2.24 

Acknowledgements The research is supported by National High-tech 863 Program of China ($$= DQG$$=) and UK Department for Innovation, Universities and Skills under the UK/China Fellowship for Excellence programme.

References [1] J. Zhang, Chemical Engineering & Technology, 29 (2006) 560-566. [2] Y. Li, Q. Li, H. Wang, and N. Ma (1995). Particle Soft Sensing Based on LS-SVM and Its Application to a Distillation Column. in Proceedings of the Sixth International Conference on Intelligent Systems Design and Applications (ISDA'06), Jinan, China. Vol 1, 177-182. [3] B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans; Society for Industrial and Applied Mathematics: Philadelphia, 1982. [4] J. Zhang, E.B. Martin, A.J. Morris, & C. Kiparissides, Computers & Chemical Engineering, 21 (1997) s1025-s1030. [5] P. Geladi and B. R. Kowalski, Analytica Chimica Acta, 185 (1986), 1-17. [6] M. Ahmed and J. Zhang (2003). Improved Inferential Feedback Control through Combining Multiple PCR Models, in Proceedings of The 2003 IEEE International Symposium on Intelligent Control, Houston, Texas, U.S.A., 878-883.

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Model-Based Linear Control of Polymerization Reactors Héctor Hernández-Escoto, Salvador Hernández-Castro, Juan Gabriel SegoviaHernández, Antonio García-Martínez. Facultad de Química - Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., 36050, México, [email protected]

Abstract This work addresses the design and performance evaluation of a control system for a class of continuous stirred tank reactors to produce homopolymers via free radicals. The control system claims to be of practical implementation in the sense that: (i) it manages both measurement types existing in this class of processes: continuous-instantaneous, and discrete-delayed with a periodic sampling-time; and (ii) its designing exploits the linear systems theory on the basis of the reactor model. The behavior of the control system, achieving stabilization of an open-loop unstable steady state, in spite of disturbances and parametric model errors, is discussed and illustrated via simulation highlighting the effect of the sampling time. Keywords: linear control, discrete-delayed measurements, polymerization reactor

Introduction The polymerization reactors, because of their industrial importance and highly nonlinear nature, have represented excellent study cases to evaluate and develop different control techniques [1]. In fact, as it can be observed in the open literature, considering the challenge that the nonlinear feature places in front, the studies follow nonlinear advanced approaches; most of them are based on the process model. However, nowadays the industrial polymerization reactors are typically operated through linear controllers that automatically maintain nominal levels of temperature and volume, and supervisory schemes that control the production rate and product quality; and, it can be said that these reactors still are not being fit with advanced control schemes. It can be argued that the nonlinear nature of most of advanced control systems makes them seem complex and of expensive implementation; besides, polymerization reactors are also monitored by discrete-delayed measurements, and the advanced control systems are designed in a framework of continuous measurements, except when model predictive control technique or Kalman filters are applied. The above mentioned has motivated a research line of automatic control systems of polymerization reactors that: (i) are based on deterministic models, (ii) manage both continuous-instantaneous and discrete-delayed measurements, and (ii) are of technically feasible and non-expensive implementation. Methodologically speaking, a linear approach must firstly be followed, but this kind of study is missing in the open literature; and even though controlling temperature and volume does not represent a challenge for linear controllers, automatically controlling production rate and product quality does. Then, in this work, on the basis of linear control elements, and regarding the discretedelayed nature of the measurement related to the production rate, a control system was

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designed for the class of free-radicals homopolymerization continuous stirred tank reactors. Next, the performance was evaluated emphasizing the effect of the samplingtime.

The Polymerization Reactor and its Control Problem In this work, the class of continuous stirred tank reactors, where a free radical homopolymerization takes place, was considered. This class of processes encloses most of the phenomenological characteristics of any polymerization reactor. Their dynamics, with respect to the production rate and safety aspects, are described by a set of four highly nonlinear equations [2]:

IÝ= −rI (I ,T ) + ε ⋅ rP (I ,M ,T ) ⋅ I + (WI /V ) − (q e /V ) ⋅ I := fI (⋅) , ti+1 = ti + δt

(1a)

MÝ= (1 − εM ) ⋅ rP (I ,M ,T ) ⋅ M + (q e /V )(M e − M ) := fM (⋅) , yM (ti ) = M(ti−1) (1b) TÝ= (−ΔH P )rP (I ,M ,T ) − U ⋅ (T − TJ ) + (q e /V )(Te − T ) := fT (⋅) , yT (t) = T (t) (1c) VÝ= −ε ⋅ rP (I ,M ,T ) ⋅V + q e − q s := fV (⋅) ,

yV (t) = V(t)

(1d)

These equations result from material and energy balances, and polymerization arguments, and point up the reactor state is given by the initiator (I) and monomer (M) concentrations, and by the temperature (T) and volume (V) of the reactor content; and the inputs are the initiator (WI) and monomer (qe) feed rates, the jacket temperature (TJ), and the output flow rate (qs). Considering a practical case, the reactor is monitored via monomer (yM), temperature (yT) and volume (yV) measurements. It must be noticed yM, at the sampling time instant ti, takes the value of M at ti-1, and δt is the periodic sampling time (ti = ti-1 + δt); say, yM is a discrete-delayed measurement resulting from a samplinganalysis activity along the reactor operation. The functionalities rI and rP represent the consumption rate of I and the polymerization rate, respectively; ε is the volume contraction factor, and U represents the heat transfer capabilty of the jacket. Then, the objective is controlling the reactor in a certain (possibly open-loop unstable) nominal state ( I ,M ,T ,V ) by the manipulation of qe, TJ, and qs, on the basis of the continuous measurements of T and V (yT(t), yV(t)), and the discrete-delayed measurement of M (yM(ti)).

The Control System The control system for the polymerization reactor is depicted in Figure 1; it can be observed that the defined control structure is the following: M is controlled through qe, which is driven by an estimate of M (ME); T is controlled through TJ, driven by yT; and V is controlled through qs, driven by yV. Then, the essential control elements are a controller, and an estimator; regarding to the discrete-delayed characteristic of yM, the estimator is added in order to provide ME(ti) each sampling time instant (ti). The Controllers The linear controllers for monomer, temperature and volume are:

qe (τ ) = q e + kPMC ⋅ (M E (ti ) − M ) + kIMC ⋅ ¦

n i= 0

(M E (ti ) − M ) ⋅ δt , τ ∈ [ti ,ti+1 ] (2a)

u(t) = u + kPX ⋅ ( y X (t) − X ) + kIX ⋅ ³ ( y X (s) − X ) ⋅ ds t

0

(2b)

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_ where u = TJ, qs, and X = T, V, respectively; the ‘ ’ symbol refers to a nominal value of the variable. The controllers have proportional and integral (sumatorial for the monomer MC X MC X controller) actions, where kP ,kP ,kI ,kI are the tuning gains. It is noticed that qe becomes a stepwise function that depends on the sequenece of the monomer estimate values {ME(t0), ME(t1), ME(t2), …}.

Figure 1. Control System of the Polymerization Reactor

The Estimator The estimator construction followed the straightforward application of the procedure given in [3] on the basis of the linearized version, at the nominal contidition, of the I and M dynamics of the reactor model (Eq. 1a, b),

Ý I˜ = aII I˜ + a IM M˜ + a IT y˜T + aIV y˜V + a Iqe q˜ e + a IWI W˜ I , amn = (∂fm / ∂n) x ,u

(3a)

Ý M˜ = aMI I˜ + a MM M˜ + a MT y˜T + a MV y˜V + a Mqe q˜ e , y˜ M (ti ) = M˜ (ti−1 )

(3b)

where the ‘∼’ symbol indicates a deviation variable between the actual and nominal ˜ = M − M ). T and V dynamics are not considered since yT and yV equal T values (i.e. M and V, respectively, and only I and M are necessary to estimate, in a reduced order estimation scheme [4]. The possibilty of the estimator construction is provided by the stable feature of the sole I-dynamics (Eq. 3a), and by the trivial observability property of the coefficients pair (aMM, 1). The estimator takes the following form:

I˜ E (ti+1 ) = ΘI ( I˜ E (ti ), M˜ E (ti ), y˜T (t), y˜V (t),W˜ I (t), q˜ e (t))

(4a)

M˜ E (ti+1) = ΘM ( I˜ E (ti ), M˜ E (ti ), y˜T (t), y˜V (t), q˜ e (t)) + kPME eM (ti ) + kIME i M (ti ) ,

(4b)

i M (ti+1) = i M (ti ) + kIME eM (ti ) , eM (ti ) = y˜ M (ti ) − M˜ E (ti )

(4c)

where ΘI and ΘM are the transition maps of the linear differential equations (3a, b). Besides the proportional action, the estimator has a sumatorial one accounted by the ME ME variable iM. kP and kI are the estimator tuning gains.

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Tuning The tuning scheme was constructed through the following procedure: (i) for the continuous controllers (Eq. 2b), the coefficients of the corresponding secondorder closed-loop linearized dynamics of T and V, in a decoupled structure, were matched with the ones of the characteristic polynomial of the stable linear dynamics of reference x + 2ξωx + ω x = 0 ; where (ξ.- damping factors, and ω.- characteristic frequencies (ii) for the discrete M-controller (Eq. 2a) and M-estimator (Eq. 4), first a characteristic polynomial of reference was constructed on the basis of the eigenvalues (γ) that result from mapping the eigenvalues (λ) of the above continuos reference dynamics into the unit circle: γ = exp(λ δt); next, the coefficients of the characteristic polynomials of the corresponding second-order closed-loop discrete linear dynamics of M, and convergence error dynamics of the M-estimator, were matched with the reference characteristic polynomial. In this way, the gains are given in terms of the well-known parameters (ξ.- damping factor, ω.- characteristic frequency) of a stable dynamics: 2

kPX = −(1/ aXu )(aXX + 2ξ X ωX ) , kIX = −(ωX / a Xu ) ,

aXu = (∂fX / ∂u) x ,u

2

kPM ,Z = (c1(δt ,ξ MZ ,ωMZ ) + p1(δt ) + 1) / p2Z (δt ) ,

X = T, V

u = qe, TJ

kIM ,Z = (c1(δt ,ξ MZ ,ωMZ ) + c 2 (δt ,ξ MZ ,ωMZ ) + 1) /(δt ⋅ p2Z (δt )) , Z = C, E

(6a) (6b) (6c)

p1 (δt ) = exp(aMM ⋅ δt ) , p2C (δt ) = aMq e (1 − p1 (δt )) / aMM , p2E = 1 c1 (δt ,ξ ,ω ) = −2 exp(δtξω ) cos(δt 1− ξ 2 ω ) , if ξ ≤ 1; c1 (δt ,ξ ,ω) = −(exp(2δt ξ 2 −1) +1) exp(−δt (ξ + ξ 2 −1)ω) , if ξ > 1,

c2 (δt ,ξ ,ω) = exp(−2δtξω) . Consequently, the controllers and the estimator are tuned in a framework of convergence rate manipulation by firstly setting the sampling time; next, choosing damping factors, and varying desired settling times with the characteristic frequencies.

Control System Performance The test of the control system was based on the study case of Alvalrez [2]. The nominal operation conditions associated to an open-loop unstable steady state were considered, (I ,M ,T ,V ,qe ,Tc ,q s ,WI ,Te ) = (0.001831 gmol/L, 0.5809, 349.58 K, 40 L/min, 315 K, 34.94 L/min, 0.08 gmol/min, 300 K); with these conditions, the polymerization is carried out at high solid fraction with gel effect, making the control system test extreme. In order to emulate the operational problems that appear in an industrial framework (i.e. change in the heat transfer capability of the reactor due to jacket fouling, and changes in the kinetics efficiency due to different raw material providers), parameter errors were introduced to the reactor model. Besides, disturbances on WI (+10% of the nominal value) and Te (+2% of the nominal value) were introduced. In Figure 2 the performance of the control system is shown for two sampling time situations: (i) δt = 5 min, with the tuning parameters (ξMC, ξT, ξV, ξME) = (2, 0.7071,

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0.7071, 2), and (ωMC, ωT, ωV, ωME) = (0.04, 0.15, 0.4, 0.4); and (ii) δt = 15 min, with the tuning parameters (ξMC, ξT, ξV, ξME) = (2, 0.7071, 0.7071, 2), and (ωMC, ωT, ωV, ωME) = (0.004, 0.15, 0.4, 0.04). It can be observed that the performance of the control system with a δt = 5 min is adequate and fast, and the required effort on the control inputs is smooth. In the case of δt = 15 min, the nominal state is still maintained; however, it takes a longer settling time and requiere more control effort (even the temperature and volume controllers) than in the case of frequent monomer mesurement. In fact, it must be said that for a δt greater than 17 min, the control system does not achieve stabilization; but, in the ideal case of non parametric errors, the control system does with a δt up to 25 min.

Figure 2. Control System Performance

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Although this control system only deals with the variables related to the production rate and safety (M, T, V), it fits to say that the control of the product quality is also achieved, but its convergence rate, and offset, is not handled in a direct form, as the I-dynamics (Figure 2). In the light of the attained performance, the approach can be extended to control the product quality; for example, driving the initiator feed rate or a transfer agent with discrete-delayed measurements of the average molecular weight of the polymeric product.

Conclusions In this work, it was designed a control system for a polymerization reactor whose linear control elements had the capability to adequately ensure its nominal operation, managing continuous-instantaneous and discrete-delayed measurements. The control system includes a systematic model-based tuning scheme that takes in account the sampling time, and whose conventional parameters provide insight into desired convergence rates. This system of linear controllers presents the least implementation cost, and a comparison of its performance with systems of nonlinear controllers would be worthwhile.

Acknowledgements We acknowledge the financial support provided by CONACyT (México) and Universidad de Guanajuato.

References [1] J. R. Richards and J. P. Congalidis, Comp. and Chem. Eng., 30 (2006) 1447. [2] J. Alvarez, AIChE Journal, 42 (1996) 2540. [3] H. Hernández and J. Alvarez, Journal of Process Control, 13 (2003) 69. [4] C.-T. Chen (3rd Edition, Oxford University Press), Linear System Theory and Design, New York, U. S. A., 1999

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Optimal bifurcation tailoring based transition control of reactor separation recycle systems Pietro Altimari,a Lucia Russo,a Erasmo Mancusi,b Costin Sorin Bildea,c a Silvestro Crescitelli a Università “Federico II” Piazzale Tecchio 80,80125 Napoli, Italy b Università del Sannio, Piazza Roma, 82100, Benevento, Italy c University “Politehnica”of Bucharest, 1-7 Polizu, 011061-Bucharest, Romania Abstract A novel method for transition control of nonlinear processes is presented. Gain scheduling is implemented to ensure stability and desired output behavior over the operating region of interest while transition between the initial and the final equilibrium is achieved by predictive reference control. In this framework, the search of a feasible reference input sequence is performed so that the closed-loop system moves along an optimal curve of equilibria. This curve is computed off-line so that its points lye far from the border of the process constraint set and correspond to satisfactory controllability of the uncontrolled plant. Moreover, bifurcation analysis of the closed loop system is carried out providing valuable indications on how to select controller parameter values preventing transition to undesired solution regimes. Effectiveness of the method is shown by application to the problem of controlling the start-up of a reactor separation recycle system. Keywords: bifurcation tailoring, gain-scheduling, predictive reference control

1. Introduction Large changes in the operating conditions typically occur in industrial practice. In polymerization reactors, for example, operating conditions are modified to attain product specifications responding to different market demands. In these operations, the transient needed for the plant to reach the desired equilibrium must be minimized to prevent large amount of off-specification products [1]. An effective approach to control transition of nonlinear processes between different equilibria relies on the implementation of gain scheduling (GS) [2]. This technique is based on the use of a family of linear feedback controllers, each of them guaranteeing desired output behavior around a different equilibrium. Plant equilibria are, in this framework, parameterized by a suitable set of reference variables. Hence, transition between different equilibria can be achieved by a step change of the reference issued to the closed-loop system. This can be thought of as switch between the feedback controllers associated to the initial and the final equilibrium and can lead to process constraints violation due to large changes in process dynamics. This can be prevented by adding to the closed loop system a predictive reference (PR) controller which on-line modifies the reference so as to enforce the fulfillment of the constraints [3]. In this paper, a novel method for transition control of nonlinear processes is presented. PR-control is implemented so that the GS-closed-loop moves along an optimal curve of equilibria. This curve is computed (or tailored) so that its points lye far from the border of the process constraint set and correspond to satisfactory controllability of the open-

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loop system. Moreover, parametric continuation is performed to select the feedback controller gains preventing transition to undesired solution regimes.

2. Control structure design Let be the plant to be controlled described by the following nonlinear system:

dx = f ( x,u ) dt

(1)

where x∈Ρn and u∈Ρn are the state and the input vectors respectively. We refer to E={(x,u)∈ Ρn Ρm: f(x,u)= 0} as the equilibrium set of (1) and assume that state and input variables are constrained within the set C= {(x,u) ∈ Ρn Ρm: xa<x< xb, ua<x< ub}. If f has non-singular Jacobian, the set E is described by an m-dimensional manifold. We refer to this manifold as the bifurcation manifold. The objective is to perform transition to pef=(xef,uef) starting from pe0= (xe0,ue0). We assume that a map Ω(σ):D⊆ΡmĺE can be constructed and refer to σ= σ(x) as the vector of scheduling variables. In this setting, the application of GS requires to design a family of feedback controllers u=u(σ,x) ensuring stability of Ω(σ) as σ varies [2]. In this paper, the following GS-control law is considered:

u (σ ,x ) = ue (σ) − Κ (σ)( x - xe (σ)) = u ff (σ) + u fb (σ, x )

(2)

where K(σ) denotes a parameterized family of gain matrices. It worth to note that (2) is composed of a feedforward uff(σ) and a feedback ufb(σ,x) control term. Accordingly, the closed-loop system can be represented by the block scheme shown in Figure-1.

uff(σ )

σs

Ω (σ )

xe(σ )

+

Ϭ

K(σ)

ufb(xσ )

- +

P

x

Figure 1. Block scheme of the gain scheduled closed loop system. Here, σs is the reference and identifies the desired equilibrium pe=Ω(σ). Moreover, the gains are scheduled according to σs to ensure stability. In accordance with Figure-1, transition to pef = Ω(σf) starting from pe0 = Ω(σ0) can be achieved by step change of σs between σ0 and σf. In so doing, constraints violation may occur due to large variations in process dynamics. This can be prevented by adding to the closed loop system a PRcontroller [3]. Such controller modifies the reference so as to enforce the fulfilment of the constraints. In particular, a constant reference σk is applied in the interval [kT, (k+1)T] ensuring that the constraints are fulfilled over the horizon [kT, kT+Th]. The search of a feasible σk is generally restricted to the segment S(α)=σ0+α(σ0−σf) connecting σ0 and σf to reduce the required computational resources. Therefore, a

Optimal Bifurcation Tailoring Based Transition Control

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feasible reference input sequence {σk}k∈Ν≡{S(αk)}k∈Ν can be computed by solving at each T the following nonlinear program [3]:

­° max α α k = ® α∈[αț ,1] °¯ s.t. p (t , x( kT ),S(α)) ∈ C

(3)

where p(t,x(kT),Γ(α)) denotes the evolution of the closed loop system for initial conditions x(kT) when the control law (2) is implemented with σ=Γ(α).

3. Optimal bifurcation tailoring The application of (3) requires that Ω(S(α)) fulfils process constraints as α varies [3]. However, equilibria Ω(S(α)) violating constraints may be found due to the nonlinearity of Ω. Moreover, equilibria Ω(S(α)) may present characteristics preventing fast transition to pef even though fulfilling process constraints. For example, they might result close to the border of C reducing the allowed variations of the manipulated variables. Motivated by these difficulties, we extend the application of (3) to parameterized curves Γ(α):[0,1]ĺD connecting σ0 and σf. Infinite curves connecting σ0 and σf are indeed available when m>1 allowing to optimize the equilibria around which the plant moves during the transition. We here compute Γ(α) so that the equilibria Ω(Γ(α)) lye far from the border of C and correspond to satisfactory controllability of the open-loop system. This leads to formulate the following problem: 1

(

min Φ (Γ ) = min ³ w1 Ψ ' Γ

Γ

0

Q

)

+ Ψ ' ( w2 L ( Ψ ) + w3 M ( Ψ ) ) d α

s.t. Ψ(α) ∈ C, L(Ψ(α)) ≤ ηa , M (Ψ(α)) ≤ ηc ∀α ∈ [0,1]; Ψ(0) = pe0 ; Ψ(1) = pef

(4) (5)

Where Ψ(α)= Ω(Γ(α)), Ψ'(α)= DαΩ(Γ(α)), L(p) and M(p) are functions providing information about the controllability and the distance of p from the border of C, ηa and ηb are vector bounds, w1, w2 and w3 are weighting constants. We note that integrating the norm of the derivative of Ψ(α) in (4) enables to prevent large excursion of Ψ(α) from the region surrounding pe0 and pef. We refer to (4)-(5) as the optimal bifurcation tailoring problem as computing Γ(α) uniquely defines the curve of the bifurcation manifold to be tracked. For the function L, the inverse of the minimum singular value of the process steady state gain matrix is used [4]. Small values for the minimum singular value indicate indeed that the plant easily moves between different equilibria. The following expression is adopted for M:

M ( p) = ¦ ª x − xa⊥,i « i =1 ¬ n

−1 Q

+ x − xb⊥,i

−1 Q

º + ª u − u⊥ a ,i »¼ ¦ « i =1 ¬ m

−1 Q

+ u − ub⊥,i

−1 Q

º »¼

(6)

where xkiŏ and ukiŏ denote the projections of x and u onto the planes x=xk,i and u=uk,i respectively. M is positive and becomes infinitely large as p approaches the border of C. Once the problem (4)-(5) is solved, a feasible sequence {σk}k∈Ν≡{Γ(αk)}k∈Ν can be computed by solving (3) with S replaced by Γ.

P. Altimari et al.

288

4. Application to a reactor-separation recycle system As a representative example, the proposed method is validated on the problem of controlling the start-up of a continuous tank reactor where the series of two first-order irreversible exothermic reactions AĺBĺC takes place. Assuming that a fraction RA of unconverted A is recovered and recycled to the reactor, that B and C are not present in the recycle and that the reactor inlet temperature is kept at a constant value, reactor dynamics can be described as follows:

dX A F § E · = 1 ( X A − X A,1 ) − k1 exp ¨ 1 ¸ X A dt MR © RT ¹

(7)

dX B F § E · §E · = 1 ( X B − X B,1 ) + k1 exp ¨ 1 ¸ X A − k2 exp ¨ 2 ¸ X B dt MR © RT ¹ © RT ¹

(8)

ΔH1k1 F dT § E = 1 (T1 − T ) + exp ¨ 1 dt M R WM C p © RT

ΔH 1 k 2 UA · §E · exp ¨ 2 ¸ X B − (T − Tc ) (9) ¸XA − WM C p WM C p ¹ © RT ¹

dTc Qc UA = (Tc ,1 − Tc ) + (T − Tc ) ρc C p,c dt Vc F1 = FA0 + FB 0 +

( FA0 + FB 0 ) RA X A 1 − RA X A

(10)

(11)

The variables in the model are the reactor molar fraction XA and XB of A and B, the reactor and the coolant temperature T and Tc, the inlet flow rate F1, the fresh feeds FA0 and FB0 of A and B, the coolant flow rate Qc. Here, we assume RA= 0.3. The other parameters have the usual meaning and are kept at constant values derived from [6]. The expression (11) for F1 is obtained by solving the external mole balance equations at the separation and the reactor inlet sections. State and input variables x= (XA, XB, T, Tc) and u=(FA0, Qc) are assumed to be constrained as follows: 0<XA<1, 0<XB<1, 300
Optimal Bifurcation Tailoring Based Transition Control

289

200 360

(b)

(a)

Qc,max 150

T

Qc

340 100

320

FA0,min 50

300 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

FA0,max Qc,min

0

10

20

30

XA

40

50

60

FA0

Figure 2. Projections of the curves Ω(S(α)) and Ω(Γ(α)); (a) reactor temperature T versus molar fraction XA; (b) coolant flow rate Qc versus fresh feed FA0. Α family of LQR controllers [5] is then designed enforcing stability around Ω(Γ(α)) as α varies. This gives the following GS-control law:

u(Γ(α),x ) = ue (Γ(α)) − 0.5BT (Ω(Γ(α))) P(Ω(Γ(α)),λ)( x - ue (Γ(α)))

(12)

where B=Du[f(x,u)] and P solves the Riccati equation ATP+PA-PBBTP-R(λ)=0 [5]. Here, R(λ) is a positive definite matrix parameterized by the scalar λ. In particular, we assume that R is the diagonal matrix defined by v=(5 λ,5λ, λ, λ). 360

360 (a)

xe1

(c)

340

T(Γ( (Γ(α))

T

340

T

320 300

α

1.0

(b)

S1

320

300

0.5 0.0 0

5

10

15

t

20

25

280 0.0

0.2

0.4

α

0.6

0.8

1.0

Figure 3. (a) Reactor temperature simulation response; (b) evolution of α imposed by the reference controller; (c) solution diagram of the closed loop system. Results of the application of the reference control scheme (3) with S replaced by the computed Γ and λ=1 are reported in Figures 3a,b. Here, the reactor temperature response (Fig. 3a) and the evolution of α imposed by the PR-controller (Fig.3b) are shown. It is apparent that the closed loop system cannot reach pe2. After an initial rise, the reactor temperature starts to decrease and an undesired stationary value is eventually reached. The reason of the observed behaviour must be imputed to the presence of equilibria coexisting with Ω(Γ(α)). This are observed in Figure-3c which shows the solution diagram of the closed-loop system. The equilibria Ω(Γ(α)) are invariably stable. Nevertheless, undesired branches are found due to the saddle node bifurcation S1. The evolution of S1 in the α-λ plane is described in Figure 4a. It can be noted that S1 vanishes at λ>18. Therefore, the scheme (3) with S replaced by Γ is applied when λ=20. The reactor temperature simulation response is, for this case, shown in Figure 4b. It is found that pe2 is reached within about 12 min.

P. Altimari et al.

290 20 360 (b)

(a)

xe2

340

T

15

λ

320 10

300 1.0

(c)

α

5

0 0.0

0.2

0.4

α

0.6

0.8

1.0

0.5 0.0 0

5

10

15

20

25

t

Figure 4 (a) Bifurcation diagram of the closed loop system; (b) Reactor temperature simulation response; (c) evolution of α imposed by the reference controller.

5. Conclusions A novel method for transition control of nonlinear processes was presented. GS is implemented to ensure stability over the operating region of interest and transition between the initial and the final equilibrium is achieved by PR-control. In this framework, the search of a feasible reference input sequence is performed so that the closed-loop system moves along an optimal curve of equilibria. This curve is computed off-line so that the its points correspond to satisfactory controllability of the uncontrolled plant and lye far from the process constraint boundaries. Moreover, bifurcation analysis of the closed loop system is performed by varying the reference signal according to the computed curve. In this way. controller parameter values preventing undesired transition regimes are selected. The proposed approach was applied to the problem of controlling the start-up of a reactor separation recycle system. In this context, the approach proved to effectively handle the presence of multiple solution regimes enabling to remove a low conversion branch responsible for reactor shut-down.

References [1] [2] [3] [4] [5] [6]

Takeda, M., and Ray, W., H., AIChE J., 45, 8, 1776, (1999). Rugh, W., J., and Smamma, J., S., Automatica, 36, 1401, (2000). Bemporad, A, IEEE Trans. Autom. Control, 43, 3, 415, (1998). Skogestad, S., Morari, M., Ind. Eng. Chem. Res., 26, 2029, (1987). Kailath, T. Linear Systems, Prentice Hall, Englewood Cliffs, NJ., (1980). Meel, A., Seider, W., D., Soroush, M., AIChE J., 52, 1, 228, (2006).

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

291

Quality by design approach in drying process organization a

a

a

Alexander Troyankin, Anton Kozlov, Alexander Voynovskiy, Natalia Menshutina a a

Mendeleyev University of Chemical-Technology of Russia, High technology department, 125047, Miusskaya sq. 9, Moscow, Russia, [email protected]

Abstract With the rapid implementation of the PAT initiatives, the role of quality control systems in pharmaceutics is going to be extremely important. The operation of such systems is closely connected with the use of various mathematical methods and information technologies directed to the achievement and maintaining required quality at every step of the production process and therefore guarantee the quality of final product. This forms a base for quality by design approach in process organization. This paper presents an approach to process organization using PAT and design of information system that can be capable to use and process data from different production levels and therefore provide production process monitoring and control. Three technological processes, with drying stage included (freeze-drying, granulation, coating) is taken as an example of the described approach application. Keywords: PAT, quality management, drying, pharmaceutics 1. Introduction Nowadays there is a great need in implementation of new innovative power saving, environmental-friendly technologies. Growth of production rates and energy consumption, high costs of raw materials, environmental pollution – all these factors force us to make efforts to the development of new green technologies and to the optimization of the current ones. Pharmaceutics always pays great attention to product quality. It is the key factor and all steps of the process should serve to provide required quality of the final product. Such shift in ideology happened when GMP were implemented in the US and Europe. Similar process is now observed in Russia. In comparison with microelectronics where the percentage of waste product is very low this value in pharmaceutical industry is relatively high and every year companies waste huge amount of money. That is why a quality management nowadays becomes a more and more important question. Organization and control of any quality management systems is closely connected to information technologies.

292

A. Troyankin et al.

IT and Quality management

Among all quality management systems three major levels of them can be discerned (See Fig. 1): ERP (Enterprise Resource planning) – manufacture level; LIMS (Laboratory Information Management System) – laboratory level; PAT (Process analytical technology) – process level. Each level is separated and can be represented by several modules, or a whole system.

Fig 1. Quality management information systems

ERP systems attempt to integrate several data sources and processes of an organization into a unified system. A typical ERP system will use multiple components of computer software and hardware to achieve the integration. A key ingredient of most ERP systems is the use of a unified database to store data for the various system modules. LIMS is computer software that is used in the laboratory for the management of samples, laboratory users, instruments, standards and other laboratory functions such as invoicing, plate management, and workflow automation. LIMS connects laboratory with other enterprise control systems, it increases data processing and research work automation. Process analytical technology is considered to be a system for designing, analyzing and controlling manufacturing through timely measurements of critical quality and performance attributes of raw and in-process materials and processes, with the goal of ensuring final product quality [1]. 2. PAT and Quality by design PAT ideology implies product quality to be considered from the very beginning in process design and optimization. In other words, the process needs to be designed and optimized taking into account continuous quality control.

Quality by Design Approach in Drying Process Organization

293

Offline process monitoring

Raw material

Mixing, Preparation

Drying

Packing

Quality assessment at the end of each stage

Fig 2. Offline quality control

For example, classic approach (See Fig. 2) to the production process organization (e.g. drying) implies offline (after the end of the stage) quality measurements. In case of any mistakes or deviations happened during processing on intermediate stages, it can results in non-quality or waste product. One of the aspects of PAT is Continuous quality assurance. System monitoring and control is being carried out in real-time (See Fig. 3) using noninvasive and indirect analysis technologies. On-line and in-line process monitoring Quality management as control element

Raw material

Mixing, Preparation

Drying

Packing

On-line quality assessment

Fig 3. Continuous quality control

All product characteristics measurements and investigations are carried out inline and on-line. Process control should be oriented to the providing stable and continuous quality of the final product. Quality control should be real-time organized and be based on dynamic quality characteristics measurements. Modern analytical equipment makes possible to collect and process huge amount of data real-time. Information technologies help to integrate gathered information and by means of modern computers and software, it is possible to apply complicated mathematical methods to analyze it. One of the relatively new and remarkable methods for process control is Multivariate Statistical Process Control (MSPC). MSPC can be defined as a set of modern mathematical and stochastical methods, algorithms for process control and optimization. Among these methods are Factor analysis (Principal Component Analysis, Partial Least Squares), process modeling (Multivariate Curve Resolution, Process Simulation), Classification methods (PLS-Discrimination, Soft Independent Modeling of Class Analogy, Hierarchical Cluster Analysis) etc. For the application of the MSPC detailed investigation of the technological process is needed. During this investigation process parameters and quality factors should be defined. Process conditions are represented as a set of parameters that can be changeable. These parameters are also particular for each type of process (drying, granulation, coating etc.) Number of them can be varied, but it is necessary to choose parameters that have influence on the product quality. Sometimes an additional task is to investigate which process conditions are vital and should be taken into account, and which are not important and can be ignored.

A. Troyankin et al.

294

The description of product quality can be done by means of quality factors, which are particular for each product (e.g. moisture content, color, density etc). All factors should be measurable and full set of them should describe product quality to a certain extent. One main quality factor can be defined, which is the most important for particular product, other factors can be ranged according to their importance or they can be equally important. After quality factors or attributes and process parameters are chosen and defined, next step is establishing a link between process parameters and product quality. Knowing these links it is possible to control or predict the quality of final product by changing process conditions and maintaining them in proper limits. This links can be established by means of various mathematical methods. This makes possible to search for alternatives that can provide required values of quality factors and therefore provide the quality product. However, the investigation of dependence between quality factors (initial raw material and final product) and process conditions can be very expensive and sometimes is not possible. Analysis of correlations of all parameters and factors is very complicated because of high dimensionality. This problem can be solved using multivariate calibration method. Data reduction (compression) and dimensionality decrease is possible by using latent projections. Now it is clear that designing the production line it is very important to pay attention and provide following facilities: facilities for monitoring of observed technological parameters; facilities for monitoring and control of adjustable technological parameters; facilities for complex and noninvasive analysis such as NIR spectroscopy. Some features of PAT Quality by Design (QbD) approach are shown in Fig. 4. Noninvasive analysis technologies

Design PAT (QbD)

Indirect measurements

Optimization Multivariate statistical process control (MSPC)

NIR / XFR / FBRM ... Calibration and quality factors assessment

Prediction and calculation of technological parameters

Fig 4. Features of PAT QbD approach

It should be noted that to provide stable product quality and to increase process efficiency data analysis from three major production levels is required. That can be possible if information systems at Manufacture level (ERP), Laboratory level (LIMS) and Process level (PAT) will be integrated and into connected. This makes a base for computer system design that is capable to use and process data from different production levels and therefore provide whole production process monitoring and control.

Quality by Design Approach in Drying Process Organization

295

3. System design and practical application Described approach to PAT Quality by design was applied to three apparatus and three processes: freeze-drying, encapsulation, coating. Each process included drying stage that is why we focused on it as an example of our approach application. Freeze-drying was carried out in special atmospheric fluid bed freeze dryer with active hydrodynamics [2], Granulation and Encapsulation processes in Huttlin Mycrolab and Mini-Glatt. As mentioned before the analysis of the process includes the definition of technological process parameters and quality factors. Gathered data is represented in Table 1. Technological parameters obtained directly from the installed equipment. Information about quality of the product comes from the analytical equipment in real-time. For discussed case special software that is integrated with process monitoring and control systems, and provides real-time quality-based processing is being developed. One-wire technology form Dallas Semiconductor, built-in equipment facilities and additional analytical equipment were used. Table 1. Process properties

Process parameters Freeze drying Air flow , Moisture content, Air temperature, Concentration and quantity of the dried product Granulation (inc. drying) Air flow, Air temperature, Dispersed liquid flow, Concentration, Microclimate pressure, Distance between nozzle and the bed Coating (inc. drying) Air flow, Air temperature, Dispersed liquid flow, Concentration, Microclimate pressure, Distance between nozzle and the bed

Quality factors Weight, Identity of the composition, Moisture Weight, Identity of the composition, Particle size

Identity of the composition, Particle size

The idea is that it is capable to monitor any deviation of critical process parameters during technological process, analyze the occurred deviation and decide if it is necessary and how to adjust the process by changing proper process parameters. So that in relatively short time the process is returned to its normal state. This allows avoiding the loss of the quality on intermediate steps and during the whole process. Described approach makes possible to create the structure of the QC Information system for pharmaceutical industry, it can be used in adaptation of the existed equipment layout, and using supposed methods of analysis and control, it is possible to implement online quality control [3]. An approach to design of such Information systems that can be capable to process and unite data from different production levels is shown in Fig. 5. This can be the base for creation knowledge base systems containing particular cases and patterns of behavior. Application of such systems can help to reduce the costs of new process and product development.

A. Troyankin et al.

296

Data acquisition from different production levels

Manufacturing level

ERP

Workflow, Input control

Laboratory level

LIMS

Results of laboratory tests

Process level

PAT

Quality by Design Continuous quality assurance

Data acquisition cycle

Data analysis cycle Process control level

Quality factors assessment

MSPC

Calibration of process parameters Prediction of process parameters values

Fig 5. General scheme of design integrated quality management intellectual system

The implementation of described tools and methods for quality management in a production scale is closely dependent on scientific research and experimental work, and thus is relatively complicated and expensive. However, it is clear that quality by design ideology is a way to provide stable quality, minimum waste product, so that the return of investment is very clear. References [1] U.S. FDA, Guidance for Industry. PAT - A Framework for Innovative Pharmaceutical Development, Manufacturing, and Quality Assurance, (2004), http://www.fda.gov/cder/guidance/6419fnl.htm [2] Menshutina N., Korneeva A., Goncharova S. and H. Leuenberger, Modeling of freeze drying in fluidized bed, Proceedings of the 14th International Drying Symposium, Sao Paolo, Brazil, 22-25 August, vol. A, (2004) pp. 680-686 [3] Degtyarev E.V., Pharmaceutical drug analysis in production and quality management, Russian Chemical Society magazine, vol. 46(4), (2002), pp. 46-51

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

297

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19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

303

Adaptation and testing of data reconciliation software for CAPE-OPEN compliance Eric Radermecker,a Marie-Noëlle Dumont,b Georges Heyen a,b BELSIM s.a., Rue Georges Berotte 24a, 4470 Saint-Georges-sur-Meuse, Belgium de Liège, Chemical engineering, Sart Tilman B6, 4000 Liège, Belgium, b [email protected] aUniversité

Abstract The experience gained in the development of a CAPE-OPEN 1.0 thermo socket for the BELSIM-VALI software is presented. VALI is a data validation and reconciliation software that provides consistent mass and energy balances, reliable and accurate Key Performance Indicators and soft sensors. It is not a simulation software per definition, but rather a powerful equation based software that is used online, to monitor and manage the operations of different processes. VALI has its own thermodynamic database of chemical compounds (> 800 fluids, > 650 solids) and methods. After demands of our clients it was decided to make VALI compliant with other thermodynamic packages via a CAPE-OPEN 1.0 thermo socket. The source code of the VALI physical property modules had to be modified, to call the Material Object components instead of built-in thermodynamic functions (thermo socket). In the user interface, we had to develop a CAPE-OPEN thermo plugs viewer to allow the selection of a CAPE-OPEN thermo plug from our Graphical User Interface (GUI). Several case studies were analysed, with performance comparison between the native thermodynamic model, and properties obtained from several CAPE-OPEN thermo plugs. We will particularly analyse here the modelling of a gas liquefaction system and a distillation case study. Keywords: Cape-Open, physical properties, data reconciliation

1. Introduction VALI is an advanced data validation and reconciliation software, used online in industry to improve the accuracy of plant data. It is not a simulation software and although process simulation and advanced data validation and reconciliation are similar on several aspects, they are quite different as well. The main difference being the way plant data are handled. In simulation, plant data are used to tune various parameters of simulation models, giving a better model, while in data validation plant data are used to check and correct measurements, giving better information of the actual state of the plant. Both process simulation and data validation and reconciliation are based on a mathematical model of a process. These models are built using predefined objects modeling the process units operations and the products that are handled. Some information must be available about the physical properties of the chemical components present in the system like their molecular weight, their density, etc. On the mathematical side, process simulation has been traditionally developed on a modular sequential approach. Each process unit is represented by a mathematical model that calculates the state of the output streams knowing the state of the input streams and

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some unit operation specifications. Each unit is modeled after the other. When some streams are recycled, convergence algorithms are to be used. Using such an approach is not possible for data validation and reconciliation. Instead the program must generate equations that relate inputs and outputs. An optimization algorithm is then used to find the set of values that are as close as possible to the measurements while satisfying the equations.

2. Learning Phase As a first step of this work, it was important to have a better understanding of both the CAPE-OPEN standards and the COM technology, before even starting the development work. A training course was followed, given by Prosim that has a long experience in implementations of CAPE-OPEN standards. 1.1. COM technology COM (Component Object Model) is an interface standard for software components introduced by Microsoft in 1993. It is used to enable inter process communication and dynamic object creation in any programming language that supports this technology. The term COM is often used in the software development industry as a term that encompasses the OLE, ActiveX, COM+ and DCOM technologies. The main advantage of COM is that it’s a language-neutral way of implementing objects that can be used in environments different from the one they were created in. Although the interface standard has been implemented on several platforms, COM is primarily used in Microsoft Environment. After discussion, Belsim decided to develop the Material Object in .NET C# 2.0. The Material Object is the central point of the architecture and the link between our software and the CAPE-Open Property Package/Thermo Systems. Based on that, two Belsim software parts have been adapted to be able to create an instance of the Material Object using COM interfaces: - ValiModeller: Graphical User interface designed to model the process. This interface is developed in C++. - ValiEngine: Calculation Engine developed in FORTRAN. Several COM interfaces in addition to the one defined for CAPE-OPEN have been developed in the Material Object to ease the communication with the calling application. 1.2. First Implementation A first CAPE-OPEN socket version 0.93 was developed in 2001 but the use of a COThermo Package was very difficult for a non-expert user. The Graphical User Interface (ValiModeller) was not able to deal with a third party thermodynamic model and we had to use a text editor to define a thermo plug. Furthermore, the compliance was not complete because Vali did not use the actual compounds of the CO-Thermo Package for all the calculations. Having had this experience, eased however the development work of a CAPE-OPEN 1.0 socket.

3. Development Phase, 4.1. The Material Object (MO) The Material Object is the communication interface between the PME (Process Modeling Environment) and the PMC (Process Modeling Components). In the CAPEOPEN 1.0 architecture, the Material Object is implemented at the PME level. In the case of our development (Thermo Socket), the Material Object was the central point of

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the architecture and the link between Belsim Software and Thermo Plugs making crucial this part of the system. It was decided to develop a proprietary Material Object in C# 2.0 using Visual Studio 2005. According the specifications of CAPE-OPEN 1.0, the Material Object developed by Belsim implements the interface “ICapeThermoMaterialObject”. All Methods defined in this interface have been implemented. 4.2. Cape-Open thermo plugs viewer The first graphical tool to be developed was a small tool based on COM technology to allow the user to see what Thermo Systems and Property Packages are available on a given computer. This tool has been developed in C# 2.0 using Visual Studio 2005. 4.3. Graphical user interface (ValiModeller) ValiModeller is the Graphical User Interface in the suite of VALI software. It is developed in C++. When defining a validation problem you need to choose a thermodynamic package (list of compounds, list of thermodynamic methods and if you have binary parameters). In ValiModeller the option of choosing between Belsim’s own thermodynamic package and a CAPE-OPEN package has been integrated. The user needs to select between the following options: Build a thermodynamic package from existing integrated databases of compounds and Thermodynamic methods (called native thermo and compounds). Select a Cape-Open 1.0 Thermo Property Package available on the computer, listed in a dialog box. ValiModeller is also able to list the compounds and properties available in the COThermo Package. The information shown in this window is collected from the Property Package through the Material Object (MO). 4.4. Vali Engine In a first step, it was necessary to verify that everywhere in the code when a pure compound property is needed, the property is given by the Thermo Package (through the MO) and not by an internal calculation. These properties are: Name, Chemical Formula, CAS number, Molecular Weight, Boiling Temperature, Enthalpy of Formation. After that, the different modules used to calculate a given property of a mixture have been modified to get the result of the calculation from the Thermo Package and not from a Vali internal routine. Here are the following properties: Liquid and Vapor Enthalpy, Volume, Entropy, Gibbs’ Free Energy, Viscosity, Conductivity and Fugacities (or Fugacity Coefficients or Activity Coefficients). The choice to perform flash calculations directly from the Thermo Package (optional) or to solve them using the native modules with the Properties obtained from the Thermo Package is also available.

4. Testing Phase Several test problems have been solved in order to test our implementation of the CAPE-OPEN 1.0 thermo socket. We selected sample flow sheets available on COCO (cape open to cape open) internet site (http://www.cocosimulator.org/index_sample.html). 4.1. Multiple flash system R.H. Cavett [1] devised a now famous problem to test tearing, sequencing and convergence procedures of flowsheet simulation programs. This process having

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multiple recycle loops has been used intensively to test tearing, sequencing and convergence procedures. The flowsheet is equivalent to a four theoretical stage near isothermal distillation (rather than a conventional near isobaric type). 4.2. Process simulation with VALI The process has been modelled with VALI software using its own (we call it native) thermodynamic database of chemical compounds (to define nitrogen, carbon dioxide, hydrogen sulphide, methane, ethane, propane, isobutene, n-butane, isopentane, npentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane and n-undecane) and methods (the classical PENG-ROBINSON equation was chosen with binary parameters available on COCO internet site). 4.3. Process simulation with VALI and CAPE-OPEN thermo plugs The next step was to substitute the native thermodynamic models with different imported CAPE-OPEN thermo plugs. The first one was a “COCO Thermodynamics for Engineering Applications” called “COCO_TEA.ThermoPack.1” containing the same compounds and a modified PENGROBINSON equation. The second one was a Simulis package containing the same compounds and a classical PENG-ROBINSON equation. 4.4. Simulation results with VALI native and CAPE-OPEN thermo plugs The simulation results were similar with 27.34 kmol/hr in feed, 12.53 kmol/hr light products and 14.81 kmol/hr heavy products. The flashes were set at the same pressure. The CPU time required for the different computations depends on the thermo plug type. The verification phase is speedier with the native one and much slower with the Simulis one, the same for the resolution phase. Verification phase implies loading all the necessary data and physical property model, and checking that all required properties can be calculated. In the resolution phase, mass and energy balance equations are solved, as well as specifications handled as pseudo measurements. In this case, the number of specified measurements is such that the problem is just calculable (no redundancy). The number of iteration needed to solve the problem with the prescribed accuracy differs slightly according to the thermo system used, even if the same equation of state was selected in all cases. We expect that the convergence criterion in the solution of the equation of state was not the same in all cases which may have an impact on the speed of convergence in the outer loop. Table 1 CPU Time and Number of Iterations Comparison for multiflash problem

Native Coco Simulis

Verification 0.22 0.37 2.98

Resolution 1.1 3.11 8.88

Total 2 5.11 16

Iterations 3 3 5

4.5. Hydro dealkylation process HDA process is another widely explored test problem. The process structure is shown in figure 1.

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The model includes reaction and separation in a 5-component mixture. Physical properties are calculated using Soave-Redlich-Kwong equation of state.

Figure 1 : HDA process

4.6. Simulation results with VALI native and CAPE-OPEN thermo plugs We compared model solution using native thermodynamics with the one obtained using CAPE-OPEN thermoplugs (COCO_TEA.ThermoPack.1 obtained with the COCO simulator, and another plug generated with the Simulis package. The same results were obtained in all cases, what demonstrates an excellent model match. The calculation time differs somewhat between cases. Verification phase, where the simulation environments calls the thermo package to verify the availability of all properties, took less time when using the native thermodynamic code. Differences could probably be reduced by optimizing the coding of the material object. In the resolution phase, mass and energy balance equations were solved, as well as specifications handled as pseudo measurements. The number of iteration needed to solve the problem with the prescribed accuracy differs slightly according to the thermo system used, even if the same equation of state was selected in all cases. We expect that the convergence criterion in the solution of the equation of state was not the same in all cases which may have an impact on the speed of convergence in the outer loop.

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Table 2 CPU Time and Number of Iterations Comparison for HAD problem

Verification

Native Coco Simulis

0.71 3.14 5.75

Resolution

3.63 3.42 2.66

Total

5.69 8.38 10.56

Iterations

4 5 3

4.7. Comparison Using a thermo socket is time consuming during the verification phase certainly to access the corresponding “dll” file. In this example it appears that the access of external modules to access physical properties implies a significant penalty. However, the difference can be much smaller, as we observed when using different test cases. The way the Thermoplugs are structured, and the programming language used in their development can also explain different behaviors.

5. Conclusions These developments were time consuming (3 month part time work), and especially estimating the time needed for the development was difficult. The development required some training provided by Prosim and COLAN. Testing and debugging were also rather challenging because all the thermo plugs were not available on the same computer as our source codes. To conclude, VALI has today a CAPE-OPEN 1.0 socket that has been successfully tested on several different CAPE-OPEN 1.0 thermo plugs. Development of an alternative socket based on the new standard 1.1 is foreseen in a near future.

References [1] Cavett, R. H., 'Application of Numerical Methods to the Convergence of Simulated Processes Involving Recycle Loops', American Petroleum Institute, 43, 57, 1963

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

309

A LabVIEW-based intelligent system for monitoring of bioprocesses Elmer Ccopa Rivera, Félix de Farias Junior, Daniel Ibraim Pires Atala, Rafael Ramos de Andrade, Aline Carvalho da Costa, Rubens Maciel Filho School of Chemical Engineering, State University of Campinas, P.O. Box 6066, 13081970, Campinas, SP, Brazil, [email protected], [email protected]

Abstract The application presented in this study illustrates the usefulness of an automated monitoring system carried out in LabVIEW environment. The results obtained have show that it is possible to infer into a real-time basis the key variables in bioethanol fermentation using pH, turbidity, CO2 flow rate and temperature on line measurements and a MLP-based Software Sensor. On-line monitoring system provided accurate online predictions of the concentrations during the fermentation process even when the secondary variables measurements were noisy. This study also will illustrate the usefulness of an automated monitoring system carried out in graphical programming environment. Keywords: Modeling, bioreactor, software sensor, artificial intelligence.

1. Introduction Artificial intelligence, such as Artificial Neural Network (ANN) has been used successfully for solving biotechnological complex problems related to the field of measurements and instrumentation. Probably, the most popular ANN used in engineering applications is the Multilayer Perceptron Neural Network (MLP) due to its easily understandable architecture and a simple mathematical form, which results in an easy tool for modeling and implementation. In addition, it is known from previous works that MLPs can be used to offer adaptive solutions, since the reestimation of their parameters is a straightforward procedure [1]. By exploiting the relationship among the process variables of bioprocesses, MLPs could be used to implement advanced control techniques, such as software sensors, algorithms for on-line estimation of state variables and model parameters that are not measurable in real-time [2, 3]. This is a promising research area with significant impact on biotechnological industry, which requires an efficient monitoring with reliable sensors to control setting of the process. Thus, for a reliable performance prediction through modeling, the MLP-based software sensor should be implemented on a platform able to provide a powerful toolset for process identification and control with interface directly to instruments, sensor and actuators. A programme to fully automate the implementation of software sensors can be developed using a graphical programming environment, called LabVIEW (Laboratory Virtual Instrument Engineering Workbench). The LabVIEW has extensive library of functions and subroutines for most programming task. It also contains an application specific library for data acquisition, serial instrument control, data processing, analysis presentation and storage. Applications created with LabVIEW are referred to as virtual instruments (VIs) [4, 5].

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In this study, it was used built-in LabVIEW function and library VIs to develop a software sensor based on MLPs for on-line monitoring of bioethanol production process. This program can be adapted to a wide range of instrumentation control and optimization applications. The proposed monitoring system is based on LabVIEW as driver software, the data acquisition system and the sensors for the secondary measurements (pH, turbidity, CO2 flow rate and temperature). The system collects the variables of the fermentation process by means of sensors. The measured values are delivered to the computer program through the data acquisition system for data processing and prediction of state variables (concentrations of biomass, product and substrate) using the MLP-based software sensor.

2. Materials and Methods 2.1. Experimental Procedure Eight batch experiments performed in the temperature range of 30- 38oC were used to develop the software sensors. Two other data sets at 36.8 and 31.2oC are then used for the validation and prediction test, respectively. Material and analytical methods for the determination of concentrations of biomass, bioethanol and substrate are described elsewhere [6]. On-line measurements were performed in the bioreactor and stored in the computer through a data acquisition board associated to a management software application implemented in LabVIEW version 6.1 (National Instruments, Austin, TX). The sample time was 3 min for all on-line data. Carbon dioxide flow rate was measured by a digital gas volumetric flow sensor, pH by glass pH-electrode, (both from ColeParmer Instrument, London, England). Production medium turbidity was measured by a turbidity transmitter (FSC 402 Mettler Toledo Ingold Inc., USA) and temperature by thermocouple (N. Brunswick Scientific Co.). 2.2. On-line monitoring system In this study, an intelligent system is developed with primary on-line sensors, which capture large volumes of real-time bioprocesses data and model building software package to use the knowledge content in the stored data. As shown in Fig. 1, the proposed on-line monitoring system comprises three essential elements: (i) An array of sensors of multisensor system, which consists of a bioreactor (Bioflow III System; New Brunswick Scientific Co., Inc., N.J., USA) of 3 L (working volume) where on-line sensors (pH, CO2 flow rate, temperature and turbidity) are placed. Features as relatively simple instrumentation, short measuring time and low prices make the primary on-line sensors to be a right choice for the approach proposed in this study. (ii) A communication module that transfers the measurement data from bioreactor to a monitoring and data acquisition system. That consists of devices to convert the protocol of the output of the primary sensors (serial digital signals from gas volumetric flow sensor, pH-electrode and thermocouple) from RS232C to TCP/IP via a National Instruments ENET-232/4. The received analog signal from Turbidimeter (analog input 0-20 mA) is also transformed to standard TCP/IP using a Field Point network module 1600. TCP/IP protocol (Transmission Control Protocol/Internet Protocol) facilitates the communication across the internet, even to remote access. (iii) The monitoring and data acquisition system, which monitor the bioprocess based on the built-in LabVIEW functions, library VIs and Artificial Neural Networks-based software sensor in a PC with a data acquisition card. This is a general-purpose graphical programming environment. Thus, the sampling and acquiring the measurement inputs from primary sensors (pH, CO2 flow rate, turbidity and temperature) and postprocessing of measured are performed in LabVIEW environment.

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Figure 1. Framework of the on-line monitoring system

This study makes use of a well-known intelligent technique such as Multilayer Perceptron Neural Network (MLP) to infer the state variables in bioethanol fermentation during the postprocessing stage. 2.3. MLP-based software sensor In this work, the structure using three neural networks, one for each output (concentration of biomass, X, substrate, S, and bioethanol, P), was chosen. The inputs for the neural networks were five: pH (pH) turbidity (Tb), CO2 flow rate (F), temperature (T) and time (t). By Cybenko's theorem [7] it follows that all continuous functions can be approximated to any desired accuracy with a network of one hidden layer of sigmoidal hidden neurons and a layer of linear output neurons. Such structure is used in this work. MLP-based software sensor can be mathematically written in the form:

· § N y j = f¨ w ji x i + ș j ¸ = ¸ ¨ ¹ © i=1

¦

§ ¨ concentration = G¨ ¨ ©

1 § −((w M1×pH)+ (w M2 ×Tb) + (w M3 ×F) · ¨ +(w ×T) + (w ×t)+ș ¸ M5 M ¹ 1 + exp © M4

· ¸ Wkj y j + ȕ k ¸ , (j = 1,...,M), (k = 1) ¸ j=1 ¹

(1)

M

¦

(2)

where wji is the weight connecting the ith neuron in the input layer and the jth neuron in hidden layer. wj is the bias of the jth neuron in the hidden layer. Wkj is the weight connecting the jth neuron in the hidden layer and the kth neuron in the output layer. Wk is the bias in the kth neuron in the output layer. f(⋅) and G(⋅) are the sigmoidal activation functions of the jth neuron in the hidden layer and of the kth neuron in the output layer, respectively.

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Small random values are used to initialization of weights and biases. Subsequently, the standard backpropagation learning algorithm, based on a gradient descendent method implemented in FORTRAN is employed to train each network describing the concentrations (Eq. 2). In this study, both input and output data were normalized to the range [0.1, 0.9]. The number neurons in the hidden layer was varied from 10 to 70, and the optimal number chosen by the cross-validation criterion with the number of epochs fixed at 2000 for all the studied architectures. The neural network with sixty hidden nodes for describing biomass concentration, forty hidden nodes for describing substrate concentration, and twenty hidden nodes for describing bioethanol concentration were found to present the lowest mean square error for the validation sample. The learning rate η, and the momentum coefficient α, used in this work were optimized both to be 0.95 in the backpropagation learning. After training, the appropriate network architecture and the parameters set (weights and biases) are saved in a file. This information is used as an input to a program that is written in Phyton to an automatic conversion of the optimal MLP model into a program based LabVIEW formula node that is used to infer the concentrations of biomass, substrate and bioethanol.

3. Results and Discussion

6.0

(m /h)

4.5 3

CO2 flow rate x 10

-6

Figure 2 shows the profiles of on-line measurements in the batch fermentation at 31.2oC used for the prediction test.

3.0 1.5 0.0 0

5

Turbidity (%)

15.0

11

16

21

26

21

26

21

26

Time (h)

12.3 9.5 6.8 4.0 0

5

6.5

11

16

Time (h)

pH

5.9 5.3 4.6 4.0 0

5

11

16

Time (h)

Figure 2. On-line primary sensor measurements at 31.2oC.

The prediction test results from the software sensor-based scheme are illustrated in Figure 3 and quantified through of the R.S.D. (Residual Standard Deviation) [2]. As can be seen in the Figure 3, the software sensor has a good agreement with the experiment data and it has not been affected by the noise of any input.

3

Biomass (Kg/m )

A LabVIEW-Based Intelligent System for Monitoring of Bioprocesses 9

R.S.D.(%) = 10.1

7 5 2 0 0

5

11

210 3

TRS (Kg/m )

313

R.S.D.(%) = 25.4

16

22

27

22

27

22

27

Time (h)

158 105 53 0 5

11

R.S.D.(%) = 17.8

3

Ethanol (Kg/m )

0 80

16

Time (h)

60 40 20 0 0

5

11

16

Time (h)

Figure 3. Experimental (cell mass, X (Ŷ); substrate, S (Ÿ) and ethanol, P (Ɣ)) and software sensors (solid lines) results.

4. Concluding Remarks This paper presents results from the implementation and testing of a PC based monitoring system for a bioethanol production process using MLP-based software sensors. The system is based on an array of primary sensor, a communication module and a monitoring and data acquisition subsystem. This integrated framework provides a real-time monitoring solution, which is one of the most important aspects of the decision making in the strategies of optimization and control of bioprocesses. A LabVIEW data acquisition module is implemented to read all influencing variables, which are first used to train the MLPs. The optimal MLPs architecture is placed in a LabVIEW based program formula node that monitors the concentration of biomass, bioethanol and substrate. The LabVIEW-based intelligent system represents thus a robust model-based approach which is expected to contribute for improving the implementation of suitable operating strategies of optimization as well as advanced control to achieve high operational performance.

5. Acknowledgements The authors acknowledge FAPESP (process number 06/51646-4), and CNPq for financial support.

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References [1] E.C. Rivera, A.C. Costa, R.R. Andrade, D.I.P. Atala, F. Maugeri Filho and R. Maciel Filho, 2007, Development of adaptive modeling techniques to describe the temperature-dependent kinetics of biotechnological processes, Biochem. Eng. J., 36, 157-166. [2] J.C.B. Gonzaga, L.A.C. Meleiro, C. Kiang and R. Maciel Filho, 2009, ANN-based softsensor for real-time process monitoring and control of an industrial polymerization process, Comput. Chem. Eng., 33, 43-49. [3] M. W. Lee, S.H. Hong, H. Choi, J.H. Kim, D.S. Lee and J.M. Park, 2008, Real-time remote monitoring of small-scaled biological wastewater treatment plants by a multivariate statistical process control and neural network-based software sensors, Process Biochem., 43, 1107-1113. [4] G.W. Johnson, LabVIEW graphical programming: Practical applications in instrumentation and control, McGraw-Hill, New York, 1994. [5] J.S. Alford, 2006, Bioprocess control: Advances and challenges, Comput. Chem. Eng., 30, 1464-1475. [6] R.R. Andrade, E.C. Rivera, A.C. Costa, D.I.P. Atala, F. Maugeri Filho, and R. Maciel Filho, 2007, Estimation of temperature dependent parameters of a batch alcoholic fermentation process, Appl. Biochem. Biotech., 136-140, 753-763. [7] G. Cybenko, 1989, Approximation by superpositions of a sigmoidal function, Math. Control Signal 2, 303-314.

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Approximate Method for Optimal Instrumentation Network Design Duy Quang Nguyen and Miguel Bagajewicz The University of Oklahoma, T-335 SEC, 100 E. Boyd, Norman, OK 73019, USA

Abstract A branch and bound procedure based on balance equations of the system (so-called equations-based method) was recently used to solve nonlinear sensor network design problem (Nguyen and Bagajewicz, 2008). The method was shown to be efficient for medium size nonlinear problem, but its computational performance for realistic large scale problems was not satisfactory. We address this deficiency by using a heuristic approximate method together with the equations-based method in a two-stage procedure. The approximate method was shown to remarkably improve computational time, and even though it does not guarantee optimality it renders good results. Two examples are provided. Keywords: Instrumentation, Sensor network, Approximate method

1. Introduction Due to economic reasons, not every process variable can be measured by a sensor. In the context that data reconciliation is used, the location of measured points has direct effect on the accuracy of estimators, which in turn affects process plant performance. The problem of optimum selection of sensor location is referred to as the sensor network design problem. Vaclavek and Loucka (1976) were the first to explore the problem, sought to achieve the observability requirements of a multicomponent network. Madron and Veverka (1992) used multiple Gauss Jordan elimination of the linear mass balance equation to achieve observability of all key variables at minimum sensor cost. Meyer et al. (1994) designed cost-optimal sensor network design with requirement on observability of key variables while Luong et al. (1994) considered several requirements; both works used graph oriented methods. Bagajewicz (1997) was the first to formulate sensor network problem as a mixed-integer programming model using binary variables to indicate whether a variable is measured or not. Chmielewski et al. (2002) showed that an unmeasured variable can be modeled in a data reconciliation formulation using a fake sensor with very high variance. Both works used branch and bound procedures to solve the problem, which guarantees optimality but its computation requirement inhibits its use in large scale problems. Finally, all literature review up to the year 2000 can be found in the book by Bagajewicz (2000). Most recently, Gala and Bagajewicz (2006a, 2006b) presented an alternative tree enumeration method where at

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each node combinations of graph cutsets are used. This method has proven to be remarkably faster, especially after a decomposition technique is used. Most of the aforementioned work was applied to linear systems. Only a few works on nonlinear sensor network design have been published. Ali & Narasimhan (1996) developed a sensor network design program specifically for bilinear systems maximizing system reliability. Single constraint of required precision was considered and genetic algorithm was used by Heyen et al. (2002) in the design of sensor network for general systems including nonlinear systems. Most recently, Nguyen and Bagajewicz (2008) presented a method to design nonlinear sensor networks for process monitoring purpose. A branch and bound procedure similar to the one presented by Gala and Bagajewicz (2006a, 2006b) was used but it is equation-based rather than cutsetbased. The method was shown to be satisfactorily efficient for medium scale problems, but not for large scale problems. In this work, we address this deficiency by using a heuristic approximate method.

2. Background The optimization model to design minimum cost sensor network as presented by Bagajewicz (1997) is (in its simplest form) as follows:

Min

¦c q

i i

∀i

s.t. σ i (q) ≤ σ i *

½ ° ¾ ∀i ∈ M S °¿

(1)

where qi , an element of vector q, is a binary variable indicating that a sensor is used to measured variable i, ci is the cost of such a sensor and Ms represents the set of variables where a performance specification is required (variables of interest or “key” variables). σ and σ * represent for network properties (e.g. precision) and their required threshold values, respectively. Our research group used a special branch and bound method to solve the above problem, which guarantees optimality. Gala and Bagajewicz (2006a, b) showed that by using cutsets instead of individual measurements as base units, one can reduce computational time considerably. Cutsets were later replaced by process balance equations in the same tree enumeration procedure for nonlinear sensor network design (Nguyen and Bagajewicz, 2008). The equations-based method (Nguyen and Bagajewicz, 2008) is briefly described as a three-step procedure as following: i) Linearization of process model equations using a Taylor expansion around the nominal operation point. ii) Finding all the equations of the problems, which include the original equations and all new equations obtained from a Gaussian elimination operation on all possible combinations of original equations. iii) Employing tree enumeration with equations as base units to find the optimal solution. A decomposition technique can also be used to further reduce computational time.

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Nguyen and Bagajewicz (2008) showed that, for nonlinear problems, computational time of equations-based tree enumeration method increases exponentially with the size of the problem, hence realistic nonlinear problems, such as the Tennessee Eastman process was not solved in an acceptable time. To overcome the limitation of the equations-based method when dealing with large scale nonlinear problems, a heuristic approximate method is proposed and presented next

3. Approximate method Two observations were drawn from the results we got with several testing problems. They are: - The global optimal solution and sub-optimal solutions belong to the same region (space of variables), that is, they share many common active variables (whose value is 1) and are different in only a few active variables. - The equation-based method is able to find sub-optimal solutions within a limited number of nodes explored. - There is a possibility of obtaining the global optimal solution from the suboptimal solutions by replacing one or more active variables present in suboptimal solutions with some other variables. Based on these observations, the following heuristic approximate method is proposed: - Employ the equations-based tree enumeration algorithm and record all the candidates for optimal solution (those with smallest cost found) in a list (the first list). - If the number of nodes explored exceeds the prespecified threshold value, stop the tree enumeration procedure and go to the next step - Find all the common active variables of the last five candidates. Exclude connecting streams if a decomposition technique is used - Find the union of all active variables in the last ten candidates. - Perform a ring-sum of these sets, that is perform “the union” minus “the common active variables” and put results to a list (the second list) - Employ a tree enumeration using the variables in the second list to find the remaining active variables. In short, the basic idea of the method is to use information from sub-optimal solutions to (hopefully) arrive at a global optimal solution: the common active (1s value) variables in sub-optimal solutions are passed directly to optimal solution and the remaining active variables are found using a tree search. The procedure is illustrated in figure 1 when no connecting stream is involved.

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S1 S2

S3

S4

S5 S6

S7

S8

Variables with same values in S-OS are passed directly to OS

1 value (active variable)

0 value (inactive variable)

S9

S10

S11 S12

S-OS (suboptimal solution)

Remaining active variable (S10) is found from {S10, S11, S12}

OS (optimal solution)

Figure 1. Illustration of approximate method Although we do not guarantee that the best solution obtained by this method is indeed the global optimum, our experience indicates it is. We performed an exhaustive (time consuming) tree search to determine this.

4. Illustrated examples Performance of the approximate method is tested using two examples: the mineral flotation process (medium scale) and Tennessee Eastman process (large scale). Process flowsheet and data for the mineral flotation process and the Tennessee Eastman example are the same as those given in Nguyen and Bagajewicz (2008). The proposed method is implemented in Fortran running on a 2.8 GHz Intel CPU, 1028 MB RAM PC computer. The number of nodes explored and the computational time for two examples are summarized in table 1. 4.1. The mineral flotation process example The process consists of four units, eight streams. For each stream, the total flowrate and two component concentrations are variables of interest, so the total number of variables is 24. The problem was solved using the approximate method and the exhaustive tree search using list of measurements (to validate the solution found by the approximate method). Only one design case is considered: Precision of 2 % in variables F1, F4, F6, F7, CA1, CB1, CB4, CA6, CB7, CA8 (10 key variables) are required. Both methods give the same results, which is to measure F4, F5, F6, F7, CA1, CB1, CB4, CA5, CB7, CA8; cost is 2010. Details of the approximate method are as follows. When terminating the tree search at 50,000 nodes explored, there are ten candidates found and the “common active variables” of the last five candidates are {F1, F3, F5, F6, F7, F8, CA1, CB1, CB4, CA5, CB7, CA8}, excluding the connecting streams results in {CA1, CB1, CB4, CA5, CB7, CA8} as “common active variables”, the list from which the remaining active variables in

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optimal solution are found is {F1, F2, F3, F4, F5, F6, F7, F8, CA2, CA3, CB3, CB6} (the second list). The tree enumeration in the last step explores 180 nodes (hence totally 50,180 nodes are explored) and finds optimal solution, which is validated by the exhaustive tree search. 4.2. The Tennessee Eastman example There are 47 variables under consideration in this example, which include flowrate and component concentrations in four streams, temperature and pressure in reactor and separator. Only approximate method (method 1) was used, method 2 (exhaustive tree search) was not used but its computational time is estimated (using the same estimation method shown in Gala and Bagajewicz, 2006b) and shown in table 1. One design case is considered: Precision of 2% is required for variables F6, yA6, yG6, yH6, F7, yG7, yH7, yA9, yG9, yH9, F11, yG11, yH11, Pr, Tr, Ps, Ts (17 key variables). The obtained solution is: measured variables are F6, yA6, yG6, yH6, F7, yA7, yA9, yG9, yH9, yG10, yH10, F11, yG11, yH11, Pr, Tr, Ps, Ts; sensors cost is 10,360. Table 1. Computational time

Approximate method Exhaustive search

Number of nodes explored Computational time tree Number of nodes explored Computational time

Example 1 50,180 9 min 48 sec 3,230,514 1 hr 51 min

Example 2 150,001 1 hour 48 min Not used (45 days estimated)

5. Conclusions In this paper, an approximate method is presented. It is used in couple with the equations-based tree search method and was shown to be an efficient method to solve large scale nonlinear sensor network design problem. Although optimality is not guaranteed, the approximate method was able to find optimal solution when the optimal solution is available for validation.

References Ali, Y., and Narasimhan, S. 1996. Sensor Network Design for Maximizing Reliability of Bilinear Processes. AIChe J., 42(9), 2563-2575. Bagajewicz, M. 1997. Design and Retrofit of Sensors Networks in Process Plants. AIChe J., 43(9), 2300-2306. Bagajewicz, M. 2000. Design and Upgrade of Process Plant Instrumentation. Technomic Publishers, Lancaster, PA. Chmielewski, D., Palmer, T., Manousiouthakis, V. 2002. On the Theory of Optimal Sensor Placement. AIChe J., 48(5), 1001-1012. Gala, M. and Bagajewicz, M. J. 2006a. Rigorous Methodology for the Design and Upgrade of Sensor Networks Using Cutsets. Ind. Eng. Chem. Res., 45(20), 6687-6697.

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Gala, M. and Bagajewicz, M. J. 2006b. Efficient Procedure for the Design and Upgrade of Sensor Networks Using Cutsets and Rigorous Decomposition. Ind. Eng. Chem. Res., 45(20), 66796686. Heyen, G., Dumont, M. and Kalitventzeff, B. 2002. Computer-aided design of redundant sensor networks, in: J. Grievink, J. van Schijndel (Eds.), Proceeding of 12th European Symposium on Computer-aided Process Engineering, Elsevier Science, Amsterdam, 2002, pp. 685–690. Luong, M.; Maquin, D.; Huynh, C. and Ragot, J. 1994. Observability, Redundancy, Reliability and Integrated Design of Measurement Systems. Proceeding of 2nd IFAC Symposium on Intelligent Components and Instrument Control Applications, Budapest, Hungary, Jun 8-10, 1994 Madron, F., and V. Veverka 1992. Optimal Selection of Measuring Points in Complex Plants by Linear Models, AIChe J., 38(2), 227. Meyer M.; Le Lann, J.; Koehret, B. and Enjalbert, M. 1994. Optimal Selection of Sensor Location on a Complex Plant Using a Graph Oriented Approach. Comput. Chem. Eng., 18 (Suppl), S535-S540. Nguyen D. and Bagajewicz M. 2008. Design of Nonlinear Sensor Networks for Process Plants. Ind. Eng. Chem. Res., 47(15), 5529-5542 Vaclavek V., and M. Loucka. 1976. Selection of Measurements Necessary to Achieve Multicomponent Mass Balances in Chemical Plant, Chem. Eng. Sc., 31, 1199.

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A software tool for design of process monitoring and analysis systems Ravendra Singha, Krist V. Gernaeyb, Rafiqul Gania a

CAPEC, bBioEng, Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark

Abstract A well designed process monitoring and analysis system is necessary to consistently achieve any predefined end product quality. Systematic computer aided methods and tools provide the means to design the necessary process monitoring and analysis systems and/or to validate any existing monitoring and analysis system. A software to achieve this has been developed. Two developed supporting tools for the design, a knowledge base (consisting of the process knowledge as well as the knowledge on measurement methods & tools) and a model library (consisting of the process operational models) have been extended rigorously and integrated with the user interface, which made the software more generic and applicable to a wide range of problems. The software for the design of a process monitoring and analysis system is presented and illustrated with a tablet manufacturing process example. Keywords: Process monitoring, quality control, PAT, software, pharmaceutical tablet

1. Introduction The necessity of the design of a suitable process monitoring and analysis system – (also called Process Analytical Technology system, or PAT system) for systematic product quality monitoring and control has been widely accepted following the publication of the FDA Process Analytical Technology guideline [1]. As reported by Singh et al. [2], the design of a PAT system involves the identification of the critical quality parameters, selection of economical and reliable on-line measurement tools and integration of these on-line sensors with the control system. Singh et al. proposed a computer-aided framework including the methods and tools through which the PAT system for product quality control can be designed, analyzed and/or validated. In this manuscript the extension of the framework of Singh et al. [2] and the corresponding software for design of PAT systems is presented. The software consists of two main supporting tools: an extended knowledge base of methods and tools for monitoring/analysis to provide the necessary information/data needed during the design of the PAT system and an extended model library to supplement the gaps in the knowledge base. Forward as well as reverse algorithms have been developed to retrieve the data/information stored in the knowledge base. The application of the software and the new framework will be illustrated through a formulation case study involving a tablet manufacturing process.

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2. Extended design framework As shown in fig. 1, the general supporting tools (protected general knowledge base and model library) as well as the user specific supporting tools (specific knowledge base and model library developed by the user) are integrated with the general user interface. The flexibility exists to either use the general supporting tools or the user specific supporting tools. The user specific supporting tools can be developed, extended and managed according to the user’s needs while administrator rights are needed to edit/replace the general supporting tools. In either case a problem specific supporting tool (consisting of the problem specific knowledge and models) can be generated and can be used for design of a PAT system. The use of problem specific knowledge/data and models reduces the data retrieval time, and therefore the final PAT system can be designed faster. As shown in fig. 1, the starting point for the new problems is to provide the problem specifications, followed by the creation of the problem specific supporting tools and then to design the PAT system according to the methodology proposed by Singh et al. [2]. For the existing case specific problems the design methodology can be used directly, or earlier case studies can be opened and consulted.

Figure 1. Overview of the extended PAT design framework which was implemented in a software

2.1. Extended supporting tools The knowledge base and the model library are the two main supporting tools of the design methodology. The knowledge base contains useful information needed for design of PAT systems. The extended knowledge base covers a wide range of industrial processes such as tablet manufacturing, fermentation, crystallization and cheese manufacturing processes. It contains information on typical unit processes in terms of the type of operation they perform, the process variables involved, the corresponding manipulating variables (actuators), the equipments typically used for on-line measurement of data (type of equipment, accuracy, precision, operating range, response time, resolution, drift, cost etc.). The model library contains a set of mathematical models of different form (steady state and dynamic) for different types of unit

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processes, sensors and controllers. They are used to generate data (e.g. in case measured data are not available) as well as for verification of the performance of the closed-loop controlled process. Similar to the knowledge base, it covers a wide range of industrial processes (fermentation, crystallization, tablet manufacturing, cheese manufacturing). 2.2. Software overview The overview of the software is shown in fig. 2 (problem specific interface). The main feature of the software is to design the PAT system. The additional features of the software provide the options to open and analyse the solved examples, to find the applications of the monitoring techniques/tools and to retrieve the knowledge/data stored in the knowledge base.

Figure 2. Software overview

2.2.1. Main feature of the software - design of PAT systems The design procedure consists of 9 steps [2] (see fig.2, left). In the first step the desired product quality is defined. Process information needs to be provided through step 2. Step 3 involves the listing of the possible process points (in general the process equipments are considered as the process points) and corresponding process variables where monitoring and control equipments might be needed. The operational limits of the process variables also need to be provided. Critical process points and the critical process variables need to be identified through step 4. Step 5 provides the actuators for each selected critical process variable. The appropriate monitoring techniques and tools for each selected critical process variable can be found through step 6. Based on the outcomes of steps 3 – 6, a PAT system can be proposed in step 7. The proposed PAT system consists of the list of critical process variables and the corresponding actuators and monitoring tools for each critical process variable. The performance of the proposed PAT system can be verified in step 8. Step 9 provides the final PAT system. Note that each design step consists of a specific interface (window) through which the required input can be provided, and the results can be accessed and analyzed.

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2.2.2. Additional features of the software (a) Open solved example: The solved problems (designed process monitoring and analysis systems) have been stored in the exercise section of the software for further access/applications. Through this option (see fig. 2, top), the stored solved case studies can be accessed and/or modified and can be used directly if a case study satisfies current user requirements. (b) Find applications of monitoring tools: This option is created based on the developed reverse algorithm. Through this option the potential application range of a particular monitoring technique/tool can be identified (e.g. to find out the different applications of the NIR/NIR based tools for monitoring of the different variables in different processes). (c) Retrieve the knowledge/data: This option is created based on the developed forward algorithm. It provides direct access to the knowledge/data stored in the knowledge base. It is specially designed for the cases where user wanted to explore the available alternatives of the process monitoring and analysis systems

3. Case study: Tablet manufacturing process – Design of PAT The process flow sheet for tablet manufacturing process (fig. 6) is adopted from the literature [3]. Step 1. Product property specifications: The desired product is a pharmaceutical tablet with the following predefined qualities: weight: 5E-04 Kg/tablet; water content: 5E-03 % w/w; coating: 1E-05 Kg/tablet; coating thickness: 1E-04 m; hardness: 145 Mpa; solubility: 14 Kg/m3; volume: 5E-07 Kg/m3; tablet thickness: 4E-03 m. Step 2. Process specifications: The basic raw materials required include: USP Water, sucrose, API, stabilizer, excipient, mannitol, flavoring, OpaDry and air. The process equipment includes: Mixing tank, milling machine, granulator, tablet press, storage tank, and tablet coater

HO (fractional)

Step 3. Process analysis: The process analysis provides the following list of process points and corresponding process variables: 1. Mixing tank: stirrer speed, stirring duration, homogeneity. 2. Milling machine: particle 1 size, milling duration, rotational speed, solid 0.8 fraction in feed, feed weight. Achieved profile 3. Granulator: granule size, Lower limit 0.6 moisture content, bed Upper limit temperature, fluidization air flow rate, fluidization air 0.4 temperature, binder flow rate, atomizing air flow rate, 0.2 true density, bulk density, tap density, dissolution, 0 porosity. 4. Tablet press: 0 0.2 0.4 0.6 0.8 1 weight, thickness, shape, Time (hr) hardness, pre-compression force, main compression Figure 3. Sensitivity analysis force, press speed, dwell time, feed volume. 5. Storage tank: level, temperature. 6. Tablet coater: coating

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thickness, inlet air flow rate, inlet air temperature, inlet air humidity, outlet air flow rate, outlet air temperature, outlet air humidity, pan air temperature, negative air pressure (pan), rotating speed of the pan, temperature of the coating liquid, flow rate of coating liquid spraying air pressure, spraying air temperature, surface roughness Step 4. Sensitivity analysis: The process variable homogeneity in the mixing tank is considered to provide an example for the sensitivity analysis. Open loop simulations (fig. 3) show that the achieved homogeneity violates the lower limit indicating thereby that this variable needs to be monitored and controlled in order to guarantee final product quality. Repeating this procedure for all process variables yields the critical process variables at each critical process point as shown in fig. 6.

% Change in control variable

Step 5. Interdependency analysis: Interdependency analysis is performed for each critical process variable to select a suitable actuator. For example, the dependency of the homogeneity (critical variable) on the mixing time and the 14 Binder flow stirrer speed (actuator rate candidates) is analysed and 12 Fluidisation air flow rate found to be equally sensitive. Fluidisation air 10 Fig. 4 shows the dependency of temperature the moisture content of the 8 granules (at the granulator process point) on three actuator 6 candidates. The moisture content is most sensitive to the binder 4 flow rate and thus it is selected 2 as an actuator for controlling the moisture content of the granules. 0 Repeating the procedure for all -16 -12 -8 -4 0 4 8 12 16 critical control variables yields %Change in actuator candidates actuators as shown in fig. 6.

Step 7. Proposed PAT system: Based on the outcomes of the steps 3.3 – 3.6, a feasible alternative of a PAT system is proposed. (e.g. Mixing tank – Homogeneity - Mixing time NIR). Step 8. Validation: A closed loop simulation has been

Figure 4. Interdependency analysis 1 0.8 HO (fractional)

Step 6. Performance analysis of monitoring tools: The performance of available monitoring tools (obtained from the knowledge base) for each measured variable is compared (based on the selected specifications) and monitoring tools are selected as shown in fig. 6.

Achieved profile Low er limit

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Figure 5. Validation

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performed to verify the performance of the control loop and to validate the final product quality. For example, the fig. 5 shows the closed loop response (on-off controller) of homogeneity in the mixing tank. The closed loop response shows that the homogeneity is now within the operational limits. Repeating the procedure for all closed loop yields the final PAT system as shown in fig. 6. Step 9. Final PAT system: A feasible alternative of the PAT system is shown in fig. 6. The critical process variables, corresponding monitoring techniques and actuators are shown in the figure.

Figure 6. Tablet manufacturing process flow sheet with designed PAT system c: controller, R: response time, T90: time for 90% response, HO: homogeneity

4. Conclusions A well-designed PAT system is essential to obtain the desired product quality consistently. In this work we presented a software for systematic design of PAT systems. The application of the developed software was demonstrated through a tablet manufacturing process case study. The supporting tools (knowledge base and model library) have been extended rigorously and therefore the developed software can be used for a wide range of applications.

5. Acknowledgements The PhD project of Ravendra Singh is financed by a PhD scholarship from the Technical University of Denmark.

References [1] FDA/CDER, 2005, Process Analytical Technology (PAT) Initiative, http://www.fda.gov/Cder/OPS/PAT.htm [2] R. Singh, K. V. Gernaey, R. Gani. Model-based computer-aided framework for design of process monitoring and analysis systems. Computers & Chemical Engineering, 33 (1) (2009) 22-43 [3] V. Papavasileiou, A. Koulouris, C. Siletti, D. Petrides. Optimize manufacturing of pharmaceutical products with process simulation and production scheduling tools. Trans IChemE, Part A, Chemical Engineering Research and Design, 85 (A7) (2007): 1086-1097

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Enhanced Predictive Modeling Using Multi Block Methods Jeong Jin Hong, Jie Zhang, Julian Morris Centre for Process Analytics and Control Technology (CPACT), School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle upon Tyne, NE1 7RU, |r E-mail: [email protected], [email protected], [email protected]

Abstract Multi block PLS (MBPLS) models have been reported to handle the complexity of data which is difficult to anlayse with the conventional PLS models. However, the conventional MBPLS models do not offer improved predictive modeling in terms of prediction performance. A data partitioning method for enhanced predictive process modeling is proposed in this paper and is called Time-MBPLS. It enables data to be separated into blocks by different measuring time. Model parameters can be used to express contributions for all variables in a certain time period and it is possible to determine data blocking structures according to variable impacts on the quality variables. The proposed method is applied to the inferential estimation of a quality variable in a bio-production process. The results demonstrate that the proposed method can improve model prediction performance on the unseen testing data Keywords: MBPLS, Time-MBPLS, Quality Prediction, Batch Processes

1. Introduction Due to the rapid development in computer technology and measurement technology, a huge amount of process operation data in a chemical process can easily be measured and stored. Furthermore, processes are now more complicated with multiple stages, units and there are usually different phases within one process stage like batch processes. Thus, interactions among process variables are typically complex and nonlinear, especially in batch processes. As there are a huge number of data samples measured from different measurements or several process units operating together, it is hard to interpret those process data as one big data matrix using standard statistical methods. Therefore, an appropriate technique that can handle and analyse those data well is required. Multi-block modelling methods can be used to address the dataintegration problem, as they enable data to be divided into blocks and it is possible to analyse unit by unit by using information extracted from blocks (MacGregor et al., 1994; Westerhuis et al., 1998). If data is divided and grouped by process units i.e. each block contains data measured from a corresponding process unit, then it might be possible to investigate the contribution of each process unit. In addition, it can also be possible to get more valuable information for improved predictive modelling as information gained from each block which is each process unit can be used to find out relationships among the units by using multi-block modelling techniques (Kourti, 2003; Westerhuis et al., 1998). Data measured from a Xylitol production system is used for this research. The purpose of modelling this process is to develop an improved inferential estimation model from

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process operation data based on MBPLS algorithm. Data is divided into two blocks as the conventional MBPLS model does. A new idea for constructing blocks for better prediction performances is introduced which is called Time-MBPLS. Sum of the absolute model parameters of MBPLS model with two blocks is used to determine data blocking structure. The same data sets are used to build PLS, MBPLS and TimeMBPLS models and the results are compared. Models are evaluated by applying to an unseen data set. The paper is organised as follows. Section 2 briefly presents background of this study. Section 3 explains the methodologies and the results. Finally, some conclusions and suggested further works are given in Section 4.

2. Background 2.1. Multiblock PLS If a process has n input variables, then these n variables can be divided into blocks, so each block has all data about one or some input variables and those blocks are related to the output. This method is usually used to model processes where data are from different stages or different phases because it is possible to put variables having the same importance or similar relations together into one space to classify or to break the process into smaller groups by using the MBPLS algorithm (Kourti, 2003). In addition, when the process has large number of variables measured, a MBPLS model can provide better interpretation of the data. A MBPLS model separates the whole data into several blocks. Each separated block calculates different scores called block scores that are combined into one matrix and then from that matrix, big scores called super scores can be calculated by block scores (Lopes et al., 2002). It is possible to see relations between a certain predictor block and predicted block using the obtained block scores. It also allows seeing relations between all predictor blocks and predicted variable block using the super scores (MacGregor et al., 1994; Westerhuis and Smilde, 2001). Unlike a PLS model, a MBPLS model can not only give overall information of an entire process but also give information of each stage or between stages (Brás et al., 2005). It might provide a better understanding about the whole process. However, the fact that the score obtained from a PLS model is exactly the same as the super score calculated from a MBPLS model developed from the same data set that is approved in (Qin et al., 2001; Westerhuis et al., 1998) means that a MBPLS model provides the same prediction capacity as a PLS model. 2.2. Time-MBPLS The method proposed here is based on a hypothesis that an enhanced predictive model could be achieved if an appropriate data partitioning is applied, and the appropriate data partitioning can be obtained when data is separated by operation time as variables measured are time-dependant. There are many interactions among the process variables at different operation times. If it is possible to extract information from all interactions occurred in the process, an enhanced process model could be achieved. If all data are put into one matrix, some interactions at a certain time containing valuable information could be offset by other interactions at different time. But if data is divided by time, it would be able to prevent the interactions being offset and enable the interactions being used for modelling. In this method, the data is separated by process time. For instance, variable 1 could be the one having the largest impact to a quality variable for the first 30 minutes and then variables 2 and 5 affect the quality variable more than any other variables for the rest of the operation time. So, the basic idea is that if data is blocked by

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different time stages, it would be possible to look at the impact of variables to the modelled quality variable at each different operating period. The proposed method is called Time-MBPLS. The idea of Time-MBPLS is briefly outlined below. Time-MBPLS (in a case of a model with two sub-blocks) 1. Data is separated into two blocks according to the measurement time: the first half of data goes to the first block and the other half goes to the second block. 2. Perform MBPLS with data blocks arranged in Step 1. 3. Obtain the sum of the absolute model parameters for each variable within a block. 4. Determine grouping order according to results of Step 3. 5. Regroup the data and perform MBPLS with new data blocks (Time-MBPLS model). As mentioned above, sum of the absolute model parameters is used to determine data blocking order because when model parameters of a certain variable have high magnitudes, it can be said that the variable has a big impact on the response variable. Although in this study the two initial data blocks in Step 1 have equal size for the simplicity of illustration, they can be of different sizes. The procedure in Step 4 is explained in detail in the next section.

3. Methodology and Results 3.1. Methodology Data from a Xylitol production process (Nahlik et al., 2003) is used for modelling. There are 13 process variables measured every minute and the quality variable is measured about every two hours by HPLC. The objective of inferential estimation is to on-line estimate the product quality variable using on-line measured process variables during the previous 212 minutes. Data were divided into three sets: training, validation, and unseen testing data sets. The training data set contains 44 samples and is used to estimate model parameters. The validation data set contains 22 samples and is used for selecting the number of latent variables. The unseen testing data set contains 22 samples and is used for evaluating the developed models. Each sample has data measured from 13 process variables for 212 minutes and each data is measured every minute. Therefore, there are 212 measured data point for each process variable in each sample. Data is initially divided into two blocks by measuring time. Data measured in the first half of the 212 minute period prior to a quality variable measurement is put into the first block and the other half is put into the second block as described in Fig. 1 as X1 and X2. Using those blocks as input data, a conventional MBPLS model is built. The sum of absolute model parameter values for each variable in each block is calculated. This leads to a total of 26 sums of absolute model parameter values. These values are arranged in ascending order and the 25th percentile and the 75th percentile are obtained. When those sum values are compared, variables having higher magnitude than the 75th percentile point are put into both blocks whereas variables having magnitude between the 25th percentile and the 75th percentile points are retained in one of the data blocks where they have higher values. The other variables having lower magnitude than 25th percentile point are not used for modelling. By using this procedure, different data partitioning structure is obtained as X1new and X2new described in Fig. 1 and a TimeMBPLS model is developed with these data blocks. In order to show the effectiveness of the proposed method, the experiment was repeated 20 times with different selections

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of the training and validation data sets. The unseen testing data set remains the same in the 20 experiments.

Fig. 1. Description of data sub-blocks X1 and X2

3.2. Results and discussions In the study, the number of latent variables giving the lowest mean squared prediction error (MSE) on the validation data is selected. All three models built in each experiment are compared by their MSE values on the testing data. Fig. 2 shows the MSE values on the unseen testing data for PLS/MBPLS models and Time-MBPLS models in the 20 cases (experiments). It can be seen that the conventional PLS models and MBPLS models represented by blue (solid) bars show the same prediction performances. This is because the score matrix calculated from the conventional PLS model is exactly same as the super scores calculated from the conventional MBPLS model developed from the same data. In 13 cases out of 20 cases, Time-MBPLS models represented by white bars show improved prediction performances than the conventional MBPLS models. One example is shown in Fig. 3 which is results of Case 5. Real measured testing data is indicated by solid line, and the dashed and dash-dot lines represent predictions from Time-MBPLS models and conventional PLS and MBPLS respectively. It can be said that data blocking by time and sum of the absolute model parameters can provide more information related to dynamics among the process variables than the conventional model having one big matrix of data on these cases. Of the other 7 cases where the conventional MBPLS models have better prediction results than Time-MBPLS models, 5 cases (Cases 3, 9, 13, 15, and 17) show that the differences between conventional MBPLS and Time-MBPLS models are insignificant. As can be seen in Fig. 2, it is possible to see the performance gap between the conventional method and the proposed method for each case. Thus, it can be said that the proposed method can generally achieve improvement in prediction capability.

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MSE on Testing Data PLS / MBPLS Time-MBPLS

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9 10 11 12 13 14 15 16 17 18 19 20 Cases

Fig. 2. MSE on unseen testing data for PLS/MBPLS models and Time-MBPLS models

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n oi t ar t n e c n o C

) d el a c s(

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-20 Measured Predicted by Time-MBPLS Predicted by PLS / MBPLS

-40 0

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10 Samples

15

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Fig. 3. Plot of results on unseen testing data in Case 5

4. Conclusions A time-MBPLS modeling method is proposed for enhancing predictive modeling and the proposed method is applied to inferential estimation of product quality in a Xylitol production process. In the proposed method, data is divided into multiple blocks by time and sums of the absolute model parameters for individual variables in each of the blocks are used to determine the variable blocking structures. By using this approach, variables providing high contributions to the quality variable at a certain period of time can be

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found and used for model building. The proposed method is compared with the conventional PLS and MBPLS models. It is shown that the proposed model shows enhanced performance in 13 out of 20 cases in terms of prediction performance on the unseen testing data. Further studies on obtaining appropriate blocking structure are required in order to further improve the performance.

5. Acknowledgements The work is supported by EU under the project Bio-production (Project no. 026515-2). The first author thanks Syngenta for partially funding his PhD study.

References L. P. Brás, et al., Chemometrics and Intell. Lab. Syst. 75, 91-99 (2005) T. Kourti, et al., Journal of Process Control. 5, 277 (1995) T. Kourti, Journal of Chemometrics. 17, 93 (2003) J. A. Lopes, et al., Biotechnology and Bioengineering. 80, 419 (2002) J. F. MacGregor, et al., AIChE Journal. 40 (1994) J. Nahlik, et al., Process Biochemistry. 38, 1695 (2003) S. J. Qin, et al., Journal of Chemometrics. 15, 715 (2001) J. A. Westerhuis, et al., Journal of Chemometrics. 12, 301 (1998) J. A. Westerhuis and A. K. Smilde, Journal of Chemometrics. 15, 485 (2001)

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Development and Experimental Verification of Model-Based Process Control using Mixed-Reality Environments Udo Schuberta, Harvey Arellano-Garciaa, Günter Woznya a

Chair of Process Dynamics and Operation, Berlin Institute of Technology, Str. d. 17.Juni 135, D-10623 Berlin, Germany , [email protected]

Abstract In this paper, an extension of the PARSEX reactor introduced by Kershenbaum & Kittisupakorn, 1994 is presented. The proposed setup improves the capabilities of the original idea and constitutes a mixed-reality environment by replacing the reactor with a virtual counterpart. Furthermore, scenarios for the application of nonlinear model predictive control under the explicitly consideration of uncertainty on the mixed-reality plant are given. Simulation studies and experiments are used to validate the characteristic dynamic behavior in order to provide challenging aspects for control and estimation algorithms.

Keywords: advanced process control, model predictive control, estimation, uncertainty 1. Introduction Model predictive control (MPC) approaches experience a continuous development because of a growing number of industrial applications. The main approach makes use of linear process models to predict the future behavior of the process to control. This approach has some well known disadvantages, e.g. if the process exhibits strong nonlinear characteristics, or requires a large region of operation. However, nonlinear model predictive control (NMPC) may overcome some limitations of linear MPC approaches. But, the number of industrial implementations is not growing as it might be expected. One reason is the uncertainty about robustness because of their complexity in industrial applications. We expect that thoroughly testing algorithms on experimental plants can improve confidence and reliability by giving more insight into implications that arise from implementation by using equipment that is comparable to industrial scenarios. To reduce costs of experiments, the process of an exothermic reactor is realized using the mixed-reality approach. It is shown that the characteristic plant behavior can be reproduced and that the reactive subsystem can be substituted without further implications. The CSTR reactor has been chosen, because it is widely accepted as a benchmark for new control approaches, since it offers complex dynamics that are challenging for the goal to establish robust estimation and optimal control [1].

2. Experimental testing of advanced process control It is a common approach to test new applications thoroughly using simulation before transferring them to the real plant. Deep insight about performance can be gained and rather obvious pitfalls may be eliminated in this stage if simulations studies are designed and carried out carefully. To move the increasingly sophisticated applications

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from simulated scenarios to the real plant certainly affords a great amount of confidence about the robustness of incorporated algorithms. Therefore, there are periods preceding the launch in production mode with extensive tests at the plant, because algorithms need to be adjusted to the arising real-world conditions. These were mostly not considered during simulation, e.g. because some of them even can’t be foreseen or imitated appropriately. Following [2,3] several aspects that cannot be comprehensively covered within simulation studies involve: x x x x x

Non modeled and unknown disturbances Uncertainty about the level of model-plant mismatch Constraints that prevent the exact implementation of control action Stochastic and time-varying behavior Implications due to the requirements of a real-time solution

In this work, we expect to improve the development process in a prospective way by incorporating these missing features into an experimental system. However, carrying out studies on experimental systems is difficult, usually expensive and potentially hazardous, in particular, if they are used for reactive systems. To overcome these drawbacks, we propose to use a mixed-reality process as an intermediate step in the development of advanced control applications. The main approach and its benefits are described in the next section and an example is used for illustration.

Figure 1: Partitioning of the CSTR-Process (left) and dimensionless design parameters compared with similar cases from [7] (right).

3. Mixed-Reality CSTR Process First attempts on creating a mixed-reality process have already been made by Kershenbaum & Kittisupakorn, 1994. They proposed the partially simulated exothermic (PARSEX) reactor to work on problems such as those in [4]. In their approach, the conventional CSTR pilot plant has been modified to substitute reactive feed with water. The amount of steam that is necessary to imitate the heat of reaction is determined using online calculation of mass balances at a high frequency. It turned out that the PARSEX reactor was an adequate replacement for the pilot plant using real chemical reaction and

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showed good performance [2,5,6]. But we suggest removing the reactor completely from the experimental setup and replacing it with a virtual counterpart. As a result, the interacting virtual and real parts can approximate all relevant characteristics of either pilot or industrial CSTR plants (nonlinearity, multiplicity, parameter sensitivity, unstable steady states) [7]. These aspects have a high practical relevance and contribute to the benefits of the mixed-reality process. 3.1. Process Description We differentiate the process into real and virtual parts by creating a system boundary as illustrated in Fig. 1. In the case of the CSTR, it is straightforward to place this boundary on the wall of the reactor, assigning all feed and product flows, as well as temperature indicators or other instruments located inside the reactor to the virtual part. In Fig. 2, the real parts (experimental devices) of the mixed-reality process are illustrated, which are connected to the virtual part. The transfer of energy across the system boundary to the coolant liquid is realized with a simple electrical heater. The heater is adjusted dynamically to produce the heat exchange rate that results from the driving temperature difference of simulated reactor temperature and measured coolant temperature. The temperature and concentrations inside the virtual reactor are calculated at a high frequency by solving mass (1) and energy (2) conservation equations depending on the measured jacket temperature. This leaves many opportunities for arbitrary choice of chemical reaction order, kinetics, feed conditions, residence time and other parameters.

Figure 2: Virtual and real parts of the mixed-reality CSTR-Process.

Since the interaction across the system boundary only involves heat transfer, a real cooling system can be attached to the virtual part easily This setup has some advances

 is time delayed because of over ordinary simulation studies. Since the heat transfer Q J the response of the heater to changing inputs, both heat transfer coefficient and jacket surface area are difficult to estimate, even though there were well defined in the virtual

 depending on the unmeasured and time part. Together with the cooling duty Q C

varying ambience temperature, unknown uncertainty is affecting all parts of the system. Additionally, varying implemented parameters e.g. kinetics of arbitrary chemical reactions can be used as deterministic uncertainty during operation. Comparable to the

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case of an industrial plant, real measurement hardware and control software are used. The plant is a FESTO Compact Workstation, designed by ADIRO Automatisierungstechnik GmbH, automated using the compact distributed control system (DCS) AC700F from ABB Automation GmbH. Both simulation for the virtual part of the plant and prediction and optimization for model-based process control are run under MATLAB® and connected to the DCS using the de facto standard of OPCinterfacing. Finally, this system allows for a focused examination of control and estimation methods under real world conditions with the possibility to perform case studies that are usually not carried out in industrial systems [2].

VR

dc A dt

VR U Ac p , A

Ff c Af  Fp cA  k1cAVR

(1)

dTR dt

(2)

U Ac p , A  Ff  Fp   'H k1c AVR  UA TR  TJ

Since the mixed-reality process should imitate conventional CSTRs, the characteristic dynamic behavior must be achieved by designing the virtual reactor appropriately. Figure 3 (left) shows the heat gain and loss diagram according to the synthesized parameters. The design value for ȕ clearly exceeds E crit 7.8398 , which determines the ability to show multiplicity behavior.

Figure 3: Heat gain/loss diagram (left) and PI-controlled transition from stable steady state C to A after disturbance in feed temperature of -10K from 1h to 1.75h (right).

3.2. Open-Loop Experiment The jacket temperature is kept constant by a standard PI-controller. A disturbance of the feed temperature can then lead to extinction behavior and a transition to stable steady state A occurs as shown in Fig. 3 (right). 3.3. Closed-Loop Simulation For closed-loop simulations, a NMPC-controller with state feedback has been implemented. Figure 5 shows simulation result for a reactor startup to the unstable steady state B. Parametric and structural uncertainties lead to the deviation of simulated process and the controller model while approaching the unstable steady state. The simulated model converges back to the stable steady state A, while the process is

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operated at B. This effect of uncertainty has been validated for open-loop simulation of the model [8], state estimation using a Kalman filter [1] and for NMPC tuning on an experimental application [6].

4. Conclusions & Outlook The simulation of the proposed mixed-reality CSTR process shows high potential to imitate conventional pilot plants. Thus, this procedure is supposed to play an important role in evaluating the performance of control and estimation algorithms under closer approximated real world conditions than using simulation. In the same time, costs for experiments can be reduced significantly compared to conventional pilot or lab-scale plants that incorporate reactive systems. The validity of the proposed framework will be shown based on an extensive experimental testing procedure. By this means, the simulated behavior and implementation of the illustrated NMPC-controller are validated.

5. Acknowledgements This work is conducted within the framework of the research training group prometei and financed by the German Research Foundation, www.prometei.de.

Figure 4: Closed loop startup simulation with set point 356K and open-loop simulation of the controller model with dotted lines.

6. References [1] [2] [3] [4] [5] [6] [7] [8]

S.I. Biagiola, J.L. Figueroa, Chem. Eng. Sci. No. 59 (2004) 4601-4612 L. Santos et al., Contr. Eng. Pract. No. 9 (2001) 847-857 L. Kershenbaum, Trans IChemE Vol. 78 (2000) 509-521 L. Kershenbaum and P. Kittisupakorn, Chem. Eng. Res. Design (1994) 55-67 C.I.C. Pinheiro and L. Kershenbaum, Comp. Chem. Eng. Suppl. (1999) 859-862 F. Xaumier et al., J. Process Contr. No. 12 (2002) 687-693 L.P. Russo, B.W. Bequette, AIChE J. Vol 41, No. 1 (1995) 135-147 P. B. Sistu and B. W. Bequette, AIChE J. Vol. 37, No. 11 (1991) 1711-1723

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Fault detection of dynamic processes using a simplified monitoring-specific CVA state space approach Shallon Stubbs, Jie Zhang, Julian Morris Centre for Process Analytics and Control Technology, School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle upon Tyne NE1 7RU, UK E-mail: [email protected], [email protected], [email protected]

Abstract There have been much reported successes with the use of state space models for process identification, control and monitoring of dynamic processes with several different approaches to deriving the state variables and a few variants of the state space model representation having been documented over the years. Typically the form of statespace model adopted is one that requires the estimation of five matrices to fully parameterize the model. This paper proposes a simplification of the state-space model for the specific purpose of process monitoring. The simplification of the representation achieved via a modified definition of the past vector of inputs and output, facilitates a simpler and more efficiently estimation of a reduced set of state space matrices. The proposed approach in conjunction with a devised filtering method gives improved fault detection performance over the established state space monitoring methods and other multivariate statistical methods.

Keywords: state space modeling, CVA, dynamic models, fault detection, process monitoring.

1. Introduction The use of state space models for process identification, control and monitoring of dynamic processes have so far been shown to be superior to other multivariate statistical methods such as principal component analysis (PCA), partial least squares (PLS) and numerical algorithms for subspace system identification (N4SID). Typically the form of state-space model adopted is the one that can generally be used in application ranging from process identification, controls and monitoring but requires the estimation of five matrices to fully parameterize the model. Thus far very little emphasis has been placed on selecting a state-space model based upon its intended application. This paper proposes an approach for adaptation of the state-space model representation and procedure for the specific purpose of process monitoring. The proposed state space model requires a significantly reduced number of parameters and in conjunction with a slightly amended method of constructing the past vector, provides for a much simpler and more efficient stochastic estimation method for deriving the state matrices. Using the benchmark Tennessee Eastman processor simulator under close-loop control, a comprehensive fault detection analysis is performed, employing the Hotelling’s T2

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statistics and square prediction error (Q) statistics on the state and output residuals, along with a proposed multi-segmented moving average window transformation technique. It is shown that the proposed model offers at least the same and in some cases better fault detection capabilities in terms of detection delay time across the 21 faults analyzed.

2. State Space Modeling and Canonical Variate Analysis The first application of the canonical correlation analysis method to stochastic realization theory was done by Akaike [1]. The state space model proposed back then, Eq(1), had a number of limitations due to its simplicity, with no system inputs, no additive measurement noise, and was computationally intensive involving numerous single value decomposition (SVD) calculations.

xt +1 = Axt + Bet ; yt = Cxt + et

(1)

Other researchers have made improvements to this state space model and Akaike’s canonical correlation method [2-3]. The improvements include accounting for the correlation between the state and output residuals and the inclusion of inputs in the representation to facilitate controls as shown in Eq(2).

x t +1 = Ax t + Bu t + wt ; yt = Cxt + Dut + Ewt + vt

(2)

Accounting for the correlation between the residuals generates a more parsimonious state space model for a given process [3]. 2.1. Deriving the states of the process The states are derived as the canonical variate between two sets of variables one set being the past vector P and the other being the future vector F, which are traditionally defined as follows:

[

PtT = y tT−1 ; y tT− 2 ,.... y tT−l y , u tT−1 , u tT− 2 ,....u tT−lu

[

Ft T = ytT+1 ; y tT+ 2 ,.... y tT+ f

]

T

]

T

(3) (4)

where ly, lu, f are the window lengths of the dynamic lag and lead elements of the input and output samples.

xt = JPt T ; GSVD(Rpf) = JSL

T

(5 )

subject to JTRppJ = Im and LTRffL = Iq, where Rpp = PPT, Rpf = PFT, and Rff = FFT

3. A simplified state space representation and parameter estimation approach The state space representation and model development approach to be proposed seeks retain the benefits of the state space representation of Eq(2) with a model that is simpler and easier to derive. Exploiting the fact that our primary objective is monitoring as opposed to control, there is essentially no need to have exogenous inputs explicitly defined in the state space model. Instead of doing away with the current input vector, it

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is instead proposed to have it incorporated in the past vector such that the vector would now take on the form:

[

PtT = ytT−1 ; ytT− 2 ,.... ytT− l y , utT , utT−1 , utT− 2 ,....utT− l u

]

T

(6)

while the vector containing the output information in the future would remain as previously defined by Eq(4). The proposed structure for the state space representation is therefore reduced to:

xt +1 = Axt + vt ; yt = Bxt + Cvt + wt

(7)

The matrices A, B and C of Eq(7) are derived so as to minimize the squared residuals of the state and output equation. Owing to the method used to derive the states, xt xtT = xt +1 xtT+1 = I k , therefore:

d (vt vtT ) T = −2 xtT+1 xt + 2 A = 0 ; A = x t +1 x t dA

(8)

Likewise given that x t v tT = v t x tT = 0 , then the output square residuals reduce to:

wt wtT = y t y tT − 2 By t x tT − 2Cy t v tT + Bx t x tT B T + Cvt v tT C T

(9)

and,

∂( wt wtT ) = −2 y t xtT + 2 B = 0 ; B = y t xtT ∂B

(10)

∂ ( wt wtT ) T −1 = −2 yt vtT + 2Cvt vtT = 0 ; C = y t vt Φ ∂C

(11)

where ĭ is the covariance matrix of the state noise vt. 3.1. Statistical Monitoring metrics Similar statistics common to those used for PCA can be adopted and applied for CVA State Space analysis. The use of Hotelling’s T2 statistics based on the first k CVA states have been proposed [4,5] also appearing in the literature are the use of Hotelling’s T2 and SPE, Q metrics based on the residuals of the state and output matrix [6]. These metrics were all employed making a total of five monitoring statistics. A sophisticated method of filtering the five monitoring metrics is also proposed in this paper to improve the reliability of the monitoring statistics. The approach uses a large moving window which is segmented into multiple small windows. By parallel computation of the small and large window averages and the use of internal thresholds, sudden level change detection by the small window was used to provide a means of actively shifting up or in effect, reduce the width of the large window so that the observed filtered output produced gave quick response to sudden level changes while giving excellent noise filtering under normal operating conditions when there are no significant magnitude changes in the monitoring statistics. The extent to which the window reference is shifted is dependent upon the internal threshold exceeded.

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4. Results of Fault Detection Analysis Study Twenty one simulated faults were tested and the detection delay was computed. The faults and a description of the open loop TE simulation is provided in [7,8]. The closeloop TE simulator adopted for the simulation runs use a control strategy proposed in [9]. The statistical model was built from the normal operation data consisting of 500 samples and the cross-validation was carried out using a second unseen data set of 900 samples. The model is defined by 33 states and uses a lag order of 4 for the past vector and 3 for the future vector. The overall mean squared error (MSE) on the output residuals for the proposed model was slightly greater than that of the full size state space model, however, for some of the process outputs the proposed model returned the lower variable specific MSE. The difference in the number of parameters is k(ny + nu) where k is the number of states, nu is the number of inputs and ny are the number of outputs. Table 1 summarizes and compares the result obtained from the simulation runs with previously published results of other statistical methods carried out on the same simulator [7,8]. CVA(1) summarizes the result of the author’s proposed modified canonical variate analysis state space model. The detection delay is expressed as the number of samples between fault introduction and its detection being confirmed. Due to reduction in variability achieved by the filtering method employed, it was possible to reduce the number of consecutive out of limit samples required to confirm a fault from 6 to 3. It was also possible to lower the control limit from 95% to one that accounted for 90% of the unfiltered statistics during normal operation and maintain the same degree of reliability. Table 1. Detection delay of simulated faults (sample rate = 3min-1)

Fault # CVA(1) CVA(2) PCA DPCA 11 11 17 17 13

1 5 8 9 11 12 4 6 14 9

2 8 21 18 19 13 37 45 43 46

3 F F F F 14 7 7 7 7

4 3 7 9 7 15 13 F 746 F

5 3 6 7 8 16 13 15 203 202

6 3 6 7 7 17 23 26 31 30

7 3 6 7 7 18 29 85 90 90

8 18 26 26 27 19 8 17 F 88

9 F F F F 20 69 72 93 90

10 23 29 55 56 21 183 279 291 292

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(a)

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Fig. 1 Fault No. 15 introduced at sample time 150. a) Detection of fault using proposed statespace model CVA(1) and filtering of the Hotelling’s T2 statistics of the output residuals; b) Misdetection of fault using traditional model CVA(2).

5. Conclusions The results indicate that the proposed state space model provides comparable if not better fault detection performance, most noticeable in the significant reduction in detection delay for the more difficult to detect faults. The proposed variable width moving average window filtering method also achieved very effectively noise filtering while retaining the dynamic characteristic of the original unfiltered monitoring statistics. For the most part, the best performing monitoring statistics of the five explored in terms of fault detection and detection delay time was the Hotelling’s T2 statistics of the output residuals.

Acknowledgement The research is supported by Dorothy Hodgkin Postgraduate Award and BP

International Ltd.

References [1] Akaike H., (1976), System Identification: Advances and Case Studies (R. K Mehra and D.G Lainoitis, Eds), p. 27, Academic Press, New York. [2] Larimore W.E. (1983), Proceedings of the American Control Conference, pp. 445 – 51. [3] Larimore, W. E., (1990), Proceedings of the IEEE Conference on Decision and Control, Vol. 2, pp, 596-604. [4] Negiz, A. and Cinar, A., (1997b), AIChE Journal, 43, (8), 2002-2020. [5] Simoglou, A., E.B Martin, A.J. Morris (1999b), Computers and Chemical Engineering, pp. 277 – 280. [6] Simoglou, A., Martin, E.B., and Morris, A.J. (2002), Computers and Chemical Engineering, Vol. 2, pp. 909 – 920.

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S. Stubbs et al. [7] Russel, E. L., L.H. Chiang, and R.D. Braatz (2000), Chemometrics and Intelligent Laboratory, Vol. 51, pp 81-3 [8] Detroja, K. P., R.D. Gudi, and S.C. Patwardhan (2007), Control Engineering Practice, Vol. 15, pp. 1468-1483 [9] Lyman, P. R. and C. Georgakis (1995), Computers & Chemical Engineering, Vol. 19, No. 3, pp. 321-331.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Fault diagnosis and process monitoring through model-based and case based reasoning Nelly Olivier-Mageta, Stéphane Negnya, Gilles Hétreuxa, Jean-Marc Le Lanna a

Laboratoire de Génie Chimique (CNRS - UMR 5503), Université de Toulouse ; INPTENSIACET 118, route de Narbonne F-31077 Toulouse Cedex 04, France, [email protected]

Abstract In this paper, we present a method for the fault detection and isolation based on the residual generation coupled with a case based reasoning approach. The main idea is to reconstruct the outputs of the system from the measurement using the extended Kalman filter. The estimations completed with qualitative information are included in a Case Based Reasoning system in order to discriminate the possible faults and to have a reliable diagnosis. The reference model is simulated by the dynamic hybrid simulator, PrODHyS. The use of this method is illustrated through an application in the field of chemical process.

Keywords: Fault Detection and Isolation, Extended Kalman Filter, Dynamic Hybrid Simulation, Distance, Case Based Reasoning 1. Introduction Nowadays, of safety and performance reasons, monitoring and supervision have an important role in process control. The complexity and the size of industrial systems induce an increasing number of process variables and make difficult the work of operators. In this context, a computer decision support tool seems to be wise. Nevertheless, the implementation of fault detection and diagnosis for stochastic system remains a challenging task. Various methods have been proposed in different industrial contexts [1] . They are generally classified as: ○ Methods without models such as quantitative process history based methods (for example, neural networks), or qualitative process history based methods (expert systems…), ○ And model-based methods which are composed of quantitative model-based methods (such as analytical redundancy) and qualitative model-based methods (such as causal methods). In this paper, the proposed approach to fault detection and isolation is a model-based approach. The first part of this communication focuses on the proposed diagnosis approach. This approach is illustrated through the simulation of the monitoring of a didactic example. This example puts in highlight the limit of this approach with a false diagnosis. Then we propose an evolution which encompasses quantitative and qualitative information to make the diagnosis more reliable.

2. Supervision module The methodology proposed in this article is more particularly designed to treat batch and semi-continuous processes which are the prevalent mode of production for low volume of high added value products. In this context, based on the research works

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performed for several years on process modeling and simulation, we have developed the object oriented environment PrODHyS dedicated to the dynamic hybrid simulation of chemical processes [2]. In this work, this platform has been exploited for monitoring studies. Then, a simulation model is used as a reference model to implement the functions of detection and diagnosis. The global principle of this system is shown in Figure 1, where the sequence of the different operations is underlined. Moreover, a distinction between the on-line and off-line operations is made. Our approach is composed of three parts: the generation of the residuals, the generation of the signatures and the generation of the fault indicators. 2.1. Residual generation

Figure 1. Supervision Architecture

The first part concerns the generation of the residuals (waved pattern in the Figure 1). Thus, it is based on the comparison between the predicted behavior obtained thanks to the simulation of the reference model (values of state variables) and the real observed behavior (measurements from the process correlated thanks to the Extended Kalman Filter). The main idea is to reconstruct the outputs of the system from the measurement and to use the residuals for fault detection [3-5]. A description of the extended Kalman filter can be found in [6,7]. Besides the residual is defined according to the following equation:

rir (t ) =

Xˆ i (t ) − X i (t ) X i (t )

with i ∈ {1, n}

(Eqn. 1.)

ˆ is the estimated state variable with the extended where Xi is the state variable, X i Kalman Filter and n is the number of state variables. Note that the generated residual rir (t ) is relative. As a matter of fact, this allows the comparison of residuals of different variables, since the residual become independent of the physical size of the variable. 2.2. Signature generation The second part is the generation of the signatures (doted pattern in the Figure 1). This is the detection stage. It determinates the presence or not of a default. This is made by a detection threshold εi (t ) . The value of ε i is chosen according to the model error covariance matrix of the Extended Kalman Filter. The generated structure S irN (t ) is denoted by Eqn. 2.

Fault Diagnosis and Process Monitoring through Model-Based and Case Based Reasoning

S irN

Max ⎡ ⎛⎜ rir (t ) − ε'i (t )⎞⎟ ; 0 ⎤ ⎢ ⎥⎦ ⎠ (t ) = n ⎣ ⎝ ∑ Max ⎡⎢ ⎛⎜⎝ rkr (t ) − ε'k (t )⎞⎟⎠ ; 0 ⎤⎥ ⎣ ⎦ k =1

εi (t ) X i (t )

with i ∈ {1, n} and ε'i (t ) =

347

(Eqn. 2.)

2.3. Fault indicator generation The last part deals with the diagnosis of the fault (hatched pattern in the Figure 1). The signature obtained in the previous part is compared with the theoretical fault signatures by means of distance. A theoretical signature T•,j of a particular default j is obtained by experience or in our case, by simulations of the process with different occurency dates of this fault. Then, a fault indicator is generated. For this, two distances are defined: the relative Manhattan distance and the improved Manhattan distance. The first distance is denoted by the following expression: n

∑ SirN (t ) − Tij

i =1 D Mr j (t ) =

(Eqn. 3.)

n

The second distance, which allows the diagnosis of many simultaneous faults, is denoted by the following expression: n

∑ SirN (t ) × m′ − Tij × n′ ⋅ Tij

i =1 D Ma j (t ) =

(Eqn. 4.)

n′

where n ′ is the number of non-zero elements of the theoretical default signature T•,j and

m ′ is the number of non-zero elements of the default signature S rN (t ) .

3. Application: the adding-evaporation unit operation 3.1. Description FB

Table 1. The operating conditions

Treactor

Ulmax

Ulmin A+B

xB

Figure 2. The studied process

Reactor

Material Feed

T (K)

298.15

263.15

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1

1

xA=eau

0.6

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0.4

0.99

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300

-

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-

1.2

The process of adding-evaporation is generally used to change solvents. Its recipe describes a succession of evaporations and adding of the new solvent (methanol). This process is studied here (Figure 2). The operation conditions are listed in the Table 1. The values of the minimum and maximum holdups Ul are respectively 200 and 800 moles. The steps of this process are the following: a feeding step during 500 seconds, a step of heating and feeding, until the holdup has reached the maximum threshold, and a heating step until the minimum holdup threshold. The pressure is supposed to be constant during this operation. The goal of this process is to have a molar composition of methanol in the reactor at 0.98.

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3.2. Results The behavior of this process is governed by thermal phenomena. A default of the reactor thermal system can damage the success of this operation. That is why, it is important to detect it as soon as possible. 3.2.1. Incidence matrix To perform a monitoring of a process, some off-line adjustments must be made. In one hand, we need to determine the covariance matrices of the model and measurement disturbances. While the measurement noises are supposed to be well-known by experiments or by the sensor manufacturer, the model disturbances is estimated by an “ensemble method”. Numerous simulations have been performed during which a model parameter has been disturbed. This allowed the estimation of statistic distribution of the model mistakes. Then, if the behavior of the system goes beyond this distribution, its behavior is abnormal. So, the detection thresholds are determined according to the model disturbances. On the other hand, the second adjustment is the learning of the incidence matrix. It is based on the same “ensemble” theory. For this, we perform a set of simulations, during which a fault is introduced at different occurency dates, for each potential state of the hybrid dynamic system. For this study, we consider seven faults: ○ Fault 1: The energy system provides no more power; ○ Fault 2: The energy system provides a power lower than the nominal one; ○ Fault 3: The energy system provides a power higher than the nominal one; ○ Fault 4: The feeding provides no more material; ○ Fault 5: The feeding provides material with a flow rate lower than the nominal one; ○ Fault 6: The feeding provides material with a flow rate higher than the nominal one; ○ Fault 7: The holdup detector detects a damaged value. The obtained incidence matrix is the following:

Signature

Table 2. Incidence matrix

Energy Power Flow Rate Temperature Holdup xWater xMethanol

1 3 2 0.92828 0.59286 0.50299 0 0 0 0.00667 0.00006 0 0.06505 0.40714 0.49695 0 0 0 0 0 0

Faults 4 5 0 0 0.84299 0.74166 0 0 0.15701 0.25834 0 0 0 0

6 0 0.97214 0 0.02786 0 0

7 0 0 0 1 0 0

We can notice that all the faults have an affect on the holdup of the mixture. The faults are differentiated thanks to the temperature, energy power or feeding flow rate information. 3.2.2. Detection results A default of the reactor heating energy feed is introduced at t = 20000 seconds. This energy feed provides a heat quantity lower than the nominal one (fault 2). We suggest that we have only a holdup sensor. So, we don’t have any information about the temperature, the flow rate and the power. In this case, the extended Kalman filter can not correct the estimated state thanks to the measurements. It only considers the holdup deviation. Figure 3 shows the detection stage. It illustrates the evolution of the residuals linked to the holdup of the mixture. From t = 80 seconds, the values of both residuals underline the abnormal behavior of the process. The diagnosis is launched at t = 21500 seconds.

Fault Diagnosis and Process Monitoring through Model-Based and Case Based Reasoning

Holdup residual (mol)

350

Detection date of the fault

Occurency date of the fault

300 Holdup residual (mol)

Maximum threshold

349

250 200 150 100 50 Confidence region

0 0

5000

10000 15000 Time (seconds)

20000

25000

Figure 3. The evolution of the holdup residual

3.2.3. Diagnosis results Table 3. The instantaneous fault signatures Energy Power 0 Flow Rate 0 Temperature 0 Holdup 1 xWater 0 xMethanol 0 Signature

The residual is then estimated and we obtain the corresponding instantaneous default signature (Table 3). We compare the instantaneous fault signature (Table 3) with the theoretical fault signatures (Table 2), by calculating the relative and improved Manhattan distances (Eqn. 3. and 4.). Then, the fault indicators are generated (Table 4). They correspond to the complement to 1 of these distances. The Manhattan relative and improved indicators detect the presence of the fault 7 with a probability of 100%. The fault 7 is a false diagnosed. So, with only the holdup measurements, a fault diagnosis is established. We must complete the system information with qualitative information in order to be more precise and relevant during the diagnosis step. Table 4. The default indicators of the example Faults 1 2 3 4 5 Manhattan relative indicator 0.688 0.802 0.832 0.719 0.753 Manhattan improved indicator 0.121 0.611 0.666 0.235 0.387

6 0.676 0.042

7 1 1

3.2.4. Improved Approach To overcome this drawback, the previous approach is coupled with the Case Based Reasoning (CBR) method. This method aims to capitalize and reuse pas experiences and knowledge for solving problem. In our case the coupling of both methods allows to have in a same problem description qualitative and quantitative information. In the CBR, illustrated on figure 4 (and detailed in [7]), the problem is described (Represent Step) with the main and most relevant characteristics, no matter the type of information. Then, the problem is compared with other ones stored in a case based and the most similar one and its associated solution are extracted to propose a solution to the initial problem (Reuse). In the previous example, the problem description is composed of the attributes given in Table 3. The model based approach allows the filling of the quantitative attributes like holdup, and the qualitative attributes like temperature, complete and detail the problem description. The qualitative information comes from detector thresholds for example.

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With this additional information, the fault 2 is identified, thus the diagnosis refined and more reliable. Target problem Represent

New Case

Retrieve

New Case

Learned case Retain

Reuse

Case base

Validated solution

Retrieved Case

Solved Case Revised and tested Case Revise

Figure 4. CBR Cycle

4. Conclusion In this research work, the feasibility of coupling qualitative methods and model based one is demonstrated for fault detection and diagnosis for chemical engineering process monitoring. These two complementary approaches improve the diagnosis phase thanks to simultaneous treatment of both qualitative and quantitative information. Unfortunately, the monitoring task is not limited to the diagnosis, after this step the operator has to take decisions in order to repair the fault under constraints: productivity, economic, security, environmental… Consequently, a relevant decision support tool must help the operator in this difficult task. Currently, in our tool, the solution to the problem encompasses only the diagnosis but it can be extended to the proposition of ways to stop (or stand by) the process until the repair, and after ways to restart it. In these conditions, these proposed ways could be easily tested and then validated by simulation (Revise step of Figure 4) because the model of the process already exists (needed for the generation of the residuals). Only, the new operating conditions must be given.

References [1] V. Venkatasubramanian, R. Rengaswamy, K. Yin and S. N. Kavuri, Comp. & Chem. Eng., 27 (2003) 293 [2] J. Perret, G. Hétreux and J.M. Le Lann, Control Eng. Practice, 12-10 (2004) 1211 [3] R.K. Mehra and J. Peschon, Automatica, 5 (1971) 637 [4] G. Welch and G. Bishop, Technical Report TR 95-041, Univ. of North Carolina, 1995 [5] S. Simani and C. Fantuzzi, Mechatronics, 16 (2006) 341 [6] N. Olivier-Maget, G. Hétreux, J.M. LeLann and M.V. LeLann, Chem. Eng. & Proc., 4711 (2008) 1942 [7] S. Negny and J.M. Le Lann, Chem. Eng. Research & Design, 86 (2008) 646

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Online monitoring of nanoparticle suspensions using dynamic light scattering, ultrasound spectroscopy and process tomography Xue Z Wanga, Lande Liua, Ruifa Lia, Richard J Tweedieb, Ken Primroseb, Jason Corbettc and Fraser McNeil-Watsonc a

Institute of Particle Science and Engineering, University of Leeds, Leeds LS2 9JT, UK, E-mail: [email protected] b Industrial Tomography Systems Limited, 39 Deansgate, Manchester M3 2BA UK c Malvern Instruments Ltd, Enigma Business Park, Worcestershire WR14 1XZ, UK

Abstract Dynamic light scattering, ultrasound spectroscopy and electrical resistance tomography were investigated for online monitoring of nanoparticle suspensions. This integrated system provides real time information about particle size distribution, zeta potential and particle concentration and visualises the mixing quality between particles and liquids. As particle size distribution is an indicator of the quality of particulate products, zeta potential measures the stability of colloidal particles and tomography shows particle concentration and the mixing quality between particles and liquids, this integrated multiple sensor system can be applied to nanoparticle manufacturing processes for online process and product quality control. Keywords: dynamic light scattering, ultrasound spectroscopy, process tomography, nanoparticle suspension, process analytical technology 1. Introduction Nanoparticle manufacturing in solid suspensions is becoming increasingly important to pharmaceutical, agrochemical and speciality chemical industries. For instance, nanonization is now used in the pharmaceutical industry to address the low solubility issue of hydrophobic pharmaceutical solids. Nano-processing in industry however faces major challenges compared to the production of larger particles. It is much more difficult to scale-up a process of nanomaterials from laboratory to industrial scale and to achieve consistency and reproducibility in product quality from batch to batch runs. An enabling technique to address the scale-up and manufacturing challenges is online sensing. The principle of using online sensing for process scale-up is that by being able to measure and understand in real-time the evolution of the product quality variables and process conditions as well as their interactions, and subsequently exercise control, product quality can be assured. However, despite the availability of various sensing techniques for measuring the size and size distribution of submicron to nano-scale particles, few of them can be applied online especially at industrial scale conditions.

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Online measurement not only creates practical challenges to the design of an instrument, it also often pushes the instrument to be used beyond its limits such as of solid concentrations. While laboratory research favours low solid concentration, to be commercially viable industrial scale operation is usually required to be at high concentration. High solid concentration can result in particle-particle interactions and multiple scattering, leading to measurement errors.

Figure 1 The experimental rig. DLS – dynamic light scattering, USS – ultrasound spectroscopy, ERT – Electrical resistance tomography

The purpose of this study is to investigate the use of two of the most promising techniques for online sensing, dynamic light scattering (DLS) and ultrasound spectroscopy (USS), for real-time measurements of particle size distribution (PSD) and zeta potential during processing of nanoparticle slurries. Electrical resistance tomography (ERT) is also integrated into this multiple sensor system for the characterisation of mixing conditions and solid concentration, the later is required by DLS and USS in PSD measurement. The focus is on studying the various variables that impact the size measurement results, including solid concentration, mixing condition and zeta potential. The experimental system is shown in Figure 1. Ultrasound spectroscopy1-3 is a sensing technique highly suitable for online measurement, in particular for dense nano sized particle systems, where the system stability may be sensitive to changes in concentration. The principle of ultrasound spectroscopy measures the attenuation (energy loss) of sound waves due to sound absorption by media when a sound wave is transmitted and propagating into the media; the attenuation is then inverted into PSD according to the theory of ECAH 4, 5 or the coupled phase model3. Laser scattering technique often provides the benchmark laboratory-based method for PSD measurement. Since light is a type of electromagnetic wave, it can be described by the wave properties e.g. amplitude, frequency, and wavelength. When the light beam is shot through the suspension, the particles in the suspension scatter the light, resulting in change in phase of the light from that of the original beam. If the particles in suspension do not move, this phenomenon is called static light scattering. While in real suspension where particles move, it is called dynamic light scattering (DLS). This phenomenon is applied to particle size measurement. The particles in suspension move as a Brownian motion which means that large particles have low velocity while the small particles

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have high velocity. The properties of scattered light change with respect to the particle velocity. Fast changing of wave of scattered light means small particles while slow change of wave is due to large particles. For concentrated slurry systems, a phenomenon called “multiple scattering” occurs. Mie theory is a methodology to address the issue. It describes the scattered intensity of spherical particle as a series of the product of Mie scattering coefficient with Legendre polynomial.6 An alternative method is to avoid multiple scattering using the back scattering technique.7 By installing a receiver close to the laser gun, the scattered light will not have to travel through the entire sample therefore reduce the multiple scattering effect. It backscatters the light via an angle, instead of passing through the samples, minimising the effect of multiple scattering. The Malvern online DLS system used in this work is based on this principle. ERT is used for cases that the continuous phase is a conductive fluid and the second phase can be either conductive or nor-conductive. Voltage is measured from a number of paired electrodes that are fitted around the inner wall of a pipe cross-section using tomographic sensors. The conductively distribution is then reconstructed to reflect the distribution of the second phase in the flow 8, 9 Frequency=20.MHz

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Figure 2. Concentration effect on the acoustic attenuation of silica suspensions (Dattenuation; I particle concentration)

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2. Experiments Experiments were carried out on the rig shown in Figure 1. The process was designed to dilute using local tap water (conductivity 407μS/cm) a concentrated silica colloid (Nissan Corporation America, 24.0%vol with conductivity 4.12mS/cm, mean size of 70-100nm in diameter). ERT measurement was carried out through the whole process. USS and DLS measurements were taken when each dilution process was completed. A simple algorithm is developed to derive the concentration from the ERT conductivities.

2 E  ( E  1)I 0  I 0  8EI 0 (I 0  1)(I 0  2)  [2 E  I 0 (I 0  E  1)] 2 2

(1) 2 E (I 0  2) where I is the volume concentration of the nonconductive phase, I0 is the initial concentration of the suspension and ȕ is the ratio of the initial conductivity to the measured conductivity.

I

USS particle sizing The relation between the acoustic attenuation and concentration for different frequencies is shown in Figure 2, the straight lines are the linear fittings of the attenuation data. It is clearly that the relationship becomes nonlinear as particle concentration is greater than 8.0% vol., and as expected3, that estimated PSD shifted to smaller mean size. PSDs for each concentration calculated by ECAH model and their mean sizes are shown in Figure 3. 120

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500.

lnm

l n m

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lQ  l -

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I 

0.15

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Figure 3. PSD and volume mean sizes of silica particles for each concentration. (a) the plots of PSD (the horizontal axial is particle size and the vertical axial is the corresponding volume fraction of the particles. The right arrow on I denotes the decrease of particle concentration). (b) volume mean size plot.

It is seen from (a) of Figure 3 that PSD gradually shifted to smaller particle size region with the increase of particle concentration and eventually became incorrect when concentration is greater than 8.0%vol. Concentration plot and ultrasound spectra The PSDs and their corresponding mean sizes measured by DLS are shown in (a) and (b) of Figure 4. (c) of Figure 4 is the comparison of the mean sizes between USS and DLS and (d) is the zeta potential measurements.

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Figure 4. Size distributions and volume means of silica particles measured by DLS. (a) size distributions (The right arrow on I denotes the decrease of particle concentration). (b) volume mean sizes. (c) comparison of mean sizes. (d) Zeta potential

From Figure 4, it is clear that for higher concentrations, the measured PSDs have slightly larger particle sizes; while the PSDs in lower concentrations as shown in (a) indicate that the dilution might have caused some changes to the system resulting in wider distributions. As seen in (c), a divergence between the two results does occur in higher concentration region (> 5.0%vol). This is due to the difference between the measurement principles. However, as can still be seen, the mean sizes in low concentration region are quite comparable. (d) indicates that with dilution going on the suspension gets more stable as the magnitude of zeta potential increases. In higher concentration region (here > 8.0%vol), the value of zeta potential indicates that the suspension is unstable. ERT results Figure 5 shows how the dispersed phase distributed in the continuous phase when flowing. As can be seen from the images in Figure 5, there was a slightly higher nonconductive area in the up left region of the images. This might be due to vortices generated in this area during the flow of the suspension resulting in particles slightly more concentrated than that in other areas.

3. Conclusions A system combining multiple sensors including dynamic light scattering (DLS), ultrasound spectroscopy (USS) and electrical resistance tomography (ERT) has been described for online characterisation of nanoparticle suspensions. ERT provides realtime information about the mixing quality of the dispersed phase in a continuous phase, and importantly solid concentration and conductivity which are required by DLS and USS for measurement of particle size distributions (PSD). The DLS sensor also measures zeta potential which is also important because its value is an indicator of stability of the suspension. Both instruments, DLS and USS, provide measurements about PSD10. Preliminary comparison was made for the two sets of data. It must be pointed out that due to the difference in measurement principles, the two sets of size

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distributions are unlikely to be identical for this specially designed experiment in high concentration region. However, they are comparable especially for the results of low concentrations in terms of their mean sizes as they appeared to be consistent. The knowledge obtained from experiments is useful for applying the instruments for online characterization of nanoparticle suspensions.

1)

2)

3)

4)

5)

6)

7)

8)

Figure 5. Constructed conductive images for each concentration of suspensions (the numbers are referring to the reference number of measurements)

4. Acknowledgements UK Technology Strategy Board (Grant Reference: TP/2/SC/6/I/10097) and EPSRC (Grant Reference: EP/E040624/1) are thanked for their financial support.

5. References 1. McClements DJ, Adv Colloid Interf Sci, 1991, 37: 33-72. 2. Povey MJW, Pharma Sci Tech Today, 2000, 3: 373-380. 3. Dukhin AS, Goetz PJ, Ultrasound for characterizing colloids. Particle sizing, Zeta potential, Rheology. Elsevier: Amsterdam-New York-Tokyo, 2002. 4. Allegra JR, Hawley SA, J. Acoust. Soc. Amer., 1972, 51: 1545-1564. 5. Estein PS, Carhart RR, J. Acoust. Soc. Amer., 1953, 25: 553-565. 6. Flesia C, Schwendimann P., Applied Physic B, 1993, 56: 157-163. 7. Malvern Instruments, www.malvern.co.uk/common/downloads/campaign/MRK65601.pdf 8. Wang M, 7th World Cong Chem Eng, Glasgow, UK, 2005. 9. Williams RA, 7th World Congr Chem Eng, Glasgow, UK, 2005. 10. Wang XZ, Liu LD, Li RF, Tweedie RJ, Primrose K, Corbett J, McNeil-Watson FK, 2009, Chem Eng Res Des, in press, doi:10.1016/j.cherd.2008.12.014.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Variance of Estimates in Dynamic Data Reconciliation Christophe Ullrich, Georges Heyen and Carine Gerkens University of Liège, Lassc, Allée de la Chimie 17, B6A, Sart-Tilman, Liège B-4000, Belgium, [email protected]

Abstract The method previously proposed to estimate the uncertainty of validated variables in steady state data reconciliation has been extended to dynamic data reconciliation. The approach used in this article to estimate a posteriori variances in the case of dynamic date validation is based on the one described in [2] for the stationary case. Orthogonal collocations are used to discretise ODE. Results are presented for an adiabatic reactor with first order kinetic.

Keywords: dynamic data reconciliation, a posteriori variances, orthogonal collocations 1. Introduction Efficient process monitoring is a key issue in plant operation, since measurement errors are always present. To address this issue, data validation is nowadays routinely performed for steady state processes, but dynamic systems still present some challenges. Data validation uses measurement redundancy and model constraints to reduce measurement uncertainty and to calculate non measured state variables of the system. A posteriori variance for validated variables compared to raw measurements can be calculated for linear or linearized steady state systems. Several methods enable to solve the dynamic data reconciliation problem [2]. We use NLP technique and orthogonal collocation [3] to discretize the ODE systems, as described in [1].

2. Estimation of a posteriori variances The algorithm uses moving horizon is used to limit the size of the optimization problem. This moving horizon is described by the following figure.

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The validation window is defined by five parameters: - h1 : measurement frequency - h2 : size of the interpolation of the input variables - h3 : discretization interval of the differential state variables - h4 : size of the moving window - h5 : the move of the window after optimization After applying function is:

orthogonal collocation to the differential system, the objective

­ ntmes ª nxmes m T m ° ¦ « ¦  xi , j  xi , j Wxi ,i , j  xi , j  xi , j j i 0 1 « ° ¬ ° nzmes T °   z i, j  zim, j Wzi ,i , j  z i, j  zim, j ° ¦ i 1 ° n ° umes º T min ®  ¦  ui , j  uim, j Wu  ui , j  uim, j » xic,k i ,i , j ° i1 »¼ ¬ªui ,ini ,ui , f ¼º interp int 1 ° nx T ¬ªui , f ¼º interp int s °  xi,0  xCIi,0 R xi ,i  xi,0  xCIi,0 ° ¦ k , s z1, i i 1 ° nu ° CI T CI °  ¦  ui ,0  u i ,0 R ui ,i  u i ,0  ui ,0 i 1 ¯

(1)

With - x: the vector of differential state variables; - z: the vector of algebraic variables; - u: the vector of input variables. This objective function is subjected to five types of constraints: - the link equations: they are algebraic relations between all process variables. Those constraints have to be satisfied as well at the measurements times as at the collocations nodes:

Variance of Estimates in Dynamic Data Reconciliation f  t j , x, z , u 0

A

t j

A

c

f

c

359

T , x , z , u c

c

c

(2-3)

0 T k

k

- the relations between the differential state variables and the Lagrange interpolation polynomials at all measurement times of the moving horizon except at the initial times of the discretization intervals tCI: n (4) B x  l (t )xc 0 i, t z t T

¦

i, j

k

j

i ,k

j

CI

k 0

- the linear interpolations of the values of input variables between times tini and tf of the interpolation horizon at the other times of that horizon: t t (5) C u  u  j ini u  u 0 i, t z t , t i, j

Cc

i ,tini

uic,k  ui ,tini



i ,t

i ,t

f ini t f  tini T t  k ini ui ,t f  ui ,tini t f  tini





j



ini

f

(6)

i, T k

0

- the residuals of the differential state equations at all collocation nodes: nT ˙

¦ l (T

D

s

s 0

k

)xic,Ts  g T k , xck , z ck , u ck 0

(7)

i, T k z tini

- the continuity constraints of the differential state variables between two discretization intervals: ª nT ª nT º c º  « ¦ l k (tini ) xic,k » « ¦ l k (t f ) x i , k » ¬k 0 ¼ t f ,discr int q 1 ¬ k 0 ¼ tini , discr int q

E

0

(8)

i

This constrained problem can be transformed into an unconstrained problem using Lagrange formulation. The necessary condition for optimality is expressed by setting to 0 the gradient of the Lagrangian. By linearising the equation system as shown in [2], one obtains a linear relation between validated variables and measurements:



M x

P x

z u m

x

Pz z m

xc

zc Pu u m

uc

/A

c

/A

0 0 0 F

/B F c

/C

/C

c

/D

/E

T



(9)

T

0 0 0 G 0

where F, Fc and G are constant terms of the linear aproximation of the constraints. One obtains the sensitivity matrix M which is the Jacobian matrix of the equation system: § ( · (10) M ¨ T ©

¸ 0¹

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360

(

§ Px ¨ ¨0 ¨0 ¨ ¨0 ¨0 ¨¨ ©0

0 0 0· ¸ 0 0 0¸ 0 Pu 0 0 0 ¸ ¸ 0 0 0 0 0¸ 0 0 0 0 0¸ ¸ 0 0 0 0 0 ¸¹ Px Wx  R x Pz Wz 0 Pz

0 0



Wu  R u

Pu

§ wǹ ¨ wx ¨ ¨ ¨ 0 ¨ ¨ wB ¨ wx ¨ ¨ 0 ¨ ¨ ¨ 0 ¨ ¨ ¨ 0 ¨ ¨ ¨ 0 ©

wǹ wz

wǹ wu

0

0

0

0

0 0

wC wu wCc wu

0

0

0

0

0

0

wA c wxc wB wxc

wA c wz c

0

0

0

0

wD wxc wE wxc

wD wz c

0

0

· 0 ¸ ¸ wA c ¸ wu c ¸ ¸ 0 ¸ ¸ ¸ 0 ¸ ¸ c ¸ wC ¸ wu c ¸ wD ¸ ¸ wu c ¸ ¸ 0 ¸ ¹

(11-12)

As for the stationary estimation [2], a posteriori variances can be deduced from this sensitivity matrix: var  x k

Nx

¦ ª¬M i 1

2 1 k ,i

Nz

2

Pxi º¼ var  xim  ¦ ª¬ M k 1,i  N x Pzi º¼ var  z im

Nu

i 1

(10)

2

 ¦ ª¬ M k1,i  N x  N z Pui º¼ var  u im i 1

Similar equations can be written for input and algebraic variables.

3. Case study: an isothermal reactor with first order kinetic This reactor with first order kinetic is defined by the following differential state equation: dCA dt

F  CAi  CA  k CA V

(14)

CA is the state variables while F and CAi are the inputs. The problem has no algebraic variable. The kinetic constant k is defined as a constant of the optimization problem; so, it can not be optimized. The parameters of the window have been chosen as follow: h1 = 1, h2 = 4, h3 = 4, h4 = 49 and h5 = 2. The Lagrange interpolation polynomials are of the second order. Input variables are varied by stepping the setpoint in following equation: dx dt

K  xSP  x

(15)

Variance of Estimates in Dynamic Data Reconciliation

Figure 1: Concentration profile

361

Figure 2: Feed flowrate profile

A Gaussian noise is added to state variables to model the measurement. As can be seen on figure 1 and 2, for the concentration and the feed flowrate profiles respectively, the validation allows to reduce the noise and the changes in the profiles are very well followed by the validated values.

Figures 3 and 4: Uncertainties comparison for concentration and feed flowrate

On figures 3 and 4, error bars show the standard deviation of the measurements and the validated values for the concentration and the feed flowrate respectively. The variances are reduced for state variables as well as for inputs. For the state variable, one has the following results: Times A priori A posteriori Reduction variances variances factor 360 0.01 0.0047 2.1 380 0.01 0.0021 4.8 400 0.01 0.0023 4.3 420 0.01 0.0022 4.5 440 0.01 0.0024 4.2 The variance reduction is similar for all measurement times of the validation window excepting for the first times for which it is less important.

362

For the incoming flowrate, one has the following results: Times A priori A posteriori variances variances 360 0.01 0.0040 380 0.01 0.0058 400 0.01 0.0034 420 0.01 0.0058 440 0.01 0.0034

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Reduction factor 2.5 1.7 2.9 1.7 2.9

The variance reduction is less important and varies more for the inputs along the validation window. We think that it is a consequence of the way input variables are defined in the validation problem.

4. Conclusions and future work The results presented in this article are for an adiabatic reactor with a first order kinetic. Similar results have been obtained for different systems including the example described in [1]. Good reductions for variances of state and algebraic variables are obtained in all cases, but for input variables the reductions of the variances are less significant. In the future, we plan to examine the influence of polynomial order used to model the input variables on the variability of the validated uncertainty.

5. Acknowledgements The authors are grateful to the Walloon Region and the European Social funds who cofinanced this research.

6. References [1] Liebman, M. J., Edgar, T. F., Lasdon, L. S., Efficient data reconciliation and estimation for dynamic processes using nonlinear programming techniques, Computers & Chemical Engineering, Vol. 16, N° 10/11, 963-986, (1992) [2] Heyen, G., Maréchal, E., Kalitventzeff, B. (1996). Sensitivity Calculations and Variance Analysis in Process Plant Measurement Reconciliation. Computers and Chemical Engineering 20S, 539-544 [3] Villadsen, J., Michelsen, M. L., Solution of differential equation models by polynomial approximation, Prentice-Hall, Englewood Cliffs, New Jersey, (1978)

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363

A Hybrid Multiple Populations Evolutionary Algorithm for Two Stage Batch Planning Problems with Disjunctive Decisions Thomas Tometzki and Sebastian Engell Process Dynamics and Operations Group, Technische Universität Dortmund, 44221 Dortmund, Germany, {t.tometzki | s.engell}@bci.tu-dortmund.de

Abstract This paper considers batch planning problems on a moving horizon with significant uncertainties in the problem data. The planning problem is represented as a two-stage stochastic integer program with linear disjunctions and solved by a stage-decomposition based hybrid algorithm with an evolutionary algorithm for the first-stage and mathematical programming for the second-stage. The first-stage problem is decomposed into a finite number of smaller subproblems by fixing some important discrete decision variables. The subproblems are solved independently by evolutionary algorithms, leading to parallel evolutions based on multiple populations. The number of subproblems is systematically reduced by comparing the current best global solution and the lower bounds of the subproblems. Numerical experiments show that the robustness is improved and the convergence to good solutions is significantly faster. Keywords: batch planning, evolutionary algorithms, disjunctive decisions

1. Introduction The information and decision structure in planning on moving horizons with uncertainties can be reflected by a mixed-integer recourse model with a finite number of scenarios in the form of a two-stage stochastic integer program. The here-and-now decisions (first-stage) which have to be made under uncertainty are compensated by recourse decisions (second-stage). In [1] the application of a hybrid stage decomposition based evolutionary algorithm to a case study (see Chapter 5.1) was presented. Compared to an exact scenario decomposition based algorithm [2] the hybrid algorithm improves the initial solution faster for a while but then in some cases it stagnates at suboptimal solutions. In [3], a more detailed analysis of this case study with regard to its complex constraints and disjunctive decisions was performed. The analysis exhibited that the integer search space of the evolutionary algorithm is highly constrained by capacity and disjunctive operational constraints. The solutions which satisfy all constraints are arranged in many small polyhedral subsets leading to a feasible search space which is disconnected. It was revealed that the generic variation operators of the evolutionary algorithm are not suitable for search spaces with disjoint subsets of feasible solutions that are separated by large infeasible regions. The aim of the present work is to remedy the shortcomings of the generic evolutionary algorithm. We describe how an appropriate representation of the disjunctive decisions can be exploited in order to significantly improve the efficiency of an evolutionary algorithm. A new multiple populations based evolutionary algorithm for disjunctive search spaces that are typical for batch planning problems is formulated.

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2. Two-stage mixed-integer disjunctive programs A two-stage mixed-integer program is used to model uncertainty in problem data. It is assumed that the uncertainty have a finite number of realizations that can be modeled by a discrete set of scenarios ω=1,…,Ω. The decisions are divided into the first-stage decisions x which have to be taken before the uncertainty is disclosed and second-stage decisions yω, which have to be taken after the uncertainty is realized. In this paper, we consider two-stage mixed-integer programs that involve linear constraints on the firstand second-stage decisions and linear disjunctions on the first-stage decisions which explicitly model operational constraints: min c x + T

x , y1 ,..., y Ω

Ax ≤ b

s.t.

∨ A

j∈J k

jk

Ω

∑π ω =1

T

ω

qω y ω

(1) (2)

x ≤ b jk , k ∈ {1,2,...,m}, J k ={1,2,...,n k }.

Wω y ω ≤ h ω - Tω x

(3) (4)

x ∈ X, y ω ∈ Y, ∀ω=1, … ,Ω. The objective of the problem (1) consists of the first-stage costs and the expected value of the second stage costs. The costs are calculated as linear functions of the first-stage variables x and the second-stage variables yω with vectors of cost parameters c and qω. The two-stage model consists of inequality constraints in both stages (2, 4) and m linear disjunctive constraints (3) on the first-stage variables. Each disjunction k∈{1,2,…,m} is composed of nk disjuncts, each containing a set of inequality terms. The disjuncts are connected together by logical exclusive OR that enforces the satisfaction of one and only one disjunct set of conditions. The finite sets X and Y may contain integrality requirements.

3. Stage decomposition based algorithmic approach The main idea of stage decomposition is to remove the ties between the second-stage scenario subproblems by fixing the first-stage decisions. The scenario subproblems are of significantly smaller size than the full two-stage problem. The master problem is a function of the vector of first-stage variables x only: min f ( x) = c x + Φ(x)

(5)

Ax ≤ b, x ∈ X

(6)

∨ A

(7)

T

x

s.t.

j∈J k

jk

x ≤ b jk , k ∈ {1,2,...,m}, J k ={1,2,...,n k }.

The second-stage value function Φ(x) for a first-stage decision x is given by the expected value of the Ω independent second-stage functions Qω(x): Ω

Φ(x)= ∑ π ω Q ω ( x )

(8)

ω =1

The evaluation of Φ(x) requires the solution of Ω subproblems over the second-stage variables yω: T

Q ω (x )= min q ω y ω yω

s.t.

Wω y ω ≤ h ω - Tω x, y ω ∈ Y, ∀ω=1, … ,Ω.

(9)

A Hybrid Multiple Populations EA for 2-Stage Batch Planning with Disjunctions

365

The constraints of the master problem (5-7) are scenario independent, while the parameters of the linear second-stage constraints in (9) may vary from scenario to scenario. The vector of the first-stage variables x appears as a vector of fixed parameters in the constraints of the second-stage scenario problems. The challenge of the master problem is that Φ(x) in general is discontinuous and non-convex due to integrality requirements and the minimization in the second stage. Additionally, first-stage feasible solutions do not necessarily have feasible solutions in the second-stage due to the implicit constraints. The main algorithmic idea of the hybrid evolutionary approach is to address the master problem given by (5-7) by an evolutionary algorithm. To evaluate f(x), the Ω subproblems given by (9) are solved independently by a MILP solver.

4. Multiple populations based evolutionary approach 4.1. Search space decomposition The idea of the proposed multiple populations evolutionary algorithm is the decomposition of the full search space of the master problem into a finite number of smaller search spaces in order to solve the subproblems independently. This may require solving a large number of problems, but they are easier to solve. Under the assumption that only the constraints of one disjunct for each disjunction in (7) must be satisfied to fulfill the first-stage constraints, the subproblems are obtained by the set of all combinations of disjuncts over all disjunctions P:=J1×…×Jk×…×Jm with Jk={1,2,…,nk}. By assigning the corresponding disjuncts to different problems, the master problem is decomposed into a finite number of smaller subproblems without disjunctions. The maximum number of subproblems is bounded by |P|=n1·n2·…·nm. 4.2. Reduction of the number of subproblems The subproblems are solved independently by evolutionary algorithms, leading to parallel evolutions based on multiple populations. Each time an evolutionary algorithm improves the best solution for a subproblem, its cost yields a new upper bound for the subproblem. The lowest upper bound of all subproblems is the current best global solution. During the parallel evolution process, each subproblem p∈P with a lower bound that is larger than the current global best solution is removed from the set: P:=P\p. This guarantees that the global optimum always remains in the union of the search spaces of the remaining subproblems. The lower bounds of the subproblems are obtained in a precalculation phase by solving of the corresponding full two-stage integer-relaxed problem. Its value obviously affects the efficiency of the reduction of number of subproblems. 4.3. Multiple Populations Evolutionary Algorithm The idea of master-problem partitioning and removing of subproblems is applied to a (μ,κ,λ)-evolution strategy [4]. An evolution strategy is a class of evolutionary algorithms which adapts the mutation strength during the course of evolution. Each individual of the population represents a search point xk=(x1,…,xn) by its object parameters, in addition to mutation strength parameters sk=(s1,…,sn) which affect the mutation operator. For each subproblem p∈P a subpopulation of μp=μ/|P| individuals is initialized randomly within the bounds of the box-constrained first-stage decision space. In the evaluation of x for a subproblem p∈P, for unsatisfied first-stage constraints (6) Ax≤b and associated disjuncts (7) Apx≤bp the fitness function f(x) is replaced by the penalty function g(x)+fmax which is defined as the sum of constraint violations according to g(x)=∑j(Ajx-bj)+∑j(Ajpx-bjp) and an upper bound fmax of f(x) for feasible solutions x. After the evaluation, for each subproblem λp=λ/|P| offspring are

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generated by λp-fold application of the mutation operator. It perturbs each variable xi by a random number drawn from a normal distribution with an expected value of zero. For integer variables, the random numbers are rounded to the nearest integer value. The distribution variance depends on parameter si which is modified log-normally. To maintain the bounds for xi, values outside the bounds are mapped onto the next bound. A truncation selection chooses the μp best (1≤μp≤λp) individuals out of the union of μp parents and λp offspring which do not exceed the maximum age of κ for the next interation loop. At the beginning of each evolutionary loop, a subproblem is removed if its lower bound is larger than the current best solution. For compensation of the overall number of individuals, the remaining populations are complemented with random copies of parental individuals to obtain not less than μ individuals in all populations together.

5. Numerical study 5.1. Chemical Batch Planning Example Fig. 1 shows the layout of a multiproduct batch plant for the production of expandable polystyrene (EPS) [5]. Two types A and B of the polymer in five grain size fractions are produced from raw materials E. The preparation stage is not considered here. The Fig. 1: The flow sheet of the multi-product batch plant. polymerization stage is operated in batch mode and is controlled by ten recipes. Each recipe defines the product (A or B) and its grain size distribution. Each batch yields a main product and four coupled products. The capacity of the polymerization stage constrains the number of batches to 12 in each two-day period. The batches are transferred into two continuously operated finishing lines which fractionate the grain sizes. The capacity of each finishing line is between 5 and 12 batches per period in case it is operated, and 0 otherwise. The operation mode has to be the same for at least two succesive periods. The planning decisions which have to be made are operational decisions on the finishing lines in each period and batching decisions on the numbers of polymerizations of each recipe in each period. The decisions in periods 1 to 3 are considered as first-stage decisions, those in periods 4 and 5 as second-stage decisions. The uncertainty in the demands is represented by 64 scenarios of equal probability. The natural representation of the first-stage search space x for the case study is given by a 30-dimensional integer vector. Each variable xipr represents the EPS-type p∈{A,B} of recipe r∈{1,…,5} in the 3 first-stage periods i∈{1,…3}. The capacity of the polymerization stage constrains the number of batches in each period:

∑x

ipr

≤ 12 , ∀i .

(10)

p,r

The discrete operational decision on the finishing lines is modeled as a disjunction of two disjuncts:

∑x r

ipr

= 0 ∨ 5 ≤ ∑ x ipr ≤ 12 , ∀i,p . r

(11)

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367

In the solution of the Ω second stage scenario problems by an MILP solver the disjunctions in the second stages are formulated as linear constraints by using auxiliary binary variables zip to represent the operational decision as follows:

5z ip ≤ ∑ x ipr ≤ 12z ip , ∀i,p .

(12)

r

In addition, the operation mode constraints decrease the number of feasible disjunct combinations, and thus the number of subproblems |P| is reduced from 64 to 25. The objective is the maximization of the profit which is calculated from variable revenues αlipr per batch for satisfying customer demands with due dates, where the lateness of the supply is denoted by l. Demands that are supplied in the same period as demanded (l=0) result in a full revenue while the revenue decreases with increasing lateness (l=1,2) of the demand satisfaction, and the accepted lateness is bounded to two periods. Furthermore, variable costs of the product inventory α+ipr per batch, variable penalties for supply shortage α-ipr per batch, fixed costs of the polymerizations βipr per batch, and costs for operating state changes of the finishing lines γip are considered in the objective function. A detailed description of the process and of the cost model can be found in [1].

5.2. Performance of the new approach The proposed approach is compared to the performance of the standard evolutionary algorithm presented in [1]. A global population size of μ=10, a global offspring/parentsratio of λ/μ=7, and a maximum age of κ=5 was chosen. The initial number of subproblems is |P|=25. Consequently the initial population size for each subproblem is μp = 1, the initial number of offspring is λp=3. Since the evolutionary algorithm is implemented for solving minimization problems, the objective of maximization of the profit is reformulated to a minimization problem. Three numerical experiments with different problem settings were carried out: Experiment 1: The revenue for the satisfaction of the demands is set to α0ipr=2.0, α1ipr=1.5 (lateness of one period) and α2ipr=1.3 (lateness of two periods). The specific costs for inventory are set to α+ipr=0.2. The variable penalties for supply shortage are set to α-ipr=0.5. The other cost coefficients are set as follows: βipr=1, γip =3. Experiment 2: The initial storage inventory for all products of type A is set to 1 batch. Otherwise the settings of experiment 1 are used. Experiment 3: The demands of types A and B are exchanged. Otherwise the settings of experiment 1 are used. For all experiments and for each algorithm 10 runs were performed. The algorithms were implemented in MATLAB 7.3. All MILPs were solved using CPLEX 10.2. The relative integrality gap of CPLEX was set to 1%. The algebraic models to be solved by CPLEX were formulated using GAMS distribution 22.5. The computational equipment for all the experiments was a dual Xeon machine with 3 GHz speed, 1.5 GB of main memory with Linux operating system. The calculation time for all experiments was limited to 7200 CPU-seconds. Fig. 2 shows the summarized evolutions of the best fitness values (top) and of the numbers of remaining subproblems (bottom) for three numerical experiments with different problem settings. The lines represent quartiles (25%, 50% and 75%) and minand max-values of the evolution distributions. The grey area in the upper charts

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25 20 15 10 5 0 0

1000

2000

3000

4000

5000

cpu-time (sec)

6000

7000

8000

30 25 20 15 10 5 0 0

1000

2000

3000

4000

5000

cpu-time (sec)

6000

7000

8000

number of remaining subproblems

30

number of remaining subproblems

number of remaining subproblems

(beginning at 0 seconds) shows the time needed to calculate the lower bounds for all subproblems.

30 25 20 15 10 5 0 0

1000

2000

3000

4000

5000

6000

7000

8000

cpu-time (sec)

Fig. 2: Results of three experiments for different problem instances (left to right). Top: Fitness evolutions of standard algorithm (dashed lines) and multiple populations based algorithm (solid lines). Bottom: Evolution of the number of subproblems for the multiple populations algorithm.

The new multiple populations based evolutionary algorithm (solid lines) performs considerably better than the standard algorithm (dashed lines) at any time. The robustness of the new approach is strengthened by the closer quartile distances. For all experiments, the initial number of 25 subproblems is reduced by a factor of approx. 5 in the course of the evolution. This leads to an efficient coverage of the search space compared to the standard algorithm.

6. Conclusions The presented work proposes a new generic hybrid approach for the solution of twostage mixed-integer disjunctive programs. The disjunctive structure is exploited to generate an efficient decomposed solution space in order to significantly improve the efficiency of the hybrid evolutionary approach. Each subset is investigated by an independent evolutionary algorithm. The number of parallel evolutions is reduced systematically by a bounding approach which guaranties that the global optimal solution remains in the search space. Numerical experiments showed that the new multiple populations based evolutionary algorithm cam improve the efficiency in terms of a faster convergence to solutions with better fitness values.

7. References [1] J. Till, G. Sand, M. Urselmann, S. Engell: A Hybrid Evolutionary Algorithm for Solving Two-stage Stochastic Integer Programs in Chemical Batch Scheduling. Computers & Chemical Engineering 31:630-647, 2007. [2] C. Carøe and R. Schultz, Operations Research Letters, 24 (1999) 37 [3] G. Sand, J. Till, T. Tometzki, M. Urselmann, S. Engell, and M. Emmerich: Engineered vs. Standard Evolutionary Algorithms: A Case Study in Batch Scheduling with Recourse. Computers & Chemical Engineering, 32:2706-2722, 2008. [4] H.P. Schwefel. Evolution and Optimum Seeking. Sixth-Generation Computer Technology. Wiley Interscience, New York, 1995. [5] G. Sand and S. Engell. Modelling and solving real-time scheduling problems by stochastic integer programming. Computers & Chemical Engineering, 28:1087-1103, 2003.

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369

A MILP Scheduling Model for Multi-stage Batch Plants Georgios M. Kopanos, Luis Puigjaner Universitat Politècnica de Catalunya - ETSEIB, Diagonal, 647, E-08028, Barcelona, Spain, E-mail: [email protected]

Abstract In the current work, a new precedence-based mixed integer linear programming (MILP) scheduling framework, based on a continuous-time representation, is developed for the scheduling in multi-stage batch plants. Advantages and special features of the proposed scheduling model are highlighted through several instances of two base case studies. Results are analyzed and further criticized towards future work.

Keywords: scheduling, batch plants, multi-stage operations, MILP 1. Introduction Multi-stage operations are found in a large number of industrial applications. The main features of multi-stage operations are the intermediate products storage strategy, such as zero wait (ZW), no intermediate storage (NIS), unlimited intermediate storage (UIS), and finite intermediate storage (FIS). Share resource constraints and sequencedependent setup times are also of great importance since they complicate the problem (especially the latter ones). Neglecting these multi-stage operations characteristics leads to poor modeling of the real industrial process resulting to poor solutions once implemented. In the PSE community a plethora of scheduling frameworks can be found.1 Among them continuous time representation strategies based on the precedence relationships between batches to be processed have been developed to deal with scheduling problems. Model variables and constraints enforcing the sequential use of shared resources are explicitly employed in these formulations. As a result, it is claimed that changeover issues can be treated in a straightforward manner.1 The three different precedence-based approaches that can be found in the literature, namely, are: i) the immediate precedence2, ii) the unit-specific immediate precedence3, and iii) the general precedence4; see Fig.1.

Figure 1. Current and proposed (in red) precedence-based frameworks. Immediate precedence explores the relation between each pair of consecutive orders in the production schedule time horizon without counting if the orders are assigned or not

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into the same unit. Unit-specific immediate precedence is based on immediate precedence concept. The difference is that it takes into account only the immediate precedence of the orders that are assigned to the same processing unit. General precedence (GP) extends the precedence concept by exploring the precedence relations of every batch regarding all the remaining batches and not only the immediate predecessor. The computational effort of this approach is significantly lower comparing it with those of the other two approaches. Nevertheless, GP scheme appears some model representation drawbacks that may moderate its implementation in industrial practice. First of all, it cannot explicitly cope with sequence-dependent setup issues, such as times and costs. In other words, if changeover issues are the optimization objective function, or a part of it, GP cannot be used to tackle the addressed problem. To continue with, GP is inappropriate for solving scheduling problems wherein some processing sequences are forbidden. Finally, even timing incoherencies resulting to myopic optimal solutions can be observed in some other cases, especially when they appeared some sequence-dependent times highly greater than some processing times.5

2. Problem statement In this work, the scheduling problem in multi-stage multiproduct batch plants with different processing units in parallel is addressed (see Fig.2). Batch-stage to unit assignment and batch sequencing in every processing stage meeting a production goal constitutes the under study scheduling problem.

Figure 2. Multi-stage process scheme. The main problem characteristics and proposed model assumptions include: - An equipment unit cannot process more than one batch at a time. - Non-preemptive operation mode is assumed. - Processing times, unit setup times and changeover times and/or costs are deterministic. - Unforeseen events are not appeared during the scheduling time horizon. - No resource constraints except for equipment availability. - Batch sizes are known a priori.

3. Mathematical formulation The proposed precedence-based MILP model is based on a continuous-time domain representation. The main concept of the proposed model aims at combining the

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advantages that general precedence and immediate precedence frameworks have, resulting to a new hybrid precedence-based formulation. In the proposed mathematical formulation, the problem constraints have been grouped according to the type of decision upon which they are imposed on. The basic set of equations are stated and briefly explained next. 3.1. Allocation constraint Every stage s of each order i can be assigned to at most one processing unit j: (1)

3.2. Timing constraints The completion time of the first stage of product i has to be greater than its processing and its setup time plus the necessary changeover time, sdi’ij, from the previous product i’, when products are consecutive into the same unit.

(2) The binary variable, Seqi’ij, becomes one when product i’ is processed exactly before of product i, while both are allocated to the same unit; otherwise is set to zero. Seqi’ij accesses the unit-specific immediate precedence of two orders. To go on, the timing of the remaining stages is given by the next expression:

(3) In eq.(3), trs-1s corresponds to the transfer time between two sequential stages of a particular product i while Storis-1 stands for the time that the stage s-1 of a product i is stored before proceeding to the following processing stage s. In ZW storage police Storis-1 is set to zero. In UIS is left free. In order to model storage policies like NIS and FIS, equations found in the literature can be easily added to the proposed MILP formulation. 3.3. Sequencing-timing constraints Binary variables Xii’j and Seqii’j, make reference to the unit-specific general precedence and the unit-specific immediate precedence notion, respectively. Roughly speaking, Xii’j is 1 when product i is processed before product i’ in the same unit j, in contrast with Seqii’j that is 1 when order i is the predecessor of order i’ in unit j. (4) Eq.(4) states that the starting time of an order i’ is greater than the completion time of whichever order i processed beforehand. The binary Seqii’j activates only the changeover times between consecutive orders, thus assessing sequence-dependent issues explicitly; and not implicitly as general precedence does.

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3.4. Sequencing-allocation constraints Equations (5)-(6) are needed in order to formulate the unit-specific general precedence concept of the proposed model. (5)

(6) These equations state that when two orders are allocated to the same unit, i.e. Yisj = Yi’sj = 1, only one of the two binary variables Xii’j and Xi’ij will be one. If the two orders are not allocated to the same unit then Xii’j = Xi’ij = 0. 3.5. Assessing consecutiveness through general precedence Obviously, two orders i and i’ are consecutive only in the case that the binary variable Xii’j=1 and, moreover, when there is no other order, i’’, between them.

Figure 3. Illustrative example for assessing consecutiveness through GP. Axiom: Two batches i and i’ are consecutive if and only if the total number of batches that are processed after batch i, if batch i’ is excluded, is equal to the total number of batches that are processed after batch i’, when batch i is excluded; see Fig.3.

(7)

(8) In Eq. (7), the auxiliary variable Posii’j is set to zero if and only if two products i and i’ are consecutive and are assigned to the same unit. In other words, when order i is processed before order i’ in unit j, i.e. Xii’j=1, and the summation term in eq.(7) is zero, i.e. there is no other order i’’ between them, then the two orders are consecutive. In any other case, Posii’j gets a value different than zero. Eq. (8) forces the Seqi’ij variable to be 1 whenever Posii’j=0; in any other case, Seqi’ij is set to zero. The 1 in the right-hand side of eq.(8) can be substituted by Xii’j. It has found that in some instances reduces the computational time.

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4. Case studies A simplified (regarding the number of products) version of an industrial case study of a multi-stage pharmaceuticals batch plant is considered. Products are processed to 5 or 6 stages and changeover times (in same stages higher than the processing times) are present. Four different instances (I.1-I.4) of this case study have been solved. Five products are scheduled in all cases but case I.2; wherein six products are considered. Table 1. Case I computational results Problem I.1 I.1 I.2 I.2 I.3 I.4

Model Obj. function. GP4 8.506 USGP 8.506 GP4 (1.83%) 8.740 USGP 8.704 USGP 29.583 USGP 905.956

N. of Eq 266 1,106 391 2,011 1,102 1,107

Bin. var Cont. var 166 26 271 485 236 31 398 730 271 485 271 486

Nodes 40 334 795,979 91,504 750,288 57,885

CPU (s) 0.365 0.575 > 600 406.680 559.100 43.160

*Solved in GAMS (CPLEX 11.0) in a Dell Inspiron 1526, 2 GHz with 2 GB RAM

Makespan minimization is the optimization goal in I.1-I.2, changeovers costs minimization in I.3, and operating plus changeovers costs minimization in I.4. ZW policy is applied. Computational results can be found Table 1. A 10-minute time limit has been imposed. Fig.4 shows the optimal schedule of I.2 problem; note that only USGP reached optimal solution.

Figure 4. Optimal schedule for I.2 problem instance (USGP optimal solution).

Afterwards, a modified case study6 found in the literature is addressed. Six 3-stage products are to be scheduled under UIS policy. Three different instances (II.1-II.3) of this case have been solved. Table 2. Case II computational results Problem II.1 II.1 II.2 II.2 II.3

Model Obj. Function. GP4 (48.7%) 32.01 USGP 31.72 GP4 26.10 USGP 26.10 USGP 48.39

N. of Eq 288 1,248 288 1,248 1,248

Bin. var 168 288 168 288 288

Cont. var 42 522 42 522 522

*Solved in GAMS (CPLEX 11.0) in a Dell Inspiron 1526, 2 GHz with 2 GB RAM

Nodes 1,404,379 47,948 2,116,139 14,068 27,452

CPU (s) > 300 103.81 452.15 22.65 66.55

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Final and intermediate inventory minimization is the objective in cases II.1-II.2. In case II.3 the minimization of both total inventory and changeover costs is desired. In II.1 example changeover times are present while in II.2 they are set to zero, in order to show how the problem difficulty decreases by not considering changeovers. GP hasn’t reached the optimal solution in II.1 case in the imposed 5-minute time limit. Computational results are included to Table 2. Fig.5 depicts the optimal schedule for II.3 problem.

Figure 5. Optimal schedule for II.3 problem instance.

5. Final discussion and future work Taking into consideration that changeover issues are usually a crucial part of the optimization goal in a large number of industries, the current work has been focused on the development of an efficient MILP model appropriate for tackling this kind of problems. In all complicated cases, the proposed model performance overwhelms that of GP; in spite of its bigger model size. USGP has been found to be much faster even in cases, e.g. I.2, II.1 and II.2, where GP was expected to perform better, mainly because of GP’s small model size. The proposed MILP scheduling framework can optimize sequence-dependent costs in contrast with GP models. The USGP model size is bigger than that of the GP formulation; however, the computational burden is significantly decreased. Future work will be focused on developing decomposition strategies in order to reduce even more the computational burden that is required to solve large-scale industrial problems, such as the complete pharmaceuticals case is.

6. Acknowledgements Financial support received from the Spanish Ministry of Education and Science (FPU grants) is fully appreciated. Authors would like to express their gratitude to Carlos Méndez for providing them with the pharmaceuticals case study.

References [1] C. Méndez, J. Cerdá, I.E. Grossmann, I. Harjunkoski, M. Fahl, 2006, Comput. Chem. Eng., 30, 913-946. [2] C. Méndez, G. Henning, J. Cerdá, 2000, Comput. Chem. Eng., 24, 2223-2245. [3] J. Cerdá, G. Henning, I.E. Grossmann, 1997, Ind. Eng. Chem. Res., 36, 1695-1707. [4] C. Méndez, J. Cerdá, 2003, Comput. Chem. Eng., 27, 1247-1259. [5] G.M. Kopanos, L. Puigjaner, AICHE Annual Meeting 2008, 554d. [6] J.M. Pinto, I.E. Grossmann, 1997, Comput. Chem. Eng., 21, 8, 801-818.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

375

Factory operations modelling methodology applied to a case study Peter M.M. Bongersa, Bas H. Bakkera b

Unilever Research Vlaardingen, Oliver van Noortlaan 120, POBox 114, 3130 AC Vlaardingen, The Netherlands, [email protected]

Abstract In many process operations the final products are manufactured in different stages and multiple product streams share the same equipment. In general, limited operations are connected by a large set of buffers. In these plants, scheduling the operations to maximise capacity, or minimizing operational costs is not straighforward. The key challenge is to design an operations model that is as simple as possible, but still represent reality of a factory. In this paper a methodology for a factory operations model is presented and discussed. In order to arrive at a simple but realistic model, a methodology needs to be complemented by knowledge of the specific domain and modelling skills-experience. Keywords: Modelling, Factory operations, Methodology, Multi-stage scheduling 1. Introduction Most of Unilever’s food processes consist of a large number of ingredients with limited storage capacity, a small number of process plants, a large number of intermediate product storage facilities and a smaller number of packing lines. The practical production scheduling inside the vast majority of these factories focuses on scheduling the packing lines on the production floor. The schedule is ‘thrown over the wall’ to the process department, in which a schedule is being made to satisfy the packing demand. This schedule is also “thrown over the wall” to the incoming materials department, etc. This way of scheduling poses three problems: 1. There is no clear insight in where the bottlenecks in the whole process are, resulting in a reduced production capacity. 2. Any change in the packing schedule might lead to an infeasible schedule in the upstream departments. As a result, packing lines may not run due to lack of intermediate products, wrong intermediates being made in the process plant, etc. 3. Each department will strive for ensuring that their department is not to blame for not packing products, hence less available capacity will be communicated to the plant. 2. Problem formulation The challenge is to reduce the impact of these problems in order to increase the capacity of the factory and reduce the product cost/tonnes. This paper describes a methodology to reduce the impact of these problems by modelling the factory operations. This is done by building a multi-stage scheduling model which describes the infra-structure of the factory, which products are being produced and how the plant is operated. The key challenge is to translate the complexity of the plant (and the operations) into a simplified, but realistic, multi-stage scheduling model. As such, the objective is not to derive the perfect model and the perfect optimal solutions, but to achieve workable and robust solutions. The model of the whole factory,

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including the constraints, is used to schedule the whole plant, maximising the production capacity and minimising the impact of the above described problems. 3. Main results This section describes a methodology to translate the complexity of the plant into a simplified model that can be used to schedule all relevant plant operations. Much of this case has been reported earlier, [1-3]. The flow scheme of the methodology is given in Fig.1. 3)'

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The methodology consists of six steps: 1. Based the process flow diagrams, interviews and standard operating procedures a factory structure model is built. 2. A material flow structure is built, including the bill of materials and product routing. 3. The factory model is built by combining the above structures and taking into account the change-over structure. 4. This factory model is used to specify which data is to be retrieved from the existing factory systems into the data model. 5. The simulation model is implemented by combining the factory model, data model and the operational inputs. 6. The model is firstly verified with the operators in the plant, followed by validation by running the plant by the model. In the remainder of this section, the different steps are elaborated and illustrated by an example. 3.1. Factory structure In this step large modelling activities are executed. It is not the purpose to describe each and every equipment that is part of the process flow diagram, but to include as little equipment as possible. The length and time scales of equipment to include need to be balanced. Interviews with the operators, and not the management, is important to

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identify the key equipment. Their information needs to be judged on the overall impact, as a local important item can be irrelevant on overall. For example, ramping-up the speed of a pump can be important locally, but not for the overall factory. Furthermore, connectivity between the equipments is important. Here also the rule is to include as little as possible, but as much as necessary. For example, if a connection is only used once a year, it is most likely not relevant in the daily operations and should be excluded. Purchase Orders Ingredient Inventory

Cone Bakers

Flavour Mixer

Cones inventory

Flavour Vessels

Sauce Mixer

Choc Grinders

Pasteurisers

Chocolate Vessels

Ageing Vessels

Sauce Vessels

Cones SKU

Choc SKU

Jelly Vessels

Mix Supply Line Freezers

Packing lines (SKU/CU) CU inventory Packing lines (MP)

Figure 2. Factory structure example

3.2. Material flow Using the bill of materials (BoM) for the final product (stock keeping unit, or SKU), for each of the key equipment used during manufacturing an intermediate BoM needs to exist (or has to be made). Often large parts of this information exist in the factory data systems. With respect to minimise complexity of the model, it is important to make a distinction between intermediate products, final products (SKU’s) and intermediates that are put on stock and used later (for example, to produce a multi-pack (a collection of various different products)).

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3.3. Factory model The factory model is an amalgamation of the material flow structure, combined with the specific equipments on which these products can be made and the change-over structure. Changing from one (intermediate) product to the other on one piece of equipment takes time, labour and products can be lost. 3.4. Data model The factory model dictates the data requirements. We separate the total data flow in static data, including equipment - and change-over structure data, and dynamic data, including all relevant parts of the BoM and changeover characteristics of products and intermediates. The actual production orders are considered to be part of the dynamic data, but require a different way of handling, as these will change at a much higher frequency and do not affect the underlying model. The dynamic data needs to be in such a format that can easy update the model, as there is a frequent inflow of new products. Additionally, the data flow diagram for this implementation is given in Fig 5.

Factory Operations Modelling Methodology Applied to a Case Study

FACTORY DATA FILES

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SCHEDULES

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Factory Structure ERP PACKAGE

weekly schedule excel file

Full BOM

Material Fow

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Ingredient order calls excel file

Structure

Weekly Planning Production weekly schedule excel file

Figure 5. Data model

3.5. Implementation The designed model is now implemented in a suitable software package. For this we have chosen INFOR Advanced Scheduler [4]. The implemented model is called the factory simulation model, which now is ready for validation. Figure 4 shows an example of a scheduling exercise in the package.

Figure 4. Multi-stage scheduling model

3.6. Validation Validation is crucial to every model. In this step, the model predictions are compared with the actual factory operations. This is achieved by running the factory with the start times of each batch generated by the model and logging the actual start-stop times (including the reasons for unexpected stopages).

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Based on experience, the difficult part is collecting the accurate capacities of the various unit operations. Often every department usually works with a different line speed for the same packing line. 4. Conclusions A methodology was developed for the design and implementation of scheduling models for factory operations. The methodology ensures the development of the simplest, but still reliable models for a given factory. The methodology was successfully tested on the optimisation of the operations in a ice-cream factories, with a 30% capacity increase as a result, without the need for capital investment.

References [1] Bongers, P.M.M., B.H. Bakker (2006). Application of multi-stage scheduling, ESCAPE 16 proceedings [2] Bongers, P.M.M., B.H. Bakker (2007). Modelling an Ice cream factory for debottlenecking, ESCAPE 17 proceedings [3] Bongers, P.M.M., B.H. Bakker (2008). Validation of an Ice cream factory operations model, ESCAPE 18 proceedings [4] INFOR (2003), Advanced Scheduling: Users Course and Modelling course, Rijswijk, The Netherlands

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

381

Integrated Operational Planning and Scheduling under Uncertainty Peter M. Verderamea, Christodoulos A. Floudasb Department of Chemical Engineering, Princeton University, Princeton, NJ 08544 USA a [email protected], [email protected]

Abstract An integrated operational planning and medium-term scheduling framework which takes into account various forms of market and process uncertainty will be presented. The framework entails the integration of a novel and robust Planning with Production Disaggregation Model with the robust counterpart of an industrially validated mediumterm scheduling model through a forward rolling horizon scheme. The operational planning and scheduling under uncertainty framework has been applied to an industrial case study in order to demonstrate that it can address relevant planning and scheduling problems.

1. Introduction Operational planning and medium-term scheduling are interrelated activities dealing with the allocation of plant resources; however, the effective integration of planning and scheduling has proven to be difficult task due to the disparate time scales of planning and scheduling. Papageorgiou and Pantelides1,2 proposed a decomposition scheme having an upper level planning model and a lower level scheduling model, which addresses the planning and scheduling of batch and semi-continuous plants. Subrahmanyam et al.3 developed an iterative framework for the planning and scheduling of a chemical plant based in part upon the premise that the aggregate planning model is a relaxation of the scheduling model. Dimitriadis et al.4 presented two frameworks related to the integration of planning and scheduling by means of a rolling horizon framework. Petkov and Maranas5 applied chance constraint programming within a multiperiod planning and scheduling framework for multiproduct batch plants with uncertain demand profiles due at the end of each period. Wu and Ierapetritou6 presented a hierarchical approach to planning and scheduling under uncertainty. Despite the recent and continued dedication to the field of planning and scheduling, the integration of planning and scheduling under uncertainty remains a challenging problem within the literature as noted in the reviews of Kallrath,7 Sahinidis,8 and Li and Ierapetritou.9 Verderame and Floudas10 developed a framework for the integration of planning and scheduling which entails interfacing the novel Planning with Production Disaggregation Model (PPDM) with the medium-term scheduling (MTS) model formulated by Janak et al.11 The PPDM provides the daily production profile, which is a tight upper bound on the production capacity of the plant in question, to the MTS, and the operational planning time horizon is iteratively scheduled through a forward rolling horizon approach. The PPDM is refined within the rolling horizon approach through the application of a novel feedback loop which entails having the production bounds generated from MTS being sent back to the planning level in order to more accurately

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reflect the true production capacity of the plant in question. This framework assumes that all demand and processing time parameters are deterministic in nature. In order to address the objective of providing a production profile and final schedule for the time horizon of interest which is immune to both processing time and demand uncertainty, the framework developed by Verderame and Floudas10 has been extended in order to explicitly take into account the aforementioned forms of uncertainty at both the planning and scheduling levels. The PPDM and MTS have been formulated into their respective robust counterparts using in part the techniques presented by Lin et al.12 and Janak et al.13 The remainder of the paper takes the following form. First, an exposition of the system under investigation will be presented. Then an overview of the proposed approach, as well as some computational results will be covered in order to validate the integrated planning and scheduling approach, and finally, some concluding remarks and key acknowledgements will be made.

2. Background The facility under investigation is a multipurpose and multiproduct batch chemical plant producing hundreds of products which are either made-to-order or made-to-store. For the made-to-order products, customers supply demand due parameters which specify the nominal date of demand enforcement, as well as the amount of required product. Uncertainty is associated with both the date of demand realization and the required amount of product. It is assumed that the required amount follows a normal distribution while the due date itself is considered to follow a discrete, uniform distribution with bounds of plus or minus one day from the nominal due date. For the made-to-store products, the customers supply the weekly demand requirements, and unlike the madeto-order products, only the required amount of product is considered to be uncertain. The required amount of product for the made-to-store states is considered to follow a normal distribution. The uncertainty related to the processing time for the various units present within the plant is assumed to follow a normal distribution and must be explicitly taken into account as well. The objective of the proposed framework is to generate a production profile and final schedule which is immune to the aforementioned forms of uncertainty, and the sections to follow will demonstrate that the given integrated planning and scheduling framework accomplishes this objective for the stated problem.

3. Integrated Planning and Scheduling Framework under Uncertainty 3.1. Planning Level Due to the nature of the uncertainty present within the problem of interest, demand uncertainty is explicitly modeled at the planning level, and as a result, the production profile supplied to the scheduling level is immune to demand uncertainty. For the made-to-order products, the demand due date parameter, rs,d, which specifies the amount of state s required on day d, is given a unique order designation which has an equal probability of being realized on the nominal day, the previous day, or the following day. In other words, the order has a 33.3% chance of having been realized on the previous day, a 66.7% chance on the nominal day, and 100% on the following day. The amount

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of required product related to a given order follows a normal distribution with the supplied order value being the mean. For the made-to-store products, the amount of required product also follows a normal distribution with the supplied order value being the mean of the given distribution while the date of realization is considered to be deterministic. Within the PPDM, the demand due parameter can be found on the right-hand side of daily demand satisfaction constraints for the made-to-order products and the weekly and monthly demand satisfaction constraints for the made-to-store products. Extending upon the techniques of Lin et al.12 and Janak et al.13, the deterministic robust counterpart of the daily underproduction and overproduction demand constraints for the made-toorder states can be seen below in Eq. (1) and Eq. (2), respectively. Overall, the deterministic robust counterpart constraints are generated by means of converting probabilistic constraints originally derived from the nominal constraints and the realization of uncertain parameters into their deterministic equivalents.

d '= d d '= d ¦ tot ( s , d ') + sla ( s , d ) ≥ ¦ ¦ ( r _ or s , d ', or − r _ or s , d ' − 1, or ) or d '=1 d ' =1 d '= d + ελ ¦ ¦ (σ ⋅r _ or ⋅r _ or )2 ) 2 − (σ s , d ', or d '− 1 s , d ' − 1, or or d '=1 d '

(1)

d '= d )] − δ max[ 1, ¦ ¦ ( r _ or − r _ or s , d ',or s , d ' − 1,or or d '=1 ∀ s s ∈ S p ∩ S bp , ∀ d d '= d d '= d ¦ tot ( s , d ') − slb ( s , d ) ≤ ¦ ¦ ( r _ or s , d ', or − r _ or s , d ' − 1,or ) or d '=1 d ' =1 d '= d − ελ ¦ ¦ (σ ⋅r _ or ⋅r _ or ) 2 − (σ )2 s , d ',or d '− 1 s , d ' − 1,or or d '=1 d '

(2)

d '= d )] + δ max[ 1, ¦ ¦ ( r _ or − r _ or s , d ',or s , d ' − 1,or or d '=1 ∀ s s ∈ S p ∩ S bp , ∀ d The reader is directed to the work of Verderame and Floudas10 and Janak et al.13 for an in-depth description of all relevant indices, sets, parameters, and variables. It should be noted that the parameter r_ors,d,or connects the nominal due date parameter rs,d with its unique order designation and possible day of realization for the made-to-order products. The parameter Ȝ can be determined from the relationship shown in Eq. 3.

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λ = Fn−1(

∏ or prob >0 s, d , or

prob ) s, d , or

(3)

where Fn-1 is the inverse normal cumulative distribution and the parameter probs,d,or is the probability of a demand due date being realized for a given order. The made-tostore products’ deterministic robust counterpart of the weekly demand constraint is the following:

tot ( s , d ) + sl 2 a ( s , w ) ≥ ¦ r _ or ¦ ¦ s , d , or or d ≤ term _ w w d ≤ term _ w w ( σ ⋅ r _ or )2 ¦ ¦ d s , d , or or d ≤ term _ w w

+ ελ

(4)

p ] ∀s s ∈ S p ∩ S p , ∀w r _ or − δ max[ 1, ¦ ¦ s , d , or or d ≤ term _ w w where

λ = Fn−1 (1 − κ )

(5)

The monthly demand constraint for the made-to-store goods which restricts the allowable amount of overproduction can also be formulated into its deterministic robust counterpart (Eq. 6).

(5 / 6 ) ⋅ − ελ

tot ( s , d ) ≤ ¦ r _ or ¦ ¦ s , d ,or or init _ m m ≤ d ≤ term _ m m init _ m m ≤ d ≤ term _ m m

(σ ⋅ r _ or )2 ¦ ¦ d s , d ,or or init _ m m ≤ d ≤ term _ m m

p + δ max[ 1, ¦ r _ or ] ∀s s ∈ S p ∩ S p , ∀m ¦ s ,d ,or or init _ m m ≤ d ≤ term _ m m (6) All of the given deterministic robust counterpart demand constraints are added to the nominal PPDM in order to explicitly model the stochastic nature of demand. 3.2. Scheduling Level The uncertainty associated with the processing time for all pertinent units is taken into account at the scheduling level through the addition of Eq. 7 and Eq. 8 to the nominal MTS. The reader is directed to Janak et al.13 for an in-depth discussion of the terms comprising the given equations.

f T (i, j, n) ≥ T s (i, j, n) + αi, j ⋅ (1 + ελ) ⋅ wv(i, j, n) ∀i, ∀j αi, j > 0, ∀n

(7)

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f T (i, j, n) ≥ T s (i, j, n) + βi, j ⋅ (1 + ελ) ⋅ B(i, j, n) ∀i, ∀j βi, j > 0, ∀n

(8)

The term Ȝ is once again derived from the relationship found in Eq. 5, and in accordance with the work of Lin et al.12 and Janak et al.13, the deterministic robust counterpart processing time constraints are added to the nominal MTS in order to take account rigorously the uncertainty associated with processing time. 3.3. Forward Rolling Horizon The forward rolling horizon approach is implemented by first discretizing the entire time horizon into planning periods. The MTS sequentially solves each planning period using the production profile supplied by the PPDM. After the MTS determines the final schedule for a planning period, production bounds are sent back to the planning level, and the PPDM is solved again now with the inclusion of the supplied production bounds. The revised production profile is then sent to MTS in order to determine the schedule for the next planning period. Once a planning period has been scheduled, no additional modifications are made within that period of time. The following approach is continued until all of the planning periods comprising the entire time horizon have been scheduled. The rolling horizon approach has the advantage of requiring fewer iterations in order to schedule the entire time horizon when compared to other iterative approaches, and the novel feedback loop allows for the refinement of the planning model ensuring that it provides a tight upper bound on the production capacity of the plant in question.

4. Computational Study The proposed framework was applied to a multipurpose and multiproduct batch plant for a time horizon of three months, and Table 1 provides for each iteration of the rolling horizon framework the production levels generated by the operational planning and medium-term scheduling models. The results indicate that the PPDM provides a tight upper bound on the production capacity of the plant, and the forward rolling horizon framework allows for the refinement of the PPDM.

Table 1. Aggregate Production Levels Planning Period

PPDM

MTS

Period 1

1847

1436

Period 2

1821

1587

Period 3

1123

1000

Period 4

1727

1466

Period 5

1061

924

Period 6

1029

848

Period 7

596

497

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5. Conclusions In this work, the framework for the integration of planning and scheduling developed by Verderame and Floudas10 has been extended in order to take into account both demand and processing time uncertainty. Both the novel PPDM and the industrially validated MTS have been reformulated into their respective robust counterparts using the techniques presented by Lin et al.12 and Janak et al.13 The resulting integrated planning and scheduling framework explicitly takes into account the aforementioned forms of uncertainty and effectively integrates the planning and scheduling levels as evidenced by the industrial case study.

6. Acknowledgements The authors gratefully acknowledge financial support from the National Science Foundation.

7. References [1] L.G. Papageorgiou and C.C. Pantelides, Optimal Campaign Operational Planning/Scheduling of Multipurpose Batch/Semicontinuous Plants. 1. Mathematical Formulation, Ind. End. Chem. Res., 35 (1996) 488. [2] L.G. Papageorgiou and C.C. Pantelides, Optimal Campaign Operational Planning/Scheduling of Multipurpose Batch/Semicontinuous Plants. 2. A Mathematical Decomposition Approach, Ind. End. Chem. Res., 35 (1996) 510. [3] S. Subrahmanyam, J.F. Pekny, and G.V. Reklaitis, Decomposition Approaches to Batch Plant Design and Operational Planning, Ind. Eng. Chem. Res., 35 (1996) 1866. [4] A.D. Dimitriadis, N. Shah, and C.C. Pantelides, RTN-based Rolling Horizon Algorithms for MediumTerm Scheduling of Multipurpose Plants, Comp. Chem. Eng., 21 (1997) S1061. [5] S.B. Petkov and C.D. Maranas, Multiperiod Plannind and Scheduling of Multiproduct Batch Plants under Demand Uncertainty, Ind. Eng. Chem. Res., 36 (1997) 4864. [6] D. Wu and M. Ierapetritou, Heirarchical approach for production planning and scheduling under uncertainty, Comp. Chem. Eng., 46 (2007) 1129. [7] J. Kallrath, Operational Planning and Scheduling in the Process Industry, OR Spectrum, 24 (2002) 219. [8] N.V. Sahinidis, Optimization under uncertainty: state-of-the-art and opportunities, Comp. Chem. Eng., 28 (2004) 971. [9] Z. Li and M. Ierapetritou, Process scheduling under uncertainty: Review and challenges, Comp. Chem. Eng., 32 (2008) 715. [10] P.M. Verderame and C.A. Floudas, Integrated Operational Planning and Medium-Term Scheduling for Large-Scale Industrial Batch Plants, Ind. Eng. Chem. Res., 47 (2008) 4845. [11] S.L. Janak, C.A. Floudas, J. Kallrath, and N. Vormbrock, Production Scheduling of a Large-Scale Industrial Batch Plant. I. Short-term and Medium-Term Scheduling, Ind. Eng. Chem. Res., 25 (2006) 8234. [12] X. Lin, S.L. Janak, and C.A. Floudas, A new robust optimization approach for scheduling under uncertainty: I. Bounded uncertainty, Comp. Chem. Eng., 28 (2004) 1069. [13] S.L. Janak, X. Lin, and C.A. Floudas, A new robust optimization approach for scheduling under uncertainty: II. Uncertainty with known probability distribution, Comp. Chem. Eng., 31 (2007) 171.

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387

Iterative learning control of a crystallisation process using batch wise updated linearised models identified using PLS Jie Zhang, Jerome Nguyan, Julian Morris School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle upon Tyne NE1 7RU, UK, E-mail: [email protected]

Abstract An iterative learning control strategy with batch wise updated linearised models identified using partial least square (PLS) regression is proposed in this paper. Taking the immediate previous batch as the reference batch, the linearised model relates the deviations in the control profiles with the deviations in the quality variable trajectories between the current and the reference batches. The linearised model is used in calculating the control policy updating for the current batch. The proposed method is applied to a batch crystallisation process and simulation results show that the proposed method can overcome the effect of disturbance and improve the process operation from batch to batch. Keywords: batch processes, crystallisation, data-driven models, iterative learning control, batch to batch control

1. Introduction Crystallisation is an important unit operation for the separation and purification of chemicals in the pharmaceutical and fine chemical industry. Crystallisation processes in the pharmaceutical industry are traditionally recipe based operation. The recipe can be such designed that the product quality is optimised. The optimised recipes are typically based on a nominal model of the crystallisation process under normal operating conditions [1]. Off-line calculated control policies (recipes) for batch crystallisation processes may not be optimal when implemented on the processes due to model plant mismatches and/or the presence of unknown disturbances [2]. Utilising the repetitive nature of batch processes, crystallisation operation recipes can be modified from batch to batch in order to overcome the detrimental effect of model-plant mismatches and unknown disturbances. This paper presents an iterative learning control strategy for a batch crystallisation process using linearised models identified from process operational data. The control policy updating is calculated using a model linearised around a reference batch. In order to cope with process variations and disturbances, the reference batch can be taken as the immediate previous batch. In such a way, the model is a batch wise linearised model and is updated after each batch. The newly obtained process operation data after each batch is added to the historical data base and an updated linearised model is re-identified. Since the control actions during different stages of a batch are usually correlated, multiple linear regression (MLR) would not lead to an appropriate model due to the colinearity among the predictor variables, i.e. the control actions at different stages of a

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batch. In order to overcome this problem, this paper proposes that the linearised model can be identified from partial least square regression (PLS). The paper is organised as follows. Section 2 presents a batch crystallisation process. A batch to batch control strategy based linearised model is presented in Section 3. Section 4 presents application results on the batch crystallisation process. Some concluding remarks are given in Section 5.

2. A batch crystallisation process The crystallisation process considered in this study is taken from [1]. The crystallizer is first charged with potash alum solution saturated at 318.1 K and slowly cooled down to 313.1 K. At the beginning, 10 g of potash alum crystals with an arithmetic mean size of 150 ȝm were added to the solution as seed crystals. The batch is cooled by a cooling fluid (water) which enters in the jacket of the batch at the inlet temperature Tjin. Crystallization kinetics are characterized by two dominant phenomena: nucleation and crystal growth. They both consume the same driving force: the supersaturation. In order to obtain larger crystals, supersaturation should be controled at a desired value aiming to supress nucleation. The supersaturation value is controlled by the temperature of the crystallizer and so the action variable to control the supersaturation will be the inlet temperature of the jacket Tjin. A mathematical model is developed based on the conservation of mass, energy and population (moments) balances in the form of a set of partial differential equations, which can be re-formualted as a set of of first-order ordinary differential equations. Details of the model and model parameters can be found in [1]. A simulation program is developed based on the above model and is used to test the proposed batch to batch control strategy.

3. Batch to batch iterative learning control with PLS models Linearised models for batch processes Consider batch processes where the batch run length (tf) is fixed and consists of N sampling intervals (i.e. N=tf/h, with h being the sampling time). Product quality variables (outputs), y∈Rn (n≥1), can be obtained off-line by analysing the samples taken during the batch run and the manipulated variable, u∈Rm (m=1 in this work), can be measured at each sampling time on-line. The product quality and control trajectories are defined, respectively, as Yk=[ykT(1), ykT(2),…, ykT(N)]T Uk=[uk(0), uk(1),…,uk(N-1)]

(1)

T

(2)

where the subscript k denotes the batch index. The desired reference trajectories of product quality are defined as Yd=[ydT(1), ydT(2),…, ydT(N)]T

(3)

A batch operation is typically modelled with a dynamic model, but it would be convenient to consider a static function relating the control sequence to the product quality sequences over the whole batch duration [3]. Due to the causality, the product quality variables at time t, yk(t), is a non-linear function of all control actions up to time t, Uk(t) =[uk(0), uk(1),…,uk(t-1)]T, i.e. yk(t)=ft(Uk(t)) + vk(t),

t=1, 2, ..., N,

yk(0)=y0

(4)

Iterative Learning Control of a Crystallisation Process Using Batch Wise Updated Linearised Models Identified Using PLS

389

where ft(⋅⋅) represents the non-linear function between Uk(t) and yk(t) and vk(t) is the measurement noise at time t. Eq(4) can be rewritten in matrix form as Yk = F(Uk) + vk

(5)

where F(⋅⋅) represents the non-linear static functions between Uk(t) and yk(t) at different sampling times and vk=[vkT(0), vkT(1),…, vkT(N-1)]T is a vector of measurement noises. Linearising the non-linear batch process model described by Eq(5) with respect to Us around the nominal trajectories (Us, Ys), the following can be obtained.

Yk = Ys +

∂F( U k ) (U k − U s ) + w k + v k ∂U k U

(6)

s

where wk=[wk (1), wk (2), …, wkT(N)]T is a sequence of model errors due to the linearisation (i.e., due to negalecting the higher oder terms) and vk represents the effects of noise and unmeasured disturbances. Define the linearised model Gs as T

Gs =

T

∂F( U k ) ∂U k U

(7) s

The structure of Gs is restricted to the following lower-block-triangular form due to the causality.

ª g10 «g 20 Gs = « «  « ¬gN 0

0 g 21  g N1

0 º 0 »  »   » »  g NN −1 ¼ 

(8)

The linearised model can be identified from historical process operation data using MLR [4]. To cope with process drift, the linearised model can be re-identified after each batch with data from the most recent batch added to the historical process data. Furthermore, the control trajectory and quality variable trajectory from the most recent batch can be used as the reference trajectories. In many batch processes, the control policies are typically determined to optimise the product quality at the end of a batch. Therefore, the control actions during different stages of a batch are usually correlated. In such cases, appropriate linearised model may not be obtained from MLR. To overcome the colinearity in the regression variables, PLS regression [5] can be used to obtain the linearised models. Batch to batch iterative learning control The batch to batch iterative learning control strategy was developed in [4] and is briefly introduced here. As batch process dynamics are non-linear and the perturbation model is linearised around the nominal operation trajectories of a batch process, offsets always occur due to modelling errors and unmeasured disturbances. The perturbation model predictions of the current batch run can be corrected by adding model prediction residuals of previous batch runs. In formulating the batch to batch iterative learning control strategy, the following quadratic objective function is considered.

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390

1 J k +1 = min [eTk +1Qe k +1 + ΔU Tk +1RΔU k +1 ] Δ U k +1 2

(9)

where ek+1 = Yd - Yk is the tracking error for the (k+1)th batch, Q and R are positive definitive matrices. Note that the objective function, Eq(9), has a penalty term on the input change ΔU k +1 (=Uk+1 - Uk) between two adjacent batch runs, the algorithm has an integral action with respect to the batch index k [4]. The weighting matrices Q and R should be selected carefully. A larger weight on the input change will lead to more conservative adjustments and slower convergence. There are also other variants of the objective function. For example, the weighting matrices Q and R may be set as Q=diag{Q(1), Q(2), …, Q(N)}, R=diag{R(0), R(1), …, R(N-1)}, where Q(i) and R(j) increase with respect to the time intervals t in proportion to its effect of the final product quality. By finding the partial derivative of the quadratic objective function Eq(9) with respect to the input change ΔU k +1 and through straightforward manipulation, the following iterative learning control (ILC) law can be obtained

ˆ T QG ˆ + R ]−1 G ˆ TQ ˆ e = [G ΔU k +1 = K k s s s where

(10)

ˆ is the linearised model identified from historical process operation data. G s

The ILC law for the control trajectory can be written as

ˆe U k +1 = U k + K k

(11)

Fig. 1 shows the structure of the run-to-run modified prediction-based optimal ILC. At the current kth batch run, the control trajectory Uk is implemented. After the completion of the batch run, the product qualities Yk are obtained by off-line analysis of samples taken during the batch run. The model prediction errors are calculated and used to correct the model predictions for the next batch. Based on the modified predictions, a new control policy Uk+1 for the next batch is calculated using the ILC law. At the next batch, this procedure is repeated. It should be emphasised here that this ILC law is for addressing the problem of model plant mismatches and unknown disturbances that present in a number of consecutive batches. Memory Δuk+1

ek+1(t)

yd(t)

_

(Q, R)

_

yk+1(t)

Plant (Gs) (Gs)

Model <

yk+1(t)

yk(t) _

+

<

∼ ek+1(t)

uk+1

<

+

+

+

Memory

+

Controller

uk

yk(t) εk(t) + + ∼ yk+1(t)

Fig 1. Structure of modified prediction-based optimal ILC

Iterative Learning Control of a Crystallisation Process Using Batch Wise Updated Linearised Models Identified Using PLS

391

4. Results The proposed technique has been successfully applied to the simulated batch crystallisation process described in Section 2. Crystallization kinetics are characterized by two dominant phenomena: nucleation and crystal growth. They both consume the same driving force: the supersaturation [1]. In order to obtain appropriate sized crystals, supersaturation should be controlled at a desired value aiming to suppress nucleation. The supersaturation value is controlled by the temperature of the crystallizer and so the manipulated variable to control the supersaturation is the reactor jacket inlet temperature (Tjin). In this process, the control objective is to keep the supersaturation following a desired trajectory throughout the batch. The batch time (4600 s) is divided in N=10 sample intervals with unequal length. The first stage is 1900 s and the remaining 9 stages are all 300 s. The iterative learning control parameters are selected as: R = 0.5I, Q = 105×diag(5, 3, 3, 3, 3, 3, 3, 3, 1, 1). The desired supersaturation profile is selected as a constant value of 0.02 kg solute/kg solvent as used in [1]. Batch to batch ILC was run for 30 batches. From the 16th batch onward, the reactor overall heat transfer coefficient was changed to 600 J/Ks from its nominal value of 800 J/Ks to represent the presence of a disturbance. Fig. 2 shows the RMSE (root mean squared errors) between the desired supersaturation profile and the actual supersaturation profiles at different batches. Fig. 3 shows the desired supersaturation profile and the supersaturation profiles at batches 1, 2, 3, and 20. It can be seen from Fig. 2 and Fig. 3 that supersaturation profiles approach the desired one from batch to batch. Fig. 1 also compares the control performance under a fixed PLS model and updated PLS models. It can be seen that control errors are lower with the updated models than those with a fixed model. o:fixed model; +:updated model 0.025

0.02

0.015

E S M R 0.01

0.005

0

0

5

Fig. 2. RMSE at different batches

10

15 Batches

20

25

30

J. Zhang et al.

392 -:target; --:1st batch; -.:2nd batch; ..:3rd batch; o:20th batch 0.08

0.07

0.06 ) t n e vl o s g k/ et ul o s g k( n oi t ar ut a sr e p u S

0.05

0.04

0.03

0.02

0.01

0

0

500

1000

1500

2000

2500 Time (s)

3000

3500

4000

4500

5000

Fig. 3. Supersaturation profiles at different batches

5. Conclusions A batch to batch iterative learning control method based on batch wise updated linearised models identified using PLS is developed. PLS can cope with the possible colinearity among control actions during different stages of a batch and identify a more appropriate model. Through batch wise updating of the linearised model, the model can adapt to process variations and is more appropriate for the current operating condition. Application to a batch crustallisation process demonstrates the effectiveness of the proposed method.

Acknowledgements The research is supported by UK Department for Innovation, Universities and Skills under the UK/China Fellowship for Excellence programme.

References [1] W. Xie, S. Rohani, & A. Phoenix, Chemical Engineering Communications, 187, (2001), 229–249. [2] J. Zhang, Ind. Eng. Chem. Res., 43 (2004), 1030-1038. [3] K. S. Lee, I. S. Chin, H. J. Lee, J. H. Lee. AIChE J. 45 (1999), 2175-2187. [4] Z. Xiong and J. Zhang, Ind. Eng. Chem. Res., 42 (2003), 6802-6814. [5] P. Geladi and B. R. Kowalski, Analytica Chimica Acta, 185 (1986), 1-17.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

393

Medium-term planning of multistage multiproduct continuous plants using mixed integer optimisation Songsong Liua, Jose M. Pintob,* , Lazaros G. Papageorgioua a

Centre for Process Systems Engineering, Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, UK, E-mail: [email protected] b Othmer-Jacobs Department of Chemical and Biological Engineering, Polytechnic University, 6 MetroTech Center, Brooklyn, New York 11201, USA

Abstract In this paper, we address the problem of medium-term planning of multistage multiproduct continuous plants with one unit per stage. A TSP-based (Traveling Salesman Problem) mixed-integer linear programming (MILP) model is proposed using a hybrid discrete/continuous time representation. In order to solve larger model instances, a rolling horizon algorithm is developed to reduce the computational expense. Case studies demonstrate the applicability of the model and solution algorithm. Keywords: planning, mixed-integer linear programming, traveling salesman problem, rolling horizon, hybrid time representation

1. Introduction A number of mathematical models for the scheduling of multiproduct plants have been proposed in the literature. However, the scheduling of continuous multiproduct plants has received less attention than their batch counterparts. Most models in the literature for multiproduct continuous plants focus either on single-stage planning/scheduling [14], or on cyclic scheduling of multistage plants [5-7]. In this paper, we extend our previous work [3] to the multistage case with one unit per stage. The goal of the work is to develop a compact and efficient mixed-integer linear programming (MILP) formulation for the medium-term planning of multistage multiproduct continuous plants that are subject to sequence-dependent changeovers based on the classic Traveling Salesman Problem (TSP) formulation, using a hybrid discrete/continuous time representation. A rolling horizon algorithm is also proposed for larger problems.

2. Problem Statement Given is a multistage multiproduct continuous plant with one unit per stage m (Fig. 1). The planning horizon ranges from several weeks to several months. Weekly demands of product i from customer c are delivered only at the end of week w. Late deliveries are *

Current address: Praxair Inc., 39 Old Ridgebury Road, Danbury, CT 06810, USA.

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394

also allowed with backlog penalties. Limited storage is used for products after the last stage M. Sequence-dependent changeover times and costs occur when switching production from product i to product j. The following assumptions are used in the problem: (1) Every product i must be processed in the same sequence throughout all stages. (2) Transition times between stages are ignored. (3) Unlimited intermediate storage is available between stages. (4) The inventory between stages is set to 0 at the end of each week.

Unit 1

Unit 2

Unit 3

Unit m

Unit M

Stage Stage 11

Stage 22 Stage

Stage Stage3 3

Stage m

Stage StageMM

Figure 1. A multistage multiproduct continuous plant

The multistage multiproduct planning problem can be stated as follows: Given are demands (Dicw), processing rates (rim), changeover costs (CCijm) and times (Wijm), product prices (PSic), backlog (CBic) and inventory costs (CIi), minimum ( Vi L ) and maximum ( ViU ) inventory levels, minimum ( T mL ) and maximum ( T mU ) processing times, and production yields (Șim); determine product assignments (Eiw), product sequences (Zijw), start times (TSimw), processing times (Timw), production amounts (Pimw), backlog (ǻicw) and inventory levels (Viw), and sales volume (Sicw); so as to maximise overall profit, 3 .

3. Mathematical Formulation The proposed MILP model is an extension of the single-unit, single-stage model by Liu et al. [3]. Due to the weekly demands in the horizon, a hybrid discrete/continuous time representation is used, in which the total planning horizon is divided into discrete weeks, and a continuous time representation is used for each week (Fig. 2). Discrete Weekly Representation of the Planning Horizon Demands

Demands

Demands

week w

week 1

week W

Continuous Representation of Week w Stage m

B 0h

C Processing

E Changeover

168 h

Figure 2. A hybrid discrete/continuous time representation

Here, the planning problem can be viewed as a TSP application. Similar to the classic TSP formulation, two binary variables Zijw and ZFijw are introduced to model the changeovers within each week and between two consecutive weeks, while ZFijw is taken as continuous variables during the implementation. Binary variables Fiw and Liw model the first and last product in week w (Fig. 3).

Medium-Term Planning of Multistage Multiproduct Continuous Plants

ZFA, B , w

Z C , A, w 1 1

E C , w1 FC , w1

1 1

E A, w 1 1 L A, w 1 1

1

Z B, D,w

1

EB , w 1 FB , w 1

A

C

395

ED , w 1 LD , w 1

B

week w-1

D

week w

Figure 3. Assignments and changeovers for all stages

Within each week, the processing of product i must be preceded by one product and followed by one product, except for the first and last one in that week:

¦Z

jiw

Eiw  Fiw and

j zi

¦Z

Eiw  Liw ,

ijw

i, w

(1)

j zi

During each week, the first and last products to be processed are assigned:

¦F

iw

i

¦L

iw

1,

w

(2)

i

If a product is not assigned in that week, it cannot be the first or last one: Fiw d Eiw , and Liw d Eiw , i, w

(3)

Between weeks w-1 and w, there is one changeover from the last product i at the end of week w-1 to the first product j at the beginning of week w:

¦

¦

ZFijw F jw , j , w z 1 , and ZFijw Li ,w1 , i, w z 1 i processing time is limited by given lower j The and upper bounds:

(4)

T mL ˜ Eiw d Timw d T mU ˜ Eiw ,

i, m, w (5) The processing of product j must start after the processing of the precedent product i and the corresponding changeover time: TS jmw  (TS imw  Timw  W ijm ˜ Z ijw ) t T mU ˜ (1  Z ijw ), TS jmw  W ijm ˜ ZFijw t T mU ˜ (1  ZFijw ),

i, j z i, m, w

i, j z i, m, w z 1

(6) (7)

The processing of product i must end before the end of each week:

TSimw  Timw d T mU ˜ Eiw ,

i, m, w

(8) The processing of product i at stage m must start (end) before the start (end) of processing of the same product at stage m+1:

TS imw d TS i ,m1,w , and TSimw  Timw d TSi ,m1,w  Ti ,m1,w , i, m z M , w The total processing and changeover time should not exceed the upper bound:

¦T

imw

i

 ¦¦W ijm ˜ Z ijw  ¦¦W ijm ˜ ZFijw d T mU , i

j

i

m, w

(9) (10)

j

The production is given by the processing rate multiplied by the processing time:

Pimw rim ˜ Timw , i, m, w (11) The production of product i in stage m+1 is equal to the production in stage m multiplied by the yield in stage m+1:

K i ,m1 ˜ Pimw

Pi ,m1,w ,

i, m z M , w

(12)

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The backlog of product i to customer c in week w are determined by its backlog in week w-1 plus its demands, minus its sales volume to that customer:

' icw ' i ,c , w1  Dicw  Sicw , c, i, w (13) Similarly, the inventory of product i after stage M is defined as the inventory in the previous week plus the production amount, minus the total sales volume: Viw

Vi ,w1  Pimw  ¦ S icw ,

i, w, m

M

(14)

c

The inventory of product i is limited by given lower and upper bounds:

Vi L d Viw d ViU ,

i, w (15) The objective is to maximise the profit, which is equal to the sales revenue minus operating costs, involving backlog, inventory and changeover costs: 3

¦¦¦ PS i

c

w

ic

˜ S icw  ¦¦¦ CBic ˜ ' icw  ¦¦ CI i ˜ Viw 

¦¦¦¦ CC i

j zi m

w

i

ijm

c

w

i

w

(16)

˜ Z ijw  ¦¦¦¦ CCijm ˜ ZFijw i

j zi m wz1

Overall, the planning problem of multiproduct plants with multistage continuous processes is formulated as an MILP model described by constraints (1)-(15) with Eq. (16) as the objective function.

4. Rolling Horizon Algorithm Because of the exponential growth in the computational effort when planning horizons and model sizes increase, here we propose a rolling horizon (RH) algorithm, which can be used to solve larger problems. In the RH algorithm, the full problem considered is divided into a set of subproblems with increasing lengths of planning horizon and solved iteratively (See Fig.4). The planning horizon of each subproblem (TH) grows successively by a pre-specified number of weeks, while the length of periods (FP) with fixed binary variables, includnig Eiw, Fiw, Liw, Zijw and ZFijw, increases by the same time increment. This iterative scheme stops when the entire planning horizon is covered. The solution of the last subproblem is considered as an approximate solution of the full problem. In the following implementation in this paper, the RH algorithm starts with a 4-week subproblem, while during each subsequential iteration, both the planning horizon and the period with fixed binary variables are increased by 2 weeks, while the peiod with non-fixed variables is 4-week in all subproblems. Fig. 4 illustrates the RH algorithm procedure to solve a problem with a planning horizon of 8 weeks. Subproblem 1 FP= 0

TH= 4

Subproblem 2 Fixed, FP= 2

TH= 6

Subproblem 3 Fixed, FP= 4 Figure 4. Rolling horizon algorithm

TH= 8

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397

5. Computational Results Given is a 3-stage polymer processing plant which produces 7 products (A-G) for 10 customers (C1-C10). The weekly demands for a horizon of 18 weeks are given in Table 1. The processing rates of products on all 3 machines (M1-M3) are given in Table 2. Table 1. Weekly demands (tons) C1/C5

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

C2/C6

C3/C7/C9

A

C

D

E

B

5

2 2 2 2 3 3 3 3 3 2 2 2 2 3 3 3 3 3

3

5

4

5

5

5

5

C4/C8/C10

G

A

B

7

C

D

E

F

G

5

10

11

8

4

5 3

5

5

11 5

3

5

4

5

4 8

7

11

4

10 3

5

3

5

5 4

7

5

5

11 10

4

11

5 3

8

4 8

5

11

4

5 3

5

4

5

7

5 5

3

11

5

4

11 5

3

8

10

5

4

7

5

4 8

10

11

4

Table 2. Processign rates (tons/week)

M1 M2 M3

A

B

C

D

E

F

G

110 80 90

70 120 100

110 100 100

90 90 90

120 100 110

80 120 110

130 120 120

The total available processing time in each week is 168 h. The changeover times (in minutes), shown in Table 3, are the same for all machines. The changeover costs are proportional to the changeover times (in hours) by a factor of 10. Table 3. Changeover times in mins (M1/M2/M3) A A B C D E F G

B

C

D

E

F

G

45/60/70

45/45/100 55/30/70

45/80/55 40/50/35 100/80/80

60/45/30 60/55/60 75/60/70 45/60/80

80/30/30 80/70/75 60/90/55 45/80/100 35/75/75

30/50/55 80/100/90 80/50/40 45/30/55 30/60/60 100/70/85

55/60/40 60/30/30 100/50/25 60/70/70 100/100/100 30/50/90 60/50/80 60/60/90 55/45/45 75/90/35 75/80/45 60/100/80 80/50/100 100/80/65 30/40/85

30/40/60 100/70/90 60/55/55

75/45/55 100/70/30

85/100/45

Table 4 shows the product prices for all customers, except for customer C10 whose price is 50% higher. The unit inventory and backlog costs are 10% and 20% of product prices, respectively.

S. Liu et al.

398 Table 4. Sale prices ($)

Price

A

B

C

D

E

F

G

10

12

13

12

15

10

8

Three cases with planning horizons of 6, 12 and 18 weeks are solved using both the proposed MILP model and RH algorithm. The models are implemented in GAMS 22.6 [8] using solver CPLEX 11.0 [9] on a Pentium 4 3.40 GHz, 1.00 GB RAM machine. The optimality tolerance is set to 0%, and the CPU time for each subproblem is limited to 3600 seconds. From Table 5, we can see that the proposed single-level MILP model finds the global optimum for the 6-week case, while it gives very good feasible solutions for the 12- and 18-week cases within the specified time limit. The proposed RH algorithm requires much less computational effort than the MILP model and returns better solutions than those given by the MILP model. Table 5. Computational results Case

Approach

No. of eqs

MILP 3062 RH 2988* MILP 6284 12-week RH 5946* MILP 9506 18-week RH 8904* * Last subproblem in the RH algorithm 6-week

No. of continuous variables

No. of binary variables

Obj

Optimality gap (%)

CPU (s)

1506 1457* 3060 2717* 4614 3977*

378 252* 756 252* 1134 252*

5583 5583 10602 10616 16493 16545

0.00 0.00* 1.13 0.00* 1.65 0.00*

742 38 3600 108 3600 151

6. Concluding Remarks A novel MILP model and a rolling horizon algorithm for medium-term planning of multistage multiproduct continuous plants with one unit per stage have been proposed. Based on a hybrid discrete/continuous time representation, a TSP-based formulation has been developed. A number of numerical examples have been presented illustrating the applicability of the proposed optimisation-based approaches.

Acknowledgements S.L. gratefully acknowledges financial support from ORSAS, the KC Wong Education Foundation, the British FCO, and the CPSE at Imperial and UCL.

References [1] M. Erdirik-Dogan and I.E. Grossmann, Ind. Eng. Chem. Res., 45 (2006) 299. [2] P. Chen, L.G. Papageorgiou and J.M. Pinto, Ind. Eng. Chem. Res., 47 (2008) 1925. [3] S. Liu, J.M. Pinto and L.G. Papageorgiou, Ind. Eng. Chem. Res., 47 (2008) 7733. [4] M. Erdirik-Dogan and I.E. Grossmann, Comput.Chem. Eng., 32 (2008) 2664. [5] J.M. Pinto and I.E. Grossmann, Comput. Chem. Eng., 18 (1994) 797. [6] A. Alle and J.M. Pinto, Ind. Eng. Chem. Res., 41 (2002) 2689. [7] A. Alle, L.G. Papageorgiou and J.M. Pinto, Comput. Chem. Eng., 28 (2004) 3. [8] A. Brooke, D. Kendrick, A. Meeraus and R. Raman, GAMS - A User’s Guide, GAMS Development Corporation, Washington, DC, 2008. [9] ILOG CPLEX 11.0 User’s Manual, ILOG SA, Gentilly, France, 2007.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

399



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19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

405

Optimal Scheduling of Multistage, Multiproduct, Batch Plants with Parallel Units and Sequence Dependent Changeovers Pedro M. Castro,a Augusto Q. Novaisb a b

DMS, INETI, 1649-038 Lisboa, Portugal, [email protected] DMS, INETI, 1649-038 Lisboa, Portugal, [email protected]

Abstract This paper deals with the optimal scheduling of multistage batch plants with parallel units and sequence dependent changeovers, together with the optimal selection of the number and size of batches to produce. A new multiple time-grid continuous-time formulation is proposed that explicitly considers a virtual, shared, intermediate storage unit per stage. Adequate material transfer between processing units belonging to consecutive stages of production is implicitly ensured through mass balances and timing constraints relating the times of event points of dissimilar grids. The new formulation is compared to a conceptually different approach with results showing that it is tighter and significantly more efficient computationally. Keywords: Mathematical programming, integrality gap, event point

1. Introduction Scheduling in the process industries has received considerable attention during the last 15 years [1]. Models are first characterized by the representation of time, be it discrete or continuous. Discrete-time models divide the time horizon into a fixed number of equal length intervals and are often the best option. However, sometimes, the problem characteristics compel us to employ a continuous-time model, which can be either time grid [2-3] or sequence based [4]. Nowadays, it is clear that single time grid, continuoustime models based on unified frameworks like the Resource-Task Network [2], are the most general, since they can handle batch and continuous tasks, resource constraints other than equipment, together with various storage policies. Yet, it is also true that they are not usually the most efficient for some classes of problems. Recent detailed computational studies [3, 5] have shown that multiple time grid (a.k.a. unit-specific) formulations can be orders of magnitude faster in problems arising from multipurpose as well as from multistage multiproduct batch plants, under an unlimited intermediate storage policy. Traditional approaches for multistage multiproduct batch plants [4] consider that the number and size of batches is known a priori. Different batches of the same product are treated as distinct entities that maintain their identity throughout the processing stages, similarly to batches belonging to different products. Hence, they can be viewed as multiproduct single batch approaches. However, decoupling batching from scheduling decisions often leads to suboptimal solutions since once cannot take advantage of batch mixing/splitting to capitalize on the different capacities from one stage to the next [6]. This paper presents a new continuous-time formulation for the simultaneous batching and scheduling of multistage batch plants with sequence dependent changeovers and

P.M. Castro and A.Q. Novais

406

unlimited intermediate storage. It uses insights from our work on single batch problems [5] and on multiple batch problems without changeovers [7]. From the former, we borrow the 4-index binary variables to identify the execution of combined processing and changeover tasks. From the latter, we take the concept of considering a shared intermediate storage unit per stage to ensure that the material transfer between stages is done properly.

2. Problem Statement Given a plant with k∈K processing stages, i∈I products and m∈MPR processing units, the goal is to determine the number and size of batches for each product, the assignment of batches to units and the sequence of batches in each unit so as to meet a certain objective. Processing times are specified by a constant Įi,m plus a term ȕi,m that is proportional to the batch size, which cannot exceed the capacity of the unit, Vmmax . Sequence dependent changeover times are given by parameter cli,i’,m. A particular unit can handle all products belonging to set Im and is allocated to a single stage, with set Mk including those belonging to stage k. Unlimited intermediate storage, and unlimited wait (UIS/UW) policies are assumed, while transfer times between units are assumed negligible. In general, multiple batches of product i can be produced and a different number of batches may be involved in dissimilar stages of production, i.e. batches can be split or mixed. Two objective functions are tested: (i) revenue maximization while meeting minimum product demands ǻi, for given selling prices vi and fixed time horizon H; (i) makespan minimization for given product demands ǻi.

I1,M1

I1_I1_M1 Duration=α1,1

I1_I2_M1 Duration=α1,1+cl1,2,1

I2_I1_M1 Duration=α2,1+cl2,1,1

I2,M1

I2_I2_M1 Duration=α2,1

...

...

I 1_I I_M1 Duration=α1,1+cl1,I,1

I2_II_M1 Duration=α2,1+cl2,I,1

II_I1_M1 Duration=αI,1+clI,1,1

. . .

II_I2_M1 Duration=αI,1+clI,2,1 ...

I I,M1

I I_II_M1 Duration=αI,1

Figure 1. Resource-Task Network representation for unit M1 showing all possible cleaning states.

3. New Approach (CN) The new unit-specific model uses binary variables N i ,i ', m,t to identify the execution of combined processing tasks in unit m starting at time t. The first index i, indicates the product being produced and the second, i’, the one that follows. The task duration comprises the processing time of i and the required changeover between i and i’ but not the processing time of i’. Before a task can be executed, the equipment unit must be at the corresponding cleaning state. Cleaning states result from the disaggregation of equipment resources. Excess resource variables Ci,m,t are used to account for cleaning states, with Ci0,m defining the initial one (eqs. 1-2). For unit M1, the several possible cleaning states are illustrated in Figure 1. Generally speaking, tasks (i,i’,m) will

Optimal Scheduling of Multistage, Multiproduct, Batch Plants

407

consume state (i,m) at the start and produce state (i’,m) at the end so that a task (i’,i’’,m) can immediately follow, see eq 3.

Ci,m,t ≤ 1 ∀i ∈ I , m ∈ M i , t ∈T ; ¦ C i0,m = 1 ∀m ∈ M PR

(1-2)

i∈I m

Ci ,m ,t = Ci0,m

t =1

+ Ci , m ,t −1 t ≠1 +

¦ N i',i,m,t −1 − ¦ N i,i ',m,t ∀i, m ∈ M i , t ∈ T

i '∈I i ,m ,t −1

(3)

i '∈I m ,i∈I i ',m ,t

The amount produced of product i is given by the continuous extent variables ξi,m,t. This amount is equal to zero if there is no task (i,i’) taking place, see eq 4. Eq 5 guarantees that all product demands are met.

ξ i ,m,t ≤ Vmmax

¦

N i ,i ',m,t i '∈I m ,i∈I i ', m , t

∀m ∈ M PR , i ∈ I m , t ∈ T

(4)

¦ ¦ν i,m ⋅ ξ i,m,t ≥ Δ i ∀i ∈ I

(5)

m∈M | K | ,i∈I m t∈T

Variables Si,m,t are used to account for the material state of product i in storage unit m at event point t. It is assumed that the states resulting from a particular stage exist in a virtual shared intermediate storage unit m∈MST. In other words, there is a 1:1 correspondence between stages and storage units, which are numbered in sequence to the processing units, M=MPR∪MST. The excess resource constraints for material states are given in eq 6. It can be seen that the availability of material state m of product i at event point t, increases by the amount generated by tasks executed in processing units m’ belonging to the same stage (m’∈ M mto ) and decreases by those executed in units m’’ belonging to the next stage (m’’∈ M mfr ), given by variable ξi,m’’,t. The yield associated to the amount produced is accounted for through parameter ν i,m . (I1,I3)

M1

T1,1 M2

T1,2

M4

(I3,I3)

cl1,3,1

(I2,I5)

A2,2

A3,1

T1,3

A6,3

(I5,I5)

T2,2 A5,2

cl2,5,2

(I4,I4)

cl6,4,3 T1,7

A T2,3 4,3

T2,7

Stage 1

(I1,I4)

Stage 2

T1,4

A1,4

(I4,I4)

cl1,4,4

A4,4

T2,4

(I6,I5)

M5

T1,5 M6

T2,1

(I6,I4)

M3 M7

A1,1

A6,5

(I2,I3)

T1,6

A2,6 cl2,3,6

(I5,I5)

cl6,5,5

T2,5

A5,5 (I3,I3)

T2,6

A3,6

Figure 2. Illustration of formulation CN (|I|=6, |MPR|=6, |MST|=1, |K|=2, |T|=2).

P.M. Castro and A.Q. Novais

408

S i ,m,t = S i ,m ,t −1 +

¦ν

ξ

i , m ' i , m ',t m '∈M mto ,i∈I m '

−

¦ξ

i , m '',t m ''∈M mfr ,i∈I m ''

∀i ∈ I , m ∈ M ST , t ∈ T

(6)

The formulation relies on one time grid for each equipment unit, with the same number of event points in all grids. Timing variables Tt,m hold the absolute time of event point t in unit m. Figure 2 shows the relationship between the time grids of the intermediate storage unit M7 and the processing units located before and after it. Each task requires one single event point. Two consecutive event points are spaced apart by a time greater than the duration of the task taking place, see eq 7, where variable MS replaces H for makespan minimization.

Tt +1,m t ≠|T | + H t =|T | − Tt , m ≥

¦ ¦[ N i,i',m,t ⋅ (α i,m + cli,i ',m )] +

i '∈I m i∈I i ',m ,t

¦ ȕi,mξi,m,t ∀m ∈ M PR , t ∈ T

(7)

i∈I m

Material transfer can occur immediately after the end of the processing part of the task. The task finishing last of all those starting at event point t in same-stage units, will set the time of storage unit event point t. In Figure 2, it is the ending time of task (I1,I3), starting at t=1 in M1, that is equal to T1,7. On the other hand, the second event point is set by task (I5,I5) in M2. The general constraint is given in eq 8 and does not involve bigM terms. The absolute time of storage unit event point t must also be greater than the lowest starting time of processing units receiving material from storage. This is ensured by eq 9. Note in Figure 2 that T1,7=T1,4=T1,6, while task (I6,I5) starts in M5 at a later time.

Tt , m ' ≥ Tt , m +

¦ ¦ α i ,m N i ,i ',m,t + ¦ β i ,mξ i ,m,t ∀m'∈ M ST , m ∈ M mto' , t ∈ T

i '∈I m i∈I i ', m , t

(8)

i∈I m

Tt ,m ' ≤ Tt ,m ∀m'∈ M ST , m ∈ M PR , m ∈ M mfr' , t ∈ T

(9)

The objective functions for revenue maximization and makespan minimization are given by eqs 10-11, respectively, where vi is the selling price of i.

max

¦ ¦¦ vi ⋅ν i,m ⋅ξ i,m,t ;min MS

(10-11)

m∈M | K | i∈I m t∈T

4. Computational Studies The performance of the new formulation is compared to the also unit-specific formulation of Shaik & Floudas (SF) [3] that models sequence dependent changeovers implicitly, through sequencing constraints. The MILP models were implemented and solved in GAMS 22.5, using CPLEX 10.2 on a Pentium-4 3.4 GHZ processor, with 2GB of RAM and running Windows XP Professional. All problems were solved to optimality (1E-6 relative tolerance) unless stated otherwise. The data for the examples considered (|K|=3) was generated using a three stage, single product problem as a basis [3]. The results are given in Table 1. Each problem was solved for consecutive values of |T| as part of the standard search procedure to find the global optimal solution. In these examples, we found that |T|SF=|T|CN+|K|-1, so the results are listed according to this formula to facilitate comparison. In terms of problem size, the total number of binaries

Optimal Scheduling of Multistage, Multiproduct, Batch Plants

409

(DV) for SF is significantly lower. This is no surprise considering that it uses 3- rather than 4-index binary variables to identify the execution of processing tasks. The drawback is that it requires substantially more constraints (EQ), mostly stemming from the need to relate the starting time of different tasks in the same unit (sequencing constraints). Concerning the integrality gap (RMIP-MIP), CN is tighter than SF, with the difference being less pronounced as the number of event points increases. Overall, the new formulation has a better computational performance being one or two orders of magnitude faster than SF, which in practice will allow solving larger problems to global optimality.

5. Conclusions This paper has looked into the optimal short-term scheduling of multistage, multiproduct batch plants with sequence dependent changeovers in cases involving multiple product batches. A new multiple time-grid continuous-time formulation has been proposed that relies on shared intermediate storage units, i.e. one virtual unit per stage, to ensure that material transfer between consecutive stages is done properly, both in terms of time as well as of quantity. Simple constraints relate the absolute time of event points belonging to dissimilar time grids. The formulation has been compared to the well-known unit-specific multipurpose formulation of Floudas and co-workers, with the results showing that the new approach is significantly more efficient overall in this class of problems.

6. References [1] [2] [3] [4] [5] [6] [7]

Méndez CA, et al.. Comput. Chem. Eng. 2006; 30: 913. Castro PM, et al. Ind. Eng. Chem. Res. 2004; 43: 105-118. Shaik MA, Floudas CA. Comput. Chem. Eng. 2008; 32: 260-274. Harjunkoski I, Grossmann I. Comput. Chem. Eng. 2002; 26: 1533-1552. Castro PM, Grossmann IE. Ind. Eng. Chem. Res. 2005; 44: 9175-9190. Sundaramoorthy A, Maravelias CT. Ind. Eng. Chem. Res. 2008; 47: 1546-1555. Castro PM, Novais AQ. Ind. Eng. Chem. Res. 2008, 47: 6126-6139.

Table 1. Computational results for revenue maximization (R) and makespan minimization (M) problem EX1_R

model |T| DV SV EQ RMIP MIP CPU s CN 6 110 307 218 6031.45 5105.74 9.2 SF 8 100 253 392 6648.77 5105.74 157 CN 7 130 358 253 6299.07 5105.74 194 SF 9 115 292 489 6783.86 5105.74 16364 EX2_R CN 6 240 514 291 5884.18 4985.29 85.2 SF 8 130 359 790 6300 4985.29 407 CN 7 285 602 338 6183.66 4985.29 1858 SF 9 150 415 1023 6738.65 4985.29 45318 EX1_M CN 10 190 511 407 29.04 30.366 3.39 SF 12 160 409 839 26.241 30.366 203 CN 11 210 562 447 27.336 29.859 70.6 SF 13 175 448 976 26.223 29.859 14730a CN 12 230 613 487 26.846 29.859 7180 EX2_M CN 6 240 514 320 11.917 15.104 207 SF 8 130 359 789 10.781 15.104 1785 CN 7 285 602 372 11.571 15.104 2314 SF 9 150 415 1022 10.781 15.314 60000b a Solver terminated with error, best possible solution (BPS)=26.76; bResource limit, BPS=12.28

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

411

Optimisation of Design, Operation and Scheduling of Batch Reactive Distillation Process with Strict Product Specification and Fixed Product Demand using gPROMS Elmahboub A. Edredera, Iqbal M. Mujtabaa, Mansour Emtirb a School of Engineering, Design and Technology, University of Bradford, Bradford, West Yorkshire, BD7 1DP, United Kingdom,[email protected] bLibyan Petroleum Institute, P.O. Box 6431Tripole, Libya,[email protected]

Abstract Optimal design, operation and scheduling of batch reactive distillation process involving esterification of ethanol and acetic acid to produce ethyl acetate (main product) and water is considered here, where the market demand for the total distillate product and its specification are fixed. For a given market demand, this work investigates how the design parameters (number of stages N and vapor load V), operation parameters (e.g. reflux ratio R; batch time, tb) and schedule in terms of number of batches NB are to be adjusted to maximize a profit function. The capability of the existing design in terms of batch time and schedule to meet variable product demands is also investigated Keywords Batch reactive distillation, fixed product demand, esterification, and optimisation

1. Introduction Due to the flexibility and lower equipment investment batch distillation processes are used in the chemical industry for production of small amount of product with high added values. Conventional batch distillation with chemical reaction (referred to as batch reactive distillation) will be suited when one of the reaction products has a lower boiling point than other products and the reactants. It allows combination of the benefits of reactive distillation and batch process. The effect of this combination has the potential to increase conversion, improve selectivity. Most studies in the past were implicit that there is an unlimited market demand for the amount of products being produced. In reality, unplanned and unlimited production of products are not sustainable and may lead to significant losses in the case of large inventory requirements of any excess products produced (Miladi and Mujtaba, 2004; Mahmud et al. 2008). This work is focused on optimal design and operation of a batch reactive distillation column for ethanol esterification process with fixed yearly product demand and strict product specifications which has not yet been explored. A profit function is maximised while the design parameters, (number of stages N and vapor load V) and operation parameters (such as reflux ratio R; batch time, tb) are optimized. The dynamic optimization problem is converted to nonlinear programming problem by Control

E.A. Edreder et al.

412

Vector Parameterization (CPV) technique and is solved by using efficient SQP method (Mujtaba, 2004) within gPROMS (general PROcess Modeling System, 2004).

2. Column model A dynamic detailed model (Edreder et al., 2008) including mass and energy balance equations, column hold-up, rigorous phase equilibria, and chemical reaction on the plates, in the reboiler and in the condenser is considered here and shown in Figure 1.

Internal Plates, j = 2, N-1 Total Mass Balance: 0 = L j −1 + V j +1 − L j − V j + Δn j H j

Condenser V2, y2

Hc

Component Mass Balance: dxji Hj = Lj−1 xj−1,i +Vj+1 yj+1,i −Lj xji −Vj yji +rjiH dt Energy Balance:

Ha, xD

0 = L j −1 h L j −1 + V j +1 hV j +1 − L j h L j − V j hV j

Equilibrium: y ji = K ji x ji Restrictions:

¦

HN, xN

Relations defining physical properties: K ji = K ji ( y j , x j , T j , P) h L j = h L j ( x j ,T j , P) hV j = hV j ( y j , T j , P )

r ji = r ji (k ji , x ji )

Δn j =

¦r

Reboiler and Reactor

y ji = 1

ji

Reboiler: j = N Total Mass Balance: dH N = LN −1 − VN + ΔnN H N dt Component Mass Balance:

Condenser and Distillate Accumulator: j=1 dH a Accumulator Total Mass Balance: = LD dt Component Mass Balance: dx a) Accumulator: H a a = LD ( xD,i − xa,i ) dt b) Condenser Holdup Tank dx Hc Di =V2y2,i + r1,i Hc − (V2 + Δn1Hc)xDi dt Energy Balance: 0 = V 2 hV 2 − (V 2 + Δn1 H c )h L1 − Qc

dx HN Ni = LN−1(xN−1,i − xNi ) −VN (yNi − xNi ) dt +rNi HN −ΔnN HN xNi Energy Balance:

0 = LN−1(hLN−1 − hLN ) −VN (hV N − hLN ) + QR

Other Equation L1 = R(V2 + Δn1H c )

LD = (V2 + Δn1H c )(1 − R) T1 = T1( xD,i , P )

h L1 = h L1( x D,i , T1, P )

Fig.1 Model equations The vapour-liquid equilibrium is calculated (Suzuki et al., 1970) as follows.

AcOH(1) + EtOH(2) ⇔ AcOEt(3) + H 2 O(4)

k1 = 2.25 × 10 −2 T − 7.812 for T > 347.6 K ; k1 = 0.001 T ≤ 347.6 K "ogk 2 = −2.3 × 10 3 / T + 6.588 "ogk 3 = −2.3 × 10 3 / T + 6.742

(1)

Optimisation of Design, Operation and Scheduling of Batch Reactive Distillation Process with Strict Product Specification and Fixed Product Demand Using gPROMS

"ogk 4 = −2.3 × 10 3 / T + 6.484

413

(2)

Catalyzed rate of reaction, gmol / (L-min) is given by (Bogacki et al., 1989)

ri = k f CAcOH CEtOH − kr C AcOEt CH 2O

(3)

The constants kf and kr are: kf = 4.76 x 10-4 and kr = 1.63 x 10-4 in (L/gmol-min)

3. Optimization Problem Formulation Figure 2 shows the design and operation optimization problem for ethanol esterification process. The objective (profit per year) function (to maximize) is defined (Miladi and Mujtaba, 2004) as follows Profit ($/yr) = P ($/yr) = (C1D1 − C2B0 − OCb) × NB − ACC

(4)

Where, OCb = Operating cost ($/batch) = (K 3 V / A) × (t b − t s ) ACC = Annualised capital cost ($/year) = K 1 V

0 .5

N

0 .8

+ K2 V

(5) 0 .6 5

NB Number of batches / year = H / (t b + t s )

(6) (7)

Where, K1 = 1,500; K2 = 9,500; K3 = 180; A = 8,000, tb = Batch time (hr); ts = Set-up time = 0.5 hr; H = Production horizon = 8000 h/year, C1 = 80, C2 = 22.45 are the prices ($/kmol) of the desired products, raw material respectively

Given:

Determine:

So as to maximize: Subject to:

the column configuration, the feed mixture, condenser vapor load, and a separation task (i.e. achieve the product with purity specification for a key distillate component, a set of product specifications (purities of key components in main products, amounts, etc.); production horizon (H, h/year); product demand the optimum design (number of stages N, and vapor load, V) and operating decisions (reflux ratio, R and batch time, tb) and schedule in terms of number of batches (NB) the objective function P. equality and inequality constraints.

Mathematically the optimization problem (OP) can be represented as: OP

Max P N, V, R, tb s.t. xc • x*c Product demand Process model equations Linear bounds on V, R

(inequality constraint) fixed (equality constraint) (inequality constraint)

Fig. 2 Optimization problem formulation

4. Case study The feed to the still consists of a mixture , with composition [0.45, 0.45, 0.00, 0.10] and amount (B0) = 5 kmol. The number of

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plates includes reboiler and a total condenser. Four percent (4 %) of the total feed charge is the total column holdup. Fifty percent (50 %) of this holdup is taken as the condenser holdup and the rest is equally divided for the plate holdup. Plates, product accumulator and reboiler compositions are initialized to those of the feed compositions. The given product purity is 0.7 mole fraction of ethyl acetate. The model was built in gPROMS Model Builder 3.0.3.

5. Results and Discussions For a given column design (i.e. number of stages) the product demand is varied (ranging from 700 to 1200 kmol/yr). For each case, the results in terms of optimum batch time, vapor load, reflux ratio, number of batches are summarized in Table 1. The maximum profit ($/ year) profile for each of these cases are shown in Figure 3. The results in Table 1 show that higher N allows the column to operate at lower reflux ratio. Moreover, for the same product demand, increase in N leads to decrease in vapor load. Figure 3 clearly shows that one single column is not optimal for the whole range of product demand. For product demand of 700 kmol/yr, comparison of the maximum profit using an existing column (e.g. N = 8) with those obtained using the optimal design (N=9, V=1.21 kmol/hr), operation (R=0.93, tb= 25.7 hr) and schedule (number of batches, NB=306) shows 20 % more profit. And, for the product demand of 1000 kmol/yr, the profit increase is by 80 %. This also shows the limit (or capability) of an existing column (i.e. fixed design) delivering products to a changing market demand. For example, it was not possible to make any Table 1. Summary of the results (N = 8) Demand

tf (hr)

V

R

700

25.4

1.28

0.930

800

22.1

1.56

0.934

(N=10) Demand

tf (hr)

V

R

NB

308.8

700

25.9

1.15

0.922

303.0

354.8

800

22.47

1.39

0.926

347.6

19.80

1.65

0.930

393.3

NB

900

19.4

1.87

0.938

402.1

900

1000

17.3

2.23

0.942

450.7

1000

17.63

1.95

0.934

440.2

501.1

1100

15.84

2.28

0.938

489.6

553.4

1200 (N = 11) Demand

14.33

2.65

0.942

540.0

tf (hr)

V

1100

15.45

2.64

0.946

1200 (N = 9) Demand

13.96

3.12

0.951

tf (hr)

V

R

NB

700

25.71

1.21

0.926

305.3

800

22.30

1.46

0.930

350.4

R

NB

700

26.0

1.12

0.920

302.3

800

22.58

1.35

0.924

346.6

900

19.66

1.75

0.934

396.8

900

19.91

1.60

0.928

392.0

1000

17.50

2.06

0.938

444.4

1000

17.74

1.89

0.932

438.5

1100

15.71

2.43

0.942

493.5

1100

15.95

2.20

0.936

486.3

1200

14.20

2.84

0.946

544.3

1200

14.43

2.55

0.939

535.7

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Fig.3 Profit vs. Demand

6. Conclusions In this work, the design, operation and schedule of batch reactive distillation column for ethanol esterification process is optimized under fixed product demand (ranging from 700-1200 kmol/yr) and strict product quality (0.7 mol fraction of ethyl acetate). The optimization problem is solved using the optimization techniques available within gPROMS. The results show that the design, operation and schedule are found to be different for all cases. Over product demand of 1150 kmol/yr no profitable operation and schedule was found for an existing column design (i.e. N=8). The column with N= 10 indicated the best profitability profile for all product demand scenarios although product demand of 1000 kg/hr was the best. Also it is interesting to note that beyond the product demand of 1000 kg/hr single column operation with any scheduling is less profitable.

7. References [1] M.B.Bogacki, , K. Alejski, and J. Szymanowski, 1989, The fast method of the solution of a reacting distillation problem. Computers Chemical Engineering., 13 (9), pp 1081. [2] E.A. Edreder, M.M. Emtir and I.M Mujtaba, 2008, Improving the Maximum Conversion of Ethanol Esterification. Chemical Product and Process Modeling, 3, (1), article 36 [3] gPROMS, 2004, Introductory User Guide, Process System Enterprise Ltd (PSE). [4] M. Miladi, and I.M. Mujtaba, 2004, Optimisation of design and operation policies of binary batch distillation with fixed product demand, Computers Chemical Engineering., 28, 2377-2390 [5] M.T. Mahmud, I.M. Mujtaba and M. Emtir, 2008, Optimal Design and Operation of Multivessel Batch Distillation Column with Fixed Product Demand and Strict Product Specifications. In Computer Aided Chemical Engineering- 25, B., Vol. 25, pp859-864, Elsevier, 2008 [6] I. Suzuki., H. Yagi, H. Komatsuand and M. Hirata, 1970, Formulation and Prediction of Quaternary Vapor-liquid Equilibrium Accompanied by Esterification. J. Chem. Engng Japan, 3, pp 152-157 [7] I.M. Mujtaba, 2004, Batch distillation: Design and operation. London: Imperial College Press.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

417

Planning and Scheduling of Solar Salt Harvest Luis Cisternasa,b, Patricio Pintoc and Karla Ossandóna a

Depto. de Ing. Química, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile. Centro de Investigación Científico y Tecnológico de la Minería, CICITEM, Chile. c SKM MinMetal, Santiago, Chile. b

Abstract Several chemicals are produced from brines by solar crystallization using solar ponds. The process of salt harvest consists on mechanically retiring the salts precipitated in the solar evaporation ponds and to leave them in its respective stockpile. In an industrial operation several ponds are used for the fractional crystallization of several salts, and therefore the harvest planning can be a nontrivial task. Therefore, the objective of this work is to plan the feeding flow to each of the solar ponds, the manipulation of solution, and the solutions and solids inventories in each pond that maximizes the production and the harvest periods. All this having as input data the evaporation rate, concentration range of the feeding, concentration range for the pond, and the operational initial conditions. The model developed corresponds to a MINLP, which includes the mass balances in each pond, equilibrium conditions, and planning & operational restrictions. The problem was solved in two steps, first the maximization of the salt harvest was determined and then, using this maximum harvest, the maximum availability of the contractor was determined. Several cases have been studied, including: ternary (NaNO3KNO3-H2O) and quaternary systems (KCl-KNO3-K2SO4-H2O), pond systems with 3 and 4 ponds and with different areas, and considering 12 and 26 operation periods per year. Keywords: solar ponds, crystallization, solar salt harvest.

1. Introduction The solar evaporation ponds are used for the production of salts or for the generation of heat energy [1]. The brines processed in solar evaporation ponds for the production of salts are obtained from different origins like seawater, natural lakes, underground brines and mining solutions. Examples of products obtained from brines include KCl, K2SO4, Na2SO4, Li2SO4, and H3BO4 [2, 3, 4]. The operation of solar pond is favorable if low cost land and arid climate are available, reason why the production depends on the location of the ponds. At the present time the solar evaporation pond are formulated and operated combining art and science. However, due to increases in the demand of some salts, space limitations and the increase in operation and capital costs, it has been forced to give a more scientific focus for the design and operation of solar evaporation ponds. For example a thermodynamic model has been developed to study the behavior of solid liquid equilibrium in aqueous electrolyte systems [5,6]. A model to optimize the process has been created together with experimental simulations that determine the best pond height depending on the climatic conditions [7]. Also a methodology has been developed based on experimental data to increase the salt production [8]. In spite of the those advances, few efforts have been carried out to improve the planning (what has to

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418

be done) and scheduling (when this has to be done) of salt harvest in solar evaporation pond systems to maximize the salt production and minimize the cost. The objective of this work consists on determining by means of planning and scheduling, the maximum precipitation of salts in solar evaporation pond systems and to distribute its harvest in such way to take advantage of the maximum use of the contractor in a year period horizon. With this objective a mathematical model was developed whose results indicate the planning and scheduling of brine flows between ponds, the brine and solid inventory in each particular pond. All of this having as data the evaporation rate, concentration operation range, concentration of the feed, and the initial pond conditions.

2. Mathematical Model In this section is presented the fundamental aspects of the MINLP model to optimize the planning and scheduling of the salt production and harvest in solar evaporation pond systems. The outlined problem consists on to determine a maximum production of salts precipitated in the solar evaporation ponds and to distribute its harvest in a such way of taking advantage of the maximum contractor's use that carries out the task. It is also looked for to determine the distribution of flows transfers among ponds. The solution strategy consists on using mathematical programming based on a superstructure of the solar evaporation process. The formulation of the mathematical model is constituted by two objective functions subject to restrictions. The first function objective considers the maximization of salt harvest and the second objective function maximize the periods of salt harvest with the objective of minimizing the costs associated to this operation. The objective function that maximizes the salt harvest is

Max

¦ ¦ ¦ CS

i ,t , k

(1)

i ∈ I t ∈T k ∈ K

Where CS i ,t ,k represents the salt harvest in the pond i in the time period t for the component k. Once the maximum harvest, CM, is determined, this is introduced as a restriction in the second model that maximizes the harvest periods, that is to say

Max

¦ ¦ (1 − y ) P i ,t

(2)

i ∈ I t ∈T

¦ ¦ ¦ CS

i ,t , k

≥ δ ⋅ CM

(3)

i ∈ I t ∈T k ∈ K

where

yiP,t is a binary variable that takes the value 1 if the pond i is in operation in the

period t, and takes the value 0 if the pond i is in harvest in the period t. į is the minimum fraction of CM that is allowed (in this work a value of į=0.9 was used). The superstructure of the solar evaporation pond system is built including a mixer in the input of each pond and a divider in the output, as it is shown in figure 1, and allowing the transfer of brines among all the pond or among those that the designer want to consider. This means that all pools could be connected. The pond model should include the mass balances and the solid-liquid equilibrium conditions between the precipitate solids and the brine. To develop this model, each pond is represented as it is shown in figure 2. Then, mass balances for each component was developed for the liquid phase

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419

and solid phase separately, considering only the flow of salt precipitated as a mass transfer from one phase to another. Each pond has two possible states in every period: operation or harvest, then its modeling is carried out using a disjunction in the following way

ªOperation º ª Harvest º « » « » « f ( x ) = 0 » ∨ « g ( x ) = 0» «¬ Ax ≤ B »¼ «¬ Bx ≤ D »¼

(4)

When the system is operating there is no harvest, and therefore the solid phase increases its inventory of salts, whereas the liquid phase may or may not receive or send brine to other ponds, which is why its brine inventory can increase or decrease. Moreover, when the harvest is in, the entire inventory of brine is sent to another pond, brine input is removed, and the salt inventory reduced to zero. Equations in the disjunction (4) represent the mass balances, equilibrium conditions, and restrictions of operation conditions, scheduling and planning. The equilibrium conditions between the solution and the precipitate solids are represented by hyperplanes according to the model developed by Pressly and Ng in 1999 [9]. That is to say,

¦a

x

n ,i , k i ,t , k

= bn ,i ∀ n ∈ N , i ∈ I , t ∈ T

(5)

k ∈K

In practice the operation conditions of evaporation ponds, in a given period, as temperature and composition, change, and therefore the relationships of the equation 5 represent medium operation conditions. Its application to pond modeling was previously studied, concluding that the hyperplanes is an appropriate tool. The operational restrictions include among others: ranges of concentrations of the solutions in ponds, ranges of operation of transfer flows among pond, maximum and minimum heights of solution and solid inventories. When the harvest is carried out in more than a period of operation, logical expressions were included to condition that the harvest is carried out in continuous periods, and to unite the last period with the first one in case that harvest is carried out in the last period.

Feed

Pond

Figure 1. Solar evaporation pond representation in the superstructure

Product

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420

Evaporation

Output brine

Input brine SOLUTION Initial inventory of brine

Precipitated salts

Final inventory of brine

SOLIDS Final inventory of solids

Initial inventory of solids

Harvest Figure 2. Solar evaporation pond representation for modeling.

3. Examples To validate the proposed methodology, two systems of solar evaporation ponds were analyzed, studying diverse scenarios. The problems outlined for each case, contain common operational data in the industry. For example, figure 3 shows the typical annual solar evaporation rate in the north of Chile. This means that higher evaporation occurs in the summer, while rainfall is almost negligible. Usually, all solutions show similar behavior but with different values depending on the concentration of the brine. The first example considered corresponds to the production of sodium nitrate in solar evaporation pond that contains NaNO3, KNO3 and H2O operating at the temperature of 25ºC. Several cases were included: the first one with a system of 3 ponds of 40,000 m2 and 12 periods of annual operation; the second, equivalent to the first one, but with 26 annual periods of operation; the cases 3 and 4 operate with 4 ponds, the third with ponds of 30,000 m2 and the fourth with ponds of 40,000 m2, both with 26 annual periods of operation. The second example corresponds to the precipitation of potassium sulfate in solar evaporation ponds that contains KCl, KNO3, K2SO4 and H2O, operating at 25ºC. In this example a single case is considered of a system that operates with 3 ponds of 40,000 m2 and 12 annual periods of operation.

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0.0065

Evaporation (m3/m2 day)

0.0060 0.0055 0.0050 0.0045 0.0040 0.0035 0.0030 0.0025 0

1

2

3

4

5

6

7

8

9

10

11

12

13

Time (month) Figure 3. Solar evaporation rate in north of Chile

The solution of the different cases was implemented in GAMS with different solvers. A total of 8 hours maximum was allowed using a processor of 2.39 GHz. With the exception of the case 1, BARON was the only solver to gives a solution in the allowed time. The table 1 shows some of the obtained results. Table 1. Result for the examples. Examples

Example 1

Cases

Case 1

Solvers CPU time [s] † CPU time[s]

‡

Salt harvest [ton/year] Harvest periods † ‡

Example 2

Case 2

Case 3

Case 4

Case 1

BARON

OQNLP

BARON

BARON

BARON

BARON

362.9

10,831.2

8,613.6

23,997.3

11,167.7

1,672.2

438.0

56,975.8

5,876.4

15,041.8

24,186.7

864.9

62,569

62,506

36,232

50,203

82,007

45,413

3

5

9

5

5

Maximum harvest objective function. Maximum harvest periods objective function.

The CPU times show that it is necessary to use other strategies or methods of optimization, and/or seek modifications or simplifications to the model to reduce CPU times. Besides these results, the planning of the solution flow handling among ponds was obtained, the inventories of brine and solids in every period and pond was determined.

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4. Conclusion and future work A procedure for the planning and scheduling of salt production and harvest in solar evaporation pond systems was developed. The use of two objective functions, one to maximize the harvest and another to maximize the harvest periods, solved in sequential form, showed to be a good strategy for the solution of this type of problems. Industrial applications and simplifications to the model or new optimization methods to reduce the CPU times correspond, at the moment, the future work.

5. Acknowledgements We thank the CONICYT for financing and support of the work reported in this manuscript (FONDECYT 1060342).

References [1] Lior N., and R. Bakish, Supply and Desalination, in Kirk-Othmer Encyclopedia of Chemical Technology, (2001). [2] Butts E., Chemicals from Brine, in “Kirk-Othmer Encyclopedia of Chemical Technology”, (2001). [3] Flotz G.E., Lithium and Lithium Compounds, in “Inorganic Chemicals Handbook”, J.J. McKetta, (1993), Marcel Dekker, New York. [4] Thieme C., and R.J. Bauer, Sodium Carbonates, in “Ullmann's Encyclopedia of Industrial Chemistry”, (2002). [5] Kwok K.S., Ka M. Ng, M.E. Taboada and L.A. Cisternas, (2008), Thermodynamics of Salt Lake System: Representation, Experiments, and Visualization, AIChE J., 54, 707-727. [6] Song P., and Y. Yan. (2003), Thermodynamics and Phase Diagram of the Salt Lake Brine System at 298.15 K, Computer Coupling of Phase Diagrams and Thermochemistry, 27, 343–352. [7] Murthy G.R. Ramakrishna and K.P. Pandey, (2003), Comparative Performance Evaluation of Fertiliser Solar Pond Under Simulated Conditions, Renewable Energy, 28, 455–466. [8] Hamzaoui A.H., A. M’nif, H. Hammi and R. Rokbani, (2003), Contribution to the Lithium Recovery from Brine, Desalination, 158, 221-224. [9] Pressly T.G., Ka M. Ng, (1999), Process Boundary Approach to Separations Synthesis, AIChE J., 45, 1939-1952

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

423

Scheduling of a Multiproduct Batch Plant under Multiperiod Demand Uncertainties by Means of a Rolling Horizon Strategy Jian Cui a and Sebastian Engell a a

Process Dynamics and Operations Group, Technische Universität Dortmund, 44221 Dortmund, Germany,{jian.cui | s.engell}@bci.tu-dortmund.de

Abstract In this contribution, a rolling horizon strategy (RHS) based on two-stage stochastic integer programming with recourse (2SSIP) for online scheduling under multiperiod uncertainties (SMU) is proposed. The RHS is applied to a polymer production plant with batch and continuous production steps where different amounts of final products are delivered by each batch according to the chosen recipes. Keywords: multiproduct batch plant, scheduling, multiperiod uncertainties, two-stage stochastic integer programming, rolling horizon strategy

1. Introduction Stochastic programming with recourse is a realistic formulation of online resource allocation problems where there is uncertainty about the future evolution, e.g. about demands, plant capacity, product yields, and this uncertainty is removed as time progresses because new information is obtained. The key idea is the representation of the information structure where the decision variables in each stage depend on deterministic information that is available at this point in time but take into account the uncertain future and in particular the potential of reacting to the future development by adapting those decision variables that do not have to be implemented immediately. Real-world problems lead to multi-stage stochastic programming problems with recourse [1] but their rigorous solution is computationally extremely demanding. A good compromise is the formulation of two-stage stochastic programming problems where the decision variables are divided into two sets. The here-and-now or first stage variables have to be fixed based on the available information but for the remaining variables it is assumed that the uncertainty is removed completely before they have to be decided. Two-stage formulations have been applied to chemical engineering problems in several contributions recently [2, 3, 4, 5, 6]. In a real-world scheduling situation, there is a continuous flow of information and decisions have to be taken upon events or periodically, so a dynamic formulation is needed. Balasubramanian and Grossmann [5] applied a shrinking-horizon approach where a series of two-stage stochastic STN models is solved in which the first stage is shrinking in each step. Here integer variables are only considered in the first stage, while continues recourse decisions are included in the second stage for the amounts sold and lost and the revenues and costs after the end of the scheduling horizon. A telescopic decomposition approach to online scheduling in which two-stage stochastic integer programming models with integer variables in the first and in the second stage was suggested by Engell et al. [2] and a cascaded two-layer model predictive framework was proposed by

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Sand et al. [3] but actual computations were only performed for static problems using the decomposition algorithm by Carøe and Schultz [7]. Till at al. [4] proposed a new solution concept for 2SSP that combines evolutionary and exact algorithms based on stage decomposition of the stochastic program. In this contribution, a 2SSIP formulation in a rolling horizon setting is presented where the evolution of uncertain demand profiles along a multi-period horizon is explicitly considered.

2. Rolling Horizon Strategy Based on 2SSIP 2.1. 2SSIP formulation in a rolling horizon setting

Fig.1 RHS: Deterministic equivalent 2SSIP in period i

Suppose a plant is scheduled under uncertainties ξ={ξ1, ξ2, . . ., ξI} which are independent discrete random variables with discrete distributions ψ(ξi) in a time horizon with I periods as shown in Fig.1. x1, x2, . . ., xI are the mixed-integer decision variables in each period. In order to reduce the computational effort, the near future within the next I1 periods and represented by f2( ) is modeled by a tree of scenarios in the combined sample space ω Ωi of the future demands whereas the more remote future within the following I2-I1 periods is represented by the expected values (EVs) of the stochastic variables (cost contribution f3( )). As the inclusion of the more distant future predominantly has the purpose to rule out unrealistic solutions that maximize the benefit over a short horizon at the expense of the long-term performance, and realistic scenarios are difficult to generate for the distant future, we consider this a reasonable simplification that does not affect the performance much. Both time horizons are rolling in the standard time coordinate i. In step i of the RHS, as shown in Fig.1, a 2SSIP model with the past optimal decisions x*1. . .i-1, actual decision variables xi, realized uncertainties ξi-1, additional uncertainties ξi+I1-1 and EVs for the distant future ξi+I1. . .i+I2-1 is solved and the first stage optimal solutions x*i are implemented. Period i is the first stage and period i+1 to period i+I2 constitute the second stage in the 2SSIP setting. Based on the formulation of two-stage stochastic integer programming with recourse in [1], the deterministic equivalent 2SSIP formulation of a maximization problem in a specific period i RHS2SSIP | Ωi is defined by: * 1i −1

max f1 ( x xi

s.t.

⎡ max f 2 ( xi , xi +1i + I1 ,ω , ξ ii + I1 −1,ω ) ⎤ xi+1i + I1 ,ω ⎥ , xi , ξ i −1 ) + EV ⎢ ⎢ + max f 3 ( xi , xi + I +1i + I ,ω , EV (ξi + I i + I −1 )) ⎥ 1 2 1 2 ⎢⎣ xi+ I1+1i+ I2 ,ω ⎥⎦

hω ( x1*i −1 , xi , xi +1i + I2 ,ω , ξi −1 , ξii + I1 −1,ω , EV (ξi + I1i + I 2 −1 )) = 0, ω = 1, 2,, Ωi

(1)

(2)

Scheduling of a Multiproduct Batch Plant under Multiperiod Demand Uncertainties by Means of a Rolling Horizon Strategy

425

gω ( x1*i −1 , xi , xi+1i + I 2 ,ω , ξi −1 , ξii +I1 −1,ω , EV (ξi + I1i + I2 −1 )) ≤ 0, ω = 1, 2,, Ωi

(3)

x1 , , xi , xi +1,ω , , xi + I 2 ,ω , xi + I 2 +1 , , x I ∈ X , ω = 1, 2,  , Ω i

(4)

ξ ω = {ξ i ,ω ,  , ξ i + I

(5)

2

−1,ω

} ∼ Ψ (ξ

{

i i + I 2 −1,ω

X = x ∈  n ' ×  n '' x lo ≤ x ≤ x up

), ω = 1, 2,  , Ω i

}

(6)

2.2. Feedback Structure of the Rolling Horizon Strategy The feedback structure of the rolling horizon strategy based on 2SSIP scheduler is shown in Fig.2.

Fig.2 RHS: Feedback structure

Starting from a given initial condition of the plant, a series of 2SSIP problems RHS2SSIP | Ωi are solved. After each step, the optimal decisions are implemented and one of the possible realizations of the uncertainties is chosen for the next period. The evolution of the plant is recorded in the database.

3. The EPS Plant The multiproduct batch plant for the production of expandable polystyrene (EPS) shown in Fig.3 is an example of a complex online scheduling problem. From a number of raw materials (E), two EPS-types (A and B) are processed on one finishing line each where fp = 5 grain size fractions (see Fig.4) are produced. The detailed description of the EPSprocess can be found in [2, 3, 4]. The scheduling problem is complicated because of the coupled production of the grain size fractions that are the final products with demands and the continuous operation of the finishing lines.

Fig.3 EPS Plant: Flow sheet

Fig.4 EPS Plant: Yields of the grain size fractions fp according to recipe rp (identical for products A and B)

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426

The model of the EPS-process scheduling problem used in this contribution is a slightly modified version of the static medium-term scheduling problem of the EPS production formulated by Till et al. [4] The model was extended by including the stored material at the beginning of the scheduling horizon in period i as well as the fact that the state of the finishing lines in the previous periods restricts the possibility of switching them on or off in the next periods (the lines have to be up or down for at least two consecutive periods). The objective function is to maximize the profit that is computed from sales revenues that are discounted if the demand is satisfied late, costs for the starts of a polymerization, costs for the change of the operating states of the finishing lines, inventory costs, and penalties for unsatisfied demands.

4. Numerical Results The modified EPS model was implemented in the 2SSIP scheduler in a rolling horizon setting where the scheduled productions and the states of the finishing lines in the next interval are the first stage variables, while the production decisions and the sales in the later periods constitute the second stage decisions. Time horizon I1 is 3 periods and time horizon I2 is 7 periods. We assume that demand uncertainties are resolved at the beginning of each time period and that they are independent of each other with the same discrete probability distribution. In each period, there are two equally probably demand scenarios. This yields 23=8 scenarios in the 2SSIP in each period i. Three successive problems were solved on a moving horizon by CPLEX 10.2.0 on a 2.4 GHz Linux machine. The problem was formulated as a monolithic MILP without decomposition. The problem size and the computation times for each step are shown in Table 1. The comparison between the 2SSIP models and their EEV models are listed in Table 2 which shows the advantages by taking recourses in 2SSIP models in facing the uncertainties where only expected values are considered in EEV models. Table 1. Three-step Rolling Horizon Problem

Constraints

Continuous Variables

Integer Variables

7367

7830

2226

Total Computation Time(H:M:S) Variables (Gap < 5%) Step 1 Step 2 Step 3 10056 00:30:07 00:11:45 00:05:36

Table 2. Comparision Between 2SSIP and EEV

Rolling Steps Step 1 Step 2 Step 3

Profits 2SSIP 55.86  63.33 66.47

EEV 54.32 61.57 64.90

The scheduling results of three rolling steps on 2SSIP and one rolling step on EEV are shown in Fig.5 to Fig.8 below. For reaching the maximum benefits, polymerization batches are scheduled in order to satisfy the demand profiles as well as possible, supply deficiencies are fulfilled as soon as possible in the future rolling steps and overall storage is kept as small as possible in each rolling steps.

Scheduling of a Multiproduct Batch Plant under Multiperiod Demand Uncertainties by Means of a Rolling Horizon Strategy

Fig.5 RHS of 2SSIP: The optimal solutions of rolling step one

Fig.6 RHS of 2SSIP: The optimal solutions of rolling step two

Fig.7 RHS of 2SSIP: The optimal solutions of rolling step three

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Fig.8 RHS of EEV: The optimal solutions of rolling step one

5. Conclusion and Future Work A 2SSIP based RHS was introduced in this contribution for online scheduling under multiperiod uncertainty. Numerical tests show that this approach is computational feasible. The computation times can be further reduced by applying decomposition techniques. In the future, also uncertainties in yields and plant capacity will be considered.

6. References [1] Birge, J. R., Louveaux, F., 1997: Introduction to Stochastic Programming. [2] Engell, S., Märkert, A., Sand, G., Schultz, R., Schulz, C., 2001: Online Scheduling of Multiproduct Batch Plants under Uncertainty. In: Online Optimization of Large Scale Systems, Springer, Berlin, 649-676. [3] Sand, G., Engell, S., 2004: Modeling and solving real-time scheduling problems by stochastic integer programming. Computers and Chemical Engineering 28 , 1087-1103. [4] Till, J., Sand, G., Urselmann, M., Engell, S., 2007: A hybrid evolutionary algorithm for solving two-stage stochastic integer programs in chemical batch scheduling. Computers and Chemical Engineering 31 (5-6), 630-647. [5] Balasubramanian, J., Grossmann I.E., 2004: Approximation to Multistage Stochastic Optimization in Multiperiod Batch Plant Scheduling under Demand Uncertainty. Ind. Eng. Chem. Res. 43, 3695-3713. [6] Guillén, G., Mele, F.D., Espuña, A., Puigjaner, L. (2006). Addressing the Design of Chemical Supply Chains under Demand Uncertainty. Ind. Eng. Chem. Res. 45, 7566-7581. [7] Carøe, C.C., Schultz, R., 1999: Dual decomposition in stochastic integer programming. Operations Research Letters 24, 37-45.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

429

Short-Term Operational Planning of Multiple-Source Refined Products Pipelines Diego C. Cafaro,a Jaime Cerdáa a

INTEC (CONICET-UNL), Güemes 3450, 3000 Santa Fe, Argentina, [email protected]

Abstract Pipelines are the most reliable, cost-effective and environmentally friendly transportation mode, and the preferred transportation option in the oil industry. Batches of different products are usually shipped from multiple refineries to several downstream terminals. Most of refined products pipelines are common carriers offering transport services to many refiners. Previous work on pipeline planning assumed single-source configurations with only one input terminal at the origin and several receiving depots. However, multiple-source pipeline configurations involving additional input terminals at non-origin points are quite usual and their operational planning raise new issues not considered before. For instance, the sequence of batches will no longer be arranged as they are pumped into the line because batches can be injected at some intermediate points. As a result, product lots and pumping runs must be handled as independent entities. Another critical matter is the batch integrity. When a new product is injected at an intermediate point, the pipeline operator is usually forbidden to split a batch in transit into a pair of non-consecutive smaller lots. The primary goal is to keep the mixing costs as low as possible. This paper presents a new MILP mathematical formulation for the short-term operational planning of refined products pipelines with multiple input and output terminals. It is based on a continuous representation in both time and volume scales. The proposed formulation was successfully applied to a practical example. Keywords: Refined products pipelines, Multiple sources, Operational planning, Mixedinteger linear programming, Continuous formulation.

1. Introduction Compared with other transportation modes like trucks, railroad cars or vessels, pipelines appear as the most efficient way to deliver huge amounts of refined petroleum products from refineries to distribution centers closer to the consuming areas. Only waterborne shipments can be price-competitive with pipelines, but they present low reliability and a much higher environmental impact.[1] Pipelines are generally owned by a number of companies and operated as common carriers to transport petroleum derivatives from different refiners. Their main purpose is to supply the required products to demanding terminals at the right time, minimizing both the product quality downgrading due to interface mixing and the energy consuming cost. Scheduling the sequence of batch injections in a multi-commodity pipeline system is a very difficult task with many constraints to be considered.[2] The pipeline industry is unique among the transportation industries because it uses stationary carriers whose cargo moves rather than moving carriers of stationary cargo.[3] As a result, conventional methods like the vehicle routing techniques fail to solve this problem. Almost every previous work on pipeline operational planning assumed that the pipeline connects a single refinery to several depots,[2-7] with some few exceptions.[8,9] Nonetheless, the common carrier pipeline

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430

problem has never been rigorously solved. Additional input terminals located at nonorigin points collect batches from downstream refineries and ship them to farther output terminals (see Figure 1). Refineries (Sources)

Distribution Centres (Destinations)

Figure 1. Multiple-source to multiple-destination pipeline

Common carrier pipelines raise numerous operational issues that were avoided on the treatment of single-source systems.[3] Since a multiple-source trunk line usually works on fungible mode, individual batches of the same product featuring common specifications, though provided by different shippers, can be joined into a single, larger batch with multiple destinations. A major difference with regards to the single-source problem is the need of additionally selecting the input terminal where the next pumping run will occur. In single-source pipelines, batches are sequenced on the line as they are injected. In contrast, batches and pumping runs are not always similarly sequenced in multiple-source pipelines and they must be handled as independent entities. An important cost in pipeline operation is the so-called mixing cost. To reduce mixing effects, it is important to generate transitions between compatible products with the less specific gravity gap. In multi-source pipelines running on fungible mode, a related key issue is the batch integrity. Pumping runs taking place at downstream input terminals can either insert a new batch or increase the size of a batch in transit. In the former case, the new batch should be injected just at the interface of two consecutive products to mostly avoid the splitting of batches in transit and keep the mixing costs as low as possible. However, a pumping run not always injects a new batch in the pipeline as assumed in previous work. Sometimes, it may increase the size of a batch in transit injected before from an upstream refinery whenever it can be accessed from the downstream terminal. This paper presents an innovative MILP mathematical formulation for the short-term operational planning of multiproduct pipelines with multiple input and output terminals, absolutely continuous in both volume and time scales.

2. Problem Statement A multiple-source pipeline system with unidirectional flow is considered. Batches are transported on fungible mode. The primary goal is to determine the size and sequence of new product lots to be pumped from multiple input terminals in order to: (a) meet every product demand at each distribution terminal over the planning horizon; (b) trace the size and location of every flowing batch; and (c) minimize the sum of pumping, transition, and underutilization costs. The pipeline operational schedule should indicate the input terminal driving each pumping run, the amount and type of product to be pumped, the starting and completion times, and the amount of product to deliver from every batch in transit to receiving terminals during every pumping run. For that purpose, the following assumptions have been made: (i) The pipeline remains completely full of incompressible liquid products at any time. The only way to get a volume of product out

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of the line is by injecting an equal volume at some input terminal. (ii) There is no physical barrier between consecutive product batches. (iii) Every batch can be pumped at a different flow rate. (iv) At most a single input terminal can be injecting a new batch at any time. (v) Product demands at output terminals to be satisfied before the end of the scheduling horizon are deterministic data. (vi) Available product inventories at input terminals are also given. A simpler, practical viewpoint is used to handle inventory management issues, usually applied by the pipeline scheduler. Nonetheless, a more rigorous analysis similar to the one reported by [6] can alternatively be performed.

3. Mathematical Formulation The proposed MILP formulation is a generalization of the mathematical model for the short-term operational planning of single-source refined products pipelines previously applied by [6] and [7]. Aside from considering multiple input terminals rather than a single one, no further assumption was required. Therefore, the optimality of the proposed schedule is guaranteed. The model involves five major entities: pumping runs (the set K), batches (the set I), oil derivatives (the set P), oil refinery sources or input terminals (the set S) and output terminals (the set J). In the set K, pumping runs k1, k2, etc., have been chronologically ordered. On the other hand, the elements of the set I have been arranged as they are sequenced into the pipeline, with the first batch i1 occupying the farthest position from the origin. Set Inew stands for new batches to be pumped in future runs. 3.1. Main Model Structure Pumping run sequencing. A pumping run k∈K must be started after the completion of the preceding run (k-1). Let Ck denote the completion time of run k and Lk represent its duration. Then,

C k − Lk ≥ C k −1

∀ k ∈ K ( k > 1)

(1)

If hmax stands for the overall length of the time horizon, then Ck ” hmax ∀k∈K. Pumping run assignment. Let us define the binary variable wi,s(k) to denote that the pumping run k inserts a new batch i∈Inew or injects material to an existing batch i∈I from refinery s whenever wi,s(k) = 1. By assumption (iv), (k ) ¦ ¦ wi ,s ≤ 1

∀k ∈ K

s∈S i∈I

(2)

Size of batch injected by a pumping run. Let Qi,s(k) denote the size of batch i injected in the pipeline from an oil refinery s through the pumping run k. Hence,

Q min wi(,ks ) ≤ Qi(,ks ) ≤ Q max wi(,ks )

∀i ∈ I , s ∈ S , k ∈ K

(3)

Admissible pumping rates vbmin/vbmax limit the injection size to,

vbmin Lk ≤ ¦ ¦ Qi(,ks ) ≤ vbmax Lk s∈S i∈I

∀k ∈ K

(4)

Tracking batch size. Wi,k is the size of a batch i at time Ck . Its value is given by,

Wi ,k = Wi ,k −1 + ¦ Qi(,ks ) − ¦ Di(,kj) s∈S

j∈J

∀k ∈ K

where Di,j(k) denotes the volume transferred from batch i to depot j during run k.

(5)

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Moreover, Fi,k is the volume between the pipeline origin and the farthest extreme of batch i at time Ck . By assumption (i) it follows that,

Fi ,k − Wi ,k = Fi +1,k

∀k ∈ K , i ∈ I ; ¦ Wi , k = PipeVol

∀k ∈ K

i∈I

(6)

Pipeline material balance. The total volume of products diverted from batches in pipeline transit to output terminal tanks must be equal to the injection size, (k ) (k ) ¦ ¦ Qi ,s = ¦ ¦ Di , j

i∈I s∈S

∀k ∈ K

i∈I j∈J

(7)

Batch location constraints. The location of a flowing batch i with regards to the input terminal coordinate (τs) is controlled by,

Fi ,k −1 ≥ τ s wi(,ks ) ; Fi ,k −1 − Wi ,k −1 ≤ τ s + ( PL − τ s ) (1 − wi(,ks ) ) ∀i ∈ I , s ∈ S , k ∈ K

(8)

Feasibility constraints for diverting in-transit batches. Similarly to the single-source case, every time a batch is diverted to an output terminal j (coordinate σj) it should feature,

Fi ,k ≥ σ j xi(,kj) ; Fi ,k −1 − Wi ,k −1 ≤ σ j + ( PL − σ j ) (1 − xi(,kj) ) ∀i ∈ I , j ∈ J , k ∈ K

(9)

xi,j(k) is a binary variable denoting that the jth-terminal is reached from batch i during pumping run k (xi,j(k) = 1). Therefore, Dmin xi,j(k) ≤ Di,j(k) ≤ Dmax xi,j(k). Assigning products to batches. Let yi,p be a binary variable denoting that batch i contains product p whenever yi,p = 1. If a pre-defined batch i∈Inew does not contain any product (yi,p = 0 ∀p∈P), it will never be injected in the pipeline. On the other hand, if it is actually injected, at least one pumping run k must supply product to it. Thus, (k ) ¦ yi , p ≤ 1 ; ¦ yi , p ≤ ¦ ¦ wi ,s ≤ K ¦ yi , p

p∈P

p∈P

s∈S k∈K

p∈P

∀i ∈ I new

(10)

3.2. Objective Function The objective function includes three terms dealing with (a) energy consuming costs depending on the active terminal and the type of product pumped (CINp,s), (b) transition costs due to interface mixing (TCi), and (c) an underutilization penalty cost (ρ),

Min

z = ¦ ¦ ¦ ¦ CIN p ,s QPi (,sk,)p + ¦ TCi + ρ ( hmax − ¦ Lk ) k∈K i∈I s∈S p∈P

i∈I

(11)

k∈K

4. Results and Discussion A practical case study involving a multiple-source common carrier pipeline with two inputs (S1, S2) and three output terminals (D1, D2, D3) has been tackled (see the top of Figure 2). The line is operated on fungible mode and transports three products (A, B, C) from both the origin and the intermediate refinery, i.e. products are interchangeable. Batch injections’ sizes are restricted between 10 and 30 units, and pumping rates may vary from 0.80 to 1.20 units per hour. The time horizon is static and comprises fivedays (120 h). The optimal pipeline operational schedule shown in Figure 2 can be found in 45.3 CPU s in an Intel 2.80 GHz PC, using GAMS/CPLEX 11.0.[10] It consists of 7

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pumping runs. Runs k2, k3, k4, k7 introduce 4 new batches B6, B3, B8, B7 containing products C, C, B, A, respectively, from refineries S1, S2, S1, S2 in that order. On the other hand, runs k1, k5, k6 enlarge batches B5, B4, B8 with products A, B, B, from refineries S1, S2, S1. The pipeline time usage raises to 100 %. 0

20

S1

¨ Ö ¤

Start

Rate

[h]

[Units/h]

40

D1 B5

End

60

S2

Volume [Units]

D2

80

D3

B4

B2

B1

B2

B1

[h]

0.00 1.20 16.67 16.67 1.20 33.33

20 20

33.33 1.20 50.00 50.00 0.86 61.67

20

B4

B6

10

B5

B4

B5

B4

B6

10

61.67 1.20 86.67 86.67 1.20 111.67

B5

30

111.67 1.20 120.00

B8

B6

B5

B8

B6

B5

20 B4

10

B1

B3

20

B1

10

B1

B3

10

30

B8 B8

B2

B6

10

B7

B5 B6

10 Products

20

B4 B4

B5

30

B4 A

B

C

Figure 2. Optimal pipeline schedule for the case study

5. Conclusions A novel continuous-time formulation for the operational planning of multiple-source pipelines has been presented. The model is capable of optimally determining the sequence and size of product injections, transported on fungible mode. The tool is quite useful to help planners combine multiple nominations into a single batch, in order to reduce interface mixing costs. Further work will focus on the dynamic aspects of the multi-source pipeline scheduling problem and the input/output terminal inventory management.

References [1] Ch.J. Trench, Allegro Energy Group, AOPL, (2001) 1-20. [2] D.C. Cafaro and J. Cerdá, Comput. Chem. Eng., 32 (2008) 728-753. [3] C.A. Hane, H.D. Ratliff, Annals of Oper. Res., 57 (1) (1995) 73-101. [4] M. Sasikumar, P.R. Prakash, S.M. Patil, S. Ramani, K-Based Syst., 10 (1997) 169-175. [5] R. Rejowski, J.M. Pinto, Comput. Chem. Eng., 27 (2003) 1229-1246. [6] D.C. Cafaro and J. Cerdá, Comput. Chem. Eng., 28 (2004) 2053-2068. [7] S. Relvas, H.A. Matos, A.P.F.D Barbosa-Póvoa, J. Fialho J., A.S. Pinheiro, Ind. Eng. Chem. Res., 45 (2006) 7841-7855. [8] D. Zyngier, J.D. Kelly, COLCE, 2006, Furman, K. C., Grossmann, I. E., Eds. [9] P. Jittamai, Ph.D. Dissertation, Texas A&M University, College Station: Texas, 2004. [10] A. Brooke, D. Kendrick, A. Meeraus, R. Raman, GAMS, Washington, 2006.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

435

How a process simulator and a rule-based system contribute to virtual reality applications for process safety Xiaolei Shanga, Paul Chunga, Jeff Frya, Luca Vezzadinib & Mauro Colomboc a

Department of Computer Science, Loughborough University, Loughborough LE11 3TU, United Kingdom b Virtual Reality & Multi Media Park, Corso Lombardia 190, Turin 10149 Italy c Politecnico di Milano, Dipartimento di Chimica, Materiali e Ingegneria Chimica "G. Natta", Piazza Leonardo da Vinci 32, 20133 Milano Italy

Abstract The VIRTHUALIS project aims to develop a number of virtual reality applications for improving safety in the process industries. The applications allow human factors experts to study how operators interact with plant, and provide a safe environment in which new safety actions can be tried and tested. Safety applications are built on the SafeVR technology platform, a distributed clientserver virtual reality system. This paper describes how two external modules - a process simulator and a rule-based system - are interfaced to the platform and the benefits they provide both separately and together. The two modules communicate with the platform’s server by exchanging messages, conforming to a simple syntax. pSimProxy provides a generic interface to an external process simulator, which in turn delivers the realistic plant behaviour. It handles bidirectional data exchange with and control of the external simulator. It can be configured at run time to use whichever available mechanisms are supported by the actual process simulator that models the plant being simulated. ClipsClient is an expert or rule-based system, based on NASA’s CLIPS expert system software that can make inferences about the information contained in the messages. It consists of a set of facts, a number of rules and an inference engine. It can be provided with a number of rules that monitor how operators are running the plant, and react in useful ways to these events. The simulator notifies the server of changes in process parameters through a message. The values may be displayed, for example as gauge readings, in the virtual environment. As operators control the plant, their actions, say opening a valve, are also reported by messages via the server to the process simulation. Messages can also be read by the rule-based system, allowing it to maintain its own representation of the plant. This in turn permits automated expert reasoning on the state of the plant and the actions of its operators which can cause further message to be sent to the server. The rule-based system is therefore, a powerful mechanism for rapidly reconfiguring the application and general rules can be written that only require new facts at run-time to change the behaviour of the entire virtual environment. The message syntaxes, the system architecture and the interfacing of the external modules are described along with examples showing their individual and joint benefits. Keywords: virtual reality, plant safety, process simulation, rule-based system

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X. Shang et al.

1. Introduction Safety is of enormous importance in many industries, especially those dealing with hazardous materials like the process industries. Virtual reality is an important visualisation technique being applied in plant safety [1]. The VIRTHUALIS project aims to develop a number of virtual reality applications for improving safety in the process industries. This will allow human factors experts to study how operators interact with plant, and provide a safe environment in which new safety actions can be tried and tested. The SafeVR platform Safety applications are built on the SafeVR technology platform (itself, originally based on Delta3D [2]), a distributed client-server system which manages a realistic, immersive, interactive, multi-user, 3D representation of a process plant, including:• collision, gravity and motion models for realistic movement and navigation; • environmental conditions, time of day, weather, etc.; • 3D audio for environmental and spatially-located equipment sounds; • controls to operate plant components (pumps, valves, PID controllers etc.); • plant instrumentation (indicators and local panels etc.). A typical deployment of the SafeVR platform elements, shown in Figure 1, consists of:• a master application (server) to co-ordinate and synchronise multiple user; • one or more satellite applications (clients) that present individual, navigable views of the plant (or control room displays) to users; • external applications (clients) that provide specific functionality; an efficient network to exchange messages between the applications.

Figure 1 Architecture of the SafeVR platform

This paper describes two external applications and the messages they exchange with the server. pSimProxy is a generic interface to a process simulation, and ClipsClient is an interface to a rule-based system. Both use the Delta3D messaging mechanism and together they provide useful functionality.

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2. pSimProxy Although virtual reality provides an immersive 3D plant environment, an external process simulator provides the realistic chemical and physical behaviour of the plant. The simulation must be dynamic to respond to the operators in the virtual world. Unlike a steady-state simulation, it responds to perturbations, and can model start-ups, shutdowns and exceptional conditions. Plant owners usually have a suitable dynamic process simulation model: a survey of the industrial partners within VIRTHUALIS found several widely used simulators. To support a real-time virtual world, we identified those capable of fast, dynamic simulation, with refresh rates comparable to VR frame rates. From those, the following fairly generic set of features, were chosen for implementation:• point-based representation of physical/chemical properties of a plant; • getting, setting, polling and ramping point values; • starting, stopping, pausing and resuming the simulation software; • faster or slower than real-time simulation speeds; • switching of simulation scenario, loading and saving simulation snapshots. pSimProxy handles bidirectional data exchange with and control of the external simulator. It is configured at run time to use whichever APIs are supported by the actual process simulator being used. It read a list of points exposed by the process simulator, their data type and flow direction. Data exchange and control of pSimProxy is provided by messages, as shown in Figure 2. The messageProcessor parses incoming messages, extracting the message type, point(s) and action etc. It then calls pSimPoint and pSimControl methods which in turn invoke methods in the pSimAbstraction layer. This layer can also translate point names, mapping the SafeVR namespace to simulator point names and vice versa.

Figure 2 pSimProxy architecture

The pSimProxy provides the following functionality: • setting process variables (pipe flows, tank levels etc.) in the simulator. As users operate the virtual plant’s controls (open valves, start pumps etc.), changes are sent to the dynamic process simulator; • getting and polling of point values from the simulator, and tolerance. Point values are returned immediately or at a specified interval, if and only if the point value has changed by more than a tolerance since last reported;

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• point ramping sets a target point value and slews to it over a specified time, simulating automated plant components and PID parameter controllers; • timescale manipulation allows the user to “fast-forward” through periods of little interest or to examine other periods in “slow-motion”.

3. ClipsClient An expert or rule-based system can monitor the information contained in the messages being exchanged by the process simulator and the server, to make inferences about the state of the plant, and how operators are controlling it. ClipsClient is an interface to NASA’s CLIPS expert system shell [3]. An expert system consists of a set of facts, a number of rules and an inference engine, allowing data and knowledge about a system to be represented separately. ClipsClient’s messageProcessor parses specific messages to extract updated point values, which it translates into a new CLIPS fact. The inference engine is then invoked to process the new fact using the current fact and rule set.

4. Message types Communication, control and data flow between the master application and the external applications is implemented by six message types. Each message contains a string, composed of a number of token-value pairs as in Figure 3. This syntax is expressive, non-restrictive and easily extensible

Figure 3 Syntax diagram of message content

Figure 4 Messages exchanged by the Master application, Simulator and Rule-based System

The message types, shown in figure 4, are:• OPERATION_MESSAGE – sent by the master to all external applications whenever the user operates a plant component (e.g. opening a valve, switching off a pump etc.). The message specifies the component, a property and a new value; • VALUE_UPDATE_MESSAGE – sent by pSimProxy to the master application to report a single updated point value; • PSIM_POLL_MESSAGE – sent by the master to pSimProxy to set or change its polling behaviour (per-point intervals or tolerances); • PSIM_CONTROL_MESSAGE – sent by the master to pSimProxy to start or stop the process simulator, change the timescale, load or save point values;

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• RULE_MESSAGE – sent by the rule-based system to the master application to return any results generated by its rules; • VALUE_RELAY_MESSAGE – a VALUE_UPDATE_MESSAGE forwarded to ClipsClient, allowing it to respond.

5. Examples of process simulator & a rule-based system interaction Previous work [4] has described how CLIPS works with VIRTHUALIS applications. Several examples may help to demonstrate the contribution of the process simulator and rule-based system when used together. Nominal sequences of actions (operations by users) can be modelled as rules, with actions in parallel, in any order, or with pre-requisite actions carried out beforehand. The sequence of operator actions can be monitored by the rule-based system, and a textbased tutor mode can give immediate operator feedback, for example as a training application. Operating point values can be monitored by the rule-based system which can raise alarms, or trigger events such as gas leaks, fires or explosions. Faulty plant can be emulated: a stuck valve for example, can be created by a rule and fact. As the user tries to open the valve, the rule-based system intervenes to reset it to the ‘sticky’ maximum and the flow is realistically restricted.

6. Conclusions and future work The combination of a process simulator and rule-based system provides dynamic, realistic plant behaviour, in response to operator actions, enriching safety applications and simplifying their construction. The VIRTHUALIS project continues to foresee their role in applications for design, training, risk assessment, accident investigation, operational safety management, even optimisation, during normal, unusual and exceptional operation.

7. Acknowledgements VIRTHUALIS (www.virthualis.org) is supported financially by the European Commission. The authors are very grateful for the technical support of Invensys.

References [1] P. Cozens, J. Waters and R. Neale, A virtual reality approach to personal safety and the design of built environment facilities. The conference proceedings of the 18th ARCOM Annual Conference, Volume 2 (2003) pp 461-473. [2] www.delta3d.org [3] J. C. Giarratano & G. Riley, Expert Systems: Principals and Programming. Third Edition. PWS Publishing Company, Boston MA. USA. (1998) ISBN: 0-534-95053-1. [4] P. W. H. Chung, X. Shang, Z. Nivolianitou and J. D. Fry, Improving Process Safety Training Through the Use of VR and Knowledge-based Technologies, Proceedings of the 17th ARRTS - Advances in Risk and Reliability Technology Symposium, L Bartlett (ed), Loughborough University (April 2007) pp 394-400 ISBN 0904947629.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

441

Data Driven Tuning of State Space Control loops with unknown state information and model uncertainty. Jakob Kjøbsted Huusoma, Niels Kjølstad Poulsenb, Sten Bay Jørgensena a

CAPEC, Department of Chemical Engineering,Technical University of Denmark, Building 229, DK-2800 Lyngby, Denmark, [email protected], [email protected] b Department of Informatics and Mathematical Modelling,Technical University of Denmark, Building 321, DK-2800 Lyngby, Denmark, [email protected]

Abstract As an alternative to model reestimation and subsequent control design for state space systems in case unsatisfactory loop performance, direct tuning is investigated. Direct tuning is shown able to optimize loop performance when the control design and state observer are based on an uncertain model estimate.

Keywords: Iterative feedback tuning, LQR, Optimal Control 1. Introduction The need for optimal process operation has rendered methods for optimization of control loop parameters an active research area. Much attention has been directed in performing control oriented system identification, which implies model estimation from closed loop data [1,2]. Optimizing the parameters in a control loop is an iterative procedure since the data from one experiment will depend on the current controller, and repeated iteration is necessary for the loop performance to converge to a minimum. An alternative would be a direct data driven approach to tuning without utilizing a model estimate. Data driven tuning methods have mainly been reported for systems given in transfer function form. The most established method is Iterative Feedback Tuning [3]. This algorithm optimizes the closed loop performance by adjusting the control parameters through a gradient based scheme. The gradient of the cost function is replaced by an unbiased estimate evaluated from special closed loop experiments. Direct tuning is often computationally less demanding than identification and model based control design. Direct tuning methods can be used when insufficient knowledge of the model structure limits nominal performance, where the system is tuned based on the certainty equivalence principle. This paper intends to investigate the use of the direct tuning method, Iterative Feedback Tuning, for optimization of the feedback and the state observer gains for a control loop based on a state space system description. Based on the certainty equivalence principle, analytical solutions for optimal values of these two gains exist. This renders the loop performance sensitive to model errors and bias. Direct controller tuning may serve as an interesting alternative, when fine tuning a control loop or when a degrading loop performance is observed.

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This paper is organized as follows. In the following section a short introduction to the system and control loop description is given. Section 3 discusses optimal control and tuning. In Section 4 an illustrative simulation example is given before final conclusions are drawn.

2. The state space control loop Given the following linear, discrete time, single input/single output, time-invariant system description:

xt +1 = Axt + But + etP ,

etp ∈ N (0, PeP )

where xt

(1)

etm ∈ N (0, σ e2m )

yt = Cxt + etm ,

is the system states, ut

is the manipulated variable and yt P t represents

measurements at discrete time instants. e

is the m

process noise and et is

measurement noise. The cross correlation between these types of noise will be assumed to be zero. It is desired to control this system using the feedback law:

ut = − Lxt + Mrt

(2)

where L is a constant feedback gain matrix and M is a controller gain for the reference signal. Since the exact value of the states are not known, an observer is used to generate the state estimates used in the control law based on measurements of the process output and a process model. The observer has the form of the predictive Kalman filter with the constant gain matrix K , assuming stationary conditions. ∧

∧ ∧

∧

∧ ∧

x t +1 t = A x t t −1 + B ut + K ( yt − C x t t −1 )

(3)

The structure of the state space feedback loop consisting of equation (1) and (3) is shown in Figure 1. In order to have a static gain from the reference to the estimated output equal to one, the following requirements can be derived ∧

∧

∧

∧

M = [C ( I − A+ B L)−1 B ]−1

(4) ∧

Introducing the state estimation error: x t = x t − x t , provides a convenient description with a more clear distinction between feedback control and state estimation dynamics [4]. If the system (1) is stabilizable and detectable a set {L, K } exists which renders the system stable [5]. Hence if optimal values for the feedback and Kalman filter gains are used stability is guaranteed.

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Figure 1. Block diagram of the closed loop state space system with state observer

3. Optimal control and tuning Optimal values for both the observer gain K and the feedback gain L exist and have known analytical solutions [6]. The optimal, stationary value for the gain matrix in the Kalman filter can be evaluated based on the process model and information of the noise intensity, from an algebraic Riccati equation. The optimal value for the controller gain will depend on the optimization criterion. In this paper the control design will minimize the value of a cost function for the loop performance for a single input/single output system:

F ( y, u ) =

1 2N

N

¦y

2 t

+ λ ut2

(5)

t =1

where λ determines the weighting between the penalty on the output and the control. For optimal tracking the output is replaced by the tracking error in the cost function. The optimal Linear Quadratic Gaussian controller (LQG) produces an optimal feedback gain which minimizes the quadratic cost function

1 FLQG ( y, u ) = 2N

N

∧T

¦x

t

∧

QR x t + λ ut2

(6)

t =1

using the linear system description in (3) with Gaussian noise, and assuming the horizon in the criterion approaches infinity. As for the observer gain the solution is given by an algebraic Riccati equation. In case

QR = C T C the cost function (6) is equivalent to (5).

In absence of an accurate process model, direct tuning of the closed loop can provide the optimal control parameters. It has been shown in [7] that Iterative Feedback Tuning can be applied to a state space control system with state observer. The iterative procedure converges towards the optimal values for the two gains, when the observer is constructed from full model information. This result has more academic than practical

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interest since analytical solutions are known when a model is available. It is on the other hand interesting to investigate the potential for using direct tuning in case of model uncertainty. Parametric model uncertainty will give the following equations for state and the estimation error

xt +1 = ( A − BL) xt + B(L x t + Mrt ) + etP ∧

∧

x t +1 = ( A− K C ) x t − Ketm + etP + Δ ∧

(7)

∧

∧

Δ = [( ǹ − ǹ) − K (C − C )] xt + ( B − B )[ Mrt − L( xt − x t )] Only if the true process and the model estimate are equivalent will the term Δ be zero. In this case the optimal closed loop performance can be achieved by solving the Riccati equations for the two gains. In case of parametric uncertainty, a certainty equivalence control design will not produce optimal closed loop performance. Hence either model re-estimation with a subsequent update of the feedback and observer gain or direct tuning can be used for optimization. The latter is illustrated by a simple numerical example.

4. Case study In order to illustrate the potential of using direct tuning in form of the Iterative Feedback Tuning method on a discrete time, state space system with state observer, a first order system, sampled every time unit is investigated:

xt +1 = 0.98 xt + 0.02ut + etP , yt = 1xt + etm ,

etP ∈ N (0,12 )

(8)

etm ∈ N (0, 0.012 )

In the optimization criterion λ = 0.001 is used. In case only the noise variance is unknown or erroneous it is the only the observer gain, Ȁ , which is not optimal. The parameters used to calculate the feedback gain and the other parameters in the observer in (3) are correct. The term Δ in (7) will be zero. Optimal performance is therefore achieved if the direct tuning converges to the value, Ȁ , which is the optimal observer gain based on full process insight and noise characteristics. In case of erroneous parameters in Ǻ the calculation of the feedback gain, L , will be affected and Δ , which is part of the state estimation error, will no longer be zero. Hence the LQR

LQR

feedback gain which produce the minimum for the cost function is not, L , which is based on the true system parameters. This is verified by figure 2 which show the performance cost as function of the feedback gain. Figure 3 show results of direct tuning for the two scenarios. It is seen that the tuning converge in few iterations. Initially equal values of 1 where use for the two noise variances in calculation of Ȁ0 . The estimate for Ǻ used to find L0 was twice the true value. Figure 3 also show that the LQR

optimal feedback gain is different from L

as shown on figure 2.

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Figure 2. Performance cost as function of the feedback gain. The full line indicate full process knowledge and the dashed line is when there are erroneous parameters in the B matrix

Figure 3. Result of ten iteration of direct tuning. To the left values of the performance cost and the tuned observer gain is given when there is erroneous noise information. To the right values of the performance cost and the tuned feedback gain is given when the B matrix is erroneous.

In the case where errors occur in the parameters in either the C or A matrix, the certainty equivalence design of both gains will be affected. Hence it is necessary to tune both gains simultaneously. This is performed and the results are given in figure 4. The ∧

∧

results in Figure 4 were produced by using C = 0.9 and A = 0.9 respectively. The results show that these gains converge to different values of the gains than calculated based on full process knowledge since the erroneous parameters are used in the observer. It is not clear from the figures that the performance is improved through the iterations. Evaluation of the cost function using long simulation time in order to improve statistics provides some more convincing results. It is seen that the cost function is F ( L0, K0 ) = 1.5075 and F ( L0, K0 ) = 1.5422 when respectively the estimate for C or A is wrong. In both cases the performance cost converges to 1.5049 which is the same as the optimal value when the model is equivalent to the true system. Hence for this case the direct tuning completely compensates for the error in the model parameters and produces a loop with optimal performance.

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Figure 4. Result of ten iteration of direct tuning of both the feedback and the observer gain. To the left the results are given when C is erroneous and to the right for an erroneous A matrix

5. Conclusions Direct tuning in form of Iterative Feedback Tuning has be use to adjust the parameters in the feedback and observer gains in a state space designed loop in order to minimize a performance cost. The achieved closed loop performance after tuning was improved compared to the nominal performance before tuning when the observer and the feedback controller were designed based on a model with parametric uncertainty.

6. References [1] R. J. P. Schrama, Accurate identification for control: The necessity of an iterative scheme. IEEE Transactions on automatic control, vol. 37, (7), pp. 991-994, 1992. [2] M. Gevers, A decade of progress in iterative process control design: from theory to practice, Journal of process control, vol. 12,(4), pp. 519-531, 2002. [3] H. Hjalmarsson, M. Gevers, S. Gunnarsson, and O. Lequin, Iterative feedback tuning: Theory and applications, IEEE Control Systems Magazine, vol. 18, (4), pp. 26-41, 1998. [4] K. J. Åström, Introduction to Stochastic Control Theory, Academic Press, 1970. [5] H. Kwakernaak and R. Sivan, Linear Optimal Control Systems. John Wiley & Sons,1972. [6] B. D. O. Anderson and J. B. Moore, Optimal Control. Linear Quadratic Methods, Prentice-Hall Int. Ed., 1989. [7] J. K. Huusom, N. K. Poulsen and S. B. Jørgensen, Data Driven Tuning of State Space Controllers with Observers. Submited for ECC 2009

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Effect of Multiple Steady-States on Operation Strategy and Control Structure for a Heat Integrated Distillation Column (HIDiC) Lin WANG, Manabu KANO, Shinji HASEBE Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan. E-mail:[email protected]

Abstract The fact that a heat integrated distillation column (HIDiC) may have multiple steadystates and unstable operating regions has been recently recognized. Practically and operationally, the existence of an unstable operating region would not be preferable, because it may cause abrupt changes in operating conditions. This paper shows two kinds of possible approaches to avoiding the multiplicity of HIDiC. The first approach is related to compressor operation strategies in LV control structure. A detailed comparison of three strategies shows that the strategy of constant compressor rotation speed is beneficial to the stable operation without multiple steady-states. The second approach is to adopt the DV or LB control structure. With one of these two configurations, there is no multiplicity in operating regions and stable operation of HIDiC can be realized. Keywords: Heat Integrated Distillation Column (HIDiC), Multiple Steady-States, Compressor, Control Structure.

1. Introduction A heat integrated distillation column (HIDiC) is an energy-efficient distillation column that has the potential for drastically reducing energy consumption [1]. Moreover, it has been recently recognized that HIDiC may have multiple steady-states and unstable operating regions [2]. From a practical and operational viewpoint, the existence of an unstable operating region would not be preferable, because it may cause abrupt changes in operating conditions. This work is based on the study of multiple steady-states in HIDiC [2] and aims to avoid unstable steady-states in order to realize stable operation. First, a detailed compressor model that can explain the nature of multiple steady-states of HIDiC is developed. Then, three compressor operation strategies are compared to clarify the influence of the multiple steady-states on operation of HIDiC. Finally, the different control structures are investigated for the existence of multiple steady-states. The analysis results are validated through simulations.

2. Dynamic model A schematic diagram of HIDiC is shown in Fig. 1. The rectifying section and the stripping section are in physical contact. A compressor is used to keep pressure in the rectifying section higher than that in the stripping section to enhance the heat transfer from the rectifying section to the stripping section.

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448

LC

Reflux drum xD

PC

C

VT

Pin

LD

Pf

12

12

F =27

L

R

Qh

S

Qc Pout

1 V LC

xB Reboiler

B

C

Qr

Fig.1 Schematic diagram of HIDiC Dynamic column model A dynamic tray column simulator was developed by using gPROMS®. In the simulation model of the rectifying section and the stripping section, equations of material balance, equilibrium, and fraction summation are taken into account. The heat which is transferred from the rectifying section to the stripping section is added into the energy balance equations. The Francis weir equation is used to calculate the liquid flow rate, and the vapor flow rate is assumed to be proportional to the square root of pressure difference on the tray. The other assumptions include that vapor holdup is negligible and liquid and vapor on each tray are perfectly mixed. The main design and operation parameters for a benzene-toluene (0.5/0.5) column are given in Table 1. Table 1. Design and operation data of HIDiC

No. of trays (rec. section / str. section) Tray diameter of rectifying section (m) Weir height of the tray (mm) Heat transfer coefficient U (J / s m2 K) Feed flow rate (mol/s)

12 / 12 1.2 50 700 27

Compressor model Compared to a conventional distillation column (CDiC), HIDiC is prone to multiplicity, which is mainly caused by the use of a compressor [2]. Therefore, a compressor model is very important. A centrifugal compressor model of HIDiC is described by the relationship between polytropic head (hp), inlet/outlet pressure (Pin/Pout), and temperature through Euler’s pump equation [3] and the following equations:

Qc = VM ∗

hp

η

= τ ∗ ωc

hp ∗ ωd 2 = hpd ∗ ωc 2

(1)

(hpd = f (VM ), ωd = cons.)

(2)

Effect of Multiple Steady-States on Operation Strategy and Control Structure for HIDiC

449

Here Qc (J/s) is the power delivered to the vapor, VM (kg/s) is the inlet mass flow rate, IJ is compressor torque and Ȧc is the rotation speed.

3. Instability conditions and compressor operation The HIDiC instability condition is equivalent to Eq. (3) [2].

(ΔH T ) 2

∂L ∂ΔH = ∂D V ∂x

∂xB ∂ΔH ΔH TV − ∂x x B ∂D V

∂ΔH ∂Qc ∂xB ΔH T − + ∂x ∂x x B ∂D V

xT

xT

∂xT ΔH1V ∂D V

∂xT Qc − (ΔH T ) 2 > 0 ∂D V

(3)

On the right side of Eq. (3), the conditions ˜xi/˜D|V and ˜ǻH/˜x are always negative [4]. The analyses of multiple steady-states have mainly focused on the third and fourth terms, which are related to the compressor heat input Qc. Here, the value of Qc depends on the operation strategies of the compressor. In this work, two operation strategies are first discussed: OS1: constant inlet pressure Pin. OS2: constant pressure difference Pout – Pin. In OS1 and OS2, the compressor inlet pressure (Pin) or the pressure difference (Pout Pin) is usually controlled by manipulating compressor rotation speed Ȧc. Multiple steady-states in different compressor operation strategies The simulation results of OS1 and OS2 show that the slope ˜Qc/˜x|xB is always negative and very steep in both strategies. Therefore, the third term on the right side of Eq. (3) is positive large and unstable operating points easily appear. Fig. 2 shows the relationship between product composition and reflux flow rate in OS1.

Fig. 2 Relationship between product composition and reflux flow rate Multiple steady-states and manual operation For the research work on manual operation of distillation, the column is operated in the sense that only the reboiler and condenser levels and column pressure are under feedback control while an operator adjusts the remaining two independent inputs to keep the product composition close to their specified values [5]. Under these circumstances, when the feed flow rate F changes to some extent during operation, it causes the HIDiC operation to change from the initial open-loop stable condition to the open-loop unstable condition. The initial operating condition of HIDiC is shown in Table 2.

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450 Table 2. Initial operating data of HIDiC L 22.2 mol/s

D 13.5 mol/s

V 27.9 mol/s

*constant

B 13.5 mol/s

xB 0.001

xD 0.999

*constant

In manual operation, Fig. 3 shows the response of Qc when feed flow rate changes along 27 ĺ 26.4 ĺ 27 mol/s. When the feed flow rate decreases, the compressor heat duty Qc increases in a relatively short time from t1=31.2 h to t2=32 h. The abrupt change of heat duty pushes the HIDiC operation to change from the unstable steadystate to another stable steady-state. Therefore, when the feed flow rate increases to 27 mol/s, the compressor heat duty cannot go back to its original value. The above analyses indicate that unstable steady-states depend on how to operate the compressor. 800 800

Qcomp (KJ/s)

Qc (KJ/s)

700 600 600

Qc

500

400 400

t1 t2

300

200 200 100

000 0

F=27 10 10

20 20

F=27

F=26.4 30 30

40 50 40 50 Time (hr) Time (hr)

60 60

70 70

80 80

90 90

Fig. 3 Compressor heat duty responses in OS1

4. Non multiple steady-states of HIDiC Non multiple steady-states and compressor operation In OS1, under the operating condition in Table 2, when the feed flow rate changes from 27ĺ26.4 mol/s, the dynamics of HIDiC is as follows: the compressor vapor flow increases, then the manipulated variable of the compressor (rotation speed Ȧc) changes considerably to keep Pin constant. The heat transfer in HIDiC increases from the rectifying section to the stripping section. Such phenomena make the compressor vapor flow increase further. It seems like a positive feedback which causes open-loop instability in HIDiC operation. During this period, from Eqs. (1) and (2), the value of Qc is significantly influenced by the ratio (Ȧc /Ȧd)2 . From the calculation results, this ratio increases 4 times its original value. For this reason, the constant rotation speed (Ȧc) strategy, which is hereafter called OS3, is more reasonable. If we can set a constant ratio (Ȧc /Ȧd), then the Qc may not change more and will not increase excessively. Simulation results validate the above analysis. In practice, HIDiC must be operated in auto-mode. Both OS1 and OS2 are suitable for compressor operation. However, when the control of product composition does not work, manual operation is inevitable. In such a case, OS3 is a good selection for compressor operation. Operation with other configurations From Fig.2, a negative slop of ˜xi/˜L|V corresponds to unstable operating points in the LV configuration. However, the ˜xi/˜D|V value is essentially negative [4]. This implies that the opposite case as compared to the LV configuration exists. Thus, instability in a given operating region with the LV configuration is avoided by using the DV configuration instead. Fig. 4 shows the relationship of product composition and

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distillate in the DV structure with constant feed flow rate. The operating conditions are the same as the LV structure. The suitability of the LB configuration can be explained in the same way as DV. The value of ˜xi/˜B|L in the reboiler is always positive, that is, there is a stability condition ˜xi/˜B|L > 0 with LB configuration. For HIDiC, both DV and LB control structures can realize stable operation whether in auto-mode or in manual mode.

Fig. 4 Relationship between product composition and distillate in DV

5. Conclusion HIDiC may have multiple steady-states, i.e., unstable operating points. This work shows two kinds of possible approaches to avoiding such multiplicity. The first approach is related to compressor operation strategies in the common LV control structure. The theoretical analysis and simulation results show that constant compressor rotation speed is beneficial to the stable operation without multiple steady-states. The second approach is based on the consideration that the multiple steady-states depend on the choice of configurations. When the DV or LB control structure is used, there is no multiplicity in operating regions, hence, the stable operation of HIDiC can be realized.

References [1] [2] [3] [4] [5]

T. Takamatsu, M.Nakaiwa et al., Kagaku Kogaku Ronbunshu, 22(1996) 985 M. Kano, T. Fukushima, H. Makita, S. Hasebe, J. Chem. Eng. Japan, 10(2007) 824 W. Jiang, J. Khan, R.A. Dougal, J. of Power Sources, 158(2006) 1333 E.W. Jacobsen and S. Skogestad, AIChE J., 4(1991) 499 E.W. Jacobsen and S. Skogestad, Ind. Eng. Chem. Res., 12(1995) 4395

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Modeling and Simulation of Gas Pipeline Network for Operational and Infrastructural Decisions Saulat Lonea, Naveed Ramzanb, Anwar Rashid Saleemib and Iftikhar A.Karimic a

Sui Northern Gas PipeLine Pakistan, Project Engineering Department, Gas house 21 Kashmir Road Lahore, Pakistan b University of Enginering and Technology, Department of Chemical Engineering, Lahore (54890) Pakistan, Pakistan, Email: [email protected] c National University of Singapore, Department of Chemical and Biomolecular Engineering, Blk E5, 4 Engineering Drive 4, #02-12, Singapore 117576, Singapore

Abstract Sui Northern Gas Pipelines Limited (SNGPL), the largest integrated gas company in Pakistan, operates the transmission system that has an annual throughput of around 575 BSCF (16.3 bscm) comprising over 3700 miles (6000 km).Thus, SNGPL needs a medium to long-term operational strategy to effectively cater for the existing and projected gas demand. In this article, the operational strategy developed on the basis of results from steady state and transient simulations of the entire gas network on a hydraulic simulator is presented. This paper also analyses various ways in which the input gas supply/demand data to the hydraulic simulator is utilized to predict the optimized operation of the gas pipeline network and infrastructure expansion requirements. The main objective is to identify infrastructure development priorities with a focus on optimizing the flow patterns from various gas fields to the demand centers utilizing the existing infrastructure, while taking into account the characteristics of the gas in individual fields; optimizing incremental expansion of the existing gas transport infrastructure to save on transmission investments. Furthermore, various options for minimizing the fuel consumption throughout the transmission network without compromising the demands from potential consumers are identified. The study furnishes SNGPL with the information required to make critical decisions for the operation of existing pipeline network and also helps in developing their future strategy of infrastructure development. Keywords: Operational Strategy, Gas transmission networks, Hydraulic simulation, Operation optimization

1. Introduction The primary objective of SNGPL is the transmission of natural gas to markets located in the Punjab and North-West Frontier Province (NWFP) provinces of Pakistan. The company manages 24 gas fields connected through an extensive pipeline network (6135 km long) that stretches all the way from Sui to Peshawar. For operational purposes, the pipeline network is divided into different segments (or 'legs' as the utility terms them). Table 1 gives the details of the major legs in the Company’s transmission system.

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454 Table 1: SNGPL Gas Transmission Network Details

Segment Name Leg A (Sui-Faisalabad) Leg B (Faisalabad – Jehlum) Leg C (Faisalabad – Peshawar – Mardan) Leg N Qadirpur Rawan – Lahore

Length Nominal Dia (miles) (in) 389

12 – 36

250

8 – 24

325

6 – 30

180

16 – 24

Compressor Stations 6 Numbers Total hp (ISO): 162,900 Bhp 1 Number Total hp (ISO): 6,000 Bhp 3 Numbers Total hp (ISO): 17,000 Bhp -

For planning purpose and for an authentic recommendation of augmentation in pipeline network, the future unconstrained gas demand figures (for the FY2006FY2025) for residential, commercial, fertilizer, cement, general industry, power and transport sector , prepared by Company’s Sales Department were selected for baseline study. Seasonal variation in gas demand was considered for the power, residential, and commercial sectors. Gas demand for the industrial sector was assumed to remain constant throughout the year. Seasonality analysis was performed for planning the network for average summer, average winter and peak winter days. To meet the seasonal swings, average annual forecasts of gross demand was translated from yearly to monthly basis for the FY2010, FY2015 and FY2020 periods. In addition to the gas demands, the list of fields supplying natural gas to the Company was obtained and their locations were identified on the network before building the hydraulic model. The gas calorific value as well as the P-90 (Expected) and P-50 (anticipated) production profiles were taken from each gas producers, and normalized on the basis of 950 Btu/scf, through to 2025. With the identification of the supply sources to the network, the P-50 supply rates were made available for immediate transfer to the pipeline modeling software. An overall gas supply/demand balance was determined based upon the average annual supply and demand rates for the Company’s transmission network. 2. Development of Hydraulic Model A state-of-the-art hydraulic simulator, PipelineStudio® version 3.0 was used to model and simulate the SNGPL pipeline system. PipelineStudio® is a hydraulic simulation package by Energy Solutions International that solves for pressures, flows and temperatures in simple or complex pipeline networks in steady as well as in transient states. In the hydraulic simulator, the entire pipeline network of the company was constructed along with all the compressor stations and supply demand points. The important input parameters includes all inflows and outflows, pipeline lengths, diameters, wall thickness, elevations, type of pipeline coating and its thicknesses, ambient temperatures for summer/winter and composition of natural gas of all gas producers. To adequately model the

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hydraulics of the networks, the demand projections were then further developed on a region, sector and node basis. 2.1 Simulation Methodology The simulation methodology was divided into following three stages: i. Calibration of existing pipeline network; steady state/transient state ii. Identification of bottlenecks and optimization of existing pipeline network iii. Network expansion studies based on forecasted supply/demand scenario 2.2.1. Calibration of existing pipeline network

After the construction of Company’s pipeline and compression network in the hydraulic simulator, the network was then calibrated by conducting hydraulic steady-state analysis to verify the operating capacities and operating scenarios. The model was calibrated for peak winter, average winter and average summer days. Panhandle-B equation and American Gas Association (AGA) equations were used for the best fit of data. Steady state simulations were carried out for the flow rate corresponding to the 24 hour average demand at each delivery point. Using the Steady State base model, transient simulations were carried out using the 24-hour demand profiles of all supply and delivery points. Here the 24-hour data were repeated for 3 successive 24-hour periods to give a 72-hour transient simulation in order to eliminate the effects of imbalances. 2.2.2. Identification of bottlenecks and optimization of existing pipeline network

After the calibration of the existing pipeline network, the results were examined for following restrictions or bottlenecks in the network: • compressor stations at, or approaching, their maximum installed power; • high gas velocity (> 10 m/s) leading to high pressure losses in the pipeline and/or excessive compressor power consumption; • inability to meet minimum pressure requirements to customers; and • low pressure at compressor suctions, again causing excessive compressor power consumption. The required necessary network enhancements were developed to remove these restrictions. Such network enhancements included: • increasing installed compression power at one or more stations; • looping existing pipelines or sections of the pipeline; and • a combination of both these enhancements. The installation of each network enhancement was also reviewed for its ability to contribute to the network’s transportation capability for future years. 2.2.3. Network expansion studies based on forecasted supply/demand scenarios

For each supply/demand scenario, the previous network was used as the basis to provide a platform on which to develop the necessary expansions to handle the increased loads. With the increased load and corresponding supply scenario, the network was inspected for pressure and flow (velocity) failures. New pipelines (new routes) and pipeline looping were then introduced to resolve the failures. Required compressor power was calculated and adjusted in all cases. For

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analysis of the expansion options, it was assumed that, once installed, compressor units would not be moved within the networks to cover shortfalls elsewhere in subsequent years. 2.3. Results & Discussions 2.3.1. Calibration

For the purposes of calibration it is necessary to minimize the errors against the pressure/flow measurements and the temperature measurements. For the former, the Panhandle ‘B’ transmission efficiency was varied to best match the measured pressures and flows and for the model conversion to use the AGA friction factor equation, the pipe wall roughness was varied. To achieve a balance against the measured temperatures, the ambient (ground) temperatures and overall heat transfer coefficient values were then adjusted. A deviation in the 24 hours simulated pressure profiles is shown in Fig-1. However, the results achieved were considered satisfactory in order to freeze the calibration models. All other studies were then conducted using these base models with the AGA friction factor equation.

Figure-1: Deviation between actual and simulated pressures in transient state (Compressor upstream pressures and intermediate pressure measurement facilities)

2.3.2. Identification of Bottlenecks and optimization of existing pipeline network

The peak winter case was used to identify all possible system bottlenecks in the transmission system. This case was considered as it represents the highest demand and throughput placed on the transmission network under its current operating practice. It was observed that the velocities at upstream of compressor stations were below 30 ft/sec (typically 20-24 ft/sec) and do not constitute as bottlenecks under the current flow conditions. However, with the increase in throughput capacity, these sections may become bottlenecks in the future. Velocities above 30 ft/sec were generally observed at the network extremities during peak demand hours. This issue was addressed in the optimization of the network. As a part of validation and optimization of the existing network, one objective was to optimize the network in terms of compressor fuel consumption across the entire company’s network. For this a new approach was developed by strengthening Leg-N. It was proposed, to shift a major portion of the gas from Leg-A to Leg-N at Qadirpur Rawan. By strengthening Leg-N, the gas which

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457

was arriving at the respective destinations after compression and recompression at AC7, AC8 and BC1 compressor stations, would arrive at the destinations through Leg-N without any compression. Steady state and transient simulations showed significant decrease in horsepower requirements (Table-2) of above mentioned compressor stations as well as addressed the high velocities problems at network extremities. In order to strengthen Leg-N, it was proposed to lay a 36-inch diameter pipeline and to uplift the existing 24-inch diameter pipeline from AV29 to Sahiwal. The uplifted 24-inch diameter pipeline was proposed to be relayed from Sahiwal to Lahore in parallel to existing 16 inch and 18 inch diameter pipelines. In addition to pipeline two compressor units were also proposed at AC-6 (Multan) compressor station. Compressor Station AC-0 - 3 units AC-1X-S - 5 units AC-1X-Q - 5 units AC-4 - 8 units AC-6 - 5 units AC-8 - 10 units AC-7 - 5 units BC-1 - 6 units NC-1 - 0 units CC-1 - 7 units CC-3 - 7 units FC-1 - 3 units Per Day Total Annual Total (MMCF)

After Optimization Winter Summer 2.01 2.18 4.23 3.60 5.47 5.30 6.04 5.60 4.23 5.46 1.25 2.39 1.27 0.37 0.33 24.87 24.86

Existing Winter Summer 1.89 1.36 4.87 4.63 3.53 2.81 6.72 5.62 4.57 2.70 4.13 1.84 3.91 1.49 1.91 1.05 1.91 2.08 0.40 35.92

0.17 0.16 0.52 22.36

Excess/(Saving) Winter Summer (0.12) 0.82 (0.64) (1.03) 1.94 2.49 (0.68) (0.02) (0.34) 2.76 (2.88) 0.55 (2.64) (1.49) (1.91) (1.05) 0.00 0.00 (1.91) (0.17) (2.08) (0.16) (0.03) (0.19) (11.05) 2.50 (306.87)

Table 2: Results showing reduction in compression fuel requirements after optimization (All figures in million standard cubic feet per day – mmcfd)

3. Future expansion studies For each supply/demand scenario, the previous network was used as the basis to provide a platform on which to develop the necessary expansions to handle the increased loads. For analysis of the expansion options, it was assumed that, once installed, compressor units would not be moved within the networks to cover shortfalls elsewhere in subsequent years. Some of the future expansion routings are described below: • from Bhong along the Indus Valley (west bank) to Kot Addu and Multan. • from Multan (Compressor Station AC-6) along the Jhelum Valley (west bank) to compressor station CC-3 (Galli Jagir) on Leg-C. • from Bhong to Faisalabad paralleling the present Leg-A. However, the new line has been considered as separate transmission line dropping off load at

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compressor stations AC-6, AC-7 and AC-8 that is then distributed using the existing system. Parts of, or all, these proposed routings would parallel the existing main transmission section, Leg-A. For these sections, a minimum pipeline diameter of 48-inch was adopted to minimize the future looping. The line would also operate up to 1380 psig. This would enable the pipeline to retain Class 600 fittings, but might require Class 900 within the compressor stations. 4. Conclusions By strengthening Leg-N, steady state and transient simulation results show a major cut in internal fuel consumption and operating costs. Moreover two systems, i.e., compression and pipeline based will be available to provide extra capacity from AV29 to Lahore. The results of the hydraulic calculations in terms of the incremental infrastructure requirements (i.e. pipeline upgrading, new pipelines, additional compression, and storage) formed the basis for the economic and financial evaluation. From these routing cases, a number of conclusions were drawn. • Company can make infrastructural decisions more easily for the optimized operation of transmission network. However, there is little to choose between the different Company routing options proposed. More detailed studies and cost analyses would be required to evaluate these options. • The different routings should be actively studied for the years beyond 2014. Up to this time, the additional imports could be handled by upgrades / additional looping to the Company’s network. After this time, new transmission lines would be required north of Bhong / Multan. • A further step of this project could be achieved by connecting this techno economic model with the real time SCADA system of the company for more precise optimization of the transmission system. 5. Acknowledgements The authors gratefully acknowledge the support of Sui Northern Gas Pipelines Limited. References [1]. Pakistan Natural Gas Supply and Demand Analysis. Prepared by Sui Northern Gas Pipelines Limited, 2006 [2]. Utilization of Gas from New Discoveries. Prepared by HBP for Sui Northern Gas Pipelines Ltd. (SNGPL) and Sui Southern Gas Company Ltd. (SSGCL), 2001 [3]. SNGPL Average-Day Unconstrained Gas Sales Projections from 2003-04 to 2024-25. Prepared by SNGPL for the Director General Gas, 2006 [4]. Saulat R. Lone, Richard Spiers, Gas Transmission Development Strategy – a modeling approach, 2006, Pipeline Simulation Interest Group

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Modeling of MSMPR crystallizer dynamics – time series prediction by neural network Krzysztof Piotrowski,a Andrzej Matynia,b Małgorzata GoĨliĔskac a

Department of Chemical & Process Engineering, Silesian University of Technology, ks. M. Strzody 7, 44-100 Gliwice, Poland, E-mail: [email protected] b Faculty of Chemistry, Wrocław University of Technology, WybrzeĪe WyspiaĔskiego 27, 50-370 Wrocław, Poland, E-mail: [email protected] c Faculty of Chemistry, Silesian University of Technology, ks. M. Strzody 7, 44-100 Gliwice, Poland

Abstract Mass crystallization process usually produces difficult for modeling oscillations of process parameters of diversified amplitude and period. For the simulation of dynamic behavior of MSMPR crystallizer in various technological conditions an artificial neural network specialized in time series prediction was originally used. The Monte Carlo simulations provided numerical data matrixes corresponded to stable and unstable process behavior, which were directly used for the neural network training and testing. Artificial neural network structures designed for both cumulative and individual parameter predictions were tested and verified in respect of their prediction ability in one-step, medium-term and long-term prognosis of the mass crystallization process dynamics. Keywords: neural network, time series modeling, mass crystallization, dynamic behavior, oscillations.

1. Introduction Mass crystallization usually produces difficult for modeling oscillations of process parameters of diversified amplitude and period. Some possible factors responsible for this cyclic behaviour should be traced and dumped or eliminated (Rawlings et al., 1993). Many mathematical approaches were adopted to identify and model this behavior. Kind and Nieken (1995) carried out dynamic simulation of crystal size distribution formed during continuous mass crystallization process with various fines removal configurations. Complex influence of many technological parameters on the stability of crystallizer’s work was reported, e.g. sensitivity of the process towards intrinsic oscillations. The model equations were solved by the method of characteristics. Under selected conditions the simulation procedure was very sensitive to numerical errors, e.g. adaptation of computational mesh size after each time step was necessary. Meadhra and van Rosmalen (1996) investigated the difference in dynamic behaviour of mass crystallization process in various scales. Their model was based on differential equation of population balance with the kinetic expressions for growth, attrition and secondary nucleation. Sheikhzadeh et al. (2008) described the dynamic optimal control methodology related to a seeded, anti-solvent semi-batch crystallization processes, based on on-line estimation of the nucleation and growth rates, as well as on the selected moments of size distribution of paracetamol crystals in isopropanol-water solutions. The crystallization model proposed, coupling population and mass balances,

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was solved using the finite difference method. Eek et al. (1996) simulated behaviour of an open-loop mass crystallization process with product classification. On the basis of dynamic controllability analysis a multiloop control structure was proposed. Neumann et al. (1999) studied the predictive capability of mechanistic model framework by comparing the simulated data concerning dynamic behaviour of median crystal size with the its experimental time profiles, including unstable oscillations during the start– up period. Kulikov et al. (2005) demonstrated original concept of sequential modular strategy for the dynamic simulation of a complex multistage process with the use of individual sub-process flowsheets representing different unit operations including mass crystallization. Various types of software (HYSYS, Parsival, gPROMS) were applied in integration platform CHEOPS. Coupling of fluid dynamics subproblem and mass crystallization subproblem for the detailed prediction of process dynamics was raised by the authors in (Kulikov et al., 2006). Only Rohani et al. (1999) developed some concept of control of a continuous cooling crystallization process suggesting application of neural network in a combined structure of a non-linear model predictive control unit.

2. Problem statement Understanding the nature of mass crystallization partial processes and their interdependencies leads to very complex nonlinear models based on multiparameter correlations. Their reliability and computational requirements depend on the level of simplifying assumptions. Necessity for fast, reliable and precise enough modeling, not limited with a set of simplifications is, however, observed. One of the modeling tools, sufficient precise and not requiring detailed information about the system under study are artificial neural networks. The possibility of time series projection by artificial neural network was thus first time used by the authors to the problem of correct prognosis of the complex dynamics of mass crystallization process in various technological conditions. Such alternative approach can be effectively used in many technological and design applications concerning mass crystallization processes since only some archival data set is necessary to identify the repeatable patterns. This procedure can be applied without any prior knowledge of the intrinsic system structure and its dynamic characteristics. The presented study focused on identification of influence of artificial neural network structure and the required number of time steps ahead (one-step, medium-term and long-term predictions) on the correctness and reliability of time series projection.

3. Simulations 3.1 Methodology Time series prediction by artificial neural network was used for the simulation of dynamic behavior of MSMPR (Mixed Suspension Mixed Product Removal) crystallizer. The network tests were preceded by preparation of some reference data. Numerical procedure based on Monte Carlo algorithm generated set of relatively large data matrixes corresponded to both stable and unstable process behavior. The original Monte Carlo algorithm, based on the strict coupling of mass, energy and population balances with the appropriate kinetic equations of growth and nucleation was used (Piotrowski et al., 2005). Each row of the resulting output-data matrix corresponded to three-element vector composed of the following parameter values: number of crystals in a computational working volume (0,1–1 mm3), suspension density and working supersaturation. Each time step (thus each row of matrix) corresponded to 20 s of real time. These matrixes of numerical data containing hidden information about process

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dynamics in the diversified technological conditions were directly used for the neural network training and testing. Neural network structures of various topologies, transfer functions, training algorithms and learning strategies, designed for cumulative and individual parameter predictions, respectively, were tested and verified (GoĨliĔska, 2008) in respect to their reproduction capabilities in one-step, medium-term and longterm projections of the process parameter oscillations. STATISTICA 7.1 Neural Networks platform was used for the computations. As input-output type variable(s) there were selected the mentioned earlier three process parameters which values were provided by Monte Carlo procedure: number of crystals in a computational working volume, suspension density and working supersaturation. These process parameters corresponded to appropriate columns of numerical data matrixes. Both one input – one output (one-column matrixes used for training the networks specialized in one process parameter projections) and three inputs – three outputs (three-column matrixes used for learning the networks capable of projection of all three process parameters at once) neural network structures were explored and statistically tested for various data sets (matrixes). 3.2 One-step prediction This prediction type forecasts one value ahead (corresponding to next time step) only using exclusively the original historic input data (corresponding to the previous time steps), thus without involving the newly estimated value into subsequent computations.

N

time steps

Fig. 1 Time series projection by artificial neural network: one-step prediction of a number of crystals in a computational working volume (N) (single process parameter course selected from the cumulative three-parameter prediction, lookahead degree: 1) – comparison of neural network prognosis with the original Monte Carlo simulation data.

The results were compared with the original reference data provided by Monte Carlo approach, which were used for the same network for its training, validating and testing (Fig. 1). It is visible that the properly trained network can predict with quite high accuracy the future value of the selected process parameter one time step ahead regardless the starting point location. Stability and instability of the mass crystallization process (incorporated within the Monte Carlo simulation results – data matrixes) seemed not to exert the significant influence on the one-step prediction quality. 3.3 Medium-term time series prediction Neural network can predict with quite high accuracy the future value one time step ahead, however quality of longer time series predictions (e.g. 100 time steps in a lookahead degree parameter defined as the number of time steps ahead of the last input

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variable values the output variable values should be predicted) is an essential indicator deciding if a given neural network model can be useful in the practice. However, to predict the values corresponding to a selected number of time steps ahead some fixed number of previous, historical values is required. It corresponds to a more or less repeatable fragment of past data which gives the network model enough information as far as concerned the relations between the consecutive elements within the time series structure under study. It must be emphasized that mass crystallization process in MSMPR crystallizer, characterized by random selection of the removing product crystals at the outlet, introduces thus some additional, stochastic element that sometimes strongly modifies the intrinsic process oscillations of diversified amplitudes and periods. This can be interpreted as introduction of some “information noise” into the “fundamental” dynamic pattern of the process. The network’s training algorithm determines the representative, repeatable fragment of data itself during the training process. This parameter is called “steps” and defined as the number of consecutive time steps from which input variable values should be drawn to be fed into the input units of neural network. It was observed, however, that for the data corresponding to a more unstable system behavior the determined values of “steps” parameter were higher, thus larger fragment of historic data was necessary to identify some repeatable structure. Better simulation results (conformity with Monte Carlo reference data) were reported in cases when one individual input/output type variable was used in the neural network structure.

Mt

KNO3-S 90 80 70 60 50 40 30 20 10 0

Mt Monte Carlo N individually

500

536

572

1004

1040

1076

1508

1544

1580

number of cycles time steps

Fig. 2 Time series projections (three courses, each composed of 100 time steps) by artificial neural network: prediction of oscillations of suspension density (Mt) (individual process parameter prediction, lookahead degree: 100) – comparison of neural network prognosis with the original Monte Carlo simulation data.

Cumulative prediction allowed one to effectively forecast the output values corresponding to just one or two time steps ahead only, whereas individual (thus more specialized) predictions of number of crystals in a computational working volume and suspension density provided very accurate results up till the assumed 100 time steps ahead (medium-term prediction) and possibly even more (Fig. 2). Oscillations of working supersaturation were the most difficult to forecast what results from the nature of this process parameter as well as from the MSMPR apparatus properties (working mode). The best results corresponded to Radial Basis Function Network (RBFN) and

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General Regression Neural Network (GRNN) types, whereas the worst ones to the Linear Network (LN), especially in the cumulative prediction variant. 3.4 Long-term time series prediction For the long–term predictions (more than 4000 time steps in a lookahead degree parameter) of number of crystals in a computational working volume, suspension density and working supersaturation the time series projections showed gradual, regular increase in the amplitude, however maintaining the same period of oscillation (Fig. 3). Such phenomenon results from the nature of a transfer function applied in the hidden layer neurons, which saturates after some simulation time due to the systematic increase in the input values. Moreover, the long–term predictions were far from the original, reference data due to accumulation of the prediction error (systematic contribution of each time step). In order to improve their reliability it seems necessary to take under consideration some hybrid structure for the effective diversification and modeling of long–term (general trend) and short–term effects. 4400 4300 4200 4100 4000

N

3900 3800 3700 3600 3500 3400 3300 3200 -500

Model Zmn1.7 0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

time steps

Fig. 3 Time series projection by artificial neural network: long-term prediction of the oscillations of a number of crystals in a computational working volume (N) (lookahead degree: 4000, single process parameter course selected from the cumulative three-parameter prediction).

4. Conclusions In the time series modeling by artificial neural network the kinetic parameters of the process are not needed since experimental or industrial data provide hidden information about the mass crystallization process dynamics, sufficient enough for the efficient simulation purposes. Nevertheless, the time profiles of the parameter changes reflect the process dynamics strictly only for the selected set of process parameters – the same for which the neural network was trained, tested and validated. Generalization, thus prediction of process parameter oscillations corresponding to other sets of process parameters is practically impossible. Further work focused on the creation of a hybrid model: strictly correlated system of – preferably – highly specialized “individual prediction” networks valid in a wide range of operating conditions is needful. This suggested approach seems to be an possible computational solution, especially when one is not able to dispose a comprehensive set of physicochemical or kinetic data indispensable for the conventional balance/kinetic models creation.

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5. Acknowledgements This work was supported by the Ministry of Science and Higher Education of Poland under grant No. N205 071 31.

References Eek, R.A., Hoogenboezem, A.J. and Bosgra, O.H., Comp. Chem. Eng., 20, 4 (1996) 427 GoĨliĔska, M., Simulation of mass crystallization process dynamics – comparison of Monte Carlo method and Artificial Neural Network approach, MSc Thesis, Silesian University of Technology, Department of Chemical & Process Engineering, Gliwice 2008 Kind, M. and Nieken, U., Chem. Eng. Proc., 34 (1995) 323 Kulikov, V., Briesen, H., Grosch, R., Yang, A., von Wedel, L. and Marquardt, W., Chem. Eng. Sci., 60 (2005) 2069 Kulikov, V., Briesen, H. and Marquardt, W., Chem. Eng. Proc., 45 (2006) 886 Piotrowski, K. and Piotrowski, J., Chem. Eng. Proc., 44 (2005) 517 Rawlings, J.B., Miller, S.B. and Witkowski, W.B., Ind. Eng. Chem., Prod. Res. Des., 32 (1993) 1275 Rohani, S., Haeri, M. and Wood, H.C., Comp. Chem. Eng., 23 (1999) 279 Meadhra, R.Ó. and van Rosmalen, G.M., Chem. Eng. Sci., 51, 16 (1996) 3943 Neumann, A.M., Bermingham, S.K., Kramer, H.J.M. and van Rosmalen, G.M., J. Cryst. Growth, 198/199 (1999) 723 Sheikhzadeh, M., Trifkovic, M. and Rohani, S., Chem. Eng. Sci., 63 (2008) 829

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Sensitivity study of a heat integrated FCC plant Mihaela Morara, Paul Serban Agachia a Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, Chemical Engineering Department, Arany Janos St., No. 11, 400028, ClujNapoca, Romania Abstract The fluid catalytic cracking (FCC) process continues to play a key role in a refinery [1]. The FCC is one of the most energy consuming processes from the refinery, especially because of the fractionator. Therefore, the goal of increasing the efficiency and the economical benefits may be achieved through continuously improving of the energy consumption and FCC operation. The results of a previous work [2] - a case study using real data from a FCC plant presently exploited in a Romanian refinery - confirmed that it is possible to save energy from the FCC plant by adding new heat exchangers, re-piping, and improving the performance of the existing heat exchangers. The investigation of the entire heat integrated FCC plant behavior has not been studied yet. Nevertheless, this kind of studies is subjected to the high complexity of a FCC process. Moreover, the thermal integration of a process may induce more instability in its operation [1]; consequently a parametric sensitivity analysis was necessary to be used in this work in order to study the influence of different operating parameters values on the behavior of the retrofitted heat integrated design of the FCC plant. The Aspen Plus has been used to create the model of the integrated FCC plant. The simulations revealed a strong nonlinearity of the FCC process [3], affecting the products separation efficiency, and identifying the behavior of the integrated plant under the presence of different kind of disturbances. Keywords: fluid catalytic cracking, heat integration, dynamic behavior, sensitivity study.

1. Introduction Fluid catalytic cracking process (FCC) is the most energy consuming process in a refinery. Even if the FCC process became a known and common process it still presents a high interest due to its influence on the profitability. A proper operation of the FCC unit determines the quality of the products and, consequently, the position on the market of the refinery. In a previous work [2] it was presented the possibility to save energy from an existing heat exchanger network (HEN) of an industrial FCC unit from a Romanian refinery. The previous study revealed that the improvement in energy reduction could be obtained through adding heat exchangers, re-piping, and improving the performance of some heat exchangers. No drastic changes had been suggested for existing HEN because the new proposed designs have been developed trying not to modify the process-toprocess heat exchangers and in the same time assuring that the process would not be affected due to its strong nonlinearity.

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The optimization of the industrial FCC’s HEN in terms of economical point of view gave a starting point to continue with the analysis of the generated designs. The aim of this work is to analyze the most economical design of the HEN obtained in the previous work. Aspen Plus was used to simulate the design called “Design E” (Figure 1).

Figure 1: Aspen Plus simulation flowsheet – Design E The sensitivity analysis was performed to show the main influences on the products in the operation of the heat integrated design of the FCC industrial plant.

2. FCC industrial process sensitivity analysis Sensitivity studies for the heat integrated FCC process have never been done. Most of the FCC studies are based on hardly constrained empirical or semi-empirical models [4] which describe the FCC process without taking into consideration heat balance and consequently the energy saving. The real industrial process presents a very complex behavior. The simulation with the constrained models revealed for a small operating parameters range a behavior that resembles with a proper operating of the real plant. The validity of the models can fail when the operating conditions are changed. That’s way the necessity of a sensitivity parameters analysis need to be done, in order to identify the optimal operation and control conditions for the proposed design E. The catalytic cracking reactions take place in the riser under well-known conditions. Further on, the products resulted in the riser need to be separated in the main fractionator. Due to the fact that in a FCC process the quantity and the quality of the main products (gasoline and diesel oils) depends firstly on the quality of the oil and secondly on the parameterization limits of the main fractionator the actions that can be done are to change the temperature, the pressure and the mass flow because the column is already designed. Therefore, due to changing of these characteristics of the output streams from the main fractionator the behavior of the HEN will be affected. For example the change in temperature of the output streams could make some of the heat exchangers to operate crossing the pinch point. But if the parameters of the main fractionator products have the values in a proper operating range according to the HEN characteristics then the HEN works properly. One of the FCC process simulation benefits using Aspen Plus is the possibility to study the process performance through sensitivity analysis. Comparing with the

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methodologies for applying the sensitivity analysis that are in the literature, with Aspen Plus it’s possible to develop this kind of studies in a more simple way. In this study the most important variables considered in the sensitivity analysis are the temperature, the pressure, the mass flow and the composition of the product stream from the riser, due to their strong influence on the heat integrated FCC process performance. Table 1 contains their values ranges. Table 1: The values of manipulated variables Values

Manipulated variable Riser stream mass flow [kg/h]

Min.

Max.

145000

152000

0

Riser stream temperature [ C]

450

550

Riser stream pressure [bar]

1.8

4

The operating conditions in the real FCC plant for the riser stream are: the temperature 515 0C; the pressure - 2.9 bars, the mass flow - 148887 kg/h. The main products of the studied industrial FCC plant are: the gasoline, the light diesel oil and the heavy diesel oil. The objective of the sensitivity analysis is finding the optimum range of the manipulated variables in order to increase the quality and the quantity of these products for the FCC plant - design E. Figure 1 shows that the only product that is not influenced by changing the operating conditions of the riser stream is the heavy diesel oil (red line).

a)

b)

c) Figure 1: The variation of the FCC main products mass flow with riser stream a) mass flow; b) temperature; c) pressure

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The light diesel oil quantity vary with the operating conditions changes due to the variation of the riser stream temperature and not only. The increasing of the temperature or the mass flow of the riser stream decreases the production of the light diesel oil with 9.64% respectively 4.28% for the studied ranges. Also, increasing the mass flow of the riser stream induces the increasing of the gasoline quantity. The variation of the temperature and pressure values considered in the sensitivity analysis doesn’t affect the quantity of the gasoline. Following the sensitivity analysis results an economical optimum could be chosen according to the market interests. If there is a high demand of gasoline the solution is to increase the mass flow from the riser, otherwise if there is an increased demand for the light diesel oil the solution is to decrease the mass flow or the temperature. If there is interest for both products the domain of the operating parameters is comprised between 147000-147500 kg/h and 480 0C. The riser stream pressure doesn’t influence the FCC plant production. From Figure 1c a very small products mass flow variation it’s observed. Besides the parameters discussed above sensitivity analysis was performed following the effect of different raw oil composition on the quantity and the quality of gasoline, light diesel oil and heavy diesel oil. There were compared four different cases. The first case was created knowing that the raw oil contains a very small percentage of heavy hydrocarbons. The second case was simulated using raw oil with mainly light hydrocarbons and in the third case it was used raw oil containing mainly heavy hydrocarbons. The last one represents the real case of the industrial FCC process.

a)

b)

c) Figure 2: The products mass flow variation at different raw oil composition: a) gasoline; b) light diesel oil; c) heavy diesel oil.

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The products separation for all four cases was made in the same conditions. Figure 2 presents how the raw oil quality affects the process productivity. It is important in a refinery to process oils with almost the same quality because it can not be possible to design a new FCC plant for each oil that present different characteristics. Considering the irregularities that appear in the lines from Figure 1 and Figure 2 it is obvious that the variation of the process parameters induce instability on some parts of the process. The sensitivity analysis results (manipulated variable: raw oil composition) are also presented in Table 2. Table 2: Main products properties for different raw oil compositions Watson

Gravity

UOP-K

88545.54

90.89

12.90

0.01

1635.04

14.60

10.25

0

-6.12

28206.96

12.25

10.15

25

0

-162.07

98923.86

92.36

13.07

80

6

0

-5.30

357.37

48.90

11.41

HCO

60

3

0

-23.14

27818.14

32.34

10.79

Gasoline

43

25

0

-64.05

49246.57

113.45

13.61

LCO

80

6

0

0.02

1559.03

14.54

10.25

HCO

60

3

0

-2.89

28502.67

13.88

10.25

Gasoline

43

25

0

-148.11

94609.35

92.33

13.05

LCO

80

6

0

0.00

1491.40

14.73

10.25

HCO

60

3

0

-4.01

28172.15

15.19

10.15

Pres.

Vapor

Enthalpy

[C]

[bar]

[frac.]

[MMBtu/h]

Gasoline

43

25

0

-123.80

LCO

80

6

0

HCO

60

3

Gasoline

43

LCO

Case

1

2

3

Real

Mass Flow

API

Temp.

[kg/h]

The variation of the quantity and quality of the FCC products can be better observed. The only production that is not influenced by changing the operating conditions of the riser stream and by changing the raw oil composition is for the heavy diesel oil. This is due to the fact that the raw oil, regardless of its composition, is mixed with slurry from the slurry decanter before entering the riser. An important aspect in the operation of the HEN of the FCC plant, beside the temperature of the output streams from the main fractionator, is the enthalpy which represents the capability of a process stream to exchange heat with other streams. From the previous work [2] it is known that the design E has the best performances regarding the costs and the quantities of energy saving. Compared with the industrial FCC plant, design E can save energy 15% of heating and 12% of cooling.

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To maintain these improvements obtained after the heat integration, the proper behaviour of the process can’t be disturbed. The disturbances applied in the sensitivity study, especially the changing of the raw oil, could affect the enthalpy of the output streams of the fractionator and consequently the heat transfer in the heat exchangers. The fractions separation in the main column is influenced and this could be induce the decreasing of energy saving in the retrofitted design E of the FCC plant HEN because the capability of the process streams to exchange heat between them is changed.

3. Conclusions The fluid catalytic cracking heat integrated process is a very complex and hard to control because of its strong nonlinearity. According to the results of the previous work [2] it was determined that the real HEN can be improved and the design named “E” is the one that will recover as much as energy as possible and reduce the utility usages. In this part the optimized HEN is evaluated in steady state under the effect of disturbances for a better understanding of the behavior of the heat integrated FCC process. It was discovered that the only product that is not influenced by changing the operating conditions of the riser stream is the heavy diesel oil but the light diesel oil quantity changes with changing of the temperature and mass flow. The gasoline productivity increases only with the increasing of the mass flow riser stream. The raw oil quality influences the fractions separation in the main column and it may induce the decreasing of energy saving in the retrofitted design E of the FCC plant HEN. This study represents the first step through an optimal control configuration that could assure a good quality of the products. The following step, taken into account the results discussed above is importing the FCC process design E from Aspen Plus in Aspen Dynamics. Aspen Dynamics reveal the fact that the heat integrated FCC process is described in dynamic state by more than 76000 equations and has 4240 states variables. Aspen Dynamics generates a control structure proper for the heat integrated FCC process – design E. New controllers can be added to the existing control structure for better improvement. Further work is needed to study the flexibility and the stability of the proposed control structure.

References [1] B. A. Al-Riyami, J. Klemes, S. Perry, Applied Thermal Engineering, 21 (2001) 1449. [2] E. Jara-Morante, M. Morar, R. Roman, S. P. Agachi, Retrofitted Heat Exchanger Network of a FCC Plant, PRES 2008, 24-29 August CHISA Prague, 2008. [3] M. V. Cristea, S. P. Agachi, V. Marinoiu, Chemical Engineering and Processing, 42 (2003) 67. [4] C. Jia, S. Rohani, A. Jutan, Chemical Engineering and Processing, 42 (2003) 311. [5] Aspen Plus User Guide 2006.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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A framework for optimal design of reactive distillation columns Rui M. Filipe,a Henrique A. Matos,b Augusto Q. Novaisc a

Departamento de Engenharia Química, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emídio Navarro, 1, 1959-007 Lisboa, Portugal, [email protected] b Centro de Processos Químicos, Departamento de Engenharia Química e Biológica, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal, [email protected] c Departamento de Modelação e Simulação de Processos, Instituto Nacional de Engenharia, Tecnologia e Inovação, Est.do Paço do Lumiar, 1649-038 Lisboa, Portugal, [email protected]

Abstract This work presents an integrated framework involving the design, multiobjective optimization and rigorous modeling of reactive distillation columns with multiple feeds and variable feed quality. An incremental approach is used, where a large number of alternatives with low design detail are followed by a reduction in alternatives with an increased detail in their design specifications. Each phase of the methodology is presented, highlighting the transition between them and the conclusions that can lead to the development of heuristic rules. Keywords: Design, reactive distillation, multi-objective optimization.

1. Introduction Process intensification usually leads to economic and environmental gains resulting therefore in systems with significantly greener engineering attributes [1]. Reactive distillation (RD) is such a successful case of process intensification where reaction and separation are combined into the same physical shell [2]. The range of application is however limited to the cases where the operating conditions for reaction and separation have some overlapping. Furthermore, bringing together reaction and separation increases the complexity of the design and operation due to the possible interactions between reaction, transport phenomena and phase equilibria. The design of RD systems can thus be a challenging task. Several methods for RD design have been published as reviewed by Almeida-Rivera [3], but no universal design methodology is still available for process design. From all possible RD column configurations it would be an enormous advantage having a preliminary methodology or procedure to select the most promising one in terms of performance and cost before the detailed design is carried out. This work presents an integrated framework that aims at facilitating the identification, modeling and selection of column designs, involving the multiobjective optimization and rigorous modeling of hybrid RD columns with arbitrary reaction distribution, multiple feeds, and variable feed quality, i.e., variable energy content. In the first step, a combination of feasible regions and multi-objective optimization techniques is used to identify potentially optimal feasible designs [4]. With this

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approach, the range of alternatives is i firstly limitted to those designs d belongging to the r holduup and a costt indicator, Pareto froont that relatees the numberr of stages, reactive named cappacity, previoously developped and testeed [4, 5]. Seccondly, and iin order to validate thhe designs, a representative r e subset of tho ose alternativees is rigorouslly modeled using Aspen Plus softw ware and a sensitivity analyssis performed to test simpliifications at he use of a riigorous dynaamic model operationaal level [6]. A third step, addresses th developedd in gPROMS environmentt to deal with h catalyst deacctivation and its control, exploring the use of varriable feed quaalities. Figure 1 presents a grraphical overrview of the methodologyy used, highliighting the u From th he analysis off the results, a number of several steeps and the sooftware tools used. design heuuristics is beiing produced. The final go oal is to gain insights into the design procedure and, simulttaneously, in an iterative fashion, inccorporate this heuristic m formulation, fo ass shown in Figgure 1. The knowledgee into a modiffied GAMS mathematical introductioon of additionnal constraintss and an impro oved cost indiicator can be eexpected to reduce thee search spacee region and ennable the iden ntification, froom the outset, of near-tofinal optim mized RD coluumn designs. The methoodology is deescribed togetther with the conclusions and heuristicc rules that have beenn formulated. The assumptiions and speccific issues related with thee transition within eacch step are alsso presented. Although thee goal is to deevelop generaal rules, for the momeent these are based on reaacting system ms with ideal vapor liquidd behavior, namely thhe olefin metaathesis system m (wherein 2--pentene reactts to form 2-bbutene and 3-hexene) and two othher scenarios with w similar structure but hypothetical substances v with differrent relative volatility.

Figure 1. Graphical G overviiew of the methhodology

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2. Multiobjective optimization using feasibility analysis Feasibility analysis, which is used to identify the design alternatives, considers the decomposition of the full column into smaller sections, for which the feasible region is built [7]. Basically, the construction process identifies the reactive and non-reactive pinch points and connects them with stage-by-stage profiles built using extreme policies for reaction distribution in the column. Steady state conditions at a specified pressure are considered. Vapor-liquid equilibrium is assumed at every stage and a single kinetically controlled reaction is considered to occur in the liquid phase only. All the heat effects are considered to be negligible which allows the decoupling of the material and energy balances. With this assumption, the sectional profiles can then be constructed using only the material balance [7]. Subsequent Aspen Plus simulations are used to evaluate the heat effects in more detail since heat integration is a major practical advantage of reactive distillation columns. The multi-objective problem is formulated using two objective functions to minimize: the reactive holdup and capacity (as a RD column cost indicator) [4]. The H-constraint method is used where, in each step, the reactive holdup is minimized subject to a limit on the maximum cost indicator value, by varying the operating parameters. The choice of step requires some careful attention. On one hand it determines the degree of detail of the Pareto surface, but on the other it affects the total number of solutions, which in the current case is of the order of several thousand. For each feasible combination of number of stages in the rectifying and stripping section, the local optimal solution gives the number and location of reactive and feed trays, feed quality and reactive holdup on each reactive tray. The Pareto surface relating the total number of stages, reactive holdup and cost indicator is then built, thus allowing the identification of an efficient set of possible configurations for the reactive distillation column. The olefin metathesis is investigated, together with two artificial pseudo systems built by modifying the relative volatility of the reactant. The effect of the relative volatilities is thus assessed. Variable and fixed reflux and reboil ratios scenarios are also investigated [4]. Feed quality is limited to the range -2 (superheated vapor) to 2 (subcooled liquid). From the analysis of the results, several conclusions can be found [4, 6], offering design guidelines, as summarized below: - The combination of feeds with extreme feed qualities, i.e. q>1 and q<0 reduces the requirement of reactive holdup. - The reactive zone is typically found near the liquid feed. - “Small” columns exhibit one saturated vapor feed, while two feeds (liquid and vapor) with extreme feed quality are obtained for “large” columns. - For the same final specifications, the reactive holdup requirements decrease in those cases of variable reflux and reboil ratios. It was also observed that the inclusion of the cost indicator, i.e. capacity, as a new objective, effectively limits the selection of the feed qualities, i.e., the feed quality is no longer limited to border values (-2/+2), which were usually selected before the inclusion of the cost indicator objective.

3. Rigorous simulation and sensitivity analysis The optimization approach used, while determining the optimal locations for the catalyst, feeds and feed quality, does not however limit the number of feeds or the minimum amount of catalyst on a tray. Consequently, many of the reported designs tend

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to be operationally unrealistic, as some trays may have too small amounts of catalyst or there are a very large number of feeds [4]. To investigate how to translate these designs to a process simulator like Aspen Plus, and to analyze the sensitivity of the solutions [6], a set of obtained solutions was used to initialize simulations in Aspen Plus. The number of stages, reboil ratio, distillate to feed ratio, location and quality of the feeds, as well as the reactive holdup distribution specifications, were taken from the former optimization results. The RadFrac model and the Ideal property method were used. Aspen Plus does not support the direct specification of the feed quality. To overcome this, a design specification was implemented: the feed temperature is adjusted to provide the required energy for the change in the internal liquid flow according to Ln = Ln-1 + q F where F is the feed flow, q the feed quality, and Ln-1 and Ln the liquid entering and leaving the n tray, respectively. The availability of such design details demonstrated to be very useful, greatly facilitating the initial convergence of the simulation. A good agreement of the results with those obtained from optimization was verified. Aspen Plus simulations show that the internal flows change over those trays with no inlets or outlets, due to different heats of vaporization of the components inside the column. As a constant molar overflow was previously assumed, by setting the reflux rather than the reboil ratio would result in significantly lower values for the latter and, consequently, degradation in the purity of the outlet streams. Besides verifying the efficiency of the design method, simulations were also used to investigate several simplifications on the designs and its effect on product purity. The most important changes that still accomplish the purity requirements with a small penalty on the cost indicator are summarized below: - Rearrangement of catalyst: catalyst equally divided over a reduced number of trays. - Rearrangement of the feeds: feeds with similar heat content can be grouped, eliminating feeds with low contribution. These new designs, although not optimal, highly increase the flexibility of the solutions. The use of less extreme feed qualities was also investigated [6]. The bounds initially used, led to temperatures that are unrealistic for industrial practice. The studies showed that for a column with two feeds and feed qualities of -2 and 2, product purity is highly dependent of the “hot” feed while the “cold” feed affects mainly the cost indicator. It was also verified that providing more energy through the reboiler instead on the feed, results in increased values of the cost indicator.

4. Dynamic simulation To investigate the dynamic behavior and the use of unconventional feed qualities to overcome catalyst deactivation a rigorous dynamic model has been developed using gPROMS. The model was built modularly and allows for different number of trays and feeds, and feed qualities. Although phase equilibrium is assumed, the model can also consider deviations from equilibrium through the built in Murphree stage efficiency equation. The physical properties are estimated using the gPROMS included package IPPFO for ideal systems. The coefficients used within IPPFO library were regressed using data from Aspen Plus. Five control loops are used. The distillate and bottoms flowrate are manipulated to control reflux drum and reboiler levels, respectively. The reflux rate is manipulated to control the purity of light component in the distillate, while the purity of the heavy component in the bottoms is controlled by manipulating the reboiler duty. In future

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work, this control configuration will be adapted to allow the manipulation of the feed energy content (feed quality) while holding constant the reboil ratio. This model was initially applied to a configuration previously obtained from the design and optimization step for the olefin metathesis system. With 14 stages and one feed, all the RD column design details were transferred from the Aspen Plus simulations performed prior to gPROMS implementation. Once again, the availability of design details from Aspen Plus simulations were instrumental for the initialization of the simulations. This model is a powerful tool to simulate the real operational RD column behavior including tasks like start-up, shutdown or sudden events such as feed quality or energy fluctuations.

5. Conclusions In this work an integrated methodology for the design and multiobjective optimization of RD columns is presented. The framework considers hybrid columns with arbitrary reaction distribution through the column and multiple feeds with variable energy content. The methodology is based on several steps, with the knowledge gained at each step informing subsequent ones, with manifest gains in its application, in particular a marked positive effect on initialization. Furthermore, in each phase of the proposed approach the design is handled in greater detail, incorporating the information previously obtained but also generating new insights, which can be instrumental for further refinements. This integrated methodology while being developed for one system, which is characterized by one reactant and two products, can be expected to be equally valuable for other reaction systems, and this will be a matter for continuing research.

6. References [1] M.F. Malone, R.S. Huss, and M.F. Doherty, Environ. Sci. Technol., 37 (2003) 5325. [2] M.F. Malone, and M.F. Doherty, Ind. Eng. Chem. Res., 39 (2000) 3953. [3] Almeida-Rivera, C.P., P.L.J. Swinkels, and J. Grievink, Comput. Chem. Eng., 28 (2004) 1997. [4] R.M. Filipe, S. Turnberg, S. Hauan, H.A. Matos, and A.Q. Novais, Ind. Eng. Chem. Res., 47 (2008) 7284. [5] R.M. Filipe, H.A. Matos, and A.Q. Novais, Performance indicators in reactive distillation design. Chem. Prod. Process Model., (2009) accepted. [6] R.M. Filipe, S. Hauan, H.A. Matos, and A.Q. Novais, Computer-Aided Chemical Engineering, B. Braunschweig and X. Joulia, Editors, 25 (2008) 211. [7] W.R. Hoffmaster and S. Hauan, Chem. Eng. Sci., 60 (2005) 7075.

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Event-Dynamic Assumptions in First-Principle Network Models and Model Reduction Heinz A Preisig Department of Chemical Enginering, NTNU, Trondheim, Norway. E-mail: [email protected]

Abstract The author's concept of network modelling based on first-principles is reviewed first. Event-assumptions in macroscopic plant models are discussed in the light of yielding a reduced-order and reduced-state space model. The assumptions can be implemented as transformations of the network model, making it generic and thus suitable for an integration into computer-aided modelling tools. Keywords: Modelling, model reduction, dynamic systems

1. What does Network Modelling Build on Building a model based on physical concepts on the macroscopic scale firstly partitions the world into pieces. These pieces are not to overlap and usually represent in the real world a spatial domain that is part of the spatial domain being occupied by the modelled plant. The subdivision is usually motivated by the existence of identifiable parts, such as equipment pieces or the like. But it may also be motivated by mechanical considerations such as phases (see for example Webster's definition of phases). The macroscopic description assumes a sharp separation between the different parts1, though the boundary itself does not have to be fixed but may move whereby one part grows as the other shrinks accordingly (Crank, 1987). This first operation of sub-dividing the plant into spatial domains is followed by a series of abstraction steps, which in most cases are done informally without paying much attention to what kind of implicit simplifying assumptions are thereby introduced into the model. This set of abstractions assumes first the nature of each individual part in terms of homogeneity with respect to all characterizing intensities. The discrete nature of the underlying nature is thereby ignored assuming continuity. The individual parts may next be seen as distributed systems, thus acknowledging that natural systems are distributed with the intensities being a function of the position. As the different spatial domains do not overlap except than in the common boundary, a boundary can only be shared between two systems. Insisting on the continuous nature of the modelled world this implies that the boundary conditions are continuity conditions in the flux of extensive quantities and the "driving force", the quantity being conjugate to the potential driving the transfer. In the next stage quite commonly a set of time-scale assumptions are introduced. Two extreme cases are important: one in which the flow is large through the system compared to internal recycle-type transfer and the opposite, where the internal cyclic transfer is dominating over the flow through the system. Making the assumption of fast transfer in the dominating streams, the two systems reduce in the first case to a pure resistance to the transfer and in the second case to a uniform distribution inside the do1

The non-sharp has already been discussed by Gibbs see Guggenheim, 1985.

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main. Some examples were previously discussed in (Preisig, 2004). It is mostly at this point that people start to generate equations representing the simplified components of the plant. Alternatively one can cast this process of developing the base model framework into a graphical representation, which we termed physical topologies, as we talk about a graphical representation of the physical containment of the plant and its relevant environment.

2. The Graph in the Model Putting this process into a pictorial form makes it possible to discuss and manipulate the base structure of the model (Preisig, 2008). A graph consists of two basic types of components, namely nodes (vertices) and arcs (edges). Assigning nodes to capacities and arcs to transfers between systems, establishes a representation of the physical topologies in the form of a graph. Adding attributes to each nodes and edges is like colouring in a child's picture book. Colours, or attributes, may indicate the nature of the capacity being represented by the node, which may be 3-D distributed, 2-D distributed or 1-D distributed or lumped, thus not distribute. For the arcs one may need to consider that they represent a distributed transfer meaning that the boundaries are distributed. As these are surfaces in the 3-D space they may at most be 2-D distributed2. Other meaningful attributes include for example the type of species being present in a node or being transferred (or not transferred) through an edge. Adding reactions generating "new" colours completes the picture. Common other attributes are heat and work streams. The topology can readily be cast into an equation representation given an equationbased representation of the capacities and the transfers. Limiting the discussion to component mass and energy and a non-reactive system, the dynamics of a capacity is described by the conservation of component mass and energy: (1) The conservation laws equate the accumulated extensive quantity with the flows of the respective quantity in and out of the spatial domain labelled as system s The two balances are coupled as mass flow induces energy flow, actually primarily internal energy combined with kinetic energy, potential energy and a volume-work stream. The quantities are either 0, -1 or 1. They reflect the reference co-ordinate being introduced for every flow. Thus the actual flow is measured relative to the reference direction. Given the graph of nodes = capacities and arcs = transfer of extensive quantity, the reflect the direction of the arc. The graph is thus a directed one. The subscript c indicates the type of transfer, which becomes an attribute to the arc. Similarly attributes can be defined for the nodes. The above equations describe one node with an arbitrary number of arcs connecting to other nodes. The representation is commonly using vectors, for example for the representation of component masses in flows or capacities. Providing the model for the whole graph thus agglomerates the equations for all nodes by stacking up the individual vectors representing each individual node. The vectors describing the individual parts are though not of the same length. For example in a plant there usually exist parts in which species are not present, whilst they are present in other places. In terms of 

On the side, this also implies connections, are always linking two and only two systems together. It also implies that network models are initially closed systems, which are "opened" by adding reservoirs and perfectly controlled subsystems

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mathematical objects, this implies that one wants only those present in the equations that are really relevant giving raise to a set of index mappings (Preisig, 2009). Introducing index maps that project the set relevant for the described object onto the base set, one gets for system s:

(2) of all respective flow vectors. The maThe flow vectors are now stacks projects the species space of vector m into the species space of species vectrix tor associate with the system s. This is the result of two projections namely the projection of the stream index sets onto the plant species set and the species index set for the system onto the plant species set. The plant species set is here defined as the base set from, which is comprises at least all the species present in the plant. This projection mechanism preserves for both conservation equations the same "flow" matrix, which by closer inspection turns out to be the part of the incidence matrix of the directed graph, which is associated with the system s. The "flow" matrices are "coloured" thus associated with particular attributes such as species, heat, work, to mention the ones used above The stacked version then extends this logically in that the incidence matrix is for the whole system. Thus assigning a global state vector to the stack appearing on the lefthand-side, the coloured incidence matrices appear on the right being conjugated with the respective flows. These dynamic matrices are augmented with a set of transfer equations and consequently a set of state variable transformations, which close the loop between the secondary state variables being introduced in this process and the conserved quantities. Parameters represent terminal nodes in the bi-partite graph representing this equation system. Since dynamics are the subject of discussion and following an old tradition, we shall in the sequel refer to these equations as constituent equations.

3. Simplifying the Model Assuming Event Dynamics Closed dynamic systems are embedded in a static world, at least from their point of view. On the other side assumptions are being made about constituent parts are acting instantaneously to stimuli. This gives rise to making assumptions about how capacities behave when measured on a time scale split into these three sub-domains (Preisig, 2008). The above indicates that in applications one actually takes different starting points for the simplification. In the most generic case one starts with all continuous system covering the modelled spatial domain and then introduces simplifying assumptions: 3.1. Event dynamic = Assuming Negligible Capacities Probably the most common assumption being made is the one of zero capacity associated with a phase boundary. In order to capture the behaviour one can start with encapsulating a phase boundary into a volume with its boundaries being inside of the respective phases. Given the continuity conditions within the phase, this volume is reduced to zero, moving the two boundaries towards the phase boundary. The result is that the above-mentioned continuity conditions for flow and conjugate to the driving potential (Preisig, 2008). Making assumptions for lumped systems, which are the result of making assumptions of a fast transfer within the system (Preisig, 2008), one obtains a node that acts instantaneously to external stimuli. In terms of the equations this implies that a set of differential equations is "converted" into a set of algebraic equations. Formally the overall network is split into two parts, one with non-negligible capacities and one with negligible ca-

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pacities. The involved multidimensional flows are including the mappings with abovedefined projection matrices. Next singular perturbation is applied to the fast capacities.

(3) yielding a set of algebraic equations that is to be solved together with the constituent part of the model. A simplified version of the constitutive equations include the description of the transfer of extensities and a set of state variable transformation, which here are assumed to be explicit in the secondary state variables z. Whilst these equations are often implicit, the secondary state variables must be the result of a mapping from the primary state space x.

(4) Putting things into context it should be noted that using the term model reduction for the implementation of this time-scale assumption implies a reduction in the dynamic order of the model but does not reduce the number of state variables (Pavliotis and Stuart 2008). A reduction in the number of state variables can only be achieved if the singularly perturbed equation and the associated parts of the constitutive equations can be solved for the fast state variables. This implies that all involved functions are linear in at least unitary functions of those fast states. Since the state space is usually not shrinking, one cannot expect significant, if at all any, reduction in the computation times when integrating these models. In contrast, computation times and possibly also reliability of the computation may be compromised by the fact that one is left with solving a system being partially in equilibrium (Van den Berg 2005, ReduceIt 2008). 3.2. Reduction using Transformations The state space can be reduced "forcefully" by using approximations for some parts of the system. A rather generic approach is described in (Li and Rabitz, 1990) which can be captured by a linear transformation for the state combined with an approximation of the inverse of the transformation matrix:

(5) A state space reduction can be obtained when choosing T non-square and substituting its inverse by the respective pseudo-inverse (Li and Rabitz, 1990). The same basic concept results when thinking in terms of approximating the stationary part of the model. Such approximations can be obtained in various ways (Ljung, 1999). Modal recution methods and proper orthogonal decomposition fit into this framework. 3.3. Lumping Lumping is a combination of transformation and singular perturbation. One first "lumps" by multiplying the balance equations with a row-vector of coloured 1s, thus adding all the dynamic equations of the same type together. Next, one system is chosen to represent all the ones being lumped. The set of equations is completed by choosing all the others and apply a singular perturbation assumption to each. This conserves the dominating constant and locates it in the chosen system, which is kind of suspended in the stationary system of the remaining systems. As mentioned above, this does not reduce the state space in general. If linearization is out of question, lower-dimensional approximations may yield acceptable ability of the model to describe the modelled plant. One should observe that as long as the steady-state description is not modified,

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the manipulation of the relative dynamics of the involved lumps is not modifying the steady state solution, but only the dynamics with which one arrives in the steady state. This can be explored in integrators so as to "robustify" solvers.

4. Conclusions 4.1. Control-Volume Network Modelling The basics of the author's network modelling approach are being reviewed. It can be seen as a straightforward, logical abstraction of first-principle models. This abstraction contains all the basic information. In particular it makes a clean link between the linkedcontrol-volume approach of physics and the mathematical representation by interpreting the linked-control volumes as a graph consisting with the nodes being the capacities and the arcs the communication across the common surfaces of adjacent control volumes. The typed incidence matrices of the graph provide this link as they appear explicitly in the representation. This eliminates the need for a mapping into a specialized environment such as Bond graphs completely. Such a mapping is only obscuring the relevant information (Preisig, 2004), which also inhibits facilitating any of the above-mentioned techniques for model simplifications and model reduction. On the other hand, the Hamiltonian view and analyses, which has been developed over the last years can certainly also possible within the network modelling framework. 4.2. Handling of Order-of-Magnitude Assumptions Event-dynamic assumptions are a natural to any model as it is always, at least intrinsically, present in the formulation of a process model. Starting formally with a network of distributed systems, event-dynamics is used to characterize phase boundaries. In the case the transport equations and the respective part of the constitutive equations are linear in the state of the singularly perturbed system, the model can be reduced, both in order and state dimension. If the latter is not possible the complexity of the model is hardly affected by making event assumptions for parts of the capacities in the plant model. 4.3. Lumping resp. Compartementalisation The simplification of compartimentalising or better lumping a section of the plant together becomes a transformation-like operation on the network model, which makes it again suitable to implement in a computer-supported network modelling tool. 4.4. Other Model Reduction Methods The alternative of "forcing" a reduction through approximations has briefly been discussed. Again the core is a transformation.

References [1] Crank, John; Free and moving boundary problems; Oxford University Press, 1987 [2] Preisig, H A; Gymnastic Exercises with Topologies Relating to Time-Scale Assumptions; ESCAPE 14 (2004), Lisabon, Portugal, 16-19/05/2004 pp 1105-1110 [3] Preisig, H A; Three Principle Model Reductions Based on Time-Scale Considerations; ESCAPE 18 (2008), Lyon, France [4] Pavliotis,Grigorios A and Stuart, Andrew M; Multiscale methods, Springer, 2008 [5] Van den Berg, J; Model reduction for dynamic real-time optimization of chemical processes; PhD thesis, TU-Delft, The Netherlands, ISBN 90-855-9152-X,2005 [6] ProMatch Workshop ReduceIt, DECHEMA, Frankfurt, Germany, November 2008. [7] Li, G and Rabitz, H; A general analysis of appxomate lumping in chemical kinetics; Chem Eng Sci, Vol 45, No 4, pp 997-1002, 1990.

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H.A. Preisig [8] Ljung, L; System Idenfication: Theory for the user, Prentice Hall, 2nd edition, 1999 [9] Preisig, H A; Modelling: Compartmental Networks and Topologies - A Comparison with Bond Graphs, ESCAPE 14 , 2004, pp 1111-1116 [10] Preisig, H A; A graph-theory-based approach to the analysis of large-scale plants, Comp & Chem Eng, 2008, (in press) [11] Preisig, H A; Constructing, modifying and maintaining consistent process models; FOCAPD, June 7-12, 2009, Beaver Run Resort, Breckenridge, Colorado.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Model-based Optimisation and Closed-loop Control of Crystal Shape in Cooling Crystallisation Jian Wan, Xue Z. Wang* and Cai Y. Ma Institute of Particle Science and Engineering, School of Process, Environmental and Materials Engineering, University of Leeds LS2 9JT, UK, Email: [email protected]

Abstract A morphological population balance (PB) model is presented which links single crystal morphology description with PB process model, therefore can be applied to simulate the dynamic evolution of crystal shape as well as size distributions in crystallisation processes. In addition, the new morphological PB model can effectively deal with multiple crystal morphological forms and transitions between them. The model is then used to derive optimal temperature and supersaturation profiles leading to the desired crystal morphology. Since tracking an optimum temperature or supersaturation trajectory can be easily implemented by manipulating the cooling water flowrate in the reactor jacket, the proposed methodology provides a feasible closed-loop mechanism for crystal shape control. The methodology is demonstrated by applying it to a case study of cooling crystallisation of potash alum.

Keywords: Crystal shape control, crystal shape optimisation, multi-scale modelling, morphological population balance equations 1. Introduction For particulate products obtained from crystallisation, crystal morphology is an important property that not only directly impacts the down-stream processability of the particles, but also affects the end-use property of the final product1. Closed-loop optimisation and control of crystal shape in a reactor however, has long been considered to be too challenging to achieve mainly due to the limitations of available measurement techniques and modelling capabilities. But there have been promising advances recently in both characterization of particle shape using imaging, e.g.2,3 and modelling of crystal shape evolution using morphological population balance, e.g.4, which could ultimately lead to practical solutions to closed-loop control of crystal shape. The objective of the paper is two fold. Firstly it is to develop a morphological population balance model for crystal shape evolution in order to handle more complicated crystallisation processes where multiple morphological forms coexist and transitions among them can take place. In addition, the new model is used to derive optimal temperature and supersaturation profiles that can be tracked to obtain desired crystal shape.

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2. Geometric description of crystal morphology The morphological PB model that can simultaneously handle multiple morphological forms is based on polytope geometry description of crystal shape. Crystals can be viewed as convex polytopes, which are mathematically represented as the intersection of half-spaces: Hx d p ,

(1)

where H is an m by n matrix, x is a column vector with n components and p is a column vector with m components. Taking the crystal of potash alum (KAl(SO4)2˜12H2O) as an example, it has a total of twenty-six crystal faces, i.e., eight octahedron {111} faces, six smaller cube {100} faces and twelve rhombdodecahedron {110} faces3. Thus the morphology of potash alum can be described by the following symmetric polytope: ª1 « «1 «1 « «1 « « « « « «1 « «1 «1 « «1 « « « ¬

3

1

3

3

1

3

3

1 1

3

3 3

1

0

0

1

0

0 2

0

2 2

0 1

2

0

1 2 1 2

0

1

2

2

ªd1 º 1 3 º » «d » 1 3» « 1» «d1 » 1 3 » » « » 1 3» «d1 » » «d 2 » 0 » « » 0 » ª x º «d 2 » »« » « » 1 » « y » d «d 2 » 1 2 » «¬ z »¼ «d 3 » » « » 1 2» «d 3 » » «d 3 » 0 » « » 0 » «d 3 » » «d » 1 2 » « 3»  1 2 »¼ ¬«d 3 ¼»

,

(2)

where d , d and d are the normal distances from the crystal geometric centre to {111} , {100} and {110} faces, respectively. Therefore potash alum crystals with a given d , d and d can be plotted using polytope geometry software5. For example, a potash alum crystal with d 7μm , d 9μm and d 8μm is shown in Figure 1(a). Furthermore, morphological transitions could happen during the crystallisation as a result of faceted growth. For instance, the six {100} and twelve {110} faces of a potash alum crystal can disappear if they grow too fast relative to the eight {111} faces, which can be easily detected using polytope geometry since it is equal to the redundancy of the constraints concerning d and d in (2). As an example, the crystal in Figure 1(a) turns to an octahedron when d , d and d grow to 8μm , 14μm and 10μm , as depicted in Figure 1(b). 1

2

1

3

2

3

1

2

3

2

3

1

2

3

Model-Based Optimisation and Closed-Loop Control of Crystal Shape in Cooling Crystallisation

(a)

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(b)

Figure 1 Polytope representation of crystal morphology and morphological transitions

3. PB modelling involving morphological transitions For a seeded crystallization process with negligible nucleation and secondary nucleation, and crystal agglomeration and breakage, a simplified version of the multi-dimensional population balance model can be illustrated as follows3: wȥ( x, t ) n w ¦ [ ȥ( x, t) g i ( x, t)] b \ ( x, t) , (3) i 1 wt

w xi

where x is an n -dimensional vector representing the size-related parameters of a crystal; ȥ is the number population density function of crystals; g (x, t ) is the growth rate and b (x, t) represents the birth term of ȥ . It is usually assumed that there only exists one morphological form in the crystallizer and thus a single population balance equation (PBE) can describe the evolution of crystal shape and size distributions during the entire crystallisation process. In practice, however, it is not uncommon to encounter crystallisation processes in which various morphological forms of crystals co-exist in the reactor6. Furthermore, morphological changes such as the disappearance of certain faces due to faceted growth can happen as well. Therefore only one PBE for modelling a single morphological form is not sufficient in such scenarios. Here, a morphological PB modelling method is further developed to consider the coexistence of multiple morphological forms and their transitions. Considering a simple case where only two morphological forms exist for cooling crystallisation of a compound: one morphological form has three independent faces, i.e., three size dimensions x , x and x ; the other has only one size dimension x . At the start of the simulation, the amount of crystals for each morphological form is known. It is also assumed that crystals that have three size dimensions can be transformed to crystals that have only one single size dimension. The morphological PB equations for these two types of crystals are given in Equations (4) and (5), respectively: wȥ (x , x , x , t) w ¦ [ ȥ (x , x , x , t) g (x , x , x , t)] b (x , x , x , t) , (4) i

ȥ

1

2

3

1

1

2

3

3

i 1 wx wt i w) (x 1 , t) w  [) (x 1 , t) g ) (x 1 , t)] wt w x1 1

2

3

i

1

b ) (x 1 , t) ,

2

3

\

1

2

3

(5)

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where x , x and x denote the normal distances to the crystal geometric centre for the three faces, respectively; ȥ( x , x , x , t ) is the number population density function of those crystals with x , x and x as their size parameters; )(x , t ) is the number population density function of those crystals with x as their size parameter. At any given time instance t t , with the known number population density functions ȥ( x , x , x , t ) and )( x , t ) for the two morphological forms, Equations (4) and (5) are to be solved simultaneously using high resolution algorithms7. Then the solution ȥ(x , x , x , t ) is split into <( x , x , x , t ) and ij( x , t ) , the later accounts for crystals that have transformed from three size dimensions to only one size dimension, while the former represents those that have not experienced such a transition therefore remaining three size dimensions. ij( x , t ) is to be further merged with )(x , t ) as they all belong to the same morphological form with a single size dimension. Thus the updated number population density functions for these two morphological forms are to be passed to Equations (4) and (5) for the next iteration. It is worth noting that mass balance is also applied to update the supersaturation in the reactor at every iteration based on the updated number population density functions. 1

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4. Optimisation of temperature and supersaturation profiles Since the morphological PB model describes the dynamic evolution of particle shape as well as particle size distribution for all crystals in the reactor as a function of the operating conditions, i.e., supersaturation or reactor temperature, it can be used to derive an optimal supersaturation or temperature profile which leads to a desired particle shape and size distribution. This section demonstrates the process of obtaining the optimal temperature and supersaturation profiles for a defined objective function related to desired crystal morphology of potash alum. Suppose the desired shape of the concerned crystals is: x /x a , x /x a , (6) where a and a are the desired aspect ratios between x and x , x and x , respectively. Then the optimisation problem can be formulated as follows: min ¦ ( ȥ (x , x , x , t )[(x /x  a )  (x /x  a ) ]) / ¦ ȥ(x , x , x , t ) (7) 1

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where r ( t ) is the cooling rate with a given lower bound r and an upper bound r ; and ȥ(x , x , x , t ) is the predicted terminal number population density function. The size-dependent growth rates of the {111} , the {100} and the {110} faces of potash alum are adopted from the literature8. It is assumed that there are initially 4843355 potash alum crystals all with twenty-six faces in a 500mL reactor and the initial temperature in the reactor is 38 0C with an initial relative supersaturation of 0.06589. The corresponding initial number population density function is shown in Figure 2(a) for the fixed x 8.06μm . The optimisation is performed for a time period of 180 seconds using Equation (7) with a a 1 , r 0.02 oC/min and r 0.3 oC/min. The resulting optimal temperature profile as well as the underlying supersaturation profile is shown in Figure 3(a) and 3(b), respectively. The terminal number population density function for the crystals with twenty-six faces is shown in Figure 2(b) and it can be seen that the number population density has dropped L

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dramatically compared to Figure 2(a) because of morphological transitions. Figure 3 shows the optimal temperature and supersaturation profiles. Taken a crystal with the maximal initial number population density in the reactor as an example, its shape evolution under the obtained supersaturation profile is shown in Figure 4, where the morphology of the selected crystal does approach to the desired shape depicted by the wireframe polytope at the end of the simulation.

(a) (b) Figure 2 The number population density function of crystals with twenty-six faces

Figure 3 The optimized temperature and supersaturation profiles

5. Concluding remarks The presented new morphological PB model has proved to be able to simulate cooling crystallization processes where multiple morphological forms co-exist in the reactor and transitions between them can happen. It also demonstrated that the model can be used to derive optimal supersaturation and temperature profiles for a given objective function related to particle shape. Since tracking a supersaturation or temperature profile can be easily achieved via a standard feedback or cascade control system using jacket cooling water flowrate as the manipulated variable, it provides a closed-loop methodology for crystal shape tailoring which can be easily implemented.

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Figure 4 The shape evolution of a crystal under the optimum supersaturation profile

6. Acknowledgements Financial support from the UK Engineering and Physical Sciences Research Council (EPSRC) for the projects of Shape (EP/C009541) and StereoVision (EP/E045707) are acknowledged. We would also like to thank the industrial collaborators for the projects including AstraZeneca, Malvern Instruments, Nexia Solutions, Pfizer, Syngenta and 3M Health Care. 7. References 1. 2. 3. 4. 5. 6. 7. 8.

Patience D. B., Rawlings J. B., AIChE Journal, 2001, 47: 2125-2130. Wang X. Z., Roberts K. J., Ma C., Chemical Engineering Science, 2008, 63: 1173-1184. Wang, X.Z., Ma, C., Roberts, K.J., 2008, 18th European Symposium on Computer Aided Process Engineering, Computer Aided Chemical Engineering, 25: 817-822. Ma C. Y., Wang X. Z., Roberts K. J., AIChE Journal, 2008, 54: 209-222. Kvasnica M., Grieder P., Baotic M., Multi-Parametric Toolbox (MPT) http://control.ee.ethz.ch/~mpt/. Cited in 2008. Matsuoka M., Journal of Physics D: Applied Physics, 1993, 26: B149-B155. Gunawan R., Fusman I., Braatz R. D., AIChE Journal, 2004, 50: 2738-2749. Ma C. Y., Wang X. Z., AIChE Journal, 2008, 54: 2321-2334.

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Multi-scale evolution of optimal process designs for the production of acetic acid via ethane oxidation Daniel Montolio-Rodrigueza , David Linkeb, Patrick Linkec,1 a

Jacobs Engineering, Process & Technology Division, Jacobs House, 427 London Road, Reading, Berkshire, RG6 1BL, United Kingdom b Leibniz-Institut for Catalysis, Catalyst Discovery and Reaction Engineering, RichardWillstätter-Str. 12, 12489 Berlin, Germany c Texas A&M University at Qatar, Chemical Engineering, PO Box 23874, Doha, Qatar, 336D Texas A&M Building, Education City, Qatar

Abstract We present an application of optimal process synthesis approach to heterogeneously catalysed gas-phase reaction systems. It enables the systematic identification of optimal conceptual process designs, the exploration of the relationships between design complexity and performance and the execution of subsequent synthesis stages that enrich the reaction models to incorporate detailed representations of phenomena so that the process designs can be evolved into optimal schemes that resemble reality closely. The technology is applied to evolve a process for the production of acetic acid via ethane oxidation, an industrially relevant process. Throughout the multi-level design cycle, information on the optimal operating envelopes is generated and can be fed back to the kinetics development team to guide additional experiments so as to ensure that kinetic models match the optimal process in which the catalyst is to be used. The evolution takes the form of an iterative process performed in multiple stages. Keywords: Modelling, Optimisation, Process Synthesis, Acetic Acid

1. Introduction To date, a number of superstructure optimization methods have been proposed to address the systematic identification of optimal chemical process designs by exploiting synergies between the reaction and separation process systems [1, 2, 3, 4, 5]. However, applications to heterogeneously catalysed reaction systems are hardly found in industry and academia due to problems in handling the mathematical complexities of realistic reaction models and the inability to incorporate practical process constraints in the problem formulations. We have addressed these shortcomings and developed a superstructure-based optimisation approach tailored to heterogeneously catalysed gasphase reaction systems. The approach follows a multi-level search strategy. At highlevel, the approach employs compact and practical process design representations to screen vast numbers of possible process configurations in order to identify promising conceptual design candidates. The framework allows the development of design performance targets and the identification of interactions between design performance and design complexity to identify those promising designs that should be considered for more detailed analysis at the following levels and eventually evolved into detailed designs. As the synthesis exercise progresses, the knowledge that has emerged about the 1

Corresponding author. Email [email protected]

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process structure is employed to reduce the number of structural alternatives to be investigated whilst more detailed process models are employed. This paper outlines the multi-level approach and presents an application in acetic acid production.

2. Production of acetic acid The ethane oxidation to produce acetic acid promises an interesting alternative to traditional routes (more than 60 % of the world production is through the methanol carbonylation route [6]) and catalyst development has received considerable research interest in this field. An encouraging novel catalyst for ethane oxidation, Mo1V0.25Nb0.12Pd0.0005Ox, has been lately investigated [7, 8]. Seven components take part in eleven reactions. The model considers two different active sites and two different pathways to form acetic acid. On one active site ethylene is transformed to acetic acid via a Wacker-like mechanism and on the other the partial oxidation of ethane occurs.

3. Decision support framework We present a Decision Support Framework (DSF) to effectively approach the process design of heterogeneously catalysed gas-phase reaction systems within a communication framework that will eventually integrate kinetic model development and process synthesis activities (Fig 1.) 3.1. Process representations The DSF relies on process network superstructure representations for heterogeneously catalysed gas-phase reacting systems that have been developed based on previous efforts in superstructure optimisation of integrated reaction and separation systems [2, 3]. The superstructure includes thorough representations of the reaction system through combinations of generic units that account for options related to mixing, temperature policies, catalyst mass, interactions between reaction and separation systems, alternative separation schemes and maximum process to process heat recovery strategies. Practical constraints linked to reactor energy management and explosion limits are also included in the representation. The superstructure optimization of integrated reaction and separation systems is carried out with the stochastic tool Tabu Search [9]. The function to optimise for the presented application is the economic potential (EP). 3.2. Synthesis strategy The synthesis strategy is based on effectively balancing the numerical and combinatorial complexities along the synthesis exercise. At the beginning of the exercise, the process structure is unknown and the combinatorial complexity is high. Therefore, simple models are employed. This early stage of the synthesis exercise is addressed in [1] with the multi-level approach. As the synthesis exercise progresses, the knowledge that has emerged about the process structure is employed to reduce the structural density and more complexity in terms of the process models can be afforded. This is the focal point of the multi-stage strategy presented here. By employing more detailed and computational demanding reactor models in later design stages, the few optimal conceptual designs resulting from the multi-level approach can be explored thoroughly. The addition of modelling detail accounts for the extra non-linearities that enable evolving the optimal conceptual designs into more realistic options. The evolution takes the form of an iterative process performed in multiple stages. The solution of each stage becomes the starting point for the next. The number of stages is not limited and the evolution could progress in as many stages as required. This study considers four stages:

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Stage 1 facilitates the screening of large numbers of design candidates with the help of superstructures that are very rich in alternative design options. Conceptual (ideal) reactor models are employed in this stage to capture major design trends whilst keeping the model complexity at moderate levels to enable a thorough search of the feasible design space. the reactor models include well mixed and plug flow units, with the letter being approximated by cascades of well mixed cells. Temperature profiles are optimized without regards to the heat transfer mechanism. This stage is described in detail in Montolio-Rodriguez et al. [1]. In Stage 2, temperature profiles for the reactors that can be attained with common co-current cooling / heating strategies found in industry are suggested. Therefore, practical solutions to the heat exchange between the reactors and their utility media are proposed. Such developments overcome previous drawbacks in non-isothermal reactor network applications where unreachable and / or unrealistic profiles were proposed. To do so a non-linear minimisation problem is solved after the simulation of each Tabu Search iteration. The formulation of the problem assumes co-current heat exchange strategies with single utilities for each reactor. In Stage 3, the radial heat propagation effects for catalytic fixed bed reactors are included in a highly effective computational approach thanks to the approximation of the radial temperature profile inside catalyst beds following [10]. Stage 4 introduces deals more detailed reactor models to better describe mixing. Cell models for fluidised beds and differential equation based models are employed to effectively optimise complex layouts.

This work focuses the efforts exclusively on the evolution of the reaction representation. A similar approach could be applied for the separation representations. Improved aggregated models could be developed to include more precise information about the separation systems as the synthesis exercise progresses. For consistency reasons, the multi-level approach presented in [1] is referred from now on as Stage 1.

Figure 1: Decision support framework to integrate kinetic model development and process synthesis.

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4. Results The design candidates proposed at the end of Stage 1 [1] are shown in Figure 2. The EP for the base case consisting of a single PFR without internal recycle is 8.5 M$/yr. The presence of internal recycle enhances the OFV of a single PFR up to 141 % (20.5 M$/yr). The presence of oxygen side feeding when more than one PFR is involved, improves the OFV of a single PFR up to 112 % (18.0 M$/yr) for the three PFRs structure. Figure 3 presents the EP for the evolution of the optimal conceptual process designs proposed at the end of Stage 1. For comparison reasons, the evolution of a single PFR without internal recycle is also presented. For the three PFRs structure cases a and b denote different diameter of the tubes that form the multi-tubular reactors. At the end of Stage 4, the single PFR with internal recycle outperforms the single PFR without internal recycle by 129.1 %. The three PFRs without internal recycle and with oxygen feed distribution outperform the single PFR without internal recycle by 60.3 % for Stage 4a and by 73.8 % for Stage 4b. Besides, the OFVs have decreased with respect to Stage 1 as follows: • • •

For the single PFR without internal recycle: 17.8 %. For the single PFR with internal recycle: 21.6 %. For the three PFRs without internal recycle and with oxygen feed distribution: 37.4 % for Stage 4a and 32.1 % for Stage 4b.

Figure 2: Optimal conceptual designs proposed at the end of Stage 1.

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5. Conclusions The described decision support framework aims to be a helpful tool in the near future to allow the computationally effective high-level coordination of process design and kinetic investigation activities. The framework will rely on a multi-level process synthesis approach that identifies the maximum performance of a system regardless its complexity, allows the engineer to understand what design trends improve process performances, and permits the engineer matching the increase of complexity of the designs with the enhancement of the objective function values. The process synthesis approach has been illustrated in this paper. It eases the understanding of the bottlenecks of the system and suggests different optimal conceptual designs for the engineer to judge. The treatment of heat and temperature management issues in the multi-level approach appears to be very ideal. Accordingly, efforts have been focussed on the development of alternative and more accurate ways to manage heat transfer complexities without compromising computational times. These developments are the

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basis of the multi-stage approach, in which during successive stages the level of detail of the reactor models is increased. The increase in the level of detail aims to capture progressively non-ideal behaviours to evolve the initial process designs into designs that can be reached in practice. Four stages illustrate the methodology proposed. It has been observed that after Stage 3, there is not much justification in increasing the level of modelling detail, as further stages result in very similar performances and require much more computational efforts. The approach developed in this stage, allows performing superstructure optimisation with highly complex process design schemes and models. It could be used to test kinetic models at advanced phases of their development in order to increase confidence in the results.

References [1] Montolio-Rodriguez, D., Linke, D., Linke, P., 2007, Chem. Eng. Sci., 62, 5602. [2] Linke, P., Kokossis, A.C., 2003a, AIChE J, 49, 1451. [3] Linke, P., Kokossis, A.C., 2003b, Comput. Chem. Eng., 27, 733. [4] Ismail, S.R., Proios, P., Pistikopoulos, E.N., 2001. AIChE J, 47, 629. [5] Kokossis, A.C., Floudas, C.A., 1991, Chem. Eng. Sci., 46, 1361–1383. [6] Yoneda, N., Kusano, S., Yasui, M., Pujado, P., Wilcher, S., 2001. Appl. Catal., A, 221. [7] Linke, D., Wolf, D., Zeiss, S., Dingerdissen, U., Baerns, M., 2002a, J. Catal. 205, 32. [8] Linke, D., Wolf, D., Zeiss, S., Dingerdissen, U., Mleczko, L., Baerns, M., 2002b, Chem. Eng. Sci., 57, 39. [9] Glover, F., 1986, Comput. Oper. Res., 13(5), 533. [10] Nagel, G. Adler, R., 1971,, Chemische Technik, 23(6), 335.

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Multiscale Modelling Framework for Chemical Product-Process Design Ricardo Morales-Rodríguez, Rafiqul Gani CAPEC, Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark, [email protected]

Abstract The objective of this paper is to present a novel computer-aided model-based framework for product-process design that also includes multiscale modelling features. To develop this framework, a combination of different computational tools, such as, property prediction packages, modelling tools, simulation engines, solvent selection software, etc, are necessary together with a set of established systematic work-flow and data-flow for various types of design problems. This framework allows the user to cover a wide range of problems at different scales (of length and time) and disciplines of chemical engineering and science in an easy and efficient manner; achieving in this way the development of a product-process with the desired end-use characteristics. Development of a pesticide formulation product where its uptake into the plant is used as a product performance measure, is used to highlight the work-flow and data-flow in the multiscale modelling framework.

Keywords: Multiscale modelling, product-process design, framework, virtual lab 1. Introduction The design, development and reliability of a chemical product and the process to manufacture it, need to be consistent with the end-use characteristics of the desired product. One of the common ways to match the desired product-process characteristics is through trial and error based experiments which can be expensive and time consuming. An alternative approach is the use of a systematic model-based framework according to an established work-flow in product-process design, replacing some of the time consuming and/or repetitive experimental steps. Furthermore, for many chemical products the appropriate models for product-process design need to have multiscale features as the properties defining the chemical structure and the product end-use characteristics are dependent on parameters of different size and time scales. The advantages of the use of multiscale modelling approach in this case is that in the design, development and/or manufacturing of a product-process, the knowledge of the applied phenomena can be provided at diverse degrees of abstractions and details. Some authors [1-4] have highlighted the importance of the multiscale and multidiciplinary approach in product-process design and identified design issues related to different scales of size, time and complexity. The development of a computer-aided framework for product-process design including a multiscale modelling option is very important for analysis, design, and/or identification of feasible chemical product candidates because it allows one to consider

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processing issues during the development of the product. The multiscale modelling framework should include the product and process design components, modelling tools and templates (work-flow) for guiding the user through the appropriate design steps. The integration of computational tools is also necessary to increase the application range of the computer-aided product-process framework; where the connection between computational tools could be established through well-defined COM-objects or the CAPE-OPEN standards. A novel computer-aided model-based framework for product-process design, that also includes multiscale modelling features, is presented in this paper. To develop this framework, a combination of different computational tools, modelling tools, simulation engines, molecular and mixture design software, solvent selection software, etc, are integrated within a set of established systematic work-flow and data-flows for various types of design problems. The performance of the multiscale model-based framework, the associated models and the work-flow for a specific product-process design is illustrated through a case study involving the modelling and design of a pesticide product; here, the pesticide uptake inside the leaf is designed and evaluated through the use of the framework, where a suite of models, database of properties, chemicals, and, a modelling tool are employed.

2. Multiscale Modelling Framework for chemical product-process design: Requirements. The multiscale modelling framework allows the user to cover a wide range of problems at different scales (of length and time) and disciplines of chemical engineering and science in an easy and efficient manner; achieving in this way the development of a product-process with the desired end-use characteristics. Another requirement of the modelling framework and the software architecture is a feature that provides the means for integration and merging of methods and tools from different sources. This architecture needs to accommodate models used for the prediction of the product behaviour/performance. Here, ICAS-MoT is the main modelling tool, which provides interactions with modelling engines, external software through the use of COM-objects, and also with external simulators through with the use of CAPE-OPEN standards. More details about this synergy is described by Morales-Rodríguez et al.[5] . Figure 1 illustrates the multiscale modelling framework for chemical product-process design where four main parts can be found: ƒ ƒ ƒ ƒ

problem definition, product design, product-process modelling, product-process evaluation.

Each of them have sub-steps that guide the user through a systematic work-flow and data-flow to solve specific design problems.

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Fig. 1. Multiscale modelling framework for chemical product-process design.

Problem definition: The multiscale modelling framework for chemical product-process design starts with the conceptual definition of the design problem, which concerns with setting the desired characteristics of the product, its properties, special qualities, ingredients to make the product, etc., that might apply for a new product or for existing products that need to be improved. Product Design: Often, information needed to perform product behaviour analysis is lacking. To overcome these gaps of information, computer-aided methods and tools are employed. That is, the use of specialized computer-aided tools such as, databases containing properties of chemicals, property prediction packages, molecular and mixture design software, solvent selection tools, etc. (all these computational tools can be found in the ICAS software developed by CAPEC at Technical University of Denmark) are employed in order to address the issue of missing information. The first sub-step involves generation of data/knowledge related to the product needs, ingredients, assumptions in the conceptual design work-flow, historical records, etc., that are needed in the subsequent steps. Another sub-step in this part consists of the selection of the materials to be added to the product taking into consideration, its application; functional property values; primary property values; main active ingredients; solvents; coatings; etc., as well as the calculation of the necessary properties (such as, diffusion coefficients, partition coefficient, surface tension, etc.) related simulation model to be used in product performance evaluation. Product-Process Modelling: Once the necessary information for evaluating the product performance through the generated models has been retrieved, a modelling tool is used to assist in the simulation and generation of alternatives and verification of the formulated properties through the ICAS-MoT (available in ICAS). ICAS-MoT is essentially a modelling tool able to generate, analyze and simulate mathematical models without extra programming efforts. In this way, the predicted product behaviour is compared against the desired targets specified at the beginning, and decided if the targets have been matched.

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Product-Process Evaluation: If the design targets are not matched, a new product design problem is started, or, a model-based analysis is made and the subsequent steps repeated to find another solution. If the targets are matched, before proceeding to manufacturing the product; an option to evaluate product-process performance is provided through the use of ICAS-MoT. Furthermore, an option to make sustainability analysis in order to evaluate the environmental and economical impact for the production and performance of the product is provided. More details of the systematic multiscale modelling framework for chemical product-process design of microcapsules for controlled release of active ingredients can be found in Morales-Rodríguez and Gani (2008) [6] .

3. Case Study for pesticide uptake prediction through the use of the multiscale modelling framework for chemical product-process design. To highlight the use of the modelling framework, a pesticide uptake example has been chosen due to its multiscale features from the modelling point of view.

Fig. 2. Multiscale description of pesticide uptake

Figure 2 shows that the modelling of the pesticide uptake can be carried out in an entire field that basically corresponds to the macroscale where the behaviour in a specific area is analyzed, and/or the impact of the pesticide to the environment is calculated; an analysis in a droplet scale is also performed, that is, the behaviour of the active ingredient inside the droplet as well as the vaporization of the liquid phase are predicted (this plays an important role in pesticide uptake); further analysis in a smaller scale (the behaviour of the pesticide uptake inside the leaf can be predicted) is performed. Here, the importance of the pesticide mass transfer phenomenon between the droplet and the leaf as well as inside the leaf is considered. A computer-aided tool called “Virtual Product-Process Design Lab” has been developed, where the multiscale modelling framework has been included, for chemical product-process design. The models at the various scales, needed for design and analysis of pesticide uptake is available in the model library. The case study involving

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the design of the pesticide formulation and the prediction of the pesticide uptake is highlighted for the active ingredient (AI) cyanazine, which is to be sprayed in a wheat field together with a surfactant called C13E11. Figs. 3a-3d depict the workflow for the design of cyanazine based pesticide formulation and the models needed at various scales, from the droplet scale to the overall pesticide uptake. Fig. 3a (problem definition) shows the step where the generation of information related with the product properties, ingredients, assumptions, etc. is carried out and saved in a documentation file for future examination and/or use.

Fig. 3. Design of one Pesticide using the multiscale modelling framework

Fig. 3b (product design) shows the selection of the plant where the pesticide will be applied, also the selection of the pesticide to be used in the formulated product as well as the surfactant. All the information that is collected in this part is transferred to the modelling tool. Fig. 3c (product-process modelling) shows the different mathematical models [7] that are available in the model-based library for this problem, each model takes into account different phenomena as well as different assumptions allowing the user to have a wider range of applicability in the pesticide formulation design. Note that this is one of the reasons for having a large model-based library. Once the virtual design has been done, an evaluation of the product behaviour performance is carried out; Fig. 3d (product-process evaluation) shows the results highlighting the calculated amounts of pesticide uptake by the leaf. Here, it is allowed to ask if the performance criteria have been satisfied. If “Yes” a new product alternative has been developed and verification

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by experiment can now be performed, if necessary. Otherwise, it is possible to return to the appropriate product design step and repeat with other options until the desired performance criteria are matched. The size of the mathematical model depends on the scenario being evaluated and the number of discretization points. The model consists of a set of differential and algebraic equations representing the phenomena of evaporation rate of the droplet, mass transfer of the pesticide AI and solvent through wax and cuticle layers of the leaf. It is important to note the multidisciplinary nature of the problem (different sources of information from different parts or fields of science, for instance, the information about the leaf conformation, diffusion coefficients for biological systems, weather conditions that effect in the behaviour of the plant, etc.) and the multiscale characteristics of the model.

4. Conclusion A systematic multiscale model-based framework for product-process design has been developed and its application illustrated through the design/analysis of the uptake cyanazine as the pesticide AI. The usual trial and error experimental-based approach has been replaced with a virtual product/process lab, which allows some of the time consuming and repetitive steps to be performed virtually through a model-based framework. In this way, the resources of experimental work are reserved for the final verification of the product, when a small number of candidates matching the desired end-use characteristics of the product have been identified. Finally, for the virtual product-process design lab to succeed, reliable multiscale models must be available in a model-library and used through an appropriate model-based framework, that can also help to generate models, when they are not available. The framework also contains models for design of devices for controlled release of active ingredients and for design/analysis of direct methanol fuel cells.

5. References [1] Charpentier, J.C., Comp. Chem. Eng., 57 (2002) 4667. [2] Charpentier, J.C., ESCAPE 17: Vol. CACE 24, (2007) 11. [3] Gani, R., Comp. Chem. Eng., 28, (2004) 2441. [4] Klatt, K.U. and Marquardt, W., ESCAPE 17: Vol. CACE 24, 19. [5] Morales-Rodríguez, R., Gani, R., Déchelotte, S., Vacher, A. and Badouin, O., Chem. Eng. Res. Des., 86 (2008) 823. [6] Morales-Rodríguez, R. and Gani, R. Proceedings of Chempor 2008. Braga Portugal. [7] Rassmusen, J.K., Prediction of Pesticide Uptake in Plants, Master Thesis, Department of Chemical engineering of Technical University of Denmark.

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System approach to modeling of pharmaceutical integrated processes: drying, layering and coating Natalia Menshutina,a Mariya Gordienko,a Yulia Makovskaya,a Alia Kasimova,a Alexei Voinovskiya a

High Technology Department, Mendeleyev University of Chemical Technology of Russia, Miusskaya sq. 9, Moscow, 125047, Russia

Abstract The paper concerns the system approach to modeling of pharmaceutical technology of drying, layering and coating in fluidized bed apparatus. The mathematical modeling bases on the statistical method for micro-level phenomena description and on heterogeneous media mechanics and non-equilibrium thermodynamics for macro-level description. Keywords: pharmaceutical integrated processes, layering and coating, modeling, system approach

1. Introduction Industrial engineering of pharmaceutics is specific and characterized by high atomization of manufacturing processes, by use of modern efficient equipment and narrow specialization of production. Fluid-bed equipment for integrated processes of mixing, drying, granulation, layering and coating allows to effective process of heatsensitive pharmaceutical substances. The other advantage is that several manufacturing stages could be done in the same equipment. Nanosystems of phospholipids micelles are universal drug delivery systems. A drug based on phospholipids restores the structure and functions of the damaged hepatocyte’s membranes. In this work the main component was phosphatidylcholine. It exists in the form of micellar structures, providing the micelle penetration to liver cells where they act as membrane glue. It is necessary to preserve pharmacological activity of phospholipids during manufacturing of solid dosage form and to deliver the active substance to intestines. The method of enteric film coating microspheres preparation containing the layer of phospholipids nanoparticles (50÷60 nm) has been investigated in this paper. The twostage process consists of: stage 1 is layering of heat and pH-sensitive active substance on placebo-pellets; stage 2 is enteric film coating. Both stages are carried out in the same fluid-bed equipment (Mycrolab, Huettlin). For scientific foundation and validation of layering and coating operation parameters it is necessary to get the clear understanding of the physical basis of phenomena which have place in apparatus, their interconnections and degree of interference between them; to take into account the specificity of biomaterial and to considerate the limitations.

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2. System approach to modeling of pharmaceutical integrated processes Layering and coating consist of micro-level phenomena such as: suspension atomization, drop and pellet collision, collision between pellets, drop adhering or rebound, spread of drop across pellet surface, infiltration, drying, particle agglomeration [1], Figure #1. The product quality is defined by physical-chemistry properties of pellets, suspension with active substances and polymer suspension; process parameters (suspension flow rate, atomization pressure, flow rate and temperature of fluidized agent and other), bed mass, size of pellet, hydrodynamics mode in apparatus. The mathematical modeling of integrated processes of drying, layering and coating is multiparametric task where all parameters have the internal relations and that could be solved by using the system approach [2]. One of the main principles of system approach is the system decomposition onto levels and revelation the relation between them. Concerning the fluid-bed system two hierarchy levels had been detected: the single particle level and apparatus level. Investigation and formalization of all microlevel phenomena is very complicated task. Therefore the statistical modeling based on experimental data was applied for description of single particle level. In this approach the mathematical description is found as system response to variation of operation parameters. The complex of experimental and analytical investigation was carried out.

3. Complex of experimental and analytical investigation Design of experiments As it was mentioned above in integrated processes the quality of product depends on lot of parameters. Some of them were used as variable (see Table #1); the other ones were not changed during experiments. The layering and coating were carried out as provided by the complete factorial design and compositional factorial design correspondingly. Table #1. Variable parameters of layering and coating experiments

Variable parameter

Value of parameter Stage 1: Drug layering Fluidized air temperature, °C 40 50 Concentration of phospholipids, % wt 5 6 Stage 2: Enteric film coating Fluidized air temperature, °C 40 50 Concentration of polymer, % wt 20 25 Flowrate of coating liquid, ml/min 0.7 1.5

60 7 60 30 2.3

Experimental results The quality of final products are characterized by concentration of phospholipids incorporated in product, the size distribution of phospholipids micelles, the shape and

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size distribution of microspheres (after the fist and the second stages), homogeneity and roughness of enteric film, residual moisture content, bulk density, flowability, coating efficiency. Figure #2 shows some of layering result. Layering at low fluidized air temperature (40 0 C) accompany be the microspheres agglomeration (two peaks on microspheres size distribution and “twins” image – see Figure #2, a-b). The higher air temperature (60 0C) allows to avoid the bridges formation and get uniform layer of active substance (Figure #2, c-d). The concentration of phospholipids molecular nanostructures incorporated in final products had been defined by UF-spectrophotometric method. Based on those data the efficiency of layering had been calculated. It was found that the drug losses not exceeded 7 %. There are some reasons of drug losses. At temperature 40°C and low concentration of preparation in initial solution the drop has no enough time to achieve the sufficient viscosity for successful adhesion before collision with a particle. After collision with particle the greater part of a drop is spattered and the small fraction fines are passed away together with the drying agent from the chamber.

Figure #2. Layered microspheres: a – size distributions; b,c – morphology; d – inner structure

At the high concentration of feed liquid and temperature 40 °C the drop has sufficient viscosity – and the greater part of drops successfully collides with a surface of microsphere. However, at this temperature the drying velocity is too low and the microspheres are located into the high compactness zone with high surface stickiness – two peaks on the microspheres size distribution plot (see Figure #2). It means a lot of particles stuck together. At temperature 60°C and low concentration of a preparation in initial solution the drop has time to get dry for successful collision with microsphere. And at the same time the drop has good flowability, which positively exerts on quality of coating. At high concentration of phosphatidylcholine the drop gets excessive hardness before collision with microsphere that promotes the rebound of drop from pellet. The mechanism of film formation during coating was similar. Some of experimental results are presented at Figure #3.

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Figure #3. Coating experimental results

The size of micellar nanostructures in product had been defined by the photon correlated spectrometer. It was found that the size of micelles after encapsulation has not changed practically and lies in the admissible range. Statistical treatment To predict the influence of fluidized air temperature (Tinlet air) and initial solution concentration (Cactive sub.), polymer concentration (Cpolymer) and flowrate of feed coating solution (Lsusp.) on the product yield (Gout), residual moisture content (W), bulk density (ρbulk), flowability (ξ) and coating efficiency (Efcoating) the experimental data had been analyzed using statistic methods. It was found that the dependence of product yield on operation condition could be described by the second order regression equation 1: Gout = 918 .67 − 5 .235 ⋅ Tinlet air − 47 .551 ⋅ C active sub . + 2 -3 2 + 0 .197 ⋅ C inlet air ⋅ Òactive sub . + 0.566 ⋅ Ñ active ⋅ Òinlet sub. - 6.483 ⋅ 10 air

(1)

The mass of losses could be calculated by using the equation 2: G Loss = 100 − G out

(2)

Dependences of residual moisture content, bulk density, flowability and coating efficiency on concentration and flowrate of feed polymer solution, inlet air temperature are following: W = 1.30 − 0.08 ⋅ C polymer + 0.23 ⋅ Lsusp. + 0.04 ⋅ Tinlet air + 0.06 ⋅ C polymer ⋅ Lsusp. + 2 2 + 0.09 ⋅ C polymer ⋅ Tinlet air + 0.29 ⋅ C polymer + 0.19 ⋅ L2susp. + 0.66 ⋅ Tinlet air

(3 )

ρbulk = 0.8544 − 0.0055 ⋅ C polymer − 0.004 ⋅ Lsusp . + 0.0075 ⋅ Tinlet air + 0.005 ⋅ Lsusp . ⋅ Tinlet air

(4 )

2 ξ = 16.09 − 0.77 ⋅ Tinlet air − 0.06 ⋅ C polymer ⋅ Lsusp . + 0.09 ⋅ C polymer ⋅ Tinlet air + 0.85 ⋅ Tinlet air

(5 )

Ef coating = 80.79 + 2.83 ⋅ Lsusp . − 1.47 ⋅ Tinlet air + 1.37 ⋅ C polymer ⋅ Lsusp . − 0.9 ⋅ Lsusp . ⋅ Tinlet air − 2 2 − 0.97 ⋅ C polymer ⋅ Tinlet air − 0.95 ⋅ C polymer − 3.15 ⋅ L2susp . − 1.66 ⋅ Tinlet air

(6 )

These dependences were included in mathematical description to predict of product quality.

4. Mathematical modelling The mathematical model based on heterogeneous media mechanics and non-equilibrium thermodynamics had been developed to choose the optimal operation parameters and to get the highest quality of final microspheres. The mathematical model consists of the mass, momentum and energy conservation equations written for gaseous and dispersed phases for nuclease and ring zones; equations described drying kinetics of layering

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biosuspensions and coating material, some additional correlations, initial and boundary conditions. The numerical solution of the system allowed to investigate the drying process and to found the distributions of basic phases parameters in dryer. The calculated velocities distribution of fluidized air and microspheres in nuclease and ring zones versus bed height are presented at Figure #4 (a). As it was mentioned above some part of phospholipids suspension is lost. The Figure #4 (b) shows the dependence of spread liquid mass and layer mass versus process time which was calculated by using the mathematical model and taken into account the possible losses.

Figure #4. Calculation results: a – velocities distribution; b – distribution of spread liquid mass and layer mass

The mathematical model was verified by using of experimental data. It was found the model is adequate to the experiment.

References [1] Stephen R.L. Werner, Jim R. Jones, Anthony H.J. Paterson, Richard H. Archer, David L. Pearce (2007) Air-suspension coating in the food industry: Part II — micro-level process approach. Powder Technology –171. –p. 34–45 [2] Kafarov V.V., Dorohov I.N. (1976) Systems analysis of chemical technology process. Strategy fundamentals. –Ɇ.: Science, –500p.

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Transport and reaction in reconstructed porous polyolefin particles Alexandr Zubov, Lucie Pechackova, Libor Seda, Juraj Kosek Department of Chemical Engineering, Institute of Chemical Technology in Prague, Technicka 5, 166 28, Prague 6, Czech Republic, [email protected]

Abstract In this contribution porous polyolefin particles were digitally reconstructed from X-ray micro-computed tomography images with spatial resolution of about 3 micrometers. Calculation of transport and polymerization processes has been carried out in these spatially 3D reconstructed porous particles. The effect of particle structure on the diffusion and reaction of monomer species was systematically investigated with real spatially 3D particle structures. Keywords: X-ray tomography, reconstruction, diffusion and rection in heterophase media

1. Introduction The knowledge of transport characteristics of monomers and diluents in porous polyolefin particles is important for the quantitative prediction of particle growth in gasand liquid-dispersion reactors for catalytic polymerization of olefins. Transport of monomers and diluents affects the rate of polymerization, the rate of particle growth, the copolymer composition distribution within the particle, and the morphology of the growing particle. Moreover, transport characteristics have a strong impact on the degassing of polyolefin powder in the post-polymerization processing.

2. Reconstruction of porous polymer particles The polymer particles used in our simulations have been digitally reconstructed from several sets of X-ray micro-tomography images where spatial resolution of one pixel corresponds approximately to 3 microns. One of the original images from tomography measurement is visualized in Fig. 1a. The next step in the processing of tomography images is their conversion from the color to the binary picture which is made by the application of a threshold function, which changes the color of each pixel in the image either to black if the preset intensity is lower than the chosen one, or to white in the opposite case. The optional modification of tomography images includes the processing of the noisy data by common binary operations of mathematical morphology, e.g., cleaning, opening, closing etc. The processed set of binarized images is then transformed by the so called phase function fg(r) to ones (porous phase) and zeros (solid phase), cf. Eq. (1).

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Figure 1. Digital reconstruction of polyolefin particles. (a) original image from X-ray tomography measurement; (b) binarized image; (c) low porous polymer particle K3_2; (d) highly porous polymer particle.

­1 if r ∈ pore f g (r ) = ® ¯0 otherwise

(1)

Symbol r = (x, y, z) represents the spatial position of the voxel.

3. Dynamics of degassing of reconstructed polyolefin particles In this contribution we aimed at the dynamics of diffusion of penetrants away from the polymer particle because this process is crucial for the post-polymerization processing of the polymer. The non-stationary diffusion in the porous particle is considered to be governed by equations

( / ∂t + ∇ ⋅ (– D

) )= 0

gas gas gas ∂cM ∇cM =0 / ∂t + ∇ ⋅ – DM pol ∂cM

pol pol M ∇cM

in pores , in polymer

(2a, b)

gas pol gas pol and DM are monomer diffusivities in gas and polymer, and cM and cM where DM are monomer concentrations in gas and polymer, respectively.

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By assuming the linear sorption equilibrium of monomer in the amorphous polymer, i.e. Henry’s law, and taking into account the polymer crystallinity, the eqs. (2) can be rewritten into form

∂c M +∇⋅ – DMgas ∇c M = 0 in pores ∂t , (1 − χ cr ) ∂c M § (1 − χ cr ) pol · + ∇ ⋅ ¨¨ – DM ∇c M ¸¸ = 0 in polymer H ∂t H © ¹

(

where

χ cr

)

(3a, b)

is the volume fraction of crystalline phase in polymer, H is Henry’s constant

gas . The detailed derivation of eqs. (3) can be found in Seda et al. (2008). and c M = c M Eqs. (2 and 3) can be further simplified by introduction of modified monomer * : diffusivity in polymer D M

(– D

pol M

) (

) (

)

∇cMpol = – (1 – χ cr )( DMpol / H ) ∇cMgas = – DM* ∇cMgas .

(4)

The diffusion in pores is much faster than in the polymer thus it can be neglected and we solve only the equation (3b) with the boundary condition of sorption equilibrium and continuity of diffusion fluxes on gas-polymer interface. The initial and boundary conditions are bulk ­°cM in polymer, f g (r ) = 0 t = 0 : cM = ® in pores, f g (r ) = 1 , °¯ 0 t > 0 : cM = 0 in pores, f g (r ) = 1

(5)

where fg(r) is the phase function defined by eq. (1). The finite volume method with multigrid algorithm was employed for processing of dynamic evolution of concentration of monomer species. The parameters used in simulation were cMbulk = 662.4 mol/m3, χcr = 0.67, H = 2.08, * gas =6×10–6 and DMpol =6×10–11 ( DM =0.9519×10–11 m2/s).The evolution of the DM amount of sorbed monomer in the polymer particle is visualized in Fig. 2a. Vertical axis in Fig. 2a displays the ratio Δm/Δm0, where Δm is the actual sorbed mass of monomer, Δm(t) = mM(t) – mM(tĺ∞), and Δm0 is the initial mass of sorbed monomer Δm0 = mM(t = 0) – mM(tĺ∞). The degassing curve of compact spherical polymer particle, with same volume of solid phase as particle K3_2, obtained by solution of second Fick’s law in spherical coordinates, cf. eq. (6), is also visualized in Fig. 2.

∂ c 1 ∂ § 2 eff ∂c · = ¨r D ¸ ∂t r 2 ∂r © ∂r ¹

(6)

Symbol Deff represents the effective diffusion coefficient and r is spatial coordinate. It is evident, that the effective diffusivity in the case of spherical particle must be higher to achieve similar evolution of degassing as in case of porous particle because of missing degassing to internal pores as visualized in Fig. 2b. However the approximation with Fick’s diffusion from spherical particle is possible only in case of very compact

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particles, for example K3_2. We showed in Seda et al. (2008) that in case of porous particles with broad distribution of solid polymer zones, cf. Fig. 1d, the degassing curve is not possible to approximate with simple Fick’s diffusion from spherical particle. 1,0 Particle K3_2 Spherical particle with same volume Deff = 1.2×10–11 m2/s

Δm/Δm0

0,8

Concentration (mol/m3)

0,6 0,4 0,2 0,0 0

1000

2000

3000

4000

5000

time / s

(a) (b) Figure 2. Evolution of amount of sorbed monomer in polymer particle. (a) full line corresponds to degassing of particle K3_2 and the dashed line corresponds to degassing of spherical particle with the same volume of solid phase; (b) concentration profile in particle K3_2 in simulation time t = 100 s.

4. Polymerization reaction in polyolefin particles In this chapter we discuss the effect of diffusion limitations on the co-polymerization reaction of ethylene and 1-hexene. We assume that the polymerization proceeds in the mature stage of its growth and its size does not evolve any more. In this case we can also assume that the catalyst is homogeneously distributed in the particle and the reaction is also considered to be homogeneous. The equation describing this pseudosteady state reaction-diffusion model can be written as

­ D gas in pores (10) 0 = ∇ ⋅ (DM ∇c M ) − k1 c M , where DM = ® M pol ¯(1 − χ cr ) ( DM /H ) in polymer where k1 is the reaction rate constant in polymer phase (k1 = 0 in pores).

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Concentration (mol/m3)

(b)

(a) Concentration (mol/m3)

Ratio chex / ceth

(c) (d) Figure 3. Concentration profiles of (b) ethylene and (c) 1-hexene in porous polymer particle (a); (d) ratio of concentration of 1-hexene to ethylene. The ratio of reactivity of ethylene to 1-hexene is chosen to be (khex/keth)=0.05 and the ratio of diffusivities is (Dhex/Deth)=0.5. Other parameters are the same as in case of dynamic degassing. These data approximately correspond to the experimental investigation of co-sorption of ethylene and 1-hexene and to composition of resulting polymer. The Galerkin version of finite element method with conjugate gradient method was employed for the steady state reaction-diffusion problem. The results of simulations are visualized in Fig. 3. It is evident, that in case of polymerization of ethylene there are significant diffusion limitations in transport into the centre of large polymer blocks. On the other hand, the diffusion limitations are not significant for co-polymerization of 1-hexane, because its reactivity is twenty times lower and diffusion can supply the consumption of monomer even in the large compact polymer blocks which significantly affects the copolymer composition in the grown particle.

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5. Conclusions The algorithms for dynamic simulation of diffusion and steady state simulations of diffusion-reaction problems in complex spatially 3D porous polyolefin particles have been developed. We demonstrate the effect of structure of real polyolefin particles reconstructed from X-ray tomography measurements on copolymer composition during mature stage of polymerization and on dynamics of degassing during postpolymerization processing of the polymer particles.

6. Acknowledgement The support from GACR 104/07/1127 and from KAN 208240651 is acknowledged.

References L. Seda, A. Zubov, M. Bobak, J. Kosek, A. Kantzas, 2008, Transport and reaction characteristics of reconstructed polyolefin particles, Macromolecular Reaction Engineering 2, 495-512. J. Kosek, F. Stepanek, M. Marek, 2005, Modeling of transport and transformation processes in porous and multiphase bodies, in Advances in Chemical Engineering, Vol. 30 „Multiscale Analysis“, edited by Marin G.B., pp. 137-203, Elsevier. M. Bobak, T. Gregor, B. Bachman, J. Kosek, 2008, Estimation of morphology characteristics of porous poly(propylene) particles from degassing measurements, Macromolecular Reaction Engineering 2, 176-189. A. Novak, M. Bobak, J. Kosek, B.J. Banaszak, T. Widya, D. Lo, W.H. Ray, J.J. de Pablo, 2006, Ethylene and 1-hexene sorption in LLDPE under typical gas-phase reactor conditions: Experiments, J. Appl. Polym. Sci. 100, 1124-1136.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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A New Parallel Tempering Algorithm for Global Optimization: Applications to Bioprocess Optimization Silvia Ochoaa,b, Jens-Uwe Repkea and Günter Woznya a

Chair of Process Dynamics and Operation, Berlin University of Technology, Sekr. KWT 9, Strasse 17. Juni 135, Berlin 10623, Germany b Research Group on Modeling, Optimization and Control (GIMOC), Universidad de Antioquia, Medellín, Colombia

Abstract A new optimization algorithm inspired in the behavior of molecules in solution is presented. The molecules are subject to different forces: intermolecular repulsion, stochastic and friction. Molecules are classified according to their objective function into explorers and refiners. Refiners are subject to higher friction values, forcing the search to a narrow region around their current position (local optimization). Explorers are strongly influenced by repulsion forces resulting in the displacement towards low molecular density zones, allowing the evaluation of unexplored regions (global optimization). The performance of the new molecular-inspired parallel tempering (MIPT) algorithm is compared to other stochastic and gradient-based methods for solving two case studies in bioprocess optimization. It is demonstrated that the MIPT algorithm is very efficient, reaches the best optimal values, explores a wider region of the solution space without requiring much computational effort and it is capable of finding different global and local optima simultaneously. Keywords: Parallel Tempering, Bioprocess Optimization, Parameter Identification, Bioprocess Dynamic Optimization.

1. Introduction Optimization is a vital tool for assuring the economic feasibility of many biotechnological processes. It has been used in bioprocess-related applications mainly for identifying reaction kinetic parameters, for solving dynamic optimization problems in fed-batch bioreactors, for designing integrated plants, for designing optimizationbased control systems, and for identifying optimal operating conditions (Banga et al., 2005; Ochoa et al., 2007). Bioprocess parameter identification and dynamic optimization of fed batch bioreactors are highly nonlinear optimization problems involving a large number of decision variables and usually presenting multiple optima. In these cases, gradient-based local optimization techniques may become trapped in local optima, especially when they are started far away from the global solution (Banga et al., 2005). On the other hand, stochastic optimization methods have shown to present a better performance converging faster to the vicinity of the global solution (Banga et al., 2005). In this work, a new stochastic optimization method based on the parallel tempering algorithm (Earl and Deem, 2005), is applied to two particular bioprocess case studies: the dynamic optimization of a fed-batch fermentation process using non-linear feeding profiles and the identification of the kinetic parameters for an ethanol production process model.

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2. Parallel Tempering Parallel tempering (PT) algorithms simulate various non interacting replicas of the original system at different temperatures. Replicas at higher temperatures are able to explore wider regions, whereas those at lower temperatures are able to perform a finer sampling in local regions of the search space (Earl and Deem, 2005). A special characteristic of PT algorithms is that it is possible to exchange temperature or information between different replicas, providing a global character by allowing escaping from local minima and exploring a wider search space. PT methods have been successfully applied in different fields (simulation of polymers, proteins, solid state, quantum and general optimization problems) for more than 20 years. However, there are still open topics regarding the algorithm, especially related to the exchange configuration mechanism, like the number of replicas and the method of temperature exchange. Regarding the last topic, it is important to notice that normally exchange is done between neighbor replicas (at adjacent temperatures), although this is not a restriction of the method. Additionally, it has been suggested that temperature may not always be the best parameter to temper, and that PT can be conducted by other parameters such as pair potentials or chemical potentials (Earl and Deem, 2005). In the following section, a new PT algorithm is introduced, in which the replicas mimic the behavior of molecules in solution, and a friction factor is the parameter used for tempering. The friction factor is related to the friction experienced by the molecules and it is inversely proportional to the temperature of the replica.

3. Molecular-Inspired Parallel Tempering (MIPT) Algorithm A new Molecular-Inspired Parallel Tempering (MIPT) algorithm is proposed in this work for finding global optima in nonlinear optimization problems. The MIPT algorithm mimics the behavior of charged molecules in solution. Each molecule is affected by three different forces as can be seen in Figure 1. The repulsion force (Frep), is a force exerted by other molecules with an electrostatic charge of the same sign, and it is inversely proportional to the square of the distance between each pair of molecules as stated by Coulomb’s law. The random force (FBm), responsible for Brownian motion of the molecule, is expressed by means of a normalized Gaussian distribution (mean zero and standard deviation one). The last force is a friction force (Ff) which has an opposite direction to the net force (Fnet=Frep+FBm) and it is proportional to the velocity (X) of the molecule. It is important to remark that the proportionality factor of the friction force, which is the friction coefficient (J), is the parameter used in this method for conducting the tempering. This proposal comes from the physical meaning of the friction coefficient, which is a function of the inverse of the temperature (J v 1/T). The friction factor J is calculated as a function of the objective function fobj to be optimized. FBm Ff

-

Frep Fnet

d ij

FBm

-

Ff

Fnet Frep

& Frep (i)

š

d ij

K1 ¦ 2 j z i d ij & & FBm (i) K 2[G (i) & Ff (i) J X & & & ¦ F(i) Frep  FBm  Ff

0

Figure 1 Representation of forces acting on charged molecules in solution. Black spheres represent molecules of the solvent. Gray spheres represent charged solute molecules

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1

K1, K2

Initialization

Data Input

-Number of decision variables, ndv -Number of molecules, nm -Number of iterations, niter

Determine new molecular positions: xnew(i) = xopt(i) + 'x(i)

Generate nm feasible molecules x0 Evaluate fobj for each molecule

Evaluate Fobj at new positions: fnew(i) = fobj(xnew(i))

iter = 0 fopt(i) = fobj(i) xopt (i)= x0(i)

Calculate free energy change as: 'G(i) = (fnew(i)-fopt(i)) / max|fopt|

Iter
No

Print results: fopt, xopt

Yes

No

exp(-EJ(i)'G(i))>rand? Metropolis condition

iter = iter + 1

Reject new position

End Classify the molecules: If fobj(i)<median(fobj) ^ x(i)= feasible: Refiner else: Explorer Calculate the friction coefficient for each molecule J(i) and the total repulsion force Frep(i)

J (i) & Frep (i )

Yes

J f obj (i)  K1 ¦ j zi

Generate a Gaussian random vector [G(i) and calculate the displacement 'x(i) of each molecule 2

1

& 'x (i)

& d ij

d ij3

& & Frep (i)  K 2 [ G (i)

Explorer Molecule?

No No

Yes

xnew feasible? Yes

Update molecular position xopt(i) = xnew(i) fopt(i) = fnew(i)

J (i)

2

Figure 2 Molecular-Inspired Parallel Tempering (MIPT) Optimization Algorithm

A detailed flow diagram of the algorithm is presented in Figure 2. The algorithm starts by generating a set of nm feasible molecules with initial positions (xi,0) determined randomly. At each iteration, the molecules are classified into refiners and explorers according to their objective function value: half of the molecules, those with the better objective function values, are designated as refiners whereas the other half as explorers. Refiner-type molecules are always feasible points subject to higher friction values that force the search to a narrow region around their current position (local character). On the other hand, explorer-type molecules are allowed to be unfeasible, to have lower friction values and they are more strongly affected by repulsive effects, which force them to move towards unexplored zones (global character). The net force (Fnet) acting on each molecule is responsible for its displacement in the space of decision variables. Such displacement is calculated as shown in (1). & & Frep (i)  K 2 [ G (i) & (1) 'x (i) 't J (i) K2 is a parameter of the system describing the magnitude of the random force acting on the molecules. [G is a random number obtained from the normalized Gaussian distribution and 't is an arbitrary time step considered for the displacement 'x of the

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molecule. In general, the time step can be chosen as one unit of time ('t=1). If 't is selected too large or too small, the effect of the different forces acting on the molecules will not be properly described by (1). After determining the displacement ('x(i)) of the i-th molecule, the Metropolis condition is used to accept or reject the new position for the explorers. In the case of the refiners, in addition to the Metropolis condition, a new position is only accepted if the new point is also feasible. After this, the molecules are reclassified according to their objective function values, exchanging their character (refiner vs. explorer) only if a previous explorer molecule becomes a feasible point with a value of the objective function better than that of a previous refiner molecule. The algorithm is stopped when the maximum number of function evaluations is reached. The main tuning parameters of the MIPT algorithm are: the number of simulated molecules nm (in order to obtain a significant molecular repulsive effect it is suggested that nmt2˜ndv, where ndv is the number of decision variables in the optimization problem); the expression used to calculate J as a function of the values of the objective function fobj; and the parameters K1 and K2 that are used in the expressions for calculating Frep and FBm, respectively (see Figure 1). K1 is a measure of the repulsion strength between molecules. K2 is related to the diffusion of the molecules in the medium. The values of K1 and K2 determine the balance of forces on the system and therefore are responsible for providing the local and global characters to the algorithm.

4. Applications of the MIPT algorithm to Bioprocess Optimization 4.1. Dynamic optimization of ethanol fed-batch fermentation Solving the dynamic optimization problem for a fed-batch bioreactor allows finding optimal feeding profiles that should be applied to the process in order to maximize a given productivity objective function. This problem is usually solved using direct dynamic optimization methods, which parameterize the control profile as piecewise polynomial functions. However, in this paper such parameterization is done using cosine functions which are nonlinear and have the advantage of being non-monotonic, which allow finding control profiles that increase and decrease smoothly and continuously. This approach is especially suitable for bioprocesses applications. The dynamic optimization problem for the fed-batch ethanol production has been previously studied in different works and the model of the process can be found elsewhere (Banga et al., 1997). Figure 3 summarizes the optimization problem solved in this section. The state variables on the process are Volume (V), Biomass (X), Glucose (S) and Ethanol (E) concentrations. The manipulated variable whose profile is found by solving the dynamic optimization problem is the input flow of glucose (F). The productivity of the process has been maximized using different optimization algorithms, taking the parameters of the cosine profile as decision variables. All the optimization algorithms were randomly initialized, that is, the starting points were randomly selected from the set of values bounded by the upper and lower limits of the decision variable(s). The results of ten different independent runs are summarized in Figure 4. It is observed that the best results were obtained using the MIPT algorithm proposed in this work, compared to the Simulated Annealing algorithm (SA), the Genetic Algorithm (GA) and the SQP gradient method (GRAD). It is important to notice that the highest productivity values of individual runs were obtained for both the MIPT algorithm and the SQP gradient method, but the average performance of the MIPT is consistently high while the performance of the gradient method is strongly dependent on the starting conditions of the optimization. In the graph of Figure 4, the best cosine feeding profile obtained from MIPT optimization is compared to the best feeding profile obtained by Banga (Banga et

A New Parallel Tempering Algorithm for Global Optimization: Applications to Bioprocess Optimization

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al., 1997) using a piecewise linear approximation. The use of a smooth non-linear profile, although similarly shaped, allows improving significantly the productivity of the ethanol fermentation process. max >Productivity@ F( t )

s.to:

min

a 0 ,a1 ,a 2 , w1 , w 2 ,I1 ,I 2

> E(t f )V(t f )@

dx f ( x (t ), u(t ), d (t )) dt x (t 0 ) x 0 x l d x (t ) d x U x ( t ) § F( t ) a 0  a 1 cos ¨¨ w 1 © 0 d F ( t ) d 12

[ V X S E]'

· § § t  t0 · ¨¨ ¸¸  I1 ¸  a 2 cos ¨ w 2 ¸ ¨ © tf  t0 ¹ ¹ ©

· § t  t0 · ¨¨ ¸¸  I 2 ¸ ¸ © tf  t0 ¹ ¹

Figure 3 Dynamic optimization problem for the ethanol fed-batch fermentation problem

12 MIPT 2-cosines (Productivity= 20559.3 g) Banga's Profile (Productivity=20423.0 g) 10

Worst

Best

MIPT

Average 20557.8

20556.1

20559.3

SA

20554.5

20551.3

20557.7

GA

18876.9

17751.9

20555.2

GRAD

19104.8

17643.8

20559.3

Feed Flow (l/h)

8

Opt. Method

6

4

2

0

0

10

20

30 time (h)

40

50

60

Figure 4 Dynamic optimization of ethanol fed-batch fermentation. MIPT vs. Simulated Annealing (SA), Genetic Algorithms (GA) and gradient-based (GRAD). In the right, the best smooth nonlinear feeding profile obtained with MIPT vs. the best piecewise linear profile by Banga et al. (1997).

4.2. Parameter identification in an ethanol production process In this section the parameter identification of an unstructured model of ethanol production is addressed. The model includes 12 parameters to be identified by minimizing the squared error between the predictions of the model and experimental data. The model and the experimental data for identification have been reported by Phisalaphong (Phisalaphong et al., 2006). The values of the objective function (squared error) for ten different independent runs (R1 to R10) obtained during the parameter identification using different optimization algorithms are presented in Figure 5. It can be observed that the best results have been obtained using the MIPT algorithm proposed in the present work. In Figure 6, the computation time (using an Intel Core 2 Duo, 1.66 GHz processor) using the four mentioned methods for the ten runs is compared. It can be observed that the average time of the MIPT method lies within the range of average values of the other methods. Therefore, an improvement in the global optimum is achieved using the MIPT method without increasing the computational effort.

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518 MIPT

0.030

SA

GA

GRAD

Objective Function

0.025 0.020 0.015 0.010 0.005

or st

Be st

W

R 1 Av 0 er ag e

8

9 R

R

R

R

7

6

5

4 R

R

2

3 R

R

R

1

0.000

Figure 5 Identification error of the kinetic parameters for an ethanol fermentation model. MIPT vs. Simulated Annealing (SA), Genetic Algorithms (GA) and gradient-based (GRAD). 450

MIPT

SA

GA

GRAD

Computation Time (s)

400 350 300 250 200 150 100 50

R 10 Av er ag e

9 R

8 R

7 R

5

6 R

R

3

4 R

R

2 R

R

1

0

Figure 6 Computation time comparison for problem 4.2. MIPT vs. Simulated Annealing (SA), Genetic Algorithms (GA) and gradient-based (GRAD).

5. Conclusions A new algorithm for parallel tempering optimization based on the behavior of charged molecules in solution was presented. This MIPT algorithm was used in two different bioprocess optimization applications, and compared to other stochastic and gradientbased methods. MIPT algorithm found the best optimal values, and its average performance was always superior to the other methods, with a comparable computation time.

6. Acknowledgements Silvia Ochoa gratefully acknowledges financial support from the Deutsche Akademischer Austausch Dienst (DAAD) and the Antioquia University of Colombia.

7. References J. Banga, A. Alonso and P. Singh, 1997, Biotechnol. Prog. 13:326-335. J. Banga, E.Balsa-Canto, C. Moles and A. Alonso, 2005, J. Biotechnology 117:407–419. D. Earl and M. Deem, 2005, Phys Chem Chem Phys.7:3910-3916. S.Ochoa, A.Yoo,J-U.Repke,G.Wozny and D.R.Yang, 2007,Biotechnol. Prog. 1454-62. M.Phisalaphong, N.Srirattana,W.Tanthapanichakoon, 2006, Biochem. Eng. J. 28: 36-43.

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Anhydrous bioethanol production using bioglycerol – simulation of extractive distillation processes Marina O.S. Dias,a Tassia L. Junqueira, a Rubens Maciel Filho, a Maria R.W. Maciel, a Carlos Eduardo Vaz Rossell b a

School of Chemical Engineering, State University of Campinas, UNICAMP, P.O. Box 6066, 13083-970, Campinas – SP, Brazil, [email protected] b Interdisciplinary Center for Energy Planning, State University of Campinas, UNICAMP, P.O. Box 6192, 13400-970, Campinas – SP, Brazil

Abstract Bioethanol has been increasingly used as fuel in the anhydrous form, mixed with gasoline. In this work, two configurations of the extractive distillation process using bioglycerol as a solvent for anhydrous bioethanol production were investigated. Simulations results show that bioglycerol is a suitable agent for the separation of ethanol-water mixtures, with low energy consumption on the column reboilers and the production of high quality anhydrous bioethanol. Keywords: bioethanol, extractive distillation, bioglycerol, simulation

1. Introduction Increase in oil prices and global concern about climate change have motivated the use of alternative forms of energy all over the world. In the transportation sector, more specifically, bioethanol and biodiesel have been increasingly used as substitutes of gasoline and diesel, respectively. Bioethanol is mainly produced from fermentation of sugars. Wine obtained after fermentation contains about 7-12 wt% ethanol. In industry, wine undergoes conventional distillation, where hydrous ethanol containing around 93 wt% ethanol is produced. In order to be used as a gasoline additive, wine must be concentrated at least to 99.3 wt% ethanol. Since water and ethanol form an azeotrope with 95.6 wt% ethanol at 1 atm, conventional distillation does not achieve the separation that meets product specification. Common separation methods used in the industry are azeotropic distillation with cyclohexane as entrainer, extractive distillation with monoethyleneglycol as solvent and adsorption onto molecular sieves. In the last years bioglycerol availability has increased, since it is obtained as a byproduct of biodiesel production process, making glycerol prices fall. Since it is not harmful to humans or the environment, and it is a suitable agent for the separation of ethanol – water mixtures [1], it can be safely used to produce anhydrous ethanol for use in food or pharmaceutical industries. In this work UniSim Design was used to simulate and investigate the performance of extractive distillation processes with glycerol for anhydrous bioethanol production. Two different configurations were studied, aiming the lowest energy consumption in the production of 1000 m³/day of anhydrous bioethanol.

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2. Extractive distillation processes In extractive distillation, also known as homogeneous azeotropic distillation, a separating agent, called solvent or entrainer, is added to the azeotropic mixture in order to alter the relative volatility of the components in the original mixture. Among possible criteria for solvent selection, the solvent used must not form a second liquid phase with the components of the mixture and should have a high boiling point. In the conventional extractive distillation process, solvent is added to the first column (extractive column), above the azeotropic feed. On the top of the extractive column, anhydrous ethanol is produced, while in the bottom a mixture containing solvent and water is obtained. The solvent is recovered in a second column (recovery column), cooled and recycled to the extractive column [2]. An alternative configuration for this process makes use of a single column to perform both removal of water and solvent recovery, by means of a side draw of water in vapor phase located a few stages above the bottom of the extractive column [3]. Thus, there is no need to use a second column to recover solvent, since anhydrous ethanol is obtained on the top of the extractive column, pure water vapor obtained as a side draw and pure solvent is produced on the bottom. Solvent is cooled down and recycled back to the column. Conventional extractive distillation processes employed in the industry for the separation of ethanol – water mixtures use monoethyleneglycol (MEG), which is a fossil and toxic solvent. Glycerol can be used as solvent in extractive distillation processes to produce anhydrous ethanol, since it eliminates the azeotrope by modifying the mixture vapor-liquid equilibrium, increasing the volatility difference between the compounds. Glycerol decomposes into acrolein when heated above 280°C [4], which is below its boiling point at atmospheric pressure. In order to avoid decomposition, extractive distillation process must be performed at sub-atmospheric pressures when needed. This is an important process condition that has to be considered.

3. Simulation of the extractive distillation processes Simulations were carried out using software UniSim Design. Hydrous ethanol in vapor phase containing 93 wt% ethanol was used as raw material. In order to produce 1000 m³/day of anhydrous ethanol (99.3 wt% ethanol), approximately 1045 m³/day of hydrous ethanol (847 kmol/h) must be fed to the extractive distillation system. UNIQUAC was the model used to calculate the activity coefficient on liquid phase and equation of state SRK was used as the vapor model. Binary coefficients for ethanolglycerol pairs are not available at UniSim database and were estimated using UNIFACVLE. Extensive studies, not shown in this paper, were carried out to characterize the possible mixtures found in the process and to find out which is the most suitable thermodynamic package to represent the interactions between components. 3.1. Conventional extractive distillation process Configuration of the conventional extractive distillation process for anhydrous bioethanol production using glycerol as a solvent is depicted in Figure 1. Firstly, a base case was considered. Optimization of the conventional process was carried out using factorial planning (26-4); the following parameters were evaluated: number of stages (N) and reflux ratio (RR) of both extractive column (EC) and recovery column (RC), solvent to feed ratio (S/F) and solvent inlet temperature (T). Sixteen simulations were carried out. Anhydrous ethanol purity and energy consumption on column reboilers were analyzed. Parameters considered on the factorial planning are shown in Table 1.

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Figure 1. Configuration of conventional extractive distillation process. Table 1. Values for the variables considered on the factorial planning - conventional process. Level

+1 -1

N-EC

38 32

N-RC

14 11

RR-EC

1.00 0.94

RR-RC

0.012 0.008

S/F

0.32 0.29

T (ºC)

150 110

Software STATISTICA 7.0 was used to generate and analyze the results. It was verified that the number of stages (N-EC and N-RC) and recovery column reflux ratio (RR-RC) are not significant in a 95 % confidence interval. Variation of energy consumption (Q) as a function of the most significant parameters (RR-EC, S/F and T) can be seen in Figure 2.

(a)

(b)

Figure 2. Energy consumption on column reboilers (Q, kJ/kg AE) on the conventional process, as a function of RR-EC and S/F (a) and T (b).

Further optimization was carried out based on the case that presented the lowest consumption of energy and met product specification, which had the following specifications: S/F=0.32, RR-EC=0.94 and T=150 ºC. Firstly, the optimization considered the reduction on energy consumption based on feed stages (solvent, hydrous ethanol and solution). After the lowest energy consumption situation was achieved,

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glycerol flow was reduced to the minimum possible value that met product specification, thus reducing even more process energy consumption. Anhydrous ethanol produced does not contain traces of solvent, so it can be safely used in different industries and as raw material. Simulation parameters and results for the optimized simulation are shown on Table 2. Table 2. Parameters of the optimized configuration - conventional extractive distillation.

(a) (b)

Process Parameter

Value

Process Parameter

Value

Solvent to feed ratio (S/F) Glycerol inlet temperature (ºC)

0.316 150

99.98 9.15x10-6

Solvent losses (%)

0.0099

Extractive column Number of stages Solvent inlet stage(b) Hydrous ethanol inlet stage(b) Reflux ratio(a) AE flow rate (kmol/h)(a) Reboiler duty (kW)

38 36 13 0.94 723.0 6073

Water stream purity (% mole) Ethanol losses (%) Energy consumption on reboilers (kJ/kg AE) Recovery column Number of stages Feed inlet stage(b) Glycerol recovery (%)(a) Reflux ratio(a) Reboiler duty (kW) Pressure (kPa)

1057 11 4 99.99 0.012 3599 50

Column specifications Stage numbering increases towards the top of the column

3.2. Alternative configuration of the extractive distillation process Alternative configuration of extractive distillation is presented in Figure 3. A base case was simulated and optimized through factorial planning (24). Parameters studied for the factorial design in this case included number of stages (N), reflux ratio (RR), solvent to feed ratio (S/F) and solvent temperature (T). Sixteen simulations were carried out; energy consumption and mass fraction of ethanol on the anhydrous ethanol were analyzed. All variables were considered significant on a 95 % confidence interval. Parameters are given in Table 3.

Figure 3. Configuration of the alternative extractive distillation process.

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Table 3. Values for the variables considered on the factorial planning – alternative process. Level

N

RR

S/F

T (ºC)

+1 -1

35 30

1.0 0.9

0.420 0.365

140 120

Optimized parameters values in the simulation that presented the lowest energy consumption were: N=30, RR=0.9, S/F=0.365 and T=140 ºC. Further optimization was carried out considering ethanol feed and solvent inlet stages, as well as side stream draw stage. It was verified that changes on these parameters did not decrease significantly the energy consumption of the process. It was possible to achieve lower energy consumption on reboilers by varying glycerol flow, but this variable must be studied with caution, since lower solvent flows increase ethanol losses on the side stream. Parameters for the optimized simulation are shown on Table 4. Table 4. Parameters of the optimized configuration - alternative extractive distillation. Process Parameter

Value

Process Parameter

Value

Solvent to feed ratio (S/F) Glycerol inlet temperature (ºC)

0.355 140

99.95 6.84x10-5

Solvent losses (%)

0.021

Water stream purity (% mole) (a) Ethanol losses (%) Energy consumption on reboilers (kJ/kg AE) Side stream stage(b) Hydrous ethanol inlet stage(b) Reboiler duty (kW) Pressure (kPa)

Number of stages 30 Solvent inlet stage(b) 29 Reflux ratio(a) 0.90 AE flow rate (kmol/h)(a) 723.0 (a) Column specifications (b) Stage numbering increases towards the top of the column

1085 2 13 9932 60

4. Discussions Energy consumption on the alternative configuration of the extractive distillation process is only 2.7 % larger than that of the conventional two-column configuration. The main disadvantage of the alternative configuration is the higher temperature of the extractive column: around 266 ºC, as opposed to the 153 ºC in the extractive column of the conventional configuration, on which the highest temperature (266 ºC) is only achieved on the recovery column. Thus, more steam (of high temperature and pressure) or another heat source must be used on the alternative column reboilers in order to maintain column at that high temperature. Ethanol losses are smaller than 0.0001 % on both studied cases; even though the alternative configuration of the extractive distillation process promotes higher glycerol losses, this should not be a problem, since glycerol is a cheap, renewable and biodegradable solvent, and on both cases losses are smaller than 0.025 %. Values obtained for the energy consumption of different processes for the separation of water – ethanol mixtures are displayed in Table 5. It can be verified that the processes studied in this work present relatively low energy consumption on column reboilers. Thus, the extractive distillation process with glycerol seems to be a competitive process and deserves further investigation.

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Table 5. Energy consumption of ethanol – water separation processes. Process

Conventional extractive distillation with glycerol Alternative extractive distillation with glycerol Extractive distillation with MEG and CaCl2 [5] Extractive distillation with MEG [6] Azeotropic distillation with pentane [7] Azeotropic distillation with benzene [7] Extractive distillation with gasoline [7]

Energy consumption (kJ/kg ethanol) 1057 1085 1425 1760 3348 4683 2695

5. Conclusions Both alternative and conventional configurations of the extractive distillation process with glycerol are suitable for anhydrous ethanol production. Glycerol, the solvent used, is derived from renewable materials and it is not harmful to humans or the environment, as opposed to the conventional solvent employed on extractive distillation process for anhydrous bioethanol production (MEG). Energy consumption on both cases are similar and relatively low, when compared to that of different processes reported in the literature, as well as ethanol and solvent losses. Anhydrous ethanol produced is not contaminated by solvent, which is of great importance when considering process sustainability and the possible use of bioethanol as raw material.

6. Acknowledgements The authors acknowledge CNPq and FAPESP for financial support.

7. References [1] F. Lee and R. Pahl, Solvent screening study and conceptual extractive distillation process to produce anhydrous ethanol from fermentation broth, Ind. Eng. Chem. Process Des. Dev., 24 (1985) 168 - 172 [2] H. Huang et al., A review of separation technologies in current and future biorefineries. Separation and Purification Technology, 62 (2008) 1 - 21 [3] R. P. Brito, M.R.W. Maciel, A.J.A. Meirelles, New extractive distillation configuration for separating binary azeotropic mixtures. In: The First European Congress of Chemical Engineering, Italy, 1 (1997) 1333 - 1336 [4] J. A. Young. CLIP: Glycerol, Journal of Chemical Education, 80 (2003) 25 [5] I. Gil et al., Separation of ethanol and water by extractive distillation with salt and solvent as entrainer: process simulation. Brazilian Journal of Chemical Engineering, 25 (2008) 207 - 215 [6] A. Meirelles, S. Weiss, H. Herfurth, Ethanol dehydration by extractive distillation. Journal of Chemical Technology and Biotechnology, 53 (1992) 181 – 188 [7] C. Black, Distillation modeling of ethanol recovery and dehydration processes for ethanol and gasohol. Chem. Eng. Prog., 76 (1980) 78-85

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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An Optimization Framework for Solving a Large Scale Scheduling Problem Toni Lastusiltaa, Oskar Frankenhaeusera, Frank Petterssonb, Tapio Westerlunda a

Process Design and Systems Engineering Laboratory, Åbo Akademi University, Biskopsgatan 8, FIN-20500 ÅBO, Finland, [email protected], [email protected], [email protected] b Heat Engineering Laboratory, Åbo Akademi University, Biskopsgatan 8, FIN-20500 ÅBO, Finland, [email protected]

Abstract Large scale scheduling problems are often difficult Mixed Integer Linear Programming (MILP) problems. The large amount of binary variables in a scheduling problem with multiple production lines sets a limit on the problem size which is solvable in a reasonable time. In this paper an efficient continuous time job precedence MILP formulation for a scheduling problem is presented and it is compactly formulated in the General Algebraic Modeling System [1]. To increase the solving capability a moving time window [2] is utilized. The base of the model is a simplification of a general N-dimensional allocation formulation in [3]. The Just-In-Time (JIT) principle is considered and is achieved by a piecewise linear objective function penalty, for each order, penalizing late and early orders. The rolling horizon implementation used a time window with 20 groups of orders, which corresponds to a 3 week schedule. The framework has been applied for production scheduling at a Finnish supplier of packaging materials based on polyethylene and polypropylene. The studied plastic producing company had over 3000 orders in 1 year to be scheduled on 4 of their printing machines. However, only a group of two machines is considered at one time, due to the similarity of these machines. In this paper the scheduling model in GAMS implementation is presented and, furthermore, the rolling horizon implementation is described. Keywords: Production scheduling, MILP, GAMS, large scale problems, industrial applications

1. Introduction During the past years scheduling models have been formulated, both with discrete and continuous time representations. An overview of the field can be found in [4]. The continuous time formulation is appealing due to its accuracy, although the increase in combinatorial complexity for larger sets of jobs is still unsolved. The exponential increase in the combinatorial complexity is due to the NP-complete nature of many scheduling problems. A large scale scheduling problem can be solved by a genetic algorithm [5] or decomposed into smaller problems and solved with the help of a heuristic [6]. Another approach is to solve it by using a moving time window [2], also called rolling horizon. The current paper uses a rolling horizon approach to solve a large scale industrial scheduling problem.

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In this paper a scheduling model, which is very similar to [6], is presented in General Algebraic Modeling System (GAMS) notation. In this formulation, compared to [6], two parallel production units are considered instead of one. Furthermore, the Just-InTime (JIT) principle [2] is considered and the rolling horizon approach is described, as well as, a heuristic approach to combine jobs.

2. Problem description The overall task is to find the optimal job sequence for the 4 printing machines at a plastic producing company in Finland. The schedule should be done in the best possible way concerning time and expenses, under given restrictions. Two of the four printing machines were fairly similar which made it possible that a job could sometimes be manufactured on either of the machines. The scheduling of the two other machines, which have mainly machine dependent orders, is not considered in this paper. The production of jobs has the following limitations. All jobs have to be produced before their due date and some orders cannot be produced before a specific release date. All jobs have a predetermined production time and a sequence dependent setup time.

3. Solving procedure The optimization procedure consists of the following phases: data collection, combining of orders heuristically and solving of the rolling horizon based optimization model. The heuristic to combine orders is done to increase the amount of orders that can be optimized in one time window. The optimization model is done in GAMS. 3.1. GAMS scheduling model for 10 jobs Sets m Machines j Jobs r Special order set 2 variables js1(j) Subset-orders possible on m1 js2(j) Subset-orders possible on m2 Alias(j, i); Alias(js1, is1); Alias(js2, is2);

/m1,m2/ /j1*j10/ /r1*r3 / *When JIT principle is considered /j1,j3,j4,j5,j6,j7,j8,j9,j10/ /j2,j3,j5,j7,j8/;

Scalars BIGM /10000/ = Constraint relaxation constant MAXTIME /60/ = Maximum production time of all jobs WEIGHT /100/; = A weight to prioritize some elements in the objective function Variables = Objective variable which is minimized obj = Lateness or earliness of job j x(j); Positive Variables = Time point when the setup of job j is performed and job j starts t(j,m) FinishT(j) = When job j is ready = Lateness of a job j Late(j) = Penalty variables * When JIT principle is considered f(j);

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Binary Variables b(i,j,m) = Decision variables for job precedence G(i,j,m) = Variable that relaxes the job precedence requirement when a job is not produced on a specific machine s(j,m); = Decision variable on which machine a job is done *The following section is defined when JIT principle is considered Sos2 Variable sos(j,r); Parameter FVAL(r) Penalty weights of different delivery times: / r1 1, r2 0.1, r3 10/; Parameter XVAL(r) Time axis in hours: /r1 -324, r2 -24, r3 324/; The alias definition enables to refer to different indices when generating equations. Job 1, “j1”, and job 2, “j2”, are not real jobs, but enables defining correct setup times for the first jobs in the rolling horizon procedure. The special order set 2 is defined as follows: only two members, positive variables, of the set can be non zero and these have to be adjacent to each other. Furthermore, the following input data is used in the model: production time (PROD1, PROD2), release time (RELEASETIME), and due time (DUETIME) vectors, as well as, setup time (SETUP1, SETUP2) matrices. Constants, including vectors and matrices, are noted with names with only big letters. Equations eq1.. obj =G= WEIGHT*sum(j,Late(j)) + sum(j, FinishT(j))/(card(j)*MAXTIME); eq2(j).. s(j,'m1')$js1(j) + s(j,'m2')$js2(j) =E= 1; eq3_1(is1,js1)$(ord(is1)ord(js1)).. G(is1,js1,'m1') =G= s(is1,'m1')+ s(js1,'m1')-1; eq4_1(js1,is1)$(ord(is1)ord(js1)).. t(js1,'m1') =G= t(is1,'m1')+ PROD1(is1)+ SETUP1(is1,js1) - BIGM*(1-b(is1,js1,'m1')) - BIGM*(1-G(is1,js1,'m1')); eq5_1(js1,is1)$(ord(is1)ord(js1)).. t(is1,'m1') =G= t(js1,'m1')+ PROD1(js1)+ SETUP1(js1,is1) - BIGM*(b(is1,js1,'m1')) - BIGM*(1-G(is1,js1,'m1')); eq6_1(js1).. FinishT(js1) =G= t(js1,'m1') + PROD1(js1)- BIGM*(1-s(js1,'m1')); eq7(j).. x(j) =E= FinishT(j) - DUETIME(j); eq8(j).. Late(j)=G= x(j); eq9_1(j)$js1(j).. t(j,'m1') =G= RELEASETIME(j)-BIGM*(1-s(j,'m1')); eq10_1.. s('j1','m1')=E= 1; eq10_2.. s('j2','m2')=E= 1; eq11_1(is1)$(ord(is1)<>1).. b('j1',is1,'m1') =E= 1; eq11_2(is2)$(ord(is2)<>1).. b('j2',is2,'m2') =E= 1; eq12(j).. f(j) =E= sum(r,FVAL(r) * sos(j,r)); *When JIT principle is considered eq13(j).. x(j) =E= sum(r,XVAL(r) * sos(j,r)); *When JIT principle is considered eq14(j).. sum(r,sos(j,r)) =E= 1; *When JIT principle is considered Solve model minimizing obj using mip ; *mip=mixed-integer programming A similar equation for machine 2 is written for equations: 3, 4, 5, 6 and 9. The objective Eq. (1) preliminary minimizes the tardiness and secondarily minimizes the production time, which means that the finishing time of the last job on both of machines should be as early as possible. This result in an even workload on the two machines, but it is not the same as minimizing the total machine time, which is the summed production time for the both machines. A shortest total machine time formulation was studied, but it was abandoned because of the significant increase in solution time. In Eq. (2) all jobs are

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required to be produced, while Eq. (3) enforces the job precedence requirement when two jobs are produced immediately after each other on a machine. Eq. (4) and Eq. (5) enforce the job precedence, which means that every job has to be produced either before or after any other job on the same machine. Eq. (6) determines the finishing time for a job, while taking in consideration that the variables t(j,m) denotes the point of time when the previous job have finished and the setup for the current job is performed. Eq. (7) denotes the earliness/tardiness and Eq. (8) denotes the tardiness. Eq. (9) enforces the release time requirement. Eq. (10) fixes the first job to be produced on a specific machine, because it is necessary to control the first jobs in order to get correct setup times when the moving time window is used. Additional constraint (11) fixes the job precedence decision variable for the first jobs on both machines. There are two limitations in the proposed model. Firstly, the release time vector must include a setup times for the orders, which is unknown. An upper limit of the setup time can be added to the actual release time. Secondly a minor limitation is that the model can give an incorrect result if the setup times are longer than job production times. The requirement to minimize the storage time of completed products is embedded in the model by introducing equations (12, 13 and 14). However, the Just-In-Time requirement was later abandoned due to the importance of minimizing the production time. When JIT principle is considered the objective function, Eq. (1), can be modified as follows: eq1. . obj =G= WEIGHT*sum(j,Late(j)) + sum(j,f(j))/(card(j)); The preferred delivery profile is controlled by the FVAL parameter values, which determines the penalty on the objective function. The special order set r values are determined by the corresponding job finishing time, see Eq. (13), within the time range given by XVAL parameter. In the current model the most preferred finishing time is 24 hours before delivery where the FVAL parameter value is 0,1. When choosing the end points of the timeline XVAL, it is necessary to take into consideration the due time, production time and release time for the jobs. In Eq. (13) the variable values of special order set r are transferred to the penalty variable f(j) according to FVAL weights. Eq. (14) is necessary to limit the possible values for r variables. The presented model was slightly modified when the heuristic to combine jobs and the rolling horizon approach was applied; the modification is not presented here due to the space limitation. 3.2. A heuristic approach to combine jobs and rolling horizon To increase the amount of orders that is possible to schedule within a reasonable time a new heuristic approach is taken. The heuristic collects a set of orders and regroups all orders into predefined groups. The groups are mainly defined by which machine a job is possible to be produced on, as follows: possible on both machines, possible on machine 1, possible on machine 2 and one group of orders which consist of products with an identical production process. The group containing orders of the same product, that is to say with an identical production process, is the actual saving that the scheduling should target. The group sized varied depending on the orders. The complexity of the problem is significantly reduced. The amount of orders considered and the group size used for

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regrouping orders will determine the solution time. The solution time for one optimization run has a significant variation depending on the input data. To simulate longer time periods the rolling horizon [2] approach, also called moving time window, is used. In this approach the problem is decomposed into smaller problems by looking only at a subset of jobs at one time, in other words a time window. The time window is chosen by the amount of considered groups of orders rather than time, because the amount of groups greatly impacted the solution time. A time window consisted typically of 15 -20 groups of orders where the solving time varied between some minutes up to one day. To be able to simulate longer time periods, a lock zone can be chosen for each run depending on the wanted solution speed. The lock zone is the amount of orders or days that the jobs are locked from the previous optimization run. A fixed amount of orders to be solved in one optimization run is used as an upper limit for one time window.

4. Conclusions The presented framework, to solve large scale scheduling problems, decomposed the problem in smaller problems and combined jobs into groups of jobs. The partial problems were successfully solved by the GAMS scheduling model. The result of the optimization relied greatly on the heuristic to combine jobs.

5. Acknowledgements The Technology Development Centre of Finland (Tekes) and the involved companies are gratefully acknowledged for their financial support.

References [1] GAMS Development Corp., GAMS – The Solver Manuals. GAMS Development Corporation, Washington, DC, USA, (2008). [2] P. Jernström, Multi-product multi-purpose machine scheduling in dynamic environments, Doctoral thesis in Process design, Åbo Akademis tryckeri (2006) ISBN 952-12-1797-9. [3] J. Westerlund , L.G. Papageorgiou and T. Westerlund, A MILP model for Ndimensional allocation, Computers and Chemical Engineering 31 (2007) 1702-1714. [4] C.A. Floudas and X. Lin, Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review, Computers and Chemical Engineering 28 (2004) 2109–2129. [5] P.A. Rubin and G.L. Ragaz, Scheduling in a sequence dependent setup environment with genetic search, Computers & Operations Research 22 (1995) 85-99. [6] J. Roslöf, I. Harjunkoski, T. Westerlund and J. Isaksson, Solving a large-scale industrial scheduling problem using MILP combined with a heuristic procedure, European Journal of Operational Research 138 (2002) 29-42.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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A Projection Approach for Optimization of Distributed Parameter Systems without Gradients Reinout Romijna, Wolfgang Marquardta a

AVT-Aachener Verfahrenstechnik, Process Systems Engg, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany, [email protected]

Abstract Simulation of complex spatially distributed processes using commercial simulation packages is widely practiced. The application of this type of models for optimization purposes is a formidable task when model equations and gradients are not accessible to the user and each model evaluation is computationally expensive. In this contribution a projection approach is proposed in which first the solution subspace of the optimization problem is computed, followed by the computation of the optimum by using substitute models. The projection approach is designed to require a minimum number of evaluations of the original model. Keywords: Model Reduction, Proper Orthogonal Computational Fluid Dynamics (CFD), Glass Melting Tank

Decomposition

(POD),

1. Introduction Simulation of complex spatially distributed process systems by detailed mathematical models using commercial finite element or Computational Fluid Dynamics (CFD) packages is widely practiced. The application of this type of models for optimization purposes suffers from two major obstacles. First, the model equations and their derivatives are typically not available for the user of commercial software and neither are the sensitivities of the outputs with respect to the inputs or parameters. Second, the computation time for solving a model is typically very high. As a result, optimization methods which use gradient information can not be applied and methods that approximate gradients locally become computationally intensive. A wide variety of direct and stochastic methods for optimization exist, which search the space of the optimization parameters without requiring gradient information [1,2]. The drawback of direct search methods is the local convergence. Stochastic methods are not efficient in the number of function evaluations required to reach the optimum and are therefore not favourable for optimization when the model is computationally expensive [1]. Response Surface Methods, utilizing approximate models, have found application in problems involving computational expensive models such as CFD models [3,4]. These methods establish a simple model for the objective function value as a function of the parameters, which replaces the original model in the optimization algorithm. The advantages of such methods are that the approximate models can be re-used for multiple optimization runs and gradient-based optimization algorithms can be employed to solve the problem. However, the quality of the results obtained with the approximate model depends on the extent to which the approximate model fits the original. Common practice in response surface modelling is to first design experiments by determining a sequence of points to be simulated in a certain way, e.g. following space filling or

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optimality criteria [4]. Then, the original model is simulated and the approximate model is identified. The steps are repeated until a valid model has been found (Fig. 1a). The number of simulations needed depends partly on the choice of the approximate model structure. In our work, the original model is simulated first, independent of the choice of approximate model structure. A measure on the generated simulation data determines the necessity of additional simulations rather than a possibly erroneous conclusion based on fitting an approximate model on the data. Furthermore, the most suitable type of approximate model is in principle not known before any data has been generated. The second step then consists of the choice for an approximate model type and an iterative identification procedure (Fig. 1b). Traditionally, surrogate models have been used to approximate the relation between parameters and objective function values. Recently, projection methods have received significant attention in the literature. They allow a considerable reduction of the model state dimension to facilitate the derivation of an approximate relation between parameters and model states. In [5], a projection space is determined after creation of an extensive CFD solution database. Persistent excitation of model inputs by a pseudorandom binary signal to obtain data for a dynamic CFD model is described in [6]. The reduction of the computational load required to generate the projection space is not specifically addressed in literature. The novelty of the method proposed in this contribution is that it is aimed at minimizing the required number of simulations and thereby the computational time, which is essential for optimization of time-consuming models.

Fig. 1a: Iterative simulation and identification.

Fig. 1b: Sequential simulation and identification.

2. Projection Approach Let the original model states be vectors x ∈ RN. Let a real vector space X be a subspace which spans all solutions xi ∈ RN of the system 0 = f(x, și) for și ∈ Ĭ. By a repetitive simulation for i=1,..,k, solutions x1,…,xk are obtained and a subspace Xk ⊂ X which spans x1,…,xk can be computed. The aim of the algorithm is to compute a reduced basis Xn of basis Xk which approximates X sufficiently well. By scanning Ĭ in an optimal way, the number of costly function evaluations is minimized. The algorithm is summarized first and will be explained in more detail in Sections 2.1, 2.2 and 2.3. 1. Determine an initial sequence of parameter vectors {ș}:={ș1,…,șk}. 2. Solve the original model f(x, și) = 0 to obtain a set of solution vectors {x}:= {x1,…,xk} corresponding to the input sequence {ș}. 3. Compute a reduced subspace Xn with dimension n ” k to approximate Xk in which the solutions {x} lie with a certain accuracy.

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4. Determine a new parameter vector șk+1 and compute solution xk+1. 5. Project xk+1 on Xn and compute the projection error. 6. If the projection error is large, i.e. if xk+1 is not contained in Xn, attach xk+1 to {x} and return to 3. If the error is small, continue to 7. 7. If Xn is a sufficient basis for xk+1 repeatedly, an accurate basis has been found and the algorithm is stopped. If not, return to 4. Determining an optimal parameter sequence (algorithm steps 1 and 4) There are two basic alternatives to determine input values șj ∈ Ĭ that should be computed. The first alternative is to design θ L based on information from prior model evaluations for șj , j < i. The second alternative, which is followed in this work, is to determine a sequence that covers Ĭ in a given manner. The coverage of Ĭ or the scattering of a set of parameter vectors {ș1,…,șk} over Ĭ is quantified by a measure of scatter d, given in [7]: G := sup min θ − θ L .

(1)

θ ∈Θ 1≤ L ≤ N

Frequently used sequences are designed for a fixed number of points (e.g. Latin hypercube designs). Others, such as the Sobol, Niederreiter and Halton sequences, determine points in a sequential way [7,8,9]. This is more suited for our approach, where the necessity of performing a new simulation is evaluated after each completed simulation (see Fig. 1b). In this work an optimization approach is used as it has been proposed in [10] for the identification of dynamic systems. After some initial simulations, the next parameter vector șk+1 is determined from

θ N +1 = arg sup min θ − θ L . θ ∈Θ 1≤ L ≤N

(2)

For each step k for which Eq. (2) has a unique solution, the scatter d is strictly decreasing. This is generally not the case for the other design methods mentioned. The performance of this approach is illustrated in Fig. 2a. A sequence of 120 points in a 3 dimensional cube was computed by the Halton, Sobol and Niederreiter algorithms and by the suggested optimization approach. For each strategy the best solution out of 20 runs is shown. The optimized sequence outperformed the other sequences after about 18 points. It should be mentioned however that the current implementation scales linearly with k but exponentially with the dimension of ș. Computation of the reduced subspace Xk (algorithm step 3) The computation of the reduced subspace is done by Proper Orthogonal Decomposition (POD). Given a data ensemble {x1,…,xk} of k vectors x ∈ RN, POD provides a way of representing x1,…,xk as expansions

xi =

¦

n j =1

α i, jϕ j ,

(3)

with n ” N, in which ijj are orthonormal basis vectors of RN which are computed in an empirical way from the data ensemble and Įi,j are the expansion coefficients. The POD expansion is optimal in the sense that the error

ε Q :=

Q 1 N [ L − ¦ α L , Mϕ M ¦ N L =1 M =1

2

(4) 2

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is minimal for all n = 1,…,N [11]. Since the error İn is averaged over all xi, some xi will typically have a larger approximation error than others. In our framework, however, we are also interested in the approximation error of each individual xi, in order to guarantee a good local fit in the entire parameter domain. Therefore, when computing basis functions iji, not the error İn of Eq. (4) is evaluated to determine the required number of basis functions, but the approximation error of each individual solution xi: Q

2

ε L ,Q := [ L − ¦ α L , M ϕ M . M =1

(5)

2

The computation of basis functions is stopped at n, when the maximum of all individual errors drops below a certain value c, i.e. max ε L ,Q < F . L

Projection and re-computation of the basis (algorithm steps 5 and 6). The projection error of state vector xk+1 is computed by Eq. (5) for i = k+1. When this projection error is small, i.e. İk+1,n < c, this means that xk+1 is contained in the reduced subspace X n. Subsequently, the reduced subspace can be tested for a new simulation point. However, if the projection error is large, a new reduced subspace has to be computed to approximate all x1,…,xk+1. This can be done by re-computing a reduced basis following algorithm step 3.

3. Case Study: Application to a CFD Model The method was applied to a case study involving a simplified 2-dimensional CFD model of a glass melting process containing around 16 thousand grid cells. The state vector in each grid cell comprised two flow velocities and a temperature. The parameter vector ș comprised the production rate ș1, a heat supply rate ș2, and a geometric shape parameter ș3. The resulting numbers of required basis functions are shown in Fig. 2b for several parameter space gridding strategies after each simulation. At the initial stage, the number of basis vectors required for a good approximation increases proportionally to the number of simulations added to the data ensemble. Eventually, the increase in the required number of basis vectors becomes small.

Fig. 2a: Comparison of distance d for several gridding strategies for increasing number of

Fig. 2b: The required number of basis vectors ε L ,Q < ε 1 for each added needed to satisfy max L

computed parameter grid points.

simulation k, for several sequences.

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The optimized parameter grid sequence seems to outperform the pseudo-random sequences slightly in the sense that the simulations 18 to 90 resulted in more required basis vectors. This means that using the optimization gridding strategy, more information has been obtained per simulation. The computation time of the 120 solutions using the CFD code was in the order of days. Having found an accurate basis for the model solutions for ș ∈ Ĭ, an approximate model gj: ș ĺ Įj was computed by polynomial regression between the parameters and each projection coefficient j. The order of the polynomial approximation function has been determined for each projection coefficient individually. In Fig. 3a, the sum of squared errors of the approximation of a validation set of simulations is shown. The order of the polynomial function with least validation error is different for each projection coefficient. The approximation of the coefficients tends to be better for the first coefficients then for the higher coefficients. However, good fits were obtained up until Į9, which is illustrated in Fig. 3b.

Fig. 3a: Sum of squared errors of projection coefficient approximations with polynomials of order 1 – 6 for a validation data set.

Fig. 3b. Example of projection coefficient approximation: gj: ș ĺ Įj, j = 9, shown in the space of (ș1, ș2, Į).

Furthermore, a polynomial function h: Į ĺ y was identified where y is a quality indicator. The quality indicator was based on particle tracing results of the used CFD software package GTM-X, a method which involves following the paths of hypothetical particles which flow through the modeled geometry [12]. The quality indicator was constrained by specified reference value. Inequality constraints on the flow velocities in original model variables were approximated by inequality constraints on the expansions Eq. (3). The optimization problem was then formulated as follows:

min

θ 1 ∈Θ 1 ,θ 2 ∈Θ 2

s.t.

− θ1 , α j = g j (θ ),

j ∈ J,

¦

i ∈ I.

h(α ) − yref ≥ 0, n j =1

α i , jϕ j ,k ≥ 0,

The parameter ș1 represents the production rate which is maximized, the first constraint is the model approximation by the projection coefficients in the set J=1,..,9. The quality indicator is constrained to be equal or larger than a reference quality indicator value yref in the second constraint. In the third constraint the flow velocity for the elements contained in a set I, which contains the points within the model geometry where the flow velocity is contrained to be positive. The optimization problem was solved using standard gradient based constrained optimization routines in MATLAB. Multiple

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optimization runs with a varying geometric parameter ș3 could be performed with computation times in the order of seconds. This shows the potential of this method in on-line applications, where benefit can be obtained or cost can be reduced when operating conditions can quickly be re-optimized after changes in process conditions, constraints or production schedules.

4. Conclusions A method for the computation of an approximate subspace of the solution space of large-scale models has been presented. Computational efficiency can be achieved by maximizing the scatter of the parameter values for which the model is simulated and by using proper orthogonal decomposition to compute a subspace which optimally approximates the data obtained. After the initially time-consuming computation of the original model solutions to identify the approximate subspace, the identification of simple approximate models becomes straightforward. These approximate models allow the solution of series of optimization case studies at very low computational effort which ultimately facilitates on-line use in real-time optimization.

5. Acknowledgements This work has been supported by the European Union within the Marie-Curie Training Network PROMATCH under grant number MRTN-CT-2004-512441. The authors greatly appreciate the use of MATLAB software provided by John Burkardt, Virginia Tech, for computing some of the results in this paper.

References [1]

M.J.D. Powell, Direct search algorithms for optimization calculations, Acta Numerica 7 (1998) 287 – 336. [2] T.F. Edgar, D.M. Himmelblau and L.S. Lasdon, Optimization of Chemical Processes, 2nd ed., McGraw-Hill, 2001. [3] G.E.P. Box and N.R. Draper, Empirical Model-Building and Response Surfaces, Wiley, 1987. [4] N.V. Queipo, R.T. Haftka, W. Shyy, T. Goel, R. Vaidyanathan and P.K. Tucker, Surrogate based analysis and optimization, Progress in Aerospace Sciences 41 (2005) 1 – 28. [5] L. Huisman, Control of Glass Melting Processes Based on Reduced CFD Models, PhD Thesis, Technische Universiteit Eindhoven, 2005. [6] K. Kunisch and S. Volkwein, Control of the Burgers equation by a reduced-order approach using Proper Orthogonal Decomposition, Journal of Optimization Theory and Applications 102 (1999) 345 – 371. [7] N.F. Trubitsyn and A.V. Shostak, Application of Halton’s sequences in the MonteCarlo method, Cybernetics and Systems Analysis 28 (1992) 804 – 807. [8] I.M. Sobol and Y.L. Levitan, A Pseudo-Random Number Generator for Personal Computers, Computers and Mathematics with Applications 37 (1999) 33 – 40. [9] P. Bratley, B.L. Fox and H. Niederreiter, Implementation and Testes of LowDiscrepancy Sequences, ACM Transactions on Modeling and Computer Simulation 2 (1992) 195 – 213. [10] M. Brendel and W. Marquardt, Experimental design for the identification of hybrid reaction models from transient data, Chemical Engineering Journal. 141 (2008) 264 – 277. [11] L. Tang and W. Shyy, Proper Orthogonal Decomposition and Response Surface Method for TPS/RLV Structural Design and Optimization: X-34 Case Study, 43 rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2005. [12] GTM-X User Manual, TNO Glass Group, Eindhoven, The Netherlands, V 4.1, 2007.

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An Evaluation of a Multi-method Tool for RealTime Implementation of Two-layer Optimization Delba N.C. Meloa, Adriano P. Marianoa, Eduardo C. Vasco de Toledob, Caliane B. B. Costaa and Rubens Maciel Filhoa a

Laboratory of Optimization, Design and Advanced Control (LOPCA).School of Chemical Engineering; University of Campinas (Unicamp). P.O. Box 6066 - 13081970, Campinas, SP, Brazil. [email protected] b Petrobras SA, Paulínia Refinery (REPLAN),Rodovia SP 332 - KM 132, P.O. Box 1, CP: 13140-000. Paulínia, SP- Brazil.

Abstract In this work an optimization tool based on Sequential Quadratic Programming (SQP), Levenberg-Marquardt (LM) and Genetic Algorithm (GA) is presented. For the matter of possible alternative computational platforms, it is convenient to have an open toll easily implemented with softwares at low costs. The tool evaluation is carried out in real-time optimization with the concept of two-layer approach. The tool is applied to a threephase catalytic slurry reactor, represented by a deterministic dynamic heterogeneous mathematical model. The kinetic law considers the hydrogenation reaction of o-cresol to obtain 2-methyl-cyclo-hexanol, in the presence of the catalyst Ni/SiO2. The advanced controller, which is based on the Dynamic Matrix Control with constraints (QDMC), is used. The present implementation aims to maintain the conversion at the exit of the reactor and to maximize the conversion. The challenge is then to conciliate better results of the optimization and less effort and computational time in the real-time process integration. The results presented showed that LM, SQP (local deterministic methods) and GA (stochastic method) algorithms were able to optimize the process both for the case of maintaining and maximizing o-cresol conversion, when perturbations are introduced into the process. The simulations showed that GA could optimize the process after perturbations were inserted but demanded a CPU time not applicable in real-ime optimizations. LM and SQP, on the other hand, optimized successfully the process, both in terms of achieved conversion and CPU time, presenting potential to be used in realtime applications for the studied three-phase catalytic reactor. Keywords: Real-time Optimization, Advanced Controller, Genetic Algorithm, Sequential Quadratic Programming, Levenberg-Marquardt Algorithm and Hydrogenation

1. Introduction Real-time operation, consisting of on-line integration of optimization and control tasks, is an essential step to achieve high profitable process operation , with maximization of profits from the processes. There are two classic approaches to integrate optimization and control tasks during process operation, to know, two-layer and one-layer ones. In the one-layer strategy, the optimization and control problems are postualted in a single objective function. In this approach the process variables set-points and parameter of the controller are obtained at the same time. The two-layer approach, on the other hand, the optimization and control problems are solved separately: the optimization of the process

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is made in an upper stage, i.e., the optimizer generates set-points for the process variables, solving a process optimization. The results are then used as new set-point values by the controller. The major challenge for real-time optimization implementations for process engineers lies mainly in the lack of robustness of the many available optimization solvers [1]. There have been many efforts to determine the parameters of decision in a process using optimization methods [2-3]. This work aims to evaluate different optimization methods performance for real-time applications. For this purpose, a multi-method optimization tool is used coupled to a mathematical model of an industrial hydrogenation unit and two-layer real-time optimization is simulated. Local deterministic (Levenberg-Marquardt, LM, and Sequential Quadratic Programming, SQP) and stochastic methods (Genetic Algorithm, GA) are used for the evaluation of two optimization problems, to know, maintenance of the process conversion at desired process operation conditions; and search for the maximal conversion.

2. Case Study- Three-phase hydrogenation catalytic slurry reactor The case study used in this work is a three-phase catalytic reactor, in which the hydrogenation of o-cresol to 2-methyl-cyclohexanol takes place. O-cresol is fed into the reactor in the liquid phase at an specified concentration and temperature. Hydrogen, part of the gas phase, is also fed to the reactor at specified concentration and temperature. The reactor is filled with catalysts particles. The process variables that are of importance on the control and process quality monitoring are reactor exit temperatue and species concentrations. The mathematical model of this process is formed by a set of partial differential equations, accounting for the energy and mass balances for all involved species. The reader interested in the methematical model development details is referred to previous works [4-5]. The model developed is therefore coupled to the optimization routine, which seeks the optimal process conditions that maximize process conversion and the ones that maintain conversion under desired specifications.

3. Optimization and Control Problems Two objective functions are evaluated: maintenance of the o-cresol conversion at ordinary operational conditions (Case 1) and maximization of conversion (Case 2). The manipulated variables are the reactant fluid feed temperature, Tfo (Case 1) and the temperature of the coolant, Tr (Case 2) and the controlled variable is the reactor exit temperature, T (because it represents an indirect measurement of conversion). Lower and upper bounds of the manipulated variables are given in Table 1. Table 1. Lower and upper bounds of the manipulated variables

Parameter Tr (K) Tfo (K)

Lower bound 350.0 378.0

Upper bound 660.0 702.0

4. Real-time implementation (RTO) The controller used in the two-layer structure already mentioned is based on the Dynamic Matrix Control with constraints (QDMC) procedure. The process integration with the two-layer approach made in a previous work [2] with SQP and LM as optimization methods is a reference to make a comparative evaluation of the RTO system implemented with GA. In the traditional two-layer optimization approach here

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adopted, the set-points of the controlled variable are calculated and sent to the control layer.

5. Results In order to make a comparison among the LM, SQP and GA optimization methods, the dynamic profiles of conversion, reactor exit temperature and manipulated variable are presented for both optimization cases; maintenance of conversion (Case 1) and maximization of conversion (Case 2). The optimization problems here were postulated in order to (1) maintain process conversion at 71.00%, even when process disturbances occur (here simulated by step perturbations in the feed concentration and in the coolant fluid temperature) and to (2) maximize conversion (simulated disturbances in feed concentration and in the reactant inlet temperature). A binary genetic algorithm (GA) code was run for 15 generations with 15 individuals, totalizing 225 evaluations of the objective function. A central composite factorial design [3] was used in order to determine the best values GA parameters that lead to the optimal solution for this case study. The best values for crossover, jump and creep mutations probabilities (the genetic algorithm parameters) were 0.8, 0.07 and 0.07, respectively. It should be here emphasized that the statistical treatment previously given to the GA parameters is general but the parameters values are valid only for this case study and indicate that GA runs with paramters set to these values tend to achieve good conversion values . The optimized values were the ones used for all optimization trials using GA in this work. Table 2 brings the characteristics of the optimal operating point found separately by GA, SQP and LM methods, as well as the computational time demanded for the search (on a 2.8 GHz 768 Mb RAM AMD Athlon processor). Table 2. Optimal response found by LM, GA and SQP in real-time optimization – Maintenance of the o-cresol conversion at ordinary operational conditions (Case 1) and maximization of the ocresol conversion (Case 2)

LM SQP GA Case 1 Case 2 Case 1 Case 2 Case 1 Case 2 o-cresol conversion (%) 71.00 95.31 71.00 95.31 71.47 86.46 Manipulated variable (K) 520.7 650.0 520.0 650.0 520.02 600.0 Computational time (min) 0.5 0.5 1 2 11 13 Set-point (K) 557.12 600.0 557.12 600.0 557.13 581.30 The conversion and set-point values were found by the LM, SQP and GA algorithms under the desired specifications for Case 1 (Table 2). Secondly, an important issue observable in Table 2 is that the computational time was significant lower for the twolayer approach with LM and SQP, with an order of magnitude compatible with real-time applications in a supervisory control structure. On the other hand, the computational time demanded for GA makes it not useful for real-time applications. The results found with local deterministic optimization methods (SQP and LM) only differ in the number of iterations and, therefore, for the sake of brevity, the presented profiles will only show comparisons among SQP and GA. From Fig. 1, it is possible to verify that both SQP+QDMC and GA+QDMC were able to bring the process back to the desired process conversion (Case 1). Due to the perturbations experienced by the process, the manipulated variable (Tfo) had to assume a new value (around 520K), which were similar for all optimization algorithms (Table 2).

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Figure 1. Real-time optimization to maintain o-cresol conversion at 71% (Case 1) and to maximize o-cresol conversion (Case 2) - Profiles of main process variables. Case 1: Manipulated variable Tfo, Step disturbance of +5% in feed concentration and in Tr ; Case 2: Manipulated variable Tr , Step disturbance of -5% in feed concentration and in Tfo

Table 2 shows that LM and SQP algorithms showed a better performance than GA in Case 2, both in terms of conversion achieved and in time of calculation. Indeed, while GA demanded 13 minutes to find the value of Tr (about 600K) that maximizes the steady-state process (86.46%), LM and SQP demanded only 30 seconds and 2 minutes, respectively, to find a value of Tr (650 K) that led to a better conversion (95.31%) than

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that found by GA. Thus, with better solutions and computational time, the SQP and LM algorithms showed to be more appropriate to be used in strategies of control in real-time of this process than the GA.

6. Conclusions The efficiency and applicability of local deterministic and stochastic optimization methods in a two-layer approach for applications in real-time control of a three-phase hydrogenation catalytic reactor were evaluated in the present work. The presented results showed that LM, SQP (local deterministic methods) and GA (stochastic method) algorithms were able to optimize the process for both cases of maintenance and maximization of o-cresol conversion, when perturbations are introduced into the process. The stochastic method, GA, however, showed to be not suitable for solving this kind of problem in real-time operation. The local deterministic methods, SQP and Levenberg-Marquardt were considerably faster than GA without showing convergence problems. Furthermore, the stochastic method was not able to maximize conversion to a value as high as the deterministic did. Therefore, the local optimization deterministic methods present a good potential to be employed in real-time applications of a threephase hydrogenation catalytic reactor. Nevertheless the initial search for finding an optimal solution may use the GA in an off-line fashion whereas the process is running under the last optimal implemented solution. The value from the GA is then used in an initial guess for the LM and SQP methods to work in on-line optimization strategies.

7. Acknowledgements The authors acknowledge FAPESP and CNPq for the financial support given to this work.

References [1] L. T. Biegler and V. M . Zavala, Comp. Chem Eng, in Press (2008) [2] D. N. C. Melo, M. M. Santos, E. C.Vasco de Toledo, S. D. M. Hasan, M. R. Wolf Maciel and R. Maciel Filho, Comp. Chem. Eng., 29 11-12(2005) 2485. [3] M. C. A. F. Rezende, C.B.B. Costa, A.C. Costa, M.R.Wolf Maciel, R. Maciel Filho, Chem. Eng. Sci. 63/2(2008) 330. [4] E.C.Vasco de Toledo, P.L. Santana, M.R. Wolf Maciel, R. Maciel Filho,Chem. Eng. Sci. 56(2001) 6055. [5] A. P. Mariano, E. C.Vasco de Toledo, J. M. F. Silva, M. R. Wolf-Maciel and R. Maciel Filho, Comp. Chem. Eng., 29 (2005), 1369.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Design and Control of New Intensified Distillation Systems for Quaternary Separations using Genetic Algorithms José Antonio Vázquez – Castilloa, Josué Addiel Venegas – Sáncheza, Juan Gabriel Segovia – Hernándeza, Salvador Hernándeza, Héctor Hernándeza, Claudia Gutiérrez – Antoniob and Abel Briones - Ramírezc,d a

Universidad de Guanajuato, Departamento de Ingeniería Química, Noria Alta s/n, Guanajuato, Gto., México 36050, [email protected] b CIATEQ, A.C., Av. del Retablo 150, Col. Fovissste, Querétaro, Querétaro, México, 76150. c Instituto Tecnológico de Aguascalientes, Departamento de Ingeniería Química, Av. Adolfo López Mateos #1801 Ote. Fracc. Bonagens, Aguascalientes, Aguascalientes, Méxic, 20256. d Innovación Integral de Sistemas S.A. de C.V., Limas No. 5 Manzana C, Fraccionamiento Don Manuel, Querétaro, Querétaro, México, 76114.

Abstract The design and optimization of a coupled distillation system is a non-linear and multivariable problem. The complexity of this kind of problem leads to the high difficulty for solving it. This paper addresses the application of genetic algorithms to the optimization of intensified distillation systems for quaternary distillations. For that purpose, we used a multi-objective genetic algorithm with restrictions, written in MatlabTM coupled to process simulator Aspen PlusTM for the evaluation of the objective function. Keywords: Genetic algorithms, dividing wall columns, design, control properties.

1. Introduction Process intensification (PI) is an area presently receiving considerable interest in the chemical engineering. Stankiewicz and Moulijn [1] provide a definition of PI, comprising novel equipment, processing techniques, and process development methods that, compared to conventional ones, offer substantial improvements in (bio)chemical manufacturing and processing as well as an extensive description of a PI toolbox, ordered along two dimensions: equipment and processing methods. Distillation handles about 3% of the total US energy consumption, more than 90% of all product recovery and purification separations in US and more than 95% of chemical industries consumption worldwide. Distillation processes are highly energy-consuming systems, and any small improvement in distillation can provide huge energy savings. Thermally coupled distillation sequences (TCDS) are an example of process intensification. Thermal coupling has been used in the design of multicomponent distillation systems to significantly reduce both energy consumption and capital costs when compared with conventional simple column configurations. Thermally coupled distillation sequences are an example of process intensification. Specifically, the thermally coupled dividing wall column (DWC) has been successfully used in many industrial separations for

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ternary mixtures. The DWC offers the possibility of both energy and capital cost savings. Capital cost savings result from a reduction in quantity of equipment (i.e., one shell instead of two in the case of the Petlyuk column). There are also indirect benefits: a DWC requires less plot area, and, therefore, shorter piping and electrical runs. Flare loads are reduced because of the lower heat input and smaller fire-case surface, leading to a smaller flare system. Amminudin et al. [2] reported the industrial acceptance and commercialization of DWC by organizations such as BASF AG, M.W. Kellogg (together with BP, later known as BP Amoco), and Sumitomo Heavy Industries Co. together with Kyowa Yuka. Linde AG constructed the world’s largest DWC for Sasol, an estimated 107 m tall and 5 m in diameter [3]. In 2004, Adrian et al. [4] reported that BASF operates about 30 DWCs worldwide in their plants. Recently, efforts have focused on finding new thermally coupled configurations based on energy savings as well as operability.

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e)

DWCS-5

Figure 1. Intensified distillation systems for quaternary separations. There are few works on extensions toward the design of DWC for mixtures of more than three components. The optimal design of DWC for separation of multicomponent mixtures is a non-linear and multivariable problem, and the objective function used as optimization criterion is generally non-convex with several local optimums. However, the task is complicated and is likely to fail to achieve convergence. In this paper, we have studied the design of five new intensified distillation systems for quaternary

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separations, with dividing walls, (Figure 1) using as a design tool a multi-objective genetic algorithm with restrictions coupled with the process simulator Aspen PlusTM [2] for the evaluation of the objective function, ensuring that all results obtained are rigorous. Numerical performance of this method has been tested in the design of columns with several mixtures to examine the effect of the relative volatilities of the feed mixtures.

2. Design Tool: Genetic Algorithm Recent years have seen increased development and application of global optimization strategies in many areas of chemical engineering. Global optimization methods can be classified as deterministic or stochastic. The first class offers a guarantee of finding the global optimum of the objective function, provided that the objective function is convex. On the other hand, stochastic optimization methods are robust numerical tools that present a reasonable computational effort in the optimization of multivariable functions; they are applicable to ill-structured or unknown structure problems, and can be used with all thermodynamic models. In the case of stochastic optimization, there are methods known as genetic algorithms (GA), which are a part of the wider field of evolutive algorithms. Optimal design of the new intensified distillation systems implies the determination of 16 variables among continues and integers, such as total number of stages, location of feed stages, location of the exits and entrances of interconnection flows, reflux ratio, product and interconnection flows. The elevated number of variables along with the enthalpy and phase equilibrium calculations for quaternary mixtures makes this problem mixed-integer non-lineal. Optimal design for these sequences means having a structure with as few as possible stages and as small as possible heat duty, but satisfying the purities required. The optimization of the intensified distillation systems implies the minimization as the number of stages in each column, Nj, as the heat duty of the reboilers presented in the sequence, Qi, subject to achieve the purities required in each stream product: Min (Qi , N j ) = f ( R, N k , N l , Fk , N F , N S ) subject to y& ≥ x& m

(1)

m

Where R is the reflux ratio, Nk is the number of stage of the outlet interconnection flow k in the column j, Nl is the number of stage of the inlet interconnection flow l in the column j, Fk is the value of the interconnection flow k, NF is the number of stage of the feed stream, NS is the number of stage of the side stream, and are the vectors of obtained and required purities for the m components, respectively. The sequences DWCS-1 and DWCS-3 have four objectives to minimize: the number of stages in the three columns and the heat duty of the unique reboiler; while in sequences DWCS-2, DWCS-4 and DWCS-5 there are five objectives: those included in the previous sequences plus the heat duty of an additional reboiler. For all sequences, minimization of these objectives includes the manipulation of 16 variables as continuous as integer, which include reflux ratio, location and values of the interconnection flows, and the feed stage of the sequence. These 4 or 5 objectives have to be minimized simultaneously, since they are in competition.

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In order to solve this problem, we used the multiobjective genetic algorithm with constraints coupled to Aspen PlusTM proposed by Gutiérrez-Antonio et al [5] to manage five and four objectives along with the 4 constraints of purities, depending on the sequence. The multiobjective genetic algorithm used allows obtaining the rigorous Pareto front of the intensified distillation systems: a set of non dominated, optimal and rigorous designs that satisfied the purities required. The term non dominated means that there is no other design that can improve one objective without worsen another one. From that set of non dominated optimal design, we choose one design for each case due to space limitations of the manuscript. The term rigorous means that all designs presented were obtained considering the complete set of MESH equations along with the phase equilibrium calculations, using the module Radfrac of Aspen PlusTM. For all sequences we employ 2000 individuals and 60 generations, as parameters of the algorithm. These parameters were obtained through a tuning process, in which we were looking to ensure the convergence in a reduced number of generations, and seeking diversity in the Pareto front. The time employed for the optimization of each sequence is between 8 and 10 hours on a Xeon 5410 workstation at 2.33 GHz with 8 GB of RAM. Figure 2 displays a block diagram for the genetic algorithm.

3. Case of Study The description of the mixtures and the composition in the feed used in this paper is given in Table 1; the feed flowrate was 45.36 kmol/h as saturated liquid, and the specified purities for the product streams were assumed to be 98.7, 98, 98 and 98.6 mole percent for A, B, C and D respectively. The design pressure for each separation was chosen to ensure the use of cooling water in the condensers. Since the feeds M1 and M2 involve a hydrocarbon mixture, the Chao-Seader correlation was used for the prediction of thermodynamic properties. In the case of M3 and M4, the UNIQUAC model was used for calculations.

Table 1. Mixtures analyzed. Mixture

Component

Feed composition

(A, B, C, D)

(mol. fraction)

M1

n-pentane, n-hexane, n-heptane, n-octane

0.15,0.35,0.35,0.15

M2

2-methyl-butane,n-pentane,2-methyl-hexane,nhexane

0.15,0.35,0.35,0.15

M3

benzene, toluene, ethylbenzene, o-xylene

0.15,0.35,0.35,0.15

M4

methanol, 1-propanol, 1-pentanol, 1-octanol

0.15,0.35,0.35,0.15

4. Results It can be noted that, for the case M1 (Table 2), the DWCS-1 sequence has the lowest energy requirement and CO2 emissions, but the DWCS-4 presents the minimum total annual cost and the highest thermodynamic efficiency. This result is in agreement with the fact that the optimum scheme must be selected in terms of the total annual cost, because the same energy requirements in complex distillation sequences can be

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translated into different costs because of their dependence on the temperatures of the integrated distillation sequence reboilers. The worst option in TAC value is DWCS-3. The analysis was conducted on the other cases of study and it can be established that, in general, DWCS-1 sequence has the lowest energy consumption and CO2 emissions, but the better option in TAC and Ș values is DWCS-4. A preliminary heuristic rule can be suggested: the best option is presented when the component A is purified in a conventional sequence. The study is complemented by a dynamic analysis (closed-loop using PI controllers). We attempted a common ground for comparison by optimizing the controller parameters, proportional gains (KC) and reset times (τi), for each conventional and integrated scheme following the integral of the absolute error (IAE) criterion.

Table 2. Energy consumption, total annual cost, thermodynamic efficiency and CO2 emissions for M1. Sequence

Energy consumption

Total Annual

Thermodynamic efficiency

CO2 Emissions

(BTU/hr)

Cost (USD)

Ș (%)

(kg/hr)

DWCS-1

2,529,918.70

531,287.1

21.4

180.7

DWCS-2

3,436,258.40

553,691.7

19.6

245.4

DWCS-3

2,537,126.50

680,975.9

21.8

181.2

DWCS-4

2,644,464.70

499,941.4

22.1

193

DWCS-5

3,521,712.80

579,412.7

17.6

251.5

0.998

0.996

DWC-3 0.994

0.992

0.99 DWC-4 0.988

0.986

0.984 0

1

2

3

4

5

6

7

Time, h

Figure 2. Dynamic responses for a feed disturbance in component A.

8

9

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The liquid compositions for the main product streams (A, B, C and D) are taken as the controlled variables. The control loops for the thermally coupled columns were chosen from an extension of the energy balance configuration for conventional distillation column. When a feed disturbance was implemented, intensified systems successfully rejected the disturbance to bring the product composition back to its design value. However, the responses of the DWCS-4 and DWCS-2 were remarkably better in comparison with DWCS-3 (Figure 2). This result is important: the best sequence in TAC value is the best in dynamic behavior.

5. Conclusions A design methodology for intensified thermally coupled distillation sequences has been presented. The design and optimization methodology used have proven to be an important tool to resolve these kinds of problems, producing results close to the global optimum and with low mathematical effort. Because of the complex nature of the studied systems, this rigorous simulation method is absolutely necessary to ensure that the best solution is chosen. As it can be seen from the results, the best option is the DWCS-4 in TAC and η values. The control properties show good dynamic closed-loop performance in the best option.

6. Acknowledgements We acknowledge the financial support provided by Universidad de Guanajuato, CONACyT and CONCyTEG (Mexico).

References [1] Stankiewicz, A., Moulijn, J. A., 2000, Process intensification: Transforming chemical engineering, CEP, 96, 22. [2] Amminudin, K.A., Smith, R., Thong, D.Y.C., Towler, G.P., 2001, Design and Optimization of Fully Thermally Coupled Distillation Columns. Part 1: Preliminary Design and Optimization Methodology. Chem. Eng. Res. Des., 79: 701. [3] Schultz, M.A., Stewart, D.G., Harris, J.M., Rosenblum, S.P., Shakur, M.S., O’Brien, D.E., 2002, Reduce Costs with Dividing Wall Columns. Chem Eng Prog, May, 64. [4] Adrian, T., Schoenmakers, H., Boll, M., 2004, Model Predictive Control of Integrated Unit Operations: Control of a Divided Wall Column. Chem Eng Process, 43, 347. [5] Gutiérrez-Antonio, C., Briones-Ramírez, A., 2009, Pareto front of ideal Petlyuk sequences using a multiobjective genetic algorithm with constraints, Computers and Chemical Engineering, in press.

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Design of Reactive Distillation with Thermal Coupling for the Synthesis of Biodiesel using Genetic Algorithms Erick Yair Miranda-Galindoa, Juan-Gabriel Segovia-Hernándeza, Salvador Hernandeza, Guadalupe de la Rosa Álvareza, Claudia Gutiérrez-Antoniob, Abel Briones-Ramírezc a

Universidad de Guanajuato, Departamento de Ingeniería Química, Noria Alta s/n, Guanajuato, Gto., México, 36050, E-mail:[email protected] b CIATEQ, A.C., Av. del Retablo 150, Col. Fovissste, 76150, Querétaro, Querétaro, México. c Innovación Integral de Sistemas S.A. de C.V., Limas No. 5 Manzana C, Fraccionamiento Don Manuel, 76114, Querétaro, Querétaro, México.

Abstract The esterification of lauric acid and methanol is explored using a thermally coupled distillation sequence with a side rectifier and the Petlyuk distillation column. The study was conducted using as a design tool a multi objective genetic algorithm with restrictions.The product of the esterification can be used as biodiesel. It was found that the thermally coupled distillation sequence involving a side rectifier can produce biodiesel with a high purity (around 0.999) and also pure water, and the excess of methanol is recovered in a side rectifier. The results indicate that the energy consumption of the complex distillation sequence with a side rectifier can be reduced significantly by varying operational conditions. These reductions in energy consumption can be interpreted as reductions in carbon dioxide emissions. Keywords: reactive distillation, biodiesel, genetic algorithm, energy consumption

1. Introduction Due to increased energy demand and environmental concerns worldwide, important research is currently underway on biofuels and alternative energies, e.g., biodiesel, biomass, bioethanol. In the case of biodiesel, it has been reported that its production can be competitive with fossil diesel when the price of crude oil reaches USD 100 per barrel [1]. As a result, important process intensification polices have been taken into account in the design of new processes, due to reduction in oil reserves, and for minimization of carbon dioxide emissions and use of alternative energies. Attention has been paid to these important aspects in the process systems engineering area of chemical engineering. For example, in a chemical plant, energy consumption in a separation process such as distillation can be up to 40% of total consumption. As a result, researchers in the field of distillation are developing new configurations that can be capable of reducing both energy consumption and carbon dioxide emissions [2]. One alternative that has been explored in detail is the use of thermally coupled distillation sequences (TCDS) that can achieve energy savings between 30 and 50 percent over conventional distillation sequences for the separation of some multicomponent mixtures. These energy savings have been predicted using steady state simulation and

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mathematical programming; also, their theoretical control properties and dynamic behavior have also been determined [3]. Based on these studies, practical implementation of thermally coupled distillation sequences has been conducted using dividing wall columns. Reactive distillation is considered to be the most representative intensification operation because it combines reactions and separation in a single process unit. As a result, TCDS options can be used to carry out reactions of esterification of fatty organic acids, and the produced esters can be used as biodiesel. This leads to important processes to produce biofuels using complex distillation systems that can reduce energy consumption, capital costs, and carbon dioxide emissions. Thus, in this paper, the production of biodiesel by esterification of methanol and lauric acid is studied using a thermally coupled distillation sequence with a side column and the fully thermally coupled distillation sequence. We have selected these distillation sequences because, for the separation of ternary mixtures, there are two types of thermally coupled distillation sequences: TCDS with side columns and the fully thermally coupled distillation sequence (Petlyuk distillation sequence). The schemes are depicted in Figure 1.

2. Strategy solution In order to optimize the thermally coupled reactive sequences we used the multiobjective genetic algorithm with constraints coupled to Aspen Plus, developed by Gutiérrez-Antonio and Briones-Ramírez [4]. Their algorithm manages the constraints using a multiobjective technique based on the concept of non dominance proposed by Coello-Coello [5]. For the reactive thermally coupled systems the optimization problem includes as objectives the minimization of the total number of stages, the size of the reactive section and the heat duty of the sequence, but it also considers the interconnection flows: Min (Qi , N i , N R ) = f ( Ri , N i , N F ,i , N r1 , N r 2 , Fk , N k ) subject to y& m ≥ x&m

(2)

Where Ri is the reflux ratio, NF,i is the number of the feed stage and Ni is the number of stages of the column i of the sequence, Nr1 and Nr2 are the initial and final stages of the reactive section NR in the column j,

y&m and x&m are vectors of obtained and required

purities for the m components, respectively. Fk and Nk are the value and location of the interconnection flow k. In the reactive thermally coupled distillation sequences, there are four objectives to minimize: the number of stages in each column, the size of the reactive section and the heat duty of the sequence. For the sequences the objectives are in competition, so they have to be optimized simultaneously. The manipulated variables include reflux ratio, total number of stages, value and location of the interconnection flows, and size of the reactive section. For the thermally coupled reactive distillation sequences we used 2000 individuals and 40 generations as parameters of the algorithm. These parameters were obtained through a tuning process, where several runs of the algorithm were performed with different number of individuals and generations.

Design of Reactive Distillation with Thermal Coupling for the Synthesis of Biodiesel Using Genetic Algorithms

551

3. Case study The esterification process can be represented conceptually by equation 3.

+

Alcohol

Fatty Acid ←⎯ → Ester

+

Water

(3)

This equilibrium reaction can be favored if the products are removed as the reaction proceeds. An additional problem may present itself, depending on the acid and the alcohol used, as binary or ternary homogeneous azeotropes can be formed in the reactive system. For highly nonideal systems, heterogeneous azeotropes can be formed. These key factors must be considered to select the appropriate thermodynamic model when the system is studied with process simulators. For this class of reactive systems, thermodynamic models such as NRTL, UNIFAC or UNIQUAC can be used to calculate vapor-liquid or vapor-liquid-liquid equilibriums. The systems include two feed streams; the first is lauric acid with a flow of 100 lbmol/h as saturated liquid at 1.5 bar, and the second is methanol with a flow of 120 lbmol/h as saturated vapor at 1.5 bar. The reactive system is catalyzed using sulphuric acid. A mass fraction of 0.999 was assumed for the purity of the biodiesel stream.

MEOH WATER B3 LAURIC-A

B2

4 5 METHANOL

BIODIESE

(a) Reactive TCDS with a side rectifier.

B5

14 LAURIC-A 18 B6 19

16 20

17 METHANOL

BIODIESE

(b) Reactive Petlyuk column. Figure 1. Reactive TCDS for the production of biodiesel.

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4. Results

Mass fraction in the liquid phase 0.3 0.4 0.5 0.6 0.7

0.8

0.9

1

The composition profiles of the optimized designs were analyzed in order to determine biodiesel composition. This is very important because the amount of acid is critical in motor vehicles. Figure 2 presents the composition profiles in the liquid phase for the reactive TCDS with side rectifier, as a representative profile of the analyzed reactive systems. In the case of the reactive TCDS option with side rectifier, it is observed that it is possible to obtain almost pure biodiesel as the bottom product of the main column (mass fraction equals 0.999). In the distillate product of this column, the water produced in the reaction is removed, and the excess of methanol is recovered in the side rectifier column. This methanol, of course, could be returned to the reactive distillation column in order to obtain a more efficient reactive distillation process. When the composition profiles for the Petlyuk distillation column are analyzed, a similar result is obtained in terms of the purity of the biodiesel.

WATER METHANOL LAURIC-A

0.1

0.2

BIODIESE

1

6

11

16 Stage

21

26

31

Figure 2. Composition profiles in the liquid phase of the main column of the reactive TCDS with a side rectifier.

For these complex reactive distillation sequences, Pareto front includes the complete set of optimal designs that satisfy the required purities: from minimum reflux ratio to minimum number of stages, and all designs between them. In this way, the engineer can establish the proper tradeoff between energy and equipment according to his particular needs, both actual and future. In this study, we choose the optimal values of 1059 and 4083 kW, for the reactive TCDS with side rectifier and the reactive Petlyuk column respectively, since, for us, they represent a good compromise between the objectives. Regarding environmental aspects, Kencse and Mizsey [6] have reported that, in fact, gas emissions are directly linked to energy consumption since, in the chemical industry, the energy required in distillation is obtained from crude oil. As a result, reductions in energy consumption can be translated into reductions in carbon dioxide emissions. This important fact can be observed in Figure 3. According to Figure 3, the carbon dioxide emission can be incremented significantly when the operational conditions are different to those corresponding to the optimum. This point is important, because in terms of control and operational aspects, it has been reported [7] that the control properties of

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553

coupled schemes can be improved when the operational conditions fall outside the optimum. This is important because in the selection of the operational conditions, the engineer must take into account the fact that savings in carbon dioxide emissions can be achieved with more efforts in the control system. Finally, regarding recent advances in the use of dividing wall distillation columns, it is possible to propose a single distillation column using a dividing wall and a side condenser. Additionally, this idea leads to reductions in capital costs. The proposed scheme is shown in Figure 4. This complex distillation scheme must be subjected to a control study in order to anticipate potential operational problems for set point tracking and load rejection. This topic is currently under study, but it is needed a kinetic model to obtain a dynamic model of the reactive system [8]. ϭϬϬ

Ɛ ϵϬ Ŷ Ž ŝƐ ϴϬ ŝƐ ϳϬ ŵ Ğ ϲϬ Ϯ

K ϱϬ   Ŷ ŝƚ ϰϬ Ŷ Ğ ϯϬ ϮϬ ŵ Ğ ƌĐ ϭϬ Ŷ / Ϭ

ZZсϲ ZZсϴ ZZсϭϬ ZZсϭϮ

ϳϵ

ϴϵ

ϵϵ

ϭϬϵ

ϭϭϵ

/ŶƚĞƌĐŽŶŶĞĐƚŝŶŐsĂƉŽƌ&ůŽǁ;ůďͲŵŽůͬŚͿ Figure 3 Increase in carbon dioxide emissions for different operational conditions in the thermally coupled distillation sequence with a side rectifier.

Figure 4. Practical implementation of the reactive TCDS with a side rectifier.

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554

5. Conclusions The esterification of methanol and lauric acid using sulphuric acid as catalyst was studied in a thermally coupled distillation sequence with a side column and the Petlyuk distillation column using a multi objective genetic algorithm with restrictions. The thermally coupled distillation sequence with a side rectifier was the best option in terms of energy consumption and purity of biodiesel in the product. The results for the reactive complex distillation sequence with a side column showed that energy consumption can be reduced drastically depending on operational conditions, and for conditions different than those of the optimal solution, carbon dioxide emissions can increase significantly. Finally, a practical implementation using a single column with a dividing wall is proposed.

6. Acknowledgements We acknowledge the financial support provided by Universidad de Guanajuato, CONACyT and CONCyTEG (Mexico).

References [1] M. Frondel and J. Peters, Energy Policy, 35 (2007) 1675 [2] M. Mascia, F. Ferrara, A. Vacca, G. Tola and M. Errico, Appl. Therm. Eng., 27 (2007) 1205 [3] J. C. Cárdenas, S. Hernández, I. R. Gudiño-Mares, F. Esparza-Hernández, C. Y. IriandaAraujo and L. M. Domínguez-Lira, Ind. Eng. Chem. Res., 44 (2005) 391 [4] C. Gutiérrez-Antonio and A. Briones-Ramírez, Computers and Chemical Engineering, In Press (2008). [5] C. A. Coello-Coello, Civil Engineering and Environmental Systems 17, (2000) 319 [6] H. Kencse and P. Mizsey, In proceedings of 17th European Symposium on Computer Aided Process Engineering (ESCAPE), Elsevier (2007) 883 [7] M. Serra, A. Spuña and L. Puigjaner, Ind. Eng. Chem. Res., 42 (2003) 1773 [8] S. Steinigeweg and J. Gmehling, Ind. Eng. Chem. Res., 42 (2003) 3612.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

555

Dividing wall distillation columns for separation of azeotropic mixtures: feasibility procedure and rigorous optimization Abel Briones-Ramíreza, b and Claudia Gutiérrez-Antonioc a

Innovación Integral de Sistemas S.A. de C.V., Calle Número 2 #125 Interior 13, Parque Industrial Jurica, Querétaro, Querétaro, 76120, México b Instituto Tecnológico de Aguascalientes, Av. Adolfo López Mateos #1801 Ote. Fracc. Bonagens, Aguascalientes, Aguascalientes, 20256, México c CIATEQ, A.C. Unidad Retablo, Av. del Retablo #150 Col. Fovissste, Querétaro, Querétaro, 76150, México, [email protected]

Abstract In this work, we propose the use of dividing wall distillation columns, DWC, to separate azeotropic mixtures. First, we present a procedure to guarantee the feasibility of the desired split, based on material balances. Once the feasibility is verified, a preliminary design is calculated considering the DWC as an arrangement of three disengaged conventional distillation columns. Then, this design is the initial solution of the optimization procedure: a multiobjective genetic algorithm with constraints coupled to Aspen Plus [1]. This algorithm is used to find optimal designs of DWC for two azeotropic mixtures of industrial importance, with just one distillation border at the operating pressure. Results show that use the DWC for separation of azeotropic mixtures is feasible, and important energy savings, until 50%, can be obtained in comparison with conventional sequences. In addition, tendencies in the location of interconnection, side and feed streams were founded. In general, results provide information that can be used for developing a short design method for these schemes. Keywords: optimization, distillation, azeotropic mixtures, feasibility

1. Introduction The 95% of the fluids of chemical and petrochemical industries are separated through distillation, which consumes 3% of the total energy world [2]. The elevated energy consumption of distillation along with the raise in fuel costs forced to seek alternatives to save energy. Dividing wall distillation columns, DWC, are an alternative to reduce operating and capital costs, Figure 1; DWC are thermodynamically equivalent to Petlyuk sequence, but just one shell is required. A lot of research has been done in DWC [3, 4, 5, 6, 7], but mostly with ideal or near ideal mixtures. Find an optimal design of a DWC is a complex problem itself; additionally, in azeotropic mixtures the feasibility of the split is a key issue that must be considered. Figure 1. Dividing wall column

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Unlike the ideal mixtures, the presence of azeotropic points generates border distillation; which limits the feasible separations. Therefore, a feasible separation implies to have feed, distillate and bottom compositions located in the same region. In the literature, there are procedures to verify feasibility of the splits for single [8] and side stream [9] distillation columns; however, there is no feasibility procedure for DWC and/or Petlyuk sequence. In this work, we present a procedure to verify the split feasibility of azeotropic DWC and/or Petlyuk sequence. This procedure is based on material balances lines, and it helps to provide a preliminary design of the DWC; for this, the method of JiménezGutiérrez et al. [10] is applied to an arrangement of three disengaged distillation columns, which are considered as a DWC. The preliminary design is feasible but is not optimal, and it becomes the initial solution of the optimization procedure.

2. Feasibility procedure For verification of the feasibility, we represent the DWC as three disengaged distillation columns, Figure 2. The feasibility is first verified in the main column (columns 2 and 3), and after on the prefractionator (column 1). The top product of column 2 is the distillate of the sequence, D, the bottom product of column 3 is the bottom of the sequence, B, while the side product, S, is the sum of the other two product streams. Calculation of feasibility zone begins locating feed composition and border distillation in the composition space. Therefore, we calculate a distillation line whose starting point is a selected bottom (or distillate) composition, depending on the topology of the composition space.

Figure 2. DWC and its representation with 3 disengaged columns

Figure 3. Feasibility zone for separation of feed F in a DWC

Then, side and distillate (or bottom) products are selected from the points included in the calculated distillation line. In this way, we ensured the feasibility in the main column. In order to satisfy the material balances of columns 2 and 3, there must be straight lines between S and B, and S and D; note that S links both material balances lines, so the material balance in the main column is also satisfied. To finish the verification, the lines B-S and D-S have to be touched by another line that contains F. This new line F1-F2 represents the material balance in the prefractionator, column 1. The feeds F1 and F2 must be located at the middle of lines D-S and B-S, respectively, in order to balance the fractionation of the mixture.

Dividing Wall Distillation Columns for Separation of Azeotropic Mixtures: Feasibility Procedure and Rigorous Optimization

557

Material balance lines give information about feed and product compositions of the three disengaged columns. With this information, we use the method of JiménezGutiérrez et al. [10] to obtain the design of these columns; it is worth of mention that columns 2 and 3 are designed with the greater value of reflux ratio resulting between them. The preliminary design is the initial solution to the optimization procedure, which is presented next.

3. Optimal design problem The optimal design problem of the azeotropic DWC implies the simultaneously optimization of three variables: heat duty of the sequence, Q, and the number of stages in both sides of the shell, Nprefr and Nmain; additionally, the purities required in each product stream must be satisfied. This optimization problem can be expressed as:

Min(Q, N prefr , N main ) = f (R, Fk , N in ,k , N out ,k , N F , N S , N i ) subject to & & y k ≥ xk

(1)

Where R is the reflux ratio, Fk is the interconnection flow k, NF is the feed stage of the sequence, NS is the side stream stage, Nin,k and Nout,k are the number of stage where comes and leaves the interconnection flow k, while the required and obtained purities are the vectors xk and yk, respectively. The optimization is performed using a multiobjective genetic algorithm with constraints coupled to Aspen Plus [1]; since the code is coupled to Aspen Plus all obtained results consider the complete set of MESH equations and rigorous calculations of phase equilibrium. The link to Aspen Plus is made with ActiveX technology, which allows the interchange of information between Windows applications. The genetic algorithm implemented is based on the NSGA-II [11], which is a multiobjective genetic algorithm very robust and easy to implement. Also, a multiobjective optimization technique is used to handle the constraints, which guides the search of the algorithm using the concept of non dominance [12]. The operation of the genetic algorithm and its coupling to Aspen Plus is as follows. From the feasible initial design, the genetic algorithm generates N designs of the azeotropic DWC, which are sent to Aspen Plus to make the simulation of all designs. After that, the results of the simulation of interest (objectives and constraints) are taken back for the genetic algorithm. Then, the entire population is divided in subpopulations according to the number of constraints satisfied; so, the best individuals are those who satisfying n constraints, and they are followed by the individual that reach n-1 constraints, and so. Inside each subpopulation, the individuals are ranked using the fitness function calculated with the algorithm based on NSGA-II. In this way, we are minimizing as the original objectives functions as the difference between the required and obtained purities and recoveries. It is worth of mention that since we are working with Aspen Plus, in some cases the results are obtained with errors or the simulation does not converge; for both cases, the

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algorithm assigns to these individuals an infinite heat duty and a value of zero to the purities and recoveries. The use of this algorithm allows the simultaneously optimization of three objectives, two integer and one continuous. Also, we handle six constraints, three of them are the purities required in each product stream; the rest of them are the recoveries of the key components in each product stream (98%), these additional constraints are considered because we manipulate the flow of product streams. In order to obtain this set of optimal designs, we manipulate six integers and three continuous variables simultaneously, basically all the variables that integrates the design of the azeotropic DWC. Since we are working with azeotropic mixtures, it is so important to give an initial design feasible to avoid that the algorithm explores in regions thermodynamically not feasible. The requirement of a feasible design is due to the nature of the mixture itself, and it is not a limitation of the genetic algorithm. As cases of study, two ternary azeotropic mixtures with one distillation boundary at 30 psia were chosen. The mixtures were acetone-isopropanol-water (M1), and methanolisopropanol-water (M2). Feed composition is equimolar for the two mixtures, and required purities are (0.94, 0.65, 0.99; M1), and (0.99, 0.60, 0.99; M2). NRTL model [13] was used for the prediction of vapor liquid equilibrium of the mixtures. For these cases, we use 1000 individuals and 60 generations. These parameters were obtained through a tuning process, where several runs of the algorithm were performed with different number of individuals and generations. The computational time employed to run each case was 3h in a Workstation Xeon 5410 at 2.33 GHz with 8 Gb of RAM.

4. Analysis of results The first step to design the azeotropic DWC is the calculation of the feasibility zone. According to the purities specified, we calculate distillation lines choosing bottom composition for mixture M1 and M2, along with the distillation boundary. Next, we select the distillate and side product compositions from the points included in the distillation lines. Once we locate the product compositions, then we draw some straight lines to assure the feasibility as in the main column as in the prefractionator, Figures 4 and 5.

Figure 4. Feasibility zone for case of mixture M1

Figure 5. Feasibility zone for case of mixture M2

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From the triangular diagrams, we read the compositions of product and feed compositions for the three columns; these data are useful to obtain the preliminary design applying the method of Jiménez-Gutiérrez et al. [10]. Preliminary designs are the initial solution to the optimization procedure, which allows obtaining Pareto fronts of azeotropic DWC, Figures 6 and 7, which include the three variables in competition.

Pareto front for mixture M1 contains 12 optimal designs that consume the minor amount of energy and havinf the minor number of stages, but satisfying purities. Figure 6. Pareto front of mixture M1 For mixture M2, the Pareto front contains 32 optimal designs: the observed minimum reflux ratio, minimum number of stages, and all designs between these extremes. Figure 7. Pareto front of mixture M2 In Figures 6 and 7, we observe that for mixture M1 the variation of the reflux ratio (energy) versus stages is abrupt, so considering a design with 1.3Rmin will conduct a design with more stages and greater energy consumption than the required. This situation is not observed in mixture M2. Also for both cases, the structure of the prefractionator remains almost constant in all designs that integrate the Pareto front. In other words, the prefractionator size remains unchanged, and the Pareto front is generated with the variations in the structure of main column. For mixture 1, the 40% of the total stages is located in the prefractionator and the rest in the main column. In contrast, for mixture M2 the prefractionator uses just the 20% of the total stages. This difference is due to in mixture M1 we have two azeotropic points, while just one in mixture M2; in other words, more stages in prefractionator are required if the mixture is more complex. Optimal interconnection flows have clear tendencies. For instance, the relation FV2/FL1 tends to one for mixture M1, and to four in mixture M2. These results are consistent to those found previously [1]: the greater values for these relations are in mixtures fewer complexes, while in mixtures more complicates this value tend to one.

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5. Concluding remarks The separation of azeotropic mixtures is feasible in dividing wall distillation columns. We presented a procedure to verify the feasibility of the split for this kind of columns, which also helps to provide a preliminary design feasible. Then, this preliminary but feasible design is provided to the optimization procedure, where nine variables are manipulated simultaneously to minimize three objectives subject to six constraints. Results show that the separation of azeotropic mixtures in DWC is feasible, and resulting optimal designs bring information to take as basis in the development of a short design method.

6. Acknowledgements Financial support of this work provided by CONACyT (México) through the Project 84552 is gratefully acknowledged.

References [1] Gutiérrez-Antonio, C., & Briones-Ramírez A. Comp. & Chem. Eng., In press (2008) [2] Hewitt, G., Quarini, J., & Morell, M. The Chemical Engineer (1999) [3] Dünnebier, G. & Pantelides, C. Ind. Eng. Chem., 38 (1999) [4] Gómez-Castro, F.I., Segovia-Hernández, J.G., Hernández, S., Gutiérrez-Antonio, C. & Briones-Ramírez, A. Chemical Engineering & Technology, 31 (2008) [5] Triantafyllou, C. & Smith, R. Chem. Eng. Res. Des., 70 (1992) [6] Yeomans, H. & Grossmann, I. Ind. Eng. Chem. Res., 39 (2000) [7] Hernández, S. & Jiménez, A. Comp. & Chem. Eng., 23 (1999) [8] Stichlmair, J.G. & Fair, J.R. Distillation: principles and practice, Wiley & Sons, 1998 [9] Rooks, R.E., Malone, M.F. & Doherty, M.F. Ind. Eng. Chem. Res., 35 (1996) [10] Gutiérrez-Antonio, C. & Jiménez-Gutiérrez, A. Ind. Eng. Chem. Res., 46 (2007) [11] Deb, K., Agrawal, S., Pratap, A. & Meyarivan, T. KanGAL report 200001, Indian Institute of Technology (2000) [12] Coello-Coello, C.A. Civil Engineering and Environmental Systems, 17 (2000) [13] Prausnitz, J. M., Lichtenthaler, R. N. & Gomes de Azevedo, E. Molecular Thermodynamics of Fluid-Phase Equilibria, Prentice-Hall International Series, 1999

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Environmental Design of IGCC through Pinch Analysis, Process Integration and Parameters Analysis M. Gadalla,a F. Emun,a T. Majozi,b L. Jiméneza a

Department of Chemical Engineering, School of Engineering, University Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Spain. [email protected] b Department of Chemical Engineering, School of Engineering, University of Pretoria, Pretoria, South Africa, [email protected]

Abstract Environmental consciousness and energy prices are both leading to revolutionary calls for energy alternatives, and cleaner power production technologies, and further to the efficient use of sources (e.g. coal, natural gas). Integrated gasification combined cycles (IGCC) are such technologies that can meet today’s power generation needs, through the combination of high environmental performance, competitive cost-of-electricity and broad fuel flexibility. In this work, systems of IGCC are modeled to provide a robust basis for studies on energy efficiency and environmental improvement. Sensitivity analyses are performed to screen a number of process parameters and operation conditions, which lead to efficient processes. Pinch analysis principles are applied to base cases such that design is better understood and improvement modifications to design are generated for best energy and environment performances. The overall performance of the system is evaluated and improved through constructing composite curves for better heat integration and energy efficiency. From both studies of sensitivity analyses and pinch analysis, emissions levels of CO2, SO2 and NOx are reduced and environmental performance is improved. Economic evaluations of modifications and improvement solutions are keys for a final decision of the optimal solutions. Moreover, further steps of detailed design of heat integration opportunities are essential to adopt a practical and feasible configuration. Keywords: IGCC, Process simulation, Process Optimization, Process Integration, Pinch Analysis.

1. Introduction Energy prices and environmental global warming are strong drivers for new technologies with more energy efficiency, and efficient use of energy sources. In coal technologies, the emission of pollutants, especially green house gases, urged the tightening environmental regulations to forcibly seek for new developments. These developments aim principally at coal based electric power technologies, where IGCC is an alternative technology to pulverized coal (PC) combustion systems (Zheng & Furinsky, 2005). IGCCs have the potential to obtain higher efficiency and better environmental performance for power generation. They also offer greater fuel flexibility (biomass, refinery residues) and can offer multiple products (electricity, hydrogen and other chemicals like methanol and higher alcohols) and byproducts (sulfur, sulfuric

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acid, slag). In addition, IGCC technology has the potential for CO2 sequestration (Zheng & Furinsky, 2005; Ordorica-Garcia et al, 2006).

2. IGCC Process Description and Modeling IGCC is developed for a base case of Texaco gasifier (Zheng & Furinsky, 2005) with radiant/convective cooling system. The process flow diagram is shown in Figure 1. The coal (Illinois #6) is crushed and mixed with water to produce slurry (35.5% w/w water) and is pumped into the gasifier with oxygen. The gasifier operates in a pressurized, down flow, entrained design and gasification takes place rapidly at temperatures higher than 1200ºC. The raw fuel gas produced is mainly composed of H2, CO, CO2, and H2O. The coal's sulfur is primarily converted to H2S and smaller quantity of COS. This raw fuel gas leaves the gasifier at 1370ºC along with molten ash and a small quantity of unburned carbon. No liquid hydrocarbons are generated. The gas/molten solids stream enters to a radiant syngas cooler (RSC) and convective syngas cooler (CSC) sections. In this design, the mix of gas/solids from the gasifier enters a radiant syngas cooling (RSC) system where cooling (≈815 ºC) is accomplished by generating a high-pressure steam. A convective syngas cooling (CSC)/gas scrubbing system cools the raw fuel stream to about 150ºC (27.5 bars) by generating additional steam. It uses a gas scrubber and a low temperature gas cooling/heat recovery section to reduce the raw fuel gas stream to 40ºC, prior to entering a cold gas cleaning unit (CGCU) for sulfur removal. The properties of Illinois #6 coal and the data are reported by the Process Engineering Division of the American Energy Institute (2000). The rest of the data (operating conditions, range of variables…) are retrieved from the literature (Christopher & Zhu, 2006; S. Sugiyama, 2006; Minchener, 2004). Coal preparation

Gasification O2

Coal

Water

Sulfur removal

Gas cooling

Sulfur

N2 Gas turbine

Air separation unit

Air BFW HRSG

Air

BFW

Steam Steam turbine

Figure 1. Simplified diagram for systems of IGCC (Booras and Holt, 2004)

3. Methodology Improvement in energy efficiency and environmental performance of IGCC systems require a rigorous simulation. All sections of the IGCC flowsheet (Figure 1) is rigorously modeled using Aspen Plus® (coal preparation, air separation unit, ASU, gasification, gas cooling and cleaning, acid gas removal, gas turbine, HRSG, steam cycle, etc). Simulation was controlled using FORTRAN routines and design specifications to reduce the number of initial conditions and to adjust variables. The

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main functional relationships (i. e. control structures) are: the amount of coal input is a function of the gas turbine net power (272 MW), the amount of slurry water depends of the coal input (35.5%), the make-up water for the steam cycle depends on the temperature of the stack gas (125oC), the air input to the ASU is determined by the gasifier net duty and the air to the gas turbine (GT) combustor is fixed by the combustor net heat duty or the stoichiometric amount of air required. Due to the seven nested loops, the five control blocks and many design specifications the model is very sensitive towards the loop’s break points (i. e. tear streams) and their initial conditions. After detailed analysis, a specific computational sequence was set up for the model, and the ranges of initial conditions were established to improve the convergence. This simulation model provide basis for sensitivity analysis, process integration, application of pinch analysis in order to improve the efficiency and environmental performance of the process.

4. Process Optimization The performance of the process for different parameters is analyzed in the following subsections. The main parameters analyzed within each analysis are thermal efficiency based on the low heating value of coal (ηt LHV), cold gas efficiency (sCG), net power output per ton of coal, O2:carbon ratio (O2:C) and air:clean syngas ratio (air:syn). Improvement 4.1. Effects of Gasification Temperature The study of the gasification temperature is performed under the operational range of temperatures where gasification can take place with slagging of the ash (1250-1550 ºC) (Zheng & Furinsky, 2005). As the gasification temperature increases, the thermal efficiency decreases due to a decrease in the cold gas efficiency. This decline in cold gas efficiency is due to a rise in the O2:C ratio in order to combust more carbon to reach high temperature. On the contrary, the total net power increases because the steam turbine power output rises due to a higher amount of the slurry used for the same quantity of gas turbine output; however, the net power output per ton of coal consumed shows a decreasing trend as the thermal efficiency. The CO2 and SOx emissions per unit of power output increases due to the rise in the coal consumption for the same level of GT power output. But the NOx emission per unit of power output decreases very slightly due to a decline in the air:clean syngas ratio, thereby lessening the thermal NOx formation. 4.2. Effects of Gas Turbine Inlet Temperature (Syngas Combustion Temperature) The analysis is performed for a range of temperatures (Tcomb) around the base case (1250-1550 oC). For an increase in Tcomb by 300 oC, thermal efficiency (ηt LHV) increases by 5%. Along with an increase in ηt LHV, the CO2 and SOx emissions per unit power output also decrease. This is due to a decrease in the level of coal consumption for the same GT power output. But, the NOx emission increases because of an increase in thermal NOx formation at higher temperatures. The carbon conversion efficiency, the cold gas efficiency and the O2:C ratio remain almost unchanged as they are independent of the combustor operating temperature. 4.3. Effects of Level of N2 injection As the fraction of N2 injection to the GT combustor increases: i) thermal efficiency increases, due to a decrease in the slurry (coal) requirement as more N2 is used to drive the turbine, ii) net power output decreases due to a decrease in the steam turbine power

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output as a result of the reduction in the coal flow, iii) net power output per ton of coal input increases because of the decrease in coal requirement for the same level of GT output, iv) CO2, SOx and NOx emissions decrease due to the decrease in the coal consumption and the diluting effect of the N2, thus inhibiting thermal NOx formation. The carbon conversion efficiency, the cold gas efficiency and the O2:C ratio remain constant because they are independent of the varying parameter. 4.4. Effects of Solid Concentration in Coal Slurry With the rise in solids concentration, the O2:carbon ratio decreases because the required energy to vaporize and superheat the water decreases. Therefore the syngas heating value increases because less coal is being used to supply energy for the gasification. Due to this, the thermal efficiency and the net power output per ton of coal input increase. The emissions per unit power of CO2, SOx and NOx slightly increase because of the slight decrease in the total net power. The net power is minimized with the rise in solids-concentration because the amount of steam produced in the HRSG decreases as the coal consumption decreases. 4.5. Simultaneous effect of N2 injection and Syngas Combustion Temperature The thermal efficiency increases almost linearly with the combustor temperature for all levels of N2 injection. Therefore, the power augmenting effect of the N2 flow is greater than its diluting effect in the combustor. N2 injection level of 98% represents the practical upper bound, as venting is inevitable and N2 can be used as a coolant in the gas turbine (Christopher & Zhu, 2006).

5. Heat Integration The complexity of the process flowsheet provides opportunities for heat integration and potentials for improved efficiency and environmental performance. In this context, the integration of the gasifier and GT combustor is analyzed. This study is complemented by the integration of the air separation unit (ASU) and the gas cleaning unit. 5.1. Heat integration of the Gasifier and the GT-Combustor In this analysis, the gasifier is integrated with the GT-combustor and the level of integration is optimized by varying the oxygen and air requirements of the gasifier and combustor, respectively. With the increase in the level of heat integration, the net power output increases, but the net power per ton of coal consumed increases until it reaches a flat maximum. The decrease in the O2:C ratio with the increase in the level of integration has a positive effect on the thermal efficiency at first, because it favors the gasification reaction (compared with the combustion reaction) and increases the cold gas efficiency. Then, with further decrease in the O2:C ratio, the carbon conversion efficiency and, in turn the cold gas efficiency, start to decrease, thereby decreasing the thermal efficiency. The last effect is to minimize the heat absorbed by the excess air, to maintain the operating temperature. 5.2. Heat integration of ASU and the gas cleaning unit The oxygen from the ASU to the gasifier is integrated with the condenser of the amine regenerator (condenser regenerator) in the gas cleaning unit. This is proposed due to the availability of high quality heat from the amine regenerator unit (Table 1). The integration is achieved together with the analysis of the process for the level of combustor and gasifier integration which is performed in section 5.1.

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The maximum efficiency is obtained at a combustor duty of 150 MW (compared with 200 MW in the previous case) due to a further decrease in the O2:C ratio as the O2 inlet temperature to the gasifier increases.

6. Pinch Analysis From simulation results, both process streams that have excess of heat and require heat are extracted. Composite and grand composite curves (CC, GCC) are generated by following pinch analysis-based approaches (graphical representations). The Problem Table Algorithm can be employed to construct the grand composite curves for the process (Smith, 2005). Figure 2 shows the composite curve CC for the overall process for a minimum temperature difference of 20°C. The indicated hot and cold energy targets are 200 and 490 MW, respectively; the pinch temperature is approximately 350oC. The minimum temperature difference can be however optimized for energycapital tradeoff. From CC, the process can be divided into two parts, one above the pinch and the other below the pinch. Each part can be integrated fulfilling the pinch analysis principles. On the other hand, GCC identifies the best matches for process-toprocess heat integration in terms of heat loads and levels of temperatures (Figure 3). As shown in Figure 3, there exist heat sources of 50 MW at 1240-760oC, 100 MW at 760570°C, 70 MW at 320-240°C, and 60 MW at 35oC, giving a total heat recovery of 280 MW. Furthermore, the excess exhaust steam from turbines at around 440oC can be utilized to satisfy the heat requirement (220 MW) of the process rather than exporting steam from utility plants. This saves money and reduces emissions in global view. In addition, steam line can be fitted on the grand composite curve such that the mass flow rate of steam can be calculated according to the match with GCC and from the properties determined from the ’steam tables’. Various levels of steam can be generated at the process. Superheated steam can be produced up to a temperature of 360oC. As an application, saturated steam at 230oC can be produced in equivalence of energy of 62 MW; steam production rate will be 123 tons/h. The heat duty on boiler feed water preheating will be 19 MW. The profile of steam is shown against the GCC in Figure 5. As a result, the amount of heat recovery achieved in the process and the steam produced will lead to substantial savings in the utility imported from external utility plants. This will correspondingly cut the emissions of CO2 to the atmosphere. 1250

1000

o

T ( C)

750

500

250

0 0

200

400

600

800

-250

H (MW)

Figure 2. Composite curve for the IGCC plant

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Interval Temperature [C]

1200 1000 HP Steam

800

760 oC 570 oC

600

50 MW

100 MW

Turbine Exhaust Steam

400 200

Steam

320 oC 70 MW 190 oC

440 oC 360 oC

240 oC

BFW

0

35 oC CW 60 MW Low temperature liquid

-2000

100

200

300

Enthalpy [MW]

-160 oC

400

500

Figure 3. Grand composite curve for IGCC

7. Conclusions A design model for IGCC systems was modeled using Aspen Plus®. Sensitivity of the process variables was studied resulting and a maximum thermal efficiency of 45% with CO2 and SOx emissions of 698 kg/MWh and 0.15 kg/MWh, respectively, was found. Heat integration of the gasifier and the combustor revealed optimal net heat duty for the integration is 200 MW. The slope of variation in thermal efficiency was high, and therefore a slight variation in operating conditions could lead to a significant loss of efficiency. Further application of Pinch Analysis to the process resulted in large savings of steam requirements of 220 MW, cut-down of global atmospheric gas emissions of 220+62 MW equivalence of steam load. Overall heat recovery within the process was achieved on 280 MW of energy; this corresponds to a saving in utility costs and a decrease in emissions; i.e. benefits to environment and profit improvement.

8. Acknowledgements The authors wish to acknowledge to AECI (A/020104/08 and A/016473/08), the Spanish Ministry of Education and Science (DPI2008-04099) for their financial support.

References G. Booras, N. Holt, 2004, Pulverised coal and IGCC plant cost and performance estimates, Gasification technologies conference, Washington DC, October 2004. H. Christopher, Y. Zhu, 2006, Improved system integration for integrated gasification combined cycle (IGCC) systems, Environ. Sci. Technol., 40, 2006, 1693-1699. J. Minchener, 2004, Coal gasification for advanced power generation, Fuel, 84, 2005, 2222-2235. G. Ordorica-Garcia, P. Douglas, E. Croiset, L. Zheng, 2005, Technoeconomic evaluation of IGCC power plants for CO2 avoidance, Energy conversion and management, 47, 2006, 2250-2259. W. Shelton , J. Lyons, 1998, Texaco gasifier base cases PED-IGCC-98-001, US Department of Energy, Process Engineering Division, 2000, 1-52. R. Smith, 2005, Chemical Process Design and Integration, John Wiley & Sons Ltd. S. Sugiyama, N. Suzuki, Y. Kato, K. Yoshikawa, A. Omina, T. Ishii, K. Yoshikawa, T. Kiga, 2005, Gasification performance of coals using high temperature air, Energy, 30, 2005, 399413. L. Zheng, E. Furinsky, 2005, Comparison of Shell, Texaco, BGL and KRW gasifiers as part of IGCC plant computer simulations, Energy conversion and management, 46, 2005, 1767-1779.

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Future potential for biomass use in blast furnace ironmaking Jarmo Söderman, Henrik Saxén, Frank Pettersson Heat Engineering Laboratory, Åbo Akademi University, Biskopsg. 8, FI-20500 Åbo, Finland,{jsoderma,hsaxen,fpetters}@abo.fi

Abstract Iron- and steelmaking is an energy intensive industrial sector using mainly coal as the heat source and reduction agent. The industry gives rise to about 7 % of the anthropogenic CO2 emissions in the world. In the absence of economically feasible and efficient methods of capturing and storing such enormous quantities of CO2, means for suppressing the emissions must be explored. The work reported in this paper studies the potential of injecting biomass to partially replace fossil reductants in the blast furnace process. The ironmaking blast furnace process is described mathematically by a thermodynamic simulation model, including realistic operational constraints. The model has been applied extensively to evaluate the use of biomass (e.g., wood chips) as auxiliary reductant, creating a simplified linear model on the basis of the results. The model is used to throw light on the feasibility of biomass injection under future price scenarios. Even though the coke replacement ratio of biomass is low, in the order of 25 %, it is demonstrated that the use of biomass as reductant can be a feasible alternative under future price scenarios of coke and emissions. Keywords: Blast furnace, biomass, optimization

1. Introduction Global concern of climate change has brought up into the discussion the role of iron and steel industry as a CO2 source. About 7 % of the anthropogenic CO2 emissions in the world are emitted from iron- and steelmaking industries. The industry uses vast amount of coal in form of coke in the blast furnaces. The purpose is not only to gain the needed heat into the ironmaking process but also to use carbon as reductant for the oxygen containing iron ore. By injection of biomass the fossil CO2 emissions could be lowered. The cost of biomass and the CO2 emission cost are main factors when optimal biomass use in blast furnace process is discussed. Biomass injection rate is, on the other hand, limited to a maximum specific rate in proportion to the hot metal production. The work reported in this paper studies the potential of injecting biomass into the blast furnace in order to partially replace fossil reductants and hereby reduce the fossil CO2 emissions.

2. Model In the present work a thermodynamic blast furnace model was applied [2,3], which is based on the fundamental concepts introduced by Rist et al. [1]. The model utilizes a division of the process into two main control volumes, with thermal and chemical equilibrium approached on the boundary, the reserve zone, between the two volumes. A

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linear model was developed with a set of binary variables to control a nonlinear relation of two process variables. The blast furnace operational costs are predicted effectively by the model. Additionally, the revenues of electric power and district heat that can be produced at the plant were obtained. The input variables in the linear process model were volumetric flow rate of air, volumetric flow rate of oxygen, specific oil rate, blast temperature, specific rate of pellets, specific rate of limestone and specific injection rate of biomass, shown in Eq. 1.

+ K i ,5

Vair

VO 2

moil T + K i ,3 + K i , 4 bl + °C kg/t hm km n/h km 3 n/h mpel m mbio + K i ,6 lime + K i ,7 kg/t hm kg/t hm kg/t hm

Yi = K i ,0 + K i ,1

3

+ K i,2

(1)

The objective function F is given by

m pel c pel m coke,own ccoke,own m coke,b c coke,b c F § m = ¨ sin ⋅ sin + ⋅ + ⋅ + ⋅ + €/t hm © t/h €/t t/h €/t t/h €/t t/h €/t VO2 cO2 m c m c m c + oil ⋅ oil + lime ⋅ lime + bio ⋅ bio + ⋅ + 3 t/h €/t t/h €/t t/h €/t km n/h € km 3 n m CO2 c CO2 c el Q c heat · m hm P ¸ + ⋅ − ⋅ + dh ⋅ t/h € t MW € MWh MW € MWh ¸¹ t hm /h

(2)

For the specific cost of hot metal production the mass and volume flow rates are multiplied by specific mass or volumetric costs, ci. Coke rate is included as own and bought coke, denoted by subscripts coke,own and coke,b. The price of electricity is denoted by cel and heat by cheat. The mass flow rate of fossil CO2 emissions is calculated as the ratio of the molecular weights of CO2 and carbon and taking also into account the share of fossil carbon in the total carbon input to the blast furnace.

3. Illustrative case The thermodynamic blast furnace model was run under a large number of input combinations, with input variables uniformly distributed within their admissible ranges. The injection rate of dry biomass was limited to max. 120 kg/t hm. The process was optimized with the price data shown at Table 1. The biomass and CO2 emission costs were varied: biomass price between 50 and 110 €/t and CO2 emission cost between 0 and 80 €/t.

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Table 1. Input price data for the test cases.

oil limestone pellets sinter coke, own coke, bought oxygen gas

150.0 €/t 30.0 €/t 110.0 €/t 90.0 €/t 200.0 €/t 300.0 €/t 50.0 €/t

El power, sold Heat, sold

50.0 €/MWh 10.0 €/MWh

biomass price CO2 emission

50.0 - 110 €/t 0.0 - 80 €/t

4. Solutions

Production cost, €/t hm

The model was first tested by a series of runs with fixed biomass price of 50 €/t and CO2 emission cost of 0 €/t at different hot metal production rates as a base case, Case 1. Secondly, a series of test runs was made by the biomass price of 100 €/t and CO2 emission cost of 30 €/t, Case 2. The optimal production costs, predicted by the MILPmodel, are shown in Figure 1 for different hot metal production rates in a blast furnace. The minimum production costs were obtained at the production rate of about 145 t hm/h.

250 case 1 case 2

200 120

130

140

150

160

Hot metal prod, t hm/h

Figure 1. Optimal production costs at different hot metal production rates. The variations of two process variables, specific injection rate of biomass and oil, with different hot metal production rates are shown in Figure 2 for Case 1 and Case 2.

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Case 1 biomass Case 1 oil

Injection rate, kg/t hm

150.0

Case 2 biomass Case 2 oil

100.0

50.0

0.0 120

130

140

150

160

Hot metal prod, t hm/h

Figure 2. Optimal specific injection rates of biomass and oil to blast furnace at different hot metal production rates.

Biomass price €/t

Biomass injection (kg/t hm)

120 100

60

80

70 80

60

90

40

110

20 0 0

10

20

30

40

50

60

70

80

CO2 cost (€/t)

Figure 3. Optimal specific injection rates of biomass at a production rate of 150 t hm/h with different prices for biomass and CO2 emissions. The optimal specific injection rates of biomass at different CO2 costs are shown in Figure 3, with fixed hot metal production rate of 150 t hm/h. The injection rates vary with the cost of CO2 emissions for a selected set of prices of biomass. The curves in Figures 2 and 3 demonstrate some aspects of the complex nature of the blast furnace process.

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Partial pyrolysis of biomass Injection of dry wood chips has been shown to be possible up to the level of about 25% of the coke. Limitation is caused by the high oxygen content of wood chips. Biomass pyrolysis has been suggested as a possible way to further increase of the biomass injection rate. A partial pyrolysis of the biomass lowers its oxygen content, but decreases the yield. Additionally there are losses of carbon and hydrogen. The blast furnace MILP-model was rewritten so that it could also take into account the pyrolysis process step. The solutions of the test series with the pyrolysis model are presented by authors in [7].

5. Conclusion An MILP-model for the blast furnace process was tested with the focus on replacement of fossil reductants oil and coke by injection of biomass under consideration of CO2 emission costs. The feasibility of biomass use was revealed at different hot metal production rates and with different price levels for biomass and CO2. A partial pyrolysis of biomass was studied with a modified model and optimal pyrolysis temperatures were found for different biomass and emission costs.

Acknowledgements The financial support from the Academy of Finland to the GreenSteel project is gratefully acknowledged.

References [1] A. Rist, N. Meysson: “A dual graphic representation of blast-furnace mass and heat balances”, Journal of Metals, 19 (1967), 50. [2] H. Saxén, M. Brämming, J.-O. Wikström and P. Wiklund: “Theoretical limits on operation under high oxygen enrichment in the blast furnace”, Proc. 60th Ironmaking Conf., ISS, Warrendale, PA, (2001), 721. [3] F. Pettersson, H. Saxén: “Model for economic optimization of iron production in the blast furnace”, ISIJ International, 46 (2006), 1297.

[4] Y. Kim and E. Worrel: “Intenational comparison of CO2 emission trends in the iron and steel industry”, Energy Policy, 30 (2002), 827. [5] T. Ariyama and M. Sato, “Optimization of ironmaking process for reducing CO2 emissions in the integrated steel works”, ISIJ International, 46 (2006), 1736. [6] M. Takekawa, K. Wakimoto, M. Matsu-ura, M. Hasegawa, M. Iwase and A. McLean: “Investigation of waste wood as a blast furnace injectant”, Steel Research, 74 (2003), 347. [7] H. Saxén, F. Pettersson, J. Söderman, M. Helle. and H. Helle, "Optimization of biomass use as auxiliary reductant in the blast furnace", Recent Progress in Mathematical modeling in Ironmaking 2008 (Ed. T. Ariyama), Tokyo, October 2008, ISIJ, pp. 95-100.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

579

Implementation of a Convexification Technique for Signomial Functions Andreas Lundella, Tapio Westerlundb Process Design and Systems Engineering, Åbo Akademi University, Biskopsgatan 8, 20500 Turku, Finland a [email protected], [email protected]

Abstract In this paper, an implementation of a global optimization framework for Mixed Integer Nonlinear Programming (MINLP) problems containing signomial functions is described. In the implementation, the global optimal solution to a MINLP problem is found by solving a sequence of convex relaxed subproblems overestimating the original problem. The described solver utilizes the General Algebraic Modeling System (GAMS) to solve the subproblems, which in each iteration are made tighter until the global optimal solution is found. Keywords: Deterministic global optimization, signomial functions

1. Introduction MINLP problems containing signomials are quite common, since for example, polynomials as well as bi- and trilinear terms can all be regarded as signomials. These are often nonconvex, making it hard to solve the problem to global optimality. A signomial function is defined as the sum of signomial terms which consist of products of power functions, i.e.,

σ ( x) =

¦c ∏ x

p ji i ,

j

j

i

where the variables xi are positive real- or integer-valued variables and the powers pji are real parameters. A MINLP problem containing signomials can then be assumed to be of the form minimize subject to

f (x) Ax = a, Bx ≤ b, g n ( x) ≤ 0 q m ( x) + σ m ( x) ≤ 0

x = ( x1 , x 2 , , x I ) n = 1,2, , J n , m = 1,2, , J m ,

where the functions f, g and q are convex and the function ı is signomial. It has previously been shown that MINLP problems of this form can be written in a relaxed and overestimated convex form using single variable transformations on the individual variables in the signomial terms (Lundell et al. 2008, Westerlund 2005). The overestimation occurs when the inverse transformations are approximated with piecewise linear functions. The initial linearization is done in one or more steps for each transformed variable. If the solution to the transformed problem does not fulfill the constraints in the original nonconvex problem, additional breakpoints are added to the piecewise linear functions in each iteration until all constraints are valid to at least an epsilon-accuracy.

580

A. Lundell and T. Westerlund

Figure 1. A flowchart of the solver

The single variable transformations mentioned above are not uniquely determined for each problem, since there, in some cases, exist different transformations applicable to the same terms. Different sets of transformations can result in approximate problems of various levels of complexity and overestimation errors. For determining an optimized set of transformations for a certain problem, a Mixed Integer Linear Programming (MILP) problem can be formulated (Lundell et al. 2007, Lundell and Westerlund 2008). Depending on the values of certain parameters in the MILP problem formulation, for example, the total number of transformations can be minimized or choosing transformations with certain properties can be emphasized. By including the MILP method in the overlaying global optimization framework as a preprocessing step, a solver, transforming the nonconvex MINLP problem to a convex overestimated form and then iteratively solving it, can be developed. The described global optimization method, with a limited preprocessing step, has been implemented previously as the GGPECP solver using AlphaECP for the convex MINLP problems (Westerlund and Westerlund 2003). However, in this paper a more general implementation is described. By interfacing the transformation techniques for signomial functions with the GAMS modeling framework, any of the MINLP solvers available in GAMS can be utilized. Since different solvers perform better on certain types of problems, this results in a more flexible solver and can significantly decrease the computational effort required to solve the optimization problem.

Implementation of a Convexification Technique for Signomial Functions

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2. The algorithm implementation in GAMS The algorithm described has been implemented in the programming language C# 3.0, a part of Microsoft’s .NET Framework 3.5. Although an implementation in, for example, C or C++ would probably provide some speed enhancements, the reduction in the time required would probably be marginal, since most of the time is spent solving the transformed MINLP problems in GAMS. A flowchart of the algorithm implementation is provided in Figure 1. 2.1. The problem file format The MINLP problem is specified in an XML format specially designed for the solver. For the sake of compatibility, a parser for the file format used in the GGPECP solver is also included. The XML format for the problem formulation is shown for a simple example in Figure 2. 2.2. Transforming the problem using the MILP method The MILP problem used for obtaining an optimized set of transformations is formulated in GAMS format. Therefore, only the strategy parameters and the powers and coefficients corresponding to the signomial terms in the MINLP problem have to be provided. Changes in the MILP method are then also simple to implement since only the GAMS problem formulation must be altered. The MILP problem can be solved using any of the available solvers, and the solution will indicate which variables need to be transformed, as well as the transformations for each variable. After the transformations have been obtained, the XML problem file is updated to include the transformations. Optionally, the solution process can now be paused, allowing the user to alter the transformations in the file. The optimization step can also be left out, in which case the user must provide the transformations manually by editing the XML file before continuing to solve the transformed problem. After the transformation step, an additional check for the convexity of the transformed signomial terms is performed to make sure the transformations are valid. 2.3. Solving the transformed problem To solve the transformed MINLP problem defined in the XML file, the problem is first automatically translated to GAMS syntax. The piecewise linear functions are defined in the main GAMS problem file, but the breakpoints are instead placed in an external parameter file. Thus, there is no need to update the problem file when adding additional breakpoints in subsequent iterations. The piecewise linear functions can be defined using either so-called Special Ordered Sets (SOS) Type 2 (Lundell et al. 2007) or binary variables (Westerlund 2005). The latter is necessary, since not all solvers in GAMS support SOS variables. After the problem and breakpoint files have been created, GAMS is called to solve the subproblem. The MINLP solver to be used by GAMS is specified by the user along with optional parameters for the individual solvers.

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minimize subject to <problem> <sigterm coeff="1"> <sigelem var="x" power="0.5" /> <sigelem var="y" power="1" />

−3 x − y y − 5 x ≤ 10 x 0.5 y ≤ 10 1≤ x ≤ 7 1≤ y ≤ 6 y∈Ν

Figure 2. An example of the XML problem file for a simple MINLP problem

After each subproblem is solved, the termination criteria are checked, and if fulfilled, the solver terminates as the global optimal solution has been found. Available termination criteria are, in addition to the convex problem fulfilling the constraints in the original nonconvex problem with epsilon-accuracy, if the solution values for the original variables involved in the transformations are close enough to existing breakpoints or a maximum iteration count has been reached. 2.4. Different strategies for adding the breakpoints Many different strategies for adding the breakpoints can be used and these often have a large impact on the number of iterations required to solve the problem, and even if it is at all possible to solve the problem to global optimality. By adding the midpoint of the interval of the breakpoints the current solution belongs to for a specific variable, it has been shown that the solutions will converge to the global optimal solution of the original nonconvex problem (Westerlund, 2005). However, depending on the problem, other strategies may prove to be more efficient, at the risk that only a local solution is found. Other strategies for selecting the breakpoints is adding the solution for the transformed variables in the current iteration as breakpoints in the next iteration, or adding the points where the approximation errors of the linearizations are maximal.

Implementation of a Convexification Technique for Signomial Functions

583

A combination of any of the above can also be used, meaning than more than one breakpoint is added to a specific piecewise linear function in each iteration. This has the drawback that the combinatorial complexity of the problem is increased more than when only adding one breakpoint per transformation variable. However, adding multiple breakpoints to the linearizations in the first iterations can allow for a shorter solution process in the long run. 2.5. Different strategies for choosing the variables to add breakpoints to The default strategy is to add breakpoints to all the linearizations of the transformation variables in the problem. However, for a problem with many different transformations, this can lead to the combinatorial complexity increasing too fast. The solution is of course to only add breakpoints to some of the piecewise linear functions in each iteration. For example, there is no need to add breakpoints to variables only appearing in constraints already fulfilled. In addition to the default strategy, two more strategies are implemented in the solver. The first is to add breakpoints only to the linearizations of the transformations occurring in the constraint with the largest deviation. The second strategy restricts the choice of variables further to only add breakpoints to the transformations having the largest impact on the error of the constraint (Westerlund 2005).

3. Conclusions and future work This paper describes a global optimization solver for global optimization of MINLP problems containing signomial functions. Although the solver is in principle fully working, some additional functions remain to be implemented. For example, it is at the moment not possible to solve problems having variables with negative domains in the signomials. Although it is possible to overcome this shortcoming by a simple translation on the variable in question, this changes the signomial functions in the process. Automatically performing the translations and calculating the new signomials would make the solver applicable to more general class of signomial problems. In addition, a parser for problems in GAMS format is also planned.

Acknowledgements A.L. gratefully acknowledges financial support from the Academy of Finland and the Research Institute of the Foundation of Åbo Akademi University.

References A. Lundell, J. Westerlund and T. Westerlund, 2007 (accepted), Some transformation techniques with applications in global optimization, Journal of Global Optimization, available online. A. Lundell and T. Westerlund, 2008, Exponential and power transformations for convexifying signomial terms in MINLP problems, Proceedings for the 27th IASTED MIC Conference. T. Westerlund, 2005, Global optimization: From theory to implementation: Some transformation techniques in global optimization, Eds. Liberti L. and Maculan N., Springer, New York. T. Westerlund and J. Westerlund, 2003, GGPECP – A global optimization algorithm, AIDIC Conference series .

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

585

Improving efficiency when solving process synthesis problems through translation of variables Marcel Ropotar,a,b Zdravko Kravanjaa a

University of Maribor, Faculty of Chemistry and Chemical Engineering, P.O. Box 219, Maribor 2000, Slovenia, [email protected] b Tanin Sevnica kemicna industrija, d.d., Hermanova cesta 1, Sevnica 8290, Slovenia, [email protected]

Abstract The aim of this contribution is to present an attempt to increase efficiency when solving large-scale discrete-continuous process synthesis problems. This was successfully achieved by incorporating a special translation of local variables within generalized disjunctive programming (GDP) applied to a logic-based outer-approximation (OA) algorithm. Different process synthesis examples were solved using a process synthesizer MIPSYN, in order to compare solution procedures with and without the translation of the variables. Keywords: generalized disjunctive programming, logic-based outer approximation algorithm, MINLP, process synthesis, translation of variables

1. Introduction GDP is regarded as one of the most advanced programming techniques for solving large-scale discrete-continuous problems. GDP problem can be solved either by transforming it into mixed-integer programs or by the development of specific solution methods, e.g. the branch and bound algorithm with convex relaxation by Lee and Grossmann[1]. It should be noted that reformulation with a convex hull is usually tighter than the one with big-M, but it has a bigger size problem[2]. The cutting plane method was applied in order to avoid this increase and yet obtain an as tight as possible lower bound[3,4]. This contribution presents another attempt to increase the efficiency of GDP by means of variable translation and the corresponding alternative convex hull representation. The motivation for the expected improvement relies on the assumption that the efficiency could be enhanced if local variables were defined in narrowed feasible space, irrespective of the discrete decisions. Variable translation is applied to the logic-based OA algorithm, where the conventional OA master problem and its converted MILP master problem are translated into alternative formulations. Different model formulations with big-M, convex hull and alternative convex hull representations are compared by solving some nontrivial synthesis examples.

2. Translation of local variables In synthesis problems, continuous local variables xs are usually defined within zero lower and non-zero upper bounds (0 ” xs ” xs,UP) and constrained by xLOy ” xs ” xUPy, in order to force non-zero bounds when alternatives are selected (y = 1). The main idea is

M. Ropotar and Z. Kravanja

586

to substitute these zero-lower-bounded variables xs with narrowed non-zero-lowerbounded variables (xLO ” xa ” xUP), through the use of the following translation equation: xs = xa – xf(1 – y)

(1)

a

where x is a nonzero-lower-bounded variable defined between the bounds (xLO ” x ” xUP), xf is an arbitrarily-forced value, defined between the same bounds, and y is a corresponding binary variable. When an alternative is selected, an integer term xf(1 – y) becomes zero and xs becomes equal to xa, and when it is rejected, a value xf is subtracted from the variable xa. By translating xs in bounding constrains xLOy ” xs ” xUPy using (1), it can be easily verified that xa takes a nonzero value xf when y=0. In this way, xa remains within the narrowed nonzero bounds irrespective of discrete decision. If a binary variable y is relaxed to a continuous variable Ȝ defined between 0 and 1, the following relaxed translation formula is obtained: xs = xa – xf(1 – Ȝ)

(2)

In addition, a logic-based variation of the variable translation in eqs. (1) and (2) is proposed: [Y: xs = xa] › [¬Y: xs = xa – xf]

(3) s

a

where in the case of the Boolean variable Y = true it follows that x = x and in the case of Y = false xs = xa – xf. It should be noted that the first variation of variable translation (1) is to be used in mixed-integer programming problems, the second one (2) in relaxed ones and the third one (3) in logic-based problems. 2.1. Translation of local variables in convex hull Consider the following GDP problem for process network problems, proposed by Turkay and Grossmann[5]: GDP: min Z s.t.

¦ ck 

f ( x)

k g

h ( x) d 0 Ag ( x) d b g

ªYk º º « h ( x ) d 0 » ª ™ Yk « k » › « B k ( x ) d 0», k  SD » « Ak ( x) d b k » « » « » «¬c k 0 ¼ ¬«c k J k ¼» :(Y ) true x  R n , c  R m , Y ^true, false`m

Note that it has only two terms in each disjunction to denote the selection (Yk is true) or rejection (Yk is false) of process units. A convex hull representation is the tightest relaxation of disjunctions k in the above (GDP) problem. It is generated by means of taking the linear combination of all the points in the feasible regions of disjunctions. By applying the convex hull relaxation to the problem (GDP) in the spirit of Lee and Grossmann[1], the (CHRP) problem given bellow is obtained. When its zero-lower-bounded variables are translated into nonzero-lower-bounded variables using the translation equation (2), the following alternative (A-CHRP) problem is obtained:

Improving Efficiency when Solving Process Synthesis Problems through Translation of Variables (CHRP): min Z

(A-CHRP):

¦¦ J ik Oik  fika  xiks  f g  xg k

A (x ) d b g

g

k

i

hg ( x g ) d 0

s.t.

Ag ( x g ) d b g

g

¦ xiks ,

xkg

¦¦ J ik Oik  fika  xika  xikf 1  Oik  f g  x g

min Z

i

hg ( x g ) d 0

s.t.

¦  xika  xikf (1  Oik ) ,

xkg

k  SD

k  SD

iDk

iDk

¦ Oik

587

¦ Oik

xs = xa – xf(1 – Ȝ)

1, 0 d Oik d 1

1, 0 d Oik d 1

iDk

iDk

EO d e

EO d e

Oik xLOik d xiks , i  Dk , k  SD

xLOik Oik  xikf 1  Oik d xika , i  Dk , k  SD

xiks d Oik xUPik , i  Dk , k  SD

xika d xUPik Oik  xikf 1  Oik , i  Dk , k  SD § xika  xikf 1  Oik · ¸ d 0, i  Dk , k  SD ¨ ¸ Oik © ¹

§ xiks · ¸¸ d 0, i  Dk , k  SD © Oik ¹

Oik gik ¨¨

Oik gik ¨

x LO d x g d x UP

x LO d x g d x UP

where xik are disaggregated variables and xLOik (xUPik) nonzero scalars forcing the nonzero bounds when an alternative is selected. When Ȝik takes zero value in the alternative formulation (A-CHRP), the corresponding variables xik in the bounding constraints are set to xik . At the same time the terms xik and xik 1  Oik in the balance f

f

equation and the objective function precisely cancel each other out, which is equivalent to obtaining zero values for xik in the original problem (CHRP).

2.2. Translation of local variables in the logic-based OA algorithm Logic-based OA problems are usually solved through MILP transformation, where Yik are replaced by binary variables yik, logical relations are formulated as integer constrains and disjunctives are represented either by a big-M or a convex hull representation. When a convex hull representation is considered, the following MILP master problem (CCH-MILP) is obtained and when it is reformulated by the mixed-integer variable translation (1), the following alternative MILP master problem (ACH-MILP) is obtained: (CCH-MILP):

(ACH-MILP):

i

i

k

T

D g t f  x l  ’ x f  x l ( x g  x l ) ½°





k

s.t.

s.t.

h xl  ’ xh xl

¦¦ cik yik  Dika  D g

min Z

¦¦  cik yik  D ika  D g

min Z

T

( xg  xl ) d 0

¾ , l 1,..., L ° ¿

A ( x g ) d bg g

T

D g t f  xl ’x f  xl ( xg  xl ) ½°





h xl ’x h xl

T

( x g  xl ) d 0

¾ , l 1,..., L ° ¿

Ag ( xg ) d bg E g ( y) d eg

E g ( y) d e g

xs = xa – xf(1 – y) Ar ( x g , x s ) d b r

Ar ( xg ,)xs ( xa , y)) d br

(4)

M. Ropotar and Z. Kravanja

588

xLOyik d xs ½° s ¾ x  Xik s x d xUPyik °¿

 f x

l T

a ik





T

T

xl  fika xl º yik ¼»



ª’ h x l «¬ x ik



T



m

x , x R , y^0,1` g

s

g

n

a ik

0 d D ,D x

LO

dx dx g

a ik

l T

l T

T

a x ik

l

f



xa d’xhik xl

ª’ h x l ¬« x ik



T

a ik

T

f

l

ik

xf 

( x l  x f )  hik x l º yik , l 1,..., L (8) ¼»



m

x g , x a  R n , y^0,1`

i  Dk , k  SD UP

a

a x ik



x l  hik x l º yik , l 1,..., L »¼

(6)

 x D d’ f  x x  ª’ f x ( x  x )  f x º y   ¼» ¬«

’xhik xl

xs d

T

(5)

(7)



’x fika xl

xs  Dika d

ª’ f a x l ¬« x ik ’x hik xl



Aik xa  xf 1  yik d bik yik

Aik xs d bik yik ’x

xf  ( xLO  xf ) yik d xa ½° a ¾x  Xik xa d xf  ( xUP  xf ) yik °¿

0 d D g ,Dika

i  Dk , k  SD

x LO d x g d x UP

Constraints (4) are introduced in order to relate global and local part of the problems. For xf being defined between nonzero lower and upper bounds, the key feature of the translated local part of the problem (ACH-MILP) is that all constraints (4,7,8) preserve feasibility when alternatives are not selected and their local variables xa take nonzero values xf, as defined by (5) and (6). This enables the definition of nonzero lower bounds for local variables. Note that if xf is set to xLO, mixed-integer lower bounding constraints (4) are reduced to simple lower bounds, and if it is set to xUP, mixed-integer upper bounding constraints (5) are reduced to upper bounds. An interesting feature of the proposed formulation of OAs (8) is that nonzero xf can be chosen such that linearization coefficients at yik become zero, and the mixed-integer OAs become pure-continuous constraints, which are easier to solve, especially when the numbers of binary variables and linearizations are very large. It becomes obvious that the selection of xf and, especially, the selection of the most suitable OA and modeling representation may not be a straightforward task and may significantly influence the efficiency of the search. This modified logic-based OA method was implemented within the unique MINLP process synthesizer, MIPSYN (Mixed-Integer Process SYNthesizer), the successor of PROSYN- MINLP[6].

3. Examples To compare efficiencies of formulations, with and without translation of variables, a network synthesis problem, a synthesis of a heat exchanger network, and allyl chloride example were solved. Example 1: The first example is a network synthesis problem with a simple model but very large-scale combinatorics with 400 binary variables. This numerical problem is an extension of the small flowsheet problem by Kocis and Grossmann[7]. Additional pairs of reactors were added to the superstructure. The solution statistics until the third major MINLP iteration are reported in Table 1. As can be seen in Table 1, it was impossible with big-M formulation to solve the problem within a reasonable time, whilst both convex hull representations enable the solving of this high-combinatorial problem very quickly. Note that with the same integrality gap and smaller number of rows (constraints other than lower and upper bounds), the alternative formulation (ACH)

Improving Efficiency when Solving Process Synthesis Problems through Translation of Variables

589

could solve the problem in only one third of the CPU time needed to solve the problem using the conventional convex hull formulation (CCH). Table 1. MILP solution statistics of the reactor network synthesis problem.

Best NLP Big-M n/a CCH 183.87 ACH 183.87

Int. gap, % n/a 0.868 0.868

No. of rows/var. 4393/1598 2797/1199 1798/1398

No. of iterations n/a 22059 4710

No. of nodes n/a 292 293

CPU for 3 it., sec. n/a 14.9 4.7

Nodes/s for 3 it. n/a 19.6 62.3

CPLEX/GAMS version 21.7, processor PENTIUM 4 2.81 GHz, 512 MB of RAM.

Example 2: The second example is the synthesis of a heat exchanger network (HEN) comprising different types of exchangers. Each match in a stage-wise superstructure is comprised of a double pipe, a plate and frame, a shell and tube exchanger, and a by-pass (Figure 1). Consideration of different types of exchanger enables the simultaneous selection of exchanger types; however, it significantly increases the number of binary variables. The model thus exhibits moderate complexity and relatively high combinatorics (249 binary variables). Table 2 shows the statistics when xf was set to xLO. With respect to the integrality gap, number of iterations, CPU time and number of nodes, both convex hull representations significantly outperform the big-M one, whilst the efficiency of the alternative convex hull formulation is approximately twice that of the conventional formulation.

Figure 1. Match superstructure. Table 2. MILP solution statistics for the HEN synthesis problem.

Best NLP Big-M 884.07 CCH 818.69 ACH 818.69

Int. gap, % 1.548 0.607 0.607

No. of rows/var. 2115/1089 1613/572 1317/884

No. of iterations 2248581 612529 321062

No. of nodes 70257 35150 19411

CPU for 15 it., sec. 500.9 163.3 83.8

Nodes/s for 15 it. 140.3 215.2 231.6

CPLEX/GAMS version 21.7, processor PENTIUM 4 2.81 GHz, 512 MB of RAM.

Example 3: The last, allyl chloride example, is the synthesis of a reactor/separator network within an overall heat integrated process scheme, with a complex model and moderate-size combinatorics (184 binary variables). The reactor/separator superstructure (Figure 2) comprises a sequence of PFR/CSTRs with side streams and intermediate separators at different locations. Each PFR consists of a train of several

M. Ropotar and Z. Kravanja

590

alternative elements. The corresponding DAE system is modeled by the orthogonal collocation on finite elements. The overall model is highly nonlinear and nonconvex. Therefore, many numerical and other issues are present which makes any comparison between formulations harder, e.g. due to the effects of nonconvexities it is impossible to compare different formulations based on an integrality gap.

C5

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Figure 2. Reactor/separator superstructure of the allyl chloride problem.

Table 3 shows solution statistics until the 17th major MINLP iteration. As can be seen from Table 3, the efficiency of the ACH formulation is almost twice as good as that of CCH and four times better than that of Big-M. It should be noted that selection of the optimal final element in PFR is formulated by big-M constraints, so that the overall process ACH and CCH formulations are, in fact, combined ACH/Big-M and CCH/BigM formulations. Table 3. MILP solution statistics of the allyl chloride problem.

Best NLP Big-M 81.924 CCH 81.836 ACH 81.769

Int. gap, % 0.190 100.00 0.343

No. of rows/var. 2307/2193 2363/2183 1230/1313

No. of iterations 4525051 1503644 854049

No. of nodes 19830 8053 7700

CPU for 17 it., sec. 2166.5 960.3 529.2

Nodes/s for 17 it. 9.2 8.4 14.6

CPLEX/GAMS version 21.7, processor PENTIUM 4 2.81 GHz, 512 MB of RAM.

4. Conclusions Initial experiences when translating variables indicate that the alternative convex hull representation, containing translation of local variables, is generally more efficient (sometimes up to an order of magnitude) when solving high-combinatorial problems than the conventional convex hull without translation of variables, and has the smallest model sizes of reduced MILP master problems. In spite of the above-mentioned efficiency, alternative convex hull formulations exhibit stronger sensitivity to the effects of nonconvexities, and the model representations are usually more complicated.

References [1] [2] [3] [4] [5] [6] [7]

S. Lee and I. E. Grossmann (2000). Comput. Chem. Eng., 24: 2125. M. Turkay and I. E. Grossmann (1996). Ind. Eng. Chem. Res., 35(8): 2611. A. Vecchietti, S. Lee and I. E. Grossmann (2003). Comput. Chem. Eng., 27(3): 433. N. W. Sawaya and I. E. Grossmann (2005). Comput. Chem. Eng., 29(9): 1891. M. Turkay and I. E. Grossmann (1996). Comput. Chem. Eng., 20(8): 959-978. Z. Kravanja and I. E. Grossmann (1994). Comput. Chem. Eng., 18(11-12): 1097. G. R. Kocis and I. E. Grossmann (1989). Comput. Chem. Eng., 13(7): 797.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

591

Increasing Throughput of Batch Distillation Zbigniew T. Fidkowski Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, PA 18195, USA, [email protected]

Abstract Batch distillation is still widely used in numerous chemical plants that make multiple products at a relatively small scale. As in continuous distillation, various combinatorial sequences of batch separations can be derived. Each of these sequences can be optimized using commercial simulator and compared with the other sequences. The objective function in optimization of batch distillation is usually the cycle time that needs to be minimized. It corresponds to the minimum energy of separation in continuous distillation, because batch distillation columns operate usually at maximum boilup. Therefore, the shorter the cycle time, the lower the energy of separation. Optimization procedure has to take into account sizes of existing tanks and other available equipment, which may lead sometimes to a classical scheduling problem. An example of selecting the optimum batch distillation sequence will be presented. The components in the feed may be lumped into five groups, ordered according to their volatilities: 1. Lights (L), 2. Product A, 3. Intermediates (I) , 4. Product B, 5. Heavies (H). Combining optimization with batch column model available in commercial simulator provides a useful tool for developing optimum batch distillation recipes. Keywords: Batch Distillation, Optimization, Separation Sequences

1. Introduction Batch distillation is one of the oldest and one of the best known separation processes. It is known by its low cost and flexible equipment, capable of performing various separations. Batch distillation is especially well-suited for small-scale processes in pharmaceuticals and specialty chemicals. Typical industrial batch distillation column is a batch rectifier. Batch stripper and middle-vessel columns, although known theoretically, are not used much in practice. Batch distillation is an unsteady state process, which means that operator actions must be performed in timely manner. There are problems with optimization of these processes, because it is not easy to determine ahead of time what is optimal. There are frequently logistical problems, because at a certain time a vessel and a clean piping connection to the vessel must be available, to store a separate cut. Finally, environmental problems arise, because frequent switches between pipes and vessels increases waste streams and increases potential for releases to environment.

2. Optimization of Batch Distillation Batch rectifier is shown in Figure 1. Distillate flow and composition and pot composition change in time. Subsequent products are obtained in so called cuts. A cut begins when distillate product is directed to a receiver and ends when distillate stops

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flowing to this receiver. It may then go to another receiver, as a next cut, or distillate may stop flowing completely, because column goes through a transition stage at total reflux or distillation is finished. Operating parameters for each cut could be, for example: 1. Reboiler heat duty (Q) 2. Reflux Ratio (R) 3. Stop Criterion for each cut (for example cut time, temperature at certain place in the column, current distillate composition). Optimization task can be formulated as follows: • Maximize Production Rate (Product Amount / Batch Time) • Subject to constraints: o Purity o Recovery o Column flooding • Vary for each cut o Q – Reboiler Duty o R – Reflux Ratio o Stop Criterion.

Figure 1. Batch rectifier

As a result, to maximize production rate (reduce batch time) • Reboiler Duty is maximized so that the column operates at the maximum allowed % of flood, • Reflux Ratio is minimized to the point where we just barely make the purity spec, • Stop Criterion must be just right, so that enough cut is taken to satisfy the recovery and purity constraints. Without using optimization it is impossible to determine the right values of Q, R and Stop Criterion.

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3. Industrial Example The objective of distillation is to make products A and B from a mixture of the following components (listed in order of decreasing volatility): Lights (L), Product A, Intermediate (I), Product B, Heavies (H). Existing sequence is shown in Figure 2. The three columns that are shown represent the same batch distillation column at different times.

Figure 2. Existing separation sequence

First (left column) the A-recovery distillation is carried out, where lights L and product A are removed and stored in the tank. With them some of intermediate component I and even product B slips through. Then there is a Front-B slope cut containing mostly I and B (but also some of A and H. Finally, product B cut is performed and heavies are left in the pot. Second column depicts purification of A. Lights are removed first and then product A cut is taken. Pot mixture, containing mostly I and B is mixed with Front B Cut and enters third distillation where I is separated from B. This is the most difficult separation, creating another slope cut IB, recycled back to the charge. Also, the initial cut containing A and I is recycled back to the second distillation. The entire sequence is complex and creates various operational problems. The major problem is with the third distillation, because component I and B are difficult to separate. That also makes it impossible to determine the end of the cut just by temperature profiles. Samples need to be taken and analyzed, which extends the time of the batch. Production of A and B had to be increased and ways of improving the existing process were sought.

4. Process Improvement Initially we tried to optimize the existing distillation sequence, but the improvements were marginal and major disadvantage of the process, difficult separation of B from I, still remained.

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Then, we noticed that the purity specs are quite relaxed: 95 mass % for component A and 97% of component B. Currently, impurities in existing product A consisted mostly of lights (L and A are easy to separate). Impurities in B consisted mostly of heavies (also easy to separate from B). So product A is really LA; product B is really BH. If we replaced light impurities in A by the intermediate component and heavies in B by the intermediate, we would not have to separate component I at all – see Figure 3. We confirmed that component I is an inert and does not really change the properties of the products. .

L Existing Prod. A

A New Prod. A I

Existing Prod. B

B

New Prod. B

H .

Figure 3. Material Balance: new products contain component I as impurity

Corresponding new separation sequence is shown in Figure 4. It is much simpler, does not contain any recycles and the most difficult separation of component I from B is no longer performed. This new distillation sequence improved the process considerably.

Figure 4. New, improved separation sequence.

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5. Acknowledgements This work was a team effort: Brendan Ackers, Bradley Cook, Dave Damminger, Craig Landis and Darryl Wise, all from Air Products, contributed to success of this project.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

597

Model and Parameter Identification in Phase Equilibria Alexander Mitsosa, George M. Bollasb and Paul I. Bartonb a

Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen, Pauwelsstr. 12, 52074 Aachen, Germany, [email protected] b Process Systems Engineering Laboratory, Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, MIT 66-464, Cambridge, MA 02139-4307, USA, [email protected], [email protected]

Abstract A formulation for parameter estimation with activity coefficient models is presented based on bilevel programs with nonconvex lower-level programs. The resulting mathematical formulation is solved numerically to global optimality with a deterministic algorithm. The formulation proposed overcomes limitations of state-ofthe-art methods for parameter estimation in liquid-liquid equilibria and vapor-liquid(liquid) equilibria, which result in qualitative and quantitative errors. The following elements of the method described are the main differences from existing methods: (i) necessary and sufficient stability criteria are imposed (as opposed to necessary only); (ii) additional constraints are introduced to ensure the experimentally observed number of phase splits and phases in each phase split; (iii) the best possible fit is guaranteed numerically. Keywords: Gibbs tangent plane, Gibbs free energy minimization, Bilevel, NRTL model, SIP, phase diagrams.

1. Introduction Excess Gibbs free energy (or activity coefficient) models are the main tool used for the description of deviation from ideality in liquid mixtures and are, therefore, essential for reliable design and modeling of separation systems. Many activity coefficient models exist, such as the modified Wilson, NRTL and UNIQUAC models. These local composition models contain adjustable parameters that describe molecular energy interactions in postulated local neighborhoods. Provided that suitable parameter values are used, the models can accurately predict the chemical potential of most liquid mixtures. The other main class of models used in phase equilibria are equation of state (EOS) models. Typically, EOS models are used for the description of vapor phases and do not contain adjustable parameters (or available parameters are set to zero). The binary case is considered in this article, in accordance with the theory of local composition models which states that multicomponent mixtures can be predicted by knowledge of only binary interaction parameters. The standard formulation for parameter estimation is to minimize the discrepancy between measurements and predictions obtained by equality of the potentials of each species in every phase. In the liquid-liquid equilibrium (LLE) case this results in isoactivity (γ-γ-method) and in the vapor-liquid-liquid equilibrium (VLLE) in isofugacity (ϕ-ϕ-method). These are necessary but not sufficient stability criteria for

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equilibrium. As a consequence the predictions may be unstable (local minima of the Gibbs free energy), in which case the parameter values obtained are unsuitable for the prediction of the mixture behavior. A sufficient stability test is typically performed a posteriori to make sure that a stable solution has been calculated. However, standard methods do not have a remedy for the case where this test fails. More generally, standard methods can result in quantitative or even qualitative errors in predictions. In addition to unstable predictions, qualitative errors observed include predicting spurious phase splits, predicting a heterogeneous azeotrope when a homogeneous is experimentally observed and failing to predict upper/lower critical solution temperatures. Moreover, the use of local optimization methods does not always lead to the best possible fit. As a consequence, unsatisfactory fits can be due either to unsuitable models or inadequate optimization solvers. In essence, standard methods can identify suitable models, but cannot exclude unsuitable ones. These issues are not only theoretical challenges, but also occur in practice. Over the last decade Stadtherr and coworkers (Gau and Stadtherr (2000); Gau et al. (2000); Simoni et al. (2007)) have demonstrated limitations of existing methods and have proposed alternative methods based on interval extensions for interesting subcases. A method, based on bilevel programming, applicable to the more general case of temperature-dependent problems was recently proposed by Mitsos et al. (2009) for LLE and Bollas et al. (2009) for VLLE. This method was applied to several binary mixtures, for which standard methods result in the aforementioned errors. The latter two references are the basis of this article. In the following the conceptual formulation is given. Further, the example of tetrahydrofuran-water LLE is described in Section 3 to demonstrate that existing methods can result in additional spurious phase splits. Finally, conclusions and potential for future work are given.

2. Formulation for Parameter Estimation in Phase Equilibria The purpose of this article is to identify parameter values for the binary interaction coefficients in excess Gibbs free energy models. These are estimated by phase-split experiments performed under various conditions, i.e., different temperature, pressure and overall composition. For simplicity, it is assumed that EOS models used for vapor phases do not contain adjustable parameters, and that the adjustable parameters in the activity coefficient models are pressure independent. Then, the task of the parameter estimation is to find temperature coefficients for the parameters in the excess Gibbs free energy model. The objective is to minimize the error between model predictions and experiments. The objective function is essentially the same as in existing methods, but the constraints are very different. Two main constraints are imposed for all measured conditions: (i) stability of the predicted phase splits and (ii) prediction of the correct number of phase splits, the correct number of phases for each phase split and the correct number of azeotropes. The stability requirement is encoded using the well-known Gibbs tangent stability criterion (Baker et al. (1982)), with special care for asymmetric models. The correct number of phase splits is imposed by requiring convexity of the Gibbs free energy in subsets of the composition range. The correct number of phases is guaranteed by a variant of the Gibbs tangent stability criterion. Azeotropes can but need not be treated in a special way. This conceptual formulation is transcribed to a bilevel program, i.e., a nested optimization problem. To be more precise, a generalized semi-infinite optimization program (GSIP) is obtained, but reformulated in a bilevel structure, see also (Stein and

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Still (2002)). The reason for this reformulation is that the GSIP has no Slater points. Bilevel programs are very challenging, especially with nonconvex lower-level programs. Note that in the formulation proposed, nonconvexity arises from the excess Gibbs free energy functions. Deterministic global optimization techniques are deemed necessary to even obtain a feasible point. Despite the relatively large size of the problems, the formulation can be solved efficiently with global optimization of both upper- and lower-level programs based on a recent algorithm by Mitsos et al. (2008). The global solution of the parameter estimation problem also enables model identification, i.e., discrimination between suitable and unsuitable models, see also (Singer et al (2006)). Since the best possible fit is obtained, model-experiment discrepancy implies an unsuitable model (assuming that the experimental error is small).

3. Case Study: tetrahydrofuran-water LLE The tetrahydrofuran(1)-water(2) mixture is very challenging. The VLLE case was considered by Bollas et al. 2009. Therein, it was discussed that standard methods predict a spurious liquid split and fail to predict the critical temperatures for solubility. In contrast, the bilevel formulation was shown to result in qualitatively and quantitatively correct predictions. Here, the LLE case is considered (at high pressures) to demonstrate the need to predict the correct number of phase splits over the composition range. Six smoothed experimental data for the LLE of this mixture are included in the DECHEMA LLE data collection (Sørensen and Arlt (1979)) and shown in Table 1. The NRTL model is used for the estimation. The NRTL nonrandomness factor α is considered adjustable in the range [0.1,0.5]. For the binary interaction parameters the temperature-dependent function

τ jm = A jm + B jm (298.15 / T − 1) + C jm (T / 298.15 − 1)

is assumed with Ajm∈[-2.5,10], Bjm∈[-30,30], Cjm∈ [-30,30] and the additional constraints − 2.5 ≤ τ jm ≤ 10. Table 1. Experimental data for tetrahydrofuran(1)-water(2) T [K]

xI

xII

T [K]

xI

xII

353.15 363.15 373.15

0.363 0.397 0.389

0.118 0.0955 0.0888

383.15 393.15 403.15

0.386 0.359 0.307

0.0875 0.0915 0.106

The isoactivity formulation has (at least) two local minima of interest. The first attained at α=0.35112, A12= 6.8079, B12= 30, C12= 24.771, A21= 1.5948, B21= -30, C21= -18.688, has an objective function of 9.9x10-4. This is seemingly a very good fit; however an additional phase split is observed, as is evident from the plot of the Gibbs free energy, Fig. 1. The second interesting set of parameter values is α=0.42209, A12=-0.22921, B12=-29.741, C12=-20.156, A21=1.5280, B21=-20.318, C21=-11.732, resulting in an objective function of 9.9x 10-5. This second set of parameter values results in a slightly better quantitative agreement, see Fig. 2. Much more importantly it gives a qualitatively correct fit. The isoactivity method with local solvers could result in either solution, especially given the small objective values. In fact, preliminary numerical experiments (not shown here) indicate that the undesired solution is obtained. The use of global solvers for the isoactivity formulation with very tight tolerances, much tighter than what would normally be used, results to the desired solution.

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However, it is rather a coincidence that the desired fit has a lower-objective function than the undesired fit. For slightly perturbed data the spurious solution gives a much better objective value than the qualitatively correct fit. For these perturbed data, global optimization using the isoactivity method would not give the qualitatively correct fit. In contrast, the GSIP constraint (i.e., imposing the correct number of phase splits by requiring convexity of the Gibbs free energy for the composition range outside of the phase split observed) can always ensure a qualitatively correct fit.

Figure 1. Left part: Gibbs free energy of spurious solution of the isoactivity method for the tetrahydrofuran-water system at 383.15K. An additional, spurious phase split (with xI ≈0.5 and xII≈1) is predicted. Right part: T-x plot for the system tetrahydrofuran(1)-water(2). Both sets of parameter values (qualitatively correct and leading to additional spurious phase split) lead to phase split prediction with relatively small discrepancies.

4. Conclusions State-of-the-art methods for parameter estimation in phase equilibria (LLE, VLLE) have several limitations. A formulation overcoming these limitations is proposed based on nested optimization, i.e., nonlinear programs embedded in the least-square-errors minimization. The formulation is solved to guaranteed global optimality using deterministic global optimization methods. The tetrahydrofuran-water mixture is shown to illustrate that excluding additional spurious phase splits is a necessity. In this article the parameter estimation is performed based on phase-split measurements. A thermodynamically more complete approach is to include additional measurements, such as heat of mixing and excess heat capacities of mixing. This would increase the statistical significance of the estimated parameters, the applicability and thermodynamic consistency of the model. No significant conceptual or numerical challenges are expected in performing this extension. On the other hand, the application of the proposed method for parameter estimation to equations of state used for description of both the liquid and vapor phases is more challenging.

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5. Acknowledgements Financial support from the Deutsche Forschungsgemeinschaft (German Research Association) through grant GSC 111 is gratefully acknowledged. This material is based upon work supported by the Department of Energy Nuclear Energy Research Initiative under Award Number DE-FC07-06ID14751. Disclaimer: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

References [1] L. E. Baker, A. C. Pierce and K. D. Luks, 1982. Gibbs energy analysis of phase equilibria. Soc. Petrol. Engrs. J. 22, 731. [2] G. M. Bollas, P. I. Barton and A. Mitsos, 2009. Bilevel optimization formulation for parameter estimation in vapor-liquid(-liquid) phase equilibrium problems. In press: Chemical Engineering Science. [3] C. Y. Gau, J. F. Brennecke and M. A. Stadtherr, 2000. Reliable nonlinear parameter estimation in VLE modeling. Fluid Phase Equilibria 168, 1. [4] C. Y. Gau and M. A. Stadtherr, 2000. Reliable nonlinear parameter estimation using interval analysis: Error-in-variable approach. Computers & Chemical Engineering 24, 631. [5] A. Mitsos, P. Lemonidis and P. I. Barton, 2008. Global solution of bilevel programs with a nonconvex inner program. Journal of Global Optimization 42, 475. [6] A. Mitsos, G. M. Bollas and P. I. Barton, 2009. Bilevel optimization formulation for parameter estimation in liquid-liquid phase equilibrium problems. Chemical Engineering Science 64, 548. [7] L. D. Simoni, Y. Lin, J. F. Brennecke and M. A. Stadtherr, 2007. Reliable computation of binary parameters in activity coefficient models for liquid-liquid equilibrium. Fluid Phase Equilibria 255, 138. [8] A. B. Singer, J. W. Taylor, P. I. Barton and W. H. Green 2006. Global Dynamic Optimization for Parameter Estimation In Chemical Kinetics, Journal of Physical Chemistry A, 110, 971. [9] J. M. Sørensen and W. Arlt, 1979. Liquid-liquid Equilibrium Data Collection: Binary Systems. DECHEMA, Deutsche Gesellschaft für Chemisches Apparatewesen, Chemische Technik und Biotechnologie eV. [10] O. Stein and G. Still, 2002. On generalized semi-infinite optimization and bilevel optimization. European Journal of Operational Research 142, 444.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Multicriteria Design framework for CO2 capture by multi-step PSA cycles Giovanna Fiandacaa, Eric S Fragaa, Stefano Brandanib a

Centre for Process Systems Engineering,Department of Chemical Engineering, University College London (UCL),[email protected] b Institute for Materials and Processes, School of Engineering and Electronics University of Edinburgh

Abstract Pressure Swing Adsorption (PSA) has recently attracted attention as an efficient separation technology for CO2 capture. However, complex multibed/multi-steps PSA cycles are necessary to obtain high purity CO2 efficiently. The complex behaviour of the performance with respect to the process variables requires the development of automated tools for the design of PSA cycles. In the present paper we introduce a multi-criteria design framework for multibed/multi-step PSA/VSA (vacuum swing adsorption) cycles for CO2 capture. A simplified, yet reliable, simulation tool has been developed to reduce computational requirements. A custom multi-objective genetic algorithm has been used to generate approximations of the Pareto front. A targeted fitness function has been defined, which encourages the evolutionary procedure to broaden the extent of the Pareto front. Keywords: Design, Multi-objective Pareto optimisation, Pressure Swing Adsorption, CO2 capture

1. CO2 Capture by Pressure Swing Adsorption The development of CO2 capture technology is necessary to decrease emissions needed to address global warming. Improvement in the efficiency of separation processes needs to be achieved. Pressure swing adsorption (PSA) is an efficient separation option for middle scale operations [1]. PSA is a cyclic separation process whose main steps are adsorption, at high pressure, and regeneration of the adsorbent, at low pressure. PSA has originally been designed to provide a high purity stream of the less strongly adsorbed component. However, CO2 is the most preferably adsorbed species on the majority of adsorbents used for the operation. Advances in adsorbent materials and development of new and more complex cycle configurations have proven PSA to be efficient and economically viable for CO2 capture [2, 3]. Nevertheless, the design of complex PSA cycles remains mainly an experimental effort due to the complexity of the simulation. Furthermore, the performance is characterized by conflicting parameters, but only a few previous papers have addressed the multi-objective optimisation of PSA cycles. The aim of this paper is to provide a tool to detect the optimal trade-offs between the parameters in a fast and reliable way. In [6], we proved the efficacy of a custom multiobjective genetic algorithm (MOGA) for the optimisation of a simple Skarstrom cycle for N2 separation from air. Here, we test the ability of the MOGA to successfully generate a Pareto front for a more complex case study: a 4-bed/4-steps VSA cycle (vacuum swing adsorption) cycles for CO2 capture, originally proposed in [3]. A vacuum swing adsorption cycle is a PSA cycle where the low pressure achieved during

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the blowdown step is subatmospheric. Evacuation to a very low absolute pressure allows a deeper regeneration of the adsorbent when the isotherm of the adsorbed species is highly favorable, as in this case.

2. Case Study

2.1. The Model The case study of interest is the separation of CO2 from a flue gas. The feed is a typical stack effluent at 575 K, containing 15% of CO2, 75% N2 and 10% of H2O. The adsorbent is a K-promoted hydrotalcite-like compound (K-HTlcs). HTlcs have a high selectivity towards CO2 and show a higher capacity at high temperatures compared to other adsorbents. The configuration (fig. 1) is a modified Skarstrom cycle, operating among 4 beds [3]. The four steps are high-pressure adsorption (PH) with feed (step I), countercurrent blowdown to a vacuum pressure (PL) (step II), desorption with lightproduct purge (step III) and repressurization with light product gas. The CO2-enriched product is collected from steps II and III, while an inert light product is collected from step I.

Figure 1. Flowsheet of the 4-beds/4-steps VSA cycle. Representation of the schedule using only one bed.

A simplified model has been used to reduce computational costs involved with the simulation. The aim of the simulations is to correctly detect the relation between the design variables and the performance, so that the optimiser can distinguish the performance at different design points in a time effective way. To this hand, a series of CSTRs (continuous stirred tank reactors) has been used to describe each bed. This simplification reduces the computational requirements since the mass balance of the fluid phase for a CSTR is not dominated by a convective term as in the case of the PFR (plug flow reactor) [5]. The mass balance of the i-th species in a CSTR is expressed by eq.1.

dni d qi +V = Fin y i ,in − Fout y i dt solid dt

(1)

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where ni is the number of moles of species i, qi is the average concentration in the solid phase, Fin and Fout are the inlet and output stream respectively, while yi,in and yi are the molar fraction of species i in the inlet and in the reactor. A good correspondence between our results and those of the more rigorous model used by Reynolds et al. [3] has been achieved using 6 CSTRs to simulate each column. A temperature dependent Langmuir isotherm (eq.2) has been used to describe the equilibrium [3, 6].

§ bPi · ¸¸ b = 2.03 exp(1.118 / T ); q = (−1.5277 *10−3 T + 1.7155)¨¨ © 1 + bPi ¹

(2)

The energy balance has been included in the model as the process is non-isothermal (eq. 3).

1 dT dq = ¦ ΔH i i C s dt dt i

(3)

where Cs is heat capacity of the bed. The linear driving force (LDF) model has been used to describe the mass transfer in the solid phase [1]. Assuming a linear driving force for mass transfer between the fluid and solid phases, the LDF approximation simplifies the model by eliminating the need to describe concentration profiles within the solid. According to the LDF model, the mass balance in the particle can be written as in eq.4.

(

d qi = κ i q i* − q i dt

)

(4)

Other assumptions are ideal gas phase and negligible pressure drop. All data used are from [3]. Overall mass balances are carried out around each bed and around the whole cycle to check the correctness of the model and of the simulation.

Figure 2. Convergence of İCSS (vertical impulses) and of the Purity (continuous curve) with the number of cycles

We achieve a fast convergence to cyclic steady state by adopting the unibed approach [7]: since at cyclic steady state all the beds undergo the same sequence of steps in an identical manner, a multibed cycle can be simulated using only one bed.

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A common method to detect CSS is to require the difference İCSS between the condition of the bed (y, e.g. concentration, temperature, pressure) at the beginning and at end of the cycle to be a very small number (İCSS = ||(yf -y0)||’ĺ0). However, such criterion might not guarantee real convergence. As shown in fig. 2, İCSS reaches very small values (Ѥ 10-5) before 30 cycles, and it then takes higher values again. On the other hand, the value of the purity reaches a plateau only after around 60 cycles. As a result, in this paper the condition for convergence to CSS is the standard deviation of the value of the objectives in the last 10 cycles to be less than 10-3.

3. Analysis and validation The analysis of the cycle has been made with respect to the same parameters used in [3]. The parameters are the purge-to-feed ratio (Ȗ), the cycle time (tc), the pressure ratio (ʌT = PH»PL) and throughput of the operation (ș). ș is defined as the amount of feed fed to one reactor during the adsorption step (step I) divided by the cycle time and the mass of adsorbent in one bed.

θ=

t ads

³ F dt in

t cVsolid

0

It is worth noting that ș is indeed independent of the cycle time as the feed inlet, Fin, is constant and tc =4*tads. The value of the high pressure has been kept constant, to the value of 1.36atm [3]. The performance of the process is judged by the value of CO2 recovery (R) and enrichment (E) in the product. Our simplified model provides a good match with the results of the rigorous model used in [3]. The comparison is shown in fig. 3. A good qualitative match is achieved. The effect of each process parameters has been analysed in [3], and confirmed by our simulations. High values of Ȗ and tf provide high recovery and low enrichment. A high value of ʌT favours both recovery and enrichment.

Figure 3. Effect of Ȗ on recovery and enrichment and comparison with literature data from [3].

4. Optimisation algorithm In [3], an attempt was made to find the conditions which simultaneously optimise both enrichment and recovery. While it is relatively easy to detect the effect of each single variable, it is complicated to understand their combined effect. We used a custom multiobjective genetic algorithm to generate a Pareto front for the cycle of interest. A Pareto front consists of equally optimal solutions with respect to the objective functions.

Multicriteria Design Framework for CO2 Capture by Multi-Step PSA Cycles

607

The implementation of a genetic algorithm for any new problem requires the definition of the following elements: a representation of (hopefully) feasible solutions, the crossover and mutation operators, a selection procedure together with an appropriate fitness function, and the properties of the evolution of the population. For the MOGA used in this work, the solution representation consists simply of real-valued design variables. A multi-point crossover operator is defined and mutation consists of selecting a single design variable and assigning it a randomly chosen value from the domain for that variable. We have used tournament selection with a tournament size of 2. The population policy is one of replacement with elitism. The key property of the MOGA presented is the definition of the fitness function. The aim is to generate as broad a Pareto set as possible. Identifying the extremes of the trade-offs between the criteria give the engineer useful information to make design decisions early in the design process. In the evolutionary procedure, the probability that an individual of the current population contribute to the evolution of the solutions is higher the more “fit” it is. The fitness of a design point in the population has then been based on a modified measure of the distance of that point to the current approximation to the Pareto front. Solutions with lower values are fitter. For our design problem, with two criteria, the distance of a dominated point to the Pareto front approximation is the minimum of the distance of that point to each of the points in the Pareto set and the distance to infinite projections from the end points parallel to the two axes. The latter gives emphasis to those solutions which may be far from any points in the current Pareto front approximation but which may help in generating new solutions that would extend the breadth of the Pareto front.

(a) Evolution and convergence of the Pareto set

(b) Average performance of MOGA and standard deviation

Figure 4. Analysis of the performance of the MOGA in terms of convergence (a) and statistic behaviour of the Pareto front (b).

5. Results The design problem is the simultaneous optimisation of CO2 recovery (R) and enrichment (E) in the product in the 4-dimensional design space defined by tc, ș, Ȗ and ʌT . The only constraint is the evaluation of R and E at cyclic steady state (CSS), which implies the dynamic simulation of the operation. The Pareto fronts have been obtained using a crossover rate of 0.7, a mutation rate 0.01, a tournament size 2, a population size of 70, and 50 generations. A statistical analysis is necessary to understand the average performance of the optimiser. Hence, in fig 4b, the average front detected via Gaussian regression of 10 Pareto front generated from the same starting point is presented. Convergence is achieved after 25 generations (fig. 4a),

G. Fiandaca et al.

608

and a good spread of solutions along the all front can be appreciated. The shape of the Pareto set suggests that we can obtain high values of recovery (over 99.9 %), for values of enrichment up to almost 2.9. After this point, an increase in the enrichment is obtained with a higher decrease of the recovery. The values of enrichment obtained are higher than those detected manually in [3], as a wider design region has been explored. The results confirm the complex interaction between the 4 design variables. High enrichment is achieved only at high value of cycle time, low Ȗ and ș values, and high value of ʌT , as expected (fig. 5b). A more complex relation between design variables and recovery has been noticed (fig. 5a). High values of the recovery have been achieved for a wide range of tc. Only high value of Ȗ can provide a high recovery. High ș and low ʌT values can allow high recovery, as well as the opposite situation, with low ș and high ʌT .

(a) High Recovery (R) solutions

(b) High Enrichment (E) solutions

Figure 5. The two sets are visualised using a parallel co-ordinate representation. Variable domains and objective function value ranges have been normalised for presentation

6. Conclusion The complexity of PSA processes for CO2 capture makes the assessment of new cycles difficult and time-consuming. The design framework we propose is able to quickly assess the performance of complex PSA cycles on the basis of a multi-criteria approach. A simplified, yet reliable, simulation tool has been developed to reduce computational requirements. A targeted fitness function has been defined, which encourages the evolutionary procedure to broaden the extent of the Pareto front. The MOGA has successfully indicated the Pareto front, providing information on the relations between the design variables and the trade-offs involved in the performance. This constitutes a valuable support during the early stages of the design process.

References [1] Ruthven, D. M., Farooq, S., and Knaebel, K. S. Pressure Swing Adsorption. VCH, (1993). [2] Zhang, J. and Webley, P. A. Environ. Sci. Technol. 42, 563–569 (2008). [3] Reynolds, S. P., Ebner, A. D., and Ritter, J. A. Adsorption 11, 531–536 (2005). [4] Fiandaca, G., Fraga, E. S., and Brandani, S. In ACDM 2008, (2008). [5] Cruz, P., Magalhães, F. D., and Mendes, A. AIChE Journal 51, 1377–1395 (2005). [6] Ding, Y. and Alpay, E. Trans IChemE 79(PArt B), 45–51 (2001). [7] Kumar, R., Fox, V. G., Hartzog, D. G., Larson, R. E., Chen, Y. C., Houghton, P. A., and Naheiri, T. Chem. Eng. Science 49(18), 3115–3125 (1994).

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

609


               

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19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

615

Optimization of combined DOC and NSRC diesel car exhaust catalysts ˇ ep´anek,a Petr Koˇc´ı,a Miloˇs Marek,a Milan Kub´ıcˇ ek,b Jan Stˇ a Department of Chemical Engineering, Institute of chemical Technology, Technick´a 3, 166 28 Prague, Czech Republic. E-mail [email protected] b Department of Mathematics, Institute of chemical Technology, Technick´ a 3, 166 28 Prague, Czech Republic. E-mail [email protected] Abstract The system of two monolithic catalytic reactors (Diesel Oxidation Catalyst, DOC, and NOx Storage Reduction Catalyst, NSRC) operating in series is studied. The catalysts are used for the conversion of exhaust gases from automobiles with Diesel engines. Several tens of catalytic reactions are considered in the description by a model based on a system of nonlinear partial differential equations (mass and enthalpy ballances). In the simulation study the effects of parameters determining the performance of the upstream-located DOC configuration (the size and effective heat capacity of the monolith, catalytic activity in individual reaction steps) on the performance of the NSRC in the European driving cycle (NEDC) are investigated. Numerical method used for solution of the resulting set of nonlinear PDEs is described. Results of the maximization of overall NOx conversion over the NEDC for several reactor configurations are presented. Keywords: NSRC, DOC, catalyst, optimization, fuel consumption

1 Introduction In recent years advanced systems enabled Diesel engines to operate efficently while producing high power output. Unfortunately, efficient engine operation requires burning of lean air/fuel mixture, which leads to increased NOx amounts in the exhaust gases. One of the aftertreatment device used for elimination of NOx from exhaust gases is the NOx -storage and reduction converter (NSRC). This type of converter must be regenerated periodically by switching the engine mode from burning lean mixture to temporarily rich mixture. During the long lean phase, the NSRC stores NOx on its surface, while during the short rich phase the stored NOx are being reduced. NSRC is usually coupled with another converter types (Diesel Oxidation catalyst for CO and HC abatement DOC, Diesel Particulate Filter for soot abatement DPF) to form an efficient apparatus for complex exhaust gas aftertreatment. In this paper, we focus on the optimization of a DOC-NSRC coupled system, where the DOC is located upstream of the NSRC. We will discuss the effects of the reactors sizes and regeneration phase control on the integral NOx conversion and fuel consumptions over the NEDC driving cycle.

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616

2 Mathematical model of catalytic monolith converters Heterogenous, spatially 1-dimensional (1D) plug-flow model of catalytic monolith channel with surface component deposition (Koˇc´ı et al. 2007, G¨uthenke et al. 2007a) has been used for the simulations of the converters. The model considers the following ballances: mass balances of individual components in the flowing gas (1), in the washcoat pores (2) and on the catalyst surface (3), total enthalpy balance of the flowing gas (4) and the enthalpy balance of the solid phase (5):  ∂(v · ck ) kc a  s ∂ck (z,t) =− + g c yk − yk , ∂t ∂z ε  1  ∂csk (z,t) kc a s = s c y − y k k + s ∂t ε (1 − εg )ϕs ε 1 ∂ψm (z,t) = cap ∂t Ψm

ρcp

J

ψ

∑ νm, j R j ,

k = 1, . . . , K

J

∑ νk, j R j ,

k = 1, . . . , K

(2)

j=1

m = 1, . . . , M

(3)

j=1

 ∂T kh a  ∂T (z,t) = −v ρcp + g T s − T ∂t ∂z ε

ρs csp

(1)

 J ∂T s (z,t) ∂2 T s kh a  s s ΔHr, j R j = λs 2 + T − T − ϕ ∑ ∂t ∂z 1 − εg j=1

(4)

(5)

Boundary conditions used at the inlet (z = 0) and at the outlet (z = L) of the monolith are: T = T in

at z = 0

(6)

∂T s = 0 at z = 0 z = L ∂z

(7)

ck = cin k , k = 1...K

(8)

at z = 0

The values of spatially distributed mass and heat transfer coefficients along the monolith channel (kc (z) and kh (z), respectively) are calculated from the correlations proposed by (Ramanathan et al. 2003). The set of partial differential equations 1 - 5 is solved by semi-implicit finite differences method, with equidistant spatial discretisation, quasi-liniarisation of reaction rates R j , and adaptive

Optimization of Combined DOC and NSRC Diesel Car Exhaust Catalysts

No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

617

Table 1: NSRC reactions.

Reaction/adsorption/desorption step

Rate law

CO + 12 O2 → CO2 H2 + 12 O2 → H2 O C3 H6 + 92 O2 → 3 CO2 + 3 H2 O

RNSRC = k1 1

yCO yO 2 G yH 1yO NSRC 2 2 R2 = k2 G yC H1 yO RNSRC = k3 3 G6 2 3 1  yCO yH  2 2 CO + H2 O  CO2 + H2 RNSRC = k4 yCO yH2 O − eq 4 Ky,4  y3CO y6H  RNSRC = k5 yC3 H6 yH2 O − eq 2 2 C3 H6 + 3 H2 O → 3 CO + 6 H2 5 K yH O y,5 2 1 NSRC R6 = k6 yCO y0.5 CO + NO → CO2 + 2 N2 NO 1 NSRC 0.5 H2 + NO → H2 O + 2 N2 R7 = k7 yH2 yNO C3 H6 + 9 NO → 3 CO2 + 3 H2 O + 92 N2 RNSRC = k8 yC3 H6 y0.5 8 NO  yNO  1 1 2 NO + 2 O2  NO2 RNSRC = k9 yNO y0.5 9 O2 − K eq G1 y,9   eq Ce2 O3 + 12 O2 → Ce2 O4 RNSRC = k10 Ψcap,O2 yO2 · ψO (T ) − ψO2 10 2 RNSRC = k Ψ y ψ Ce2 O4 + CO → Ce2 O3 + CO2 11 cap,O2 CO O2 11 Ce2 O4 + H2 → Ce2 O3 + H2 O RNSRC = k12 Ψcap,O2 yH2 ψO2 12 1 1 1 NSRC Ce2 O4 + 9 C3 H6 → Ce2 O3 + 3 CO2 + 3 H2 O R13 = k13 Ψcap,O2 · yC3 H6 ψO2  eq  2 NO2 + BaCO3 + 12 O2 → Ba(NO3 )2 + CO2 RNSRC = k14 Ψcap,NOx yNO2 · y0.1 14 O2 ψNOx − ψNOx eq 3 NSRC 0.1 R15 = k15 Ψcap,NOx yNO · yO ψNOx − ψNOx 2 NO + BaCO3 + 2 O2  Ba(NO3 )2 + CO2 2 y ψ Ba(NO3 )2 + 5 CO → N2 + 5 CO2 + BaO RNSRC = k16 Ψcap,NOx · COG NOx 16 yH ψ2NOx Ba(NO3 )2 + 5 H2 → N2 + 5 H2 O + BaO RNSRC = k17 Ψcap,NOx · 2 G 17 yC H2 ψNOx Ba(NO3 )2 + 59 C3 H6 → N2 + 53 CO2 + 53 H2 O + BaO RNSRC = k18 Ψcap,NOx · 3 6G 18 2 y ψ Ba(NO3 )2 + 3 CO → 2 NO + 3 CO2 + BaO RNSRC = k19 Ψcap,NOx · COG NOx 19 3 yH ψNOx Ba(NO3 )2 + 3 H2 → 2 NO + 3 H2 O + BaO RNSRC = k20 Ψcap,NOx · 2 G 20 3 yC H ψNOx Ba(NO3 )2 + 13 C3 H6 → 2 NO + CO2 + H2 O + BaO RNSRC = k21 Ψcap,NOx · 3 6G 21 3 NSRC BaO + CO2 → BaCO3 RNSRC = ∑21 22 j=16 R j 2      2 2 0.7 G1 = 1 + Ka,1 yCO + Ka,2 yC3 H6 · 1 + Ka,3 yCO yC H · 1 + Ka,4 yNOx T 3 6 G2 = 1 + Ka,6 yO2

   G3 = 1 + 0.1Ka,6 yO2 1 + Ka,7 yNOx

time-step control. Analytical expressions for the derivatives of reaction rates have been used to further decrease the computational demands. In the equations (2, 3, 5) the reaction rates R j are considered individually in dependence on the simulated catalyst (reaction kinetics). The employed reactions and rate laws are listed in Tables 1 (NSRC) and 2 (DOC) and discussed in more detail by (Koˇc´ı et al. 2007) and (Kryl et al. 2005), respectively. The considered NSRC reaction set is given in Table 1. The model developed earlier (Koˇc´ı et al. 2007, see) is employed. The model has been also validated by driving cycle tests (G¨uthenke et al. 2007b, see). It has been observed experimentally that higher amount of NO2 in the inlet NOx mixture enhances the effective NOx storage in NSRC, mainly at lower temperatures (Epling et al. 2004). It is also known, that the activity of the NOx reduction agents is H2 > CO > C3 H6 (Koˇc´ı et al. 2007, 2008). The reaction set of the DOC is shown in Table 2. It has been validated by an engine test driving cycle (Kryl et al. 2005, see). The original DOC model (Kryl et al. 2005) has been extended by the following reactions that need to be considered under temporarily rich conditions (during the NSRC regeneration phase): oxygen storage effects (reactions 13-16 in Table 2), and water gas shift and steam reforming reactions (reactions 17-18 in Table 2). The oxidation of H2 has been

J. Sˇ teˇpa´nek et al.

618

Table 2: DOC reactions.

No. 1

Reaction/adsorption/desorption step CO + 12 O2 → CO2

2 4

H2 + 12 O2 → H2 O C3 H6 + 92 O2 → 3 CO2 + 3 H2 O C10 H22 + 31 2 O2 → 10 CO2 + 11 H2 O

5

C6 H5 CH3 + 9 O2 → 7 CO2 + 4 H2 O

6

C3 H6 + 2 NO + 72 O2 → N2 + 3 CO2 + 3 H2 O

7

C10 H22 + 2 NO + 19 2 O2 → N2 + 10 CO2 + 11 H2 O

8

C6 H5 CH3 + 2 NO + 8 O2 → N2 + 7 CO2 + 4 H2 O

9

NO + 12 O2  NO2

3

10

C10 H22 + Zeol  C10 H22 ·Zeol

11

13

C6 H5 CH3 + Zeol  C6 H5 CH3 ·Zeol 1 NO2 + O2 + Alu  NO3 ·Alu 2 Ce2 O3 + 12 O2 → Ce2 O4

14 15 16

Ce2 O4 + CO → Ce2 O3 + CO2 Ce2 O4 + H2 → Ce2 O3 + H2 O Ce2 O4 + 19 C3 H6 → Ce2 O3 + 13 CO2 + 13 H2 O

17

CO + H2 O  CO2 + H2

18

C3 H6 + 3 H2 O → 3 CO + 6 H2

12

Rate law RDOC = k1 yCO yO2 G1 1

1

RDOC = k2 yH2 yO2 G1 2

1

RDOC = k3 yC3 H6 yO2 G1 3

1

1 1 RDOC = k4 yC10 H22 yO2 · (1+K · 4 a,4,C10 H22 yC10 H22 ) (1+Ka,4,NO yNO ) 1 1 RDOC = k y y · · 5 C6 H5 CH3 O2 (1+K 5 a,5,C H CH yC H CH ) (1+Ka,5,NO yNO ) 6 5

3

6 5

3

1 sel y RDOC = RDOC K6,NO NO · (1+K 3 6 a,6,O2 yO2 )(1+Ka,6,NO yNO ) 1 sel y RDOC = RDOC K7,NO NO · (1+K 7 4 y )(1+K y ) a,7,O2 O2

a,7,NO NO

1 sel y RDOC = RDOC K8,NO NO · (1+K 8 5 a,8,O2 yO2 )(1+Ka,8,NO yNO )  yNO  1 DOC 0.5 2 R9 = k9 yNO yO − eq G 2 2 K   y,9 ads des RDOC 10 = Ψcap,C10 H22 · k10 yC10 H22 (1 − ψC10 H22 ) − k10 ψC10 H22  DOC ads des R11 = Ψcap,C6 H5 CH3 · k11 yC6 H5 CH3 (1 − ψC6 H5 CH3 ) − k11 ψC6 H5 CH3   ads des RDOC 12 = Ψcap,NOx k12 yNO2 · (1 − ψNO2 ) − k12 ψNO2   eq RDOC = k Ψ y · ψ (T ) − ψ 13 cap,O O O 13 O 2 2 2 2

RDOC 14 = k14 Ψcap,O2 yCO ψO2 RDOC 15 = k15 Ψcap,O2 yH2 ψO2 RDOC y ψ 16 = k16 Ψ  cap,O2 C3 H6y O2y  CO2 H2 RDOC eq 17 = k17 yCO yH2 O − Ky,13

  y3CO y6H 2 RDOC 18 = k18 yC3 H6 yH2 O − K eq y2 y,14 H2 O  2     G1 = 1 + Ka,1 yCO + Ka,2 yC3 H6 · 1 + Ka,3 y2CO y2C H · 1 + Ka,4 y0.7 NOx T 3 6           G2 = 1 + Ka,CO yCO · 1 + Ka,C3 H6 yC3 H6 · 1 + Ka,C10 H22 yC10 H22 · 1 + Ka,C6 H5 CH3 yC6 H5 CH3 · 1 + Ka,NO yNO

Table 3: Parameters of DOC the model monolith converters.

Length of DOC (metallic monolith) Length of NSRC (ceramic monolith) Diameter of DOC and NSRC Wall thickness Washcoat thickness Channel dimension Average washcoat porosity Effective density of the solid Effective heat capacity of the solid Specific surface area Regeneration phase length

L LNSRC σ δwall δwashcoat dh εs ρs csp a treg

5-20 cm in 1 cm steps 5-20 cm in 1 cm steps 10 cm 110 (ceramic) / 50 (metallic) 30 μm 1.13 mm (400 cpsi) 0.7 2700 (ceramic) / 4320 (metallic) kg.m−3 1000 (ceramic) / 790 (metallic) J.kg−1 .K−1 2728 (ceramic) / 2876.8 (metallic) m2 .m−3 0-7 s in 1s steps

also added to the reaction scheme (reaction 2 in Table 2). Because the original inhibition term for propene oxidation (Ansell et al. 1996) is valid only under lean conditions, the common inhibition term valid also under rich conditions (Voltz et al. 1973) has been used instead. Parameters of the model converters are shown in Table 3. 3 Simulation results Simulations studying the effect of reactor size and regeneration phase length (corresponding to fuel consumption penalty) have been conducted. Engine test NEDC driving cycle data (Kryl et al. 2005) with added active regeneration phases have been utilized as the inlet gas data definition. Dynamic evolution of the NOx outlet concentration and spatiotemporal concentration profile of the stored NOx can be seen in Fig. 1. From the comparison of the DOC and NSRC outlet concentrations can be seen that the NSRC function is essential for an efficient NOx reduction.

Optimization of Combined DOC and NSRC Diesel Car Exhaust Catalysts

619

Each regeneration phase is reflected in decrease of the surface NOx concentrations (cf. Fig. 1-right. Results of the simulation parametric study are illustrated in Fig. 2, which show the influence of the particular reactor and regeneration phase length on the integral NOx conversion during the NEDC driving cycle. The DOC‘s

Figure 1: Left: Gas NOx concentrations during the NEDC driving cycle with 3s regenerations. Right: Calculated surface NOx concentration profile in the NSRC reactor. Inlet - measured raw engine emision data. Outlet - calculated tailpipe emissions. ability to catalyze water gas shift, steam reforming and HC-SCR improves the NOx conversion in the DOC+NSRC system. However, for a larger DOC the thermal inertia of the converter becomes a limiting factor. Furthermore, for very short regeneration phases (1s) the oxygen storage capacity of the DOC consumes a relatively large part of the available reducing agents (cf. reactions 14-16 in Table 2. In Fig. 2, the NOx conversion maximum with respect to DOC size is marked with a symbol ). The interplay between the positive and negative DOC effects then results in a maximum of the catalytic system efficiency when considering the DOC size. This optimum DOC size depends also on the applied regeneration phase length. Of course, increasing the NSRC size results always in an increased

Figure 2: Influence of NSRC and DOC size on NOx conversion for two lengths of the regeneration phase (left - 1s, right - 4s.)

J. Sˇ teˇpa´nek et al.

620

NOx storage capacity and reduction efficiency. The effect of the regeneration phase length on the NOx conversion is more important for small NSRC converters that work closer to the NOx saturation limit. While the NOx conversion for systems with 5 cm NSRC grew approximately by half after introducing 4 seconds long regeneration phases compared with 1s regeneration, the NOx conversion of systems with 25 cm NSRC grew only by approximately one sixth. Fig. 3 illus85 80 75

65

x

XNO (%)

70

60 55 50 45 40 0

1

2 3 4 5 Regeneration phase length (s)

6

7

Figure 3: Influence of regeneration phase length on the integral NOx conversion for LDOC = 15 cm, LNSRC = 15 cm. trates the influence of regeneration phase length on integral NOx conversion in the DOC+NSRC system with the length 15+15 cm. It can be seen in Fig. 3 that the regeneration phase length positively influences the NOx conversion. However, it negatively influences the fuel consumption of the engine, thus it should be kept as short as possible. Furthermore, the increase of the conversion is not proportional to the regeneration length. The increments gradually decrease and we can observe only a very small difference for 5 seconds and longer regeneration phases.

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4 Conclusions Based on the presented simulation study, the active NSRC regeneration phase length can be adaptively controlled to maintain sufficient NOx conversion while minimizing fuel consumption. Depending on the particular car application, optimum DOC+NSRC configuration can be found. Acknowledgements The work was supported by the Czech Grant Agency (grant No. 104/05/2616) and the Czech Ministry of Education (project MSM 6046137306). References Koˇc´ı P., Schejbal M., Gregor T., Trdliˇcka J., Kub´ıcˇ ek M., Marek M. Transient behaviour of catalytic monolith with NOx storage capacity. Catal. Today 119, 64 (2007). G¨uthenke A., Chatterjee D., Weibel M., Krutzsch B., Koˇc´ı P., Marek M., Nova I., Tronconi E. Current status of modelling lean exhaust gas aftertreatment catalysts. Adv. Chem. Eng. 33, 103-211 (2007b). Ramanathan K., Balakotaiah V., West D.H. Light-off criterion and transient analysis of catalytic monoliths. Chem. Eng. Sci. 58, 1381 (2003). Kryl D., Koˇc´ı P., Kub´ıcˇ ek M., Marek M., Maunula T., H¨ark¨onen M. Catalytic converters for automobile diesel engines with adsorption of hydrocarbons on zeolites. Ind. Eng. Chem. Res. 44, 9524 (2005). G¨uthenke A., Chatterjee D., Weibel M., Waldb¨usser N., Koˇc´ı P., Marek M., Kub´ıcˇ ek M. Development and application of a model for a NOx storage and reduction catalyst. Chem. Eng. Sci. 62, 5357 (2007a). Epling W.S, Campbell L.E, Yezerets A., Currier N.W., Parks J.E. Overview of the fundamental reactions and degradation mechanisms of NOx storage/reduction catalysts. Catal. Rev. 46, 163 (2004). ˇ ep´anek J., Kub´ıcˇ ek M., Marek M. Dynamics and selectivity Koˇc´ı P., Pl´at F., Stˇ of NOx reduction in NOx storage catalytic monolith. Catal. Today 137, 253 (2008). Ansell G.P., Bennett P.S., Cox J.P., Frost J.C., Gray P.G., Jones A.-M., Rajaram R.R., Walker, A.P., Litorell M., Smedler G. The development of a model capable of predicting diesel lean NOx catalyst performance under transient conditions. Appl. Catal. B: Environ. 10, 183 (1996). Voltz S.E., Morgan C.R., Leiderman D., Jacob S.M. Kinetic study of carbon monoxide and propylene oxidation on platinum catalysts. Ind. Eng. Chem. Prod. Res. Dev. 12, 294 (1973).

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Optimization of Molasses and Air Feeding Profiles in Fed-Batch Baker’s Yeast Fermentation ølknur ATASOYa, Mehmet YÜCEERb, Ridvan BERBER*+ Ankara University, Faculty of Engineering, Dept. of Chemical Engineering, 06100 Tandogan/Ankara, Turkey E-mail: [email protected] a Currently at: Refik Saydam Hygiene Center, Department of Environment Health Research, 06100 Sıhhiye/Ankara, Turkey E-mail: [email protected] b Currently at: ønönüUniversity, Dept of. Chemical Engineering, 44280 Malatya ,Turkey E-mail: [email protected]

Abstract This work focuses on maximization of the amount of biomass in the production of baker’s yeast in fed-batch fermenters while minimizing the undesirable alcohol formation, by regulating the molasses and air feed rates. An optimization mechanism coupled with a state estimation algorithm and an Artificial Neural Network model based on original industrial data has been designed. As substrate and biomass concentrations required within this structure can not be measured on-line, these variables were predicted by an artificial neural network model using other measurable variables. Nonmeasurable substrate concentrations were successfully estimated by Kalman filtering using industrial data and thus, obtained new data sets were used for training the neural network model. Subsequently, through an SQP based optimization algorithm feeding profiles yielding maximum biomass and minimum alcohol formation were obtained. When computed results were compared to the industrial data, it was seen that molasses feeding profiles were compatible whereas aeration profiles were considerably different. The reason of this discrepancy was due to the agitation of the industrial fermenter with air at high air flow rates in order to provide better mixing in the reactor. Since the aeration profile obtained is associated with only the reproduction of microorganisms, it is postulated that the suggested optimization strategy may be industrially applicable for the maximization of biomass where enough agitation is provided by other means., Keywords: Baker’s yeast, Kalman filter, neural network, dynamic optimization

1. Introduction Predetermined constant feeding profiles relying on operating experience are still being used for the fed batch production of Saccharomyces cerevisiae, known also as baker’s yeast. However, it becomes compulsory to operate industrial processes at their optimum conditions because of rapidly growing economic competitions and frequently-changing customer expectations that need to be satisfied. Maximization of product i.e. biomass is of great importance for baker’s yeast production in an industrial fed-batch fermenter. On the other hand, optimization of these processes is relatively more difficult than the steady state optimization owing to the fact that dynamic model has to be satisfied as a constraint in the optimization. Although there is limited number of methods in literature, each of them has its own complexities. In order to achieve maximum yield at the highest possible productivity, a well designed feeding strategy is thus needed [1]. In latest studies, an evolutionary algorithm, together with a model updating procedure was used for obtaining optimal feeding profile in a fed batch process [2]. A methodology

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was proposed by Peters et al. [3] for designing and implementing a real time optimizing controller for nonlinear batch processes. Optimization problem was solved by a Lyapunov based extremum seeking approach. Karakuzu et al. [4] developed two soft sensors for the estimation of biomass concentration and specific growth rate in fedbatch baker’s yeast fermentation; one based on estimation of specific growth rate from process model, the other based on actual measurements. A fuzzy controller was then designed and tested on a simulated fed-batch production scale fermenter to determine the molasses and air flow rates. A new control mechanism has been designed in this work, for computing the molasses and air feeding profiles in real time. In the first step of the suggested strategy, unmeasurable variables were predicted by an artificial neural network model using other measurable variables. Molasses and air feeding were optimized by using predicted and measurable state variables in the second step. The results are industrially applicable for the maximization of biomass where enough agitation is provided.

2. Dynamic Model The process considered here is fed-batch culture of Saccharomyces cerevisiae, commercially known as baker’s yeast. The model assumes that the reactor is a single phase (liquid) isothermal system omitting the gas phase and micro organisms, and its contents are homogenous in axial and radial directions. Under these assumptions; glucose, oxygen, substrate, ethanol and cell mass balances were used to describe the liquid phase. Model equations and parameters were taken from literature [4]. The metabolism of yeast growth is based on the bottleneck hypothesis [5].

3. Optimization Strategy, Results and Conclusion Due to the fact that industrial baker’s yeast production is dependent on the medium conditions and other parameters like the behaviour of micro-organisms, the process may behave unexpectedly. One of the main operational difficulties that may lead to decrease in production yield is attributed to ethanol production. Predetermined constant feeding profiles (F) relying on operating experience are still being used for the fed batch production of Saccharomyces cerevisiae in order to control the biomass yield and ethanol production. The drawback associated with this practice is such that operator intervention may be required in cases of the occurrence of unexpected situations. Therefore, an automated optimization strategy would be required in order to eliminate the reliance on human experience. Thus, this work aims at maximizing the amount of biomass in the production of baker’s yeast in industrial fed-batch fermenters while minimizing the undesirable alcohol formation in real time, by regulating the molasses and air feed rates. The control mechanism that is designed for achieving this goal by determining the optimal molasses and air feeding rates is depicted in Figure 1.

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Figure 1. Control strategy

State Estimation by Kalman Filtering State estimation is a necessary component of sophisticated monitoring and control techniques, which attempts to reconstruct the needed information from the available measurements and prior knowledge in the form of a dynamic model. As the substrate concentration is not measured in baker’s yeast production process considered, the mathematical model was first linearized and Kalman Filtering (KF) was applied to the system in order to obtain the substrate concentration from available measurements (biomass, ethanol, dissolved oxygen concentration and fermenter volume). Fig. 2 shows the substrate concentrations predicted by state estimation from five different industrial data sets. Inner figure in Fig. 2 illustrates early changes in detail.

Figure 2. Estimation of substrate concentration by Kalman filter

Prediction of Substrate and Biomass Concentrations with ANN ANNs are powerful tools that have the abilities to identify underlying highly complex relationships from input output data only [6]. They have been extensively studied to present process models, and their use in industry has been rapidly growing [7]. Here, a three-layer feed-forward network was created to predict the substrate and biomass concentrations. The first layer has six sigmoid neurons, the second layer has fifteen

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sigmoid neurons and last layer have two linear neurons. The ANN model used for the reactor consists of six input nodes corresponding to fermentation time, molasses feed rate, air feed rate, dissolved oxygen concentration, ethanol concentration, fermentation volume. The two outputs were the biomass concentration and substrate concentration in the reactor. For training, fifteen industrial data sets were used. Testing was accomplished during three real time runs in the plant. The developed ANN model was used for obtaining the molasses and air feeding profiles with on-line optimization. Testing results are shown in Figure 3 and 4, which demonstrates close agreement of the model predictions with the industrial data.

Figure 3. ANN testing results for biomass concentrations

Figure 4. ANN testing results for substrate concentrations

Training and testing performances were evaluated statistically through R2 and mean absolute percentage error (MAPE %). The results demonstrate that the ANN model accurately predicts the substrate and biomass concentrations of industrial yeast fermentation process.

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Optimization of Molasses Feeding and Aeration Profiles The amount of biomass in the production of baker’s yeast in fed-batch fermenters was intended to be maximized while minimizing the unwanted alcohol formation, by regulating the molasses and air feed rates. The following objective function was used in optimization;

Max J = X bio (t f )

(1)

u

where u is the manipulated variable defined as molasses feeding rate (Fmolasses) and Xbio(tf) is biomass concentration at the end of production time. This multiobjective problem has been tackled earlier only from the point of view of finding optimum molasses feeding rate [8], but no account of air feed rate profiles has been provided. A control vector parameterization approach combined with Sequential Quadratic Programming (SQP) was applied here for solution of this optimization problem [9]. The optimization problem was at first expressed in discrete time domain by dividing the batch time into hourly time intervals (17 totals) each with a constant molasses and air feed rate, conforming to the initial values of the control vector. Starting from the beginning of the process, the dynamic model was integrated with these decision variables. Meanwhile, the state variables computed at the end of each time interval were taken as initial values for the subsequent time interval for integration. When the end of overall process time domain was reached, the objective function was evaluated. This strategy revealed the molasses (i.e. glucose) feed profile to the reactor. Molasses feeding values obtained for each time interval by optimization was used to determine oxygen uptake rate required by microorganisms in the corresponding time interval. Gas-liquid interface mass transfer coefficient was computed with this oxygen uptake rate using an empirical mass transfer coefficient equation [4]. The suggested control strategy was implemented in the industrial baker’s yeast plant in real time during three industrial fermentation processes. Fig. 5 and 6 compare predicted optimal control profiles to the real industrial data. Air feed rate obtained with this study is concerned only with growing of biomass according to the model. If air is used for agitation and mixing in the fermentation liquid, this needs to be taken into account separately as a mechanical requirement for reactor hydrodynamics. These figures indicate that predicted molasses feeding profiles were compatible whereas aeration profiles were considerably different.

Figure 5. Comparison of predicted control effort and industrial data for molasses feed

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Figure 6. Comparison of predicted control effort and industrial data for air feed

The reason of this discrepancy was agitation of the industrial fermenter with air, and keeping the air flow rate high in order to provide better mixing. Aeration profile predicted in this work is based on the amount of air required for reproduction of microorganisms. It is concluded that the results are industrially applicable for the maximization of biomass where enough agitation is provided by other than aeration means.

4. Acknowledgement The support provided by the Scientific Research Projects Fund of Ankara University through grant no 2001-07-05-056 for this work is gratefully acknowledged. The authors are thankful to Dr. Mustafa TURKER for his support and provision of industrial data.

References [1] H.Y.Wang, C.L. Cooney, and D.I.C. Wang, Biotechnol. and Bioeng. 19 (1977), 69 [2] Ronen, Y. Shabtai, H. Guterman, J. of Biotechnology, 97 (2002) 253. [3] N. Peters, M. Guay, D. DeHaan, Int. Symposium on Advanced Control of Chemical Processes, ADCHEM 2006 Proceedings, Gramado, Brazil, (2006) 227. [4] C. Karakuzu, M. Türker and S. Öztürk, Control Engineering Practice, 14 (2006) 959. [5] B. Sonnleitner and O. Kappeli, Biotechnol. Bioeng. 26 (1986) 1176. [6] S. Haykin, Neural Networks, A comprehensive foundation, (2nd ed.). Prentice Hall, USA, 1999. [7] L. H. Ungar, E. J. Hartman, J. D. Keeler and G. D. Martin, Am. Inst. Chem. Eng. Symp. Ser., 92 (1996), 57. [8] R. Berber, C. Pertev, M. Turker, Bioprocess Engineering 20 (1999) 263. [9] M. Yuceer, I. Atasoy and R. Berber, Computer Aided Chemical Engineering, 20 (2005) 631.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Optimization Studies of an Oil Well Drilling Process Marcia P. Vega, Frederico R. B. Vieira, Mauricio C. Mancini Departamento de Engenharia Química - Universidade Federal Rural do Rio de Janeiro, BR 465, km7 – CEP: 23890-000 – Seropédica – RJ – Brasil, E-mail: [email protected]

Abstract Noninferior or Pareto sets of optimal solutions were determined for the dual objectives of maximizing the annulus solid concentration and minimizing mud invasion into the reservoir or migration of reservoir fluids into the well annulus. The following set of time varying control inputs to the process were analyzed: choke valve opening index, pump mixture mass flow rate or mud density and drilling rate. The formulation of the oil well drilling control problem as a multiobjective optimization problem and solving the Pareto set was the most appropriate way to understand all the competitions among the various objectives. Keywords: multi-objective optimization, mud invasion, kick 1. Introduction A drilling system consists of a rotating drill string, which is placed into the well (Fig. 1). The drill fluid is pumped through the drill string and exits through the choke valve. An important scope of the drill fluid is to maintain a certain pressure gradient along the length of the well. During drilling, disturbances that produce fluctuations in the well pressure might occur. As the well is drilled, the hydrostatic pressure increases because of the well length grow. In addition, the reservoir fluid influx changes the well flow rate and density of the well fluid mixture. Finally, the pipe connection procedure, which requires stopping and starting of the drill fluid, produces severe fluctuations in the well flow rates. The pressure balance between the well section and the reservoir is important. If the pressure in the well is higher than the reservoir pressure, it is referred to as over-balanced drilling. This condition causes the circulation fluids to penetrate into the reservoir formation. On the other hand, if the pressure in the well is lower than the reservoir pressure, it is referred to as under-balanced drilling, and the reservoir fluids migrate into the well annulus. Over-balanced drilling is the most used method for drilling oil wells. The reason for this is that it nearly eliminates the risk for an uncontrolled ‘‘blow-out’’ situation, where the pressure in the reservoir causes large amounts of the reservoir fluids to penetrate into the

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well and follow the well to the surface. Today, different type of equipment such as blow-out preventers, gives the possibility of reducing the well pressure lower than the reservoir pressure [1]. Drilling the oil well having under-balanced conditions has the benefit that the porous formation is less damaged, since the particles from the drilling process do not penetrate into the formation. This leads to a higher production rate when the oil well is set into production.

Figure 1 – Oil well drilling scheme. An optimization analysis of a drilling process constitutes a powerful tool for operating under desired pressure levels and simultaneously maximizing the penetration rate, which reduces costs, as oil derrick operation demands around U$220,000.00/day. The procedure traditionally adopted in optimization studies is the formulation of a single objective function combining all performance measurements with weighting functions chosen a priori. The a priori choice of weights do not successfully demonstrates which optimum trajectory the manipulated variable should follow for dealing with conflicting objectives; in addition, there are no evidences that the specific use of certain manipulated variables will produce superior quality results. Wang et al. [2] pointed out that traditional mathematical programming algorithms use two strategies for solving optimization problems: single objective optimization, using the others objectives as constraints; and the altogether objectives optimization, using weighting factors. For the second approach, the arbitrary choose of weights and the diverse quantities unification (cost, product quality, environmental effects) in a common measure produce criticism. Besides, the second strategy is not able to find the optimal solution for a non convex objective function. The majority of real-world problems present complex nature and conflicting objectives, being rarely convex. Therefore, a judicious solution of optimization problems requires the use of multi-criterion approach, producing a family of solutions named optimum Pareto set. As a result, the multi-objective optimization, which seeks to harmonize conflicting objectives, appears as an interesting approach, being also called as efficient or multi-criterion optimization. The solutions are named Pareto optimum, maxima vector, efficient points, non inferior solutions or non dominant solutions. The major objective of this paper is applying multi-criterion dynamic optimization to an oil well drilling process. The interaction in the mapping

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between input and output variables is analyzed through multi-objective optimization, employing a dynamic mathematical model. The presence of conflicting objectives was identified, that is, an objective function could not be improved without sacrificing the other. Pareto optimization (İ-constraint method) is implemented by initializing the optimization algorithm with distinct initial guesses, for attaining global optimum according to the methodology of Madsen [3]. Various schemes were analyzed, including drilling rate, choke valve opening index, pump circulation rate or mud density (input variables) in order to evaluate the process performance (annulus bottom hole pressure and annulus solid concentration). 2. Pareto optimization There are several methods described in the literature about the Pareto set generation [4]. They basically transform the original multi-objective problem into many single objective optimization related problems. The transformation is done under conditions that guarantee the construction of the Pareto set. Also this transformation enables a numerical solution for the original multi-objective problem. The simplest and the most usually applied technique is the İ-constraint approach [5]. In this method, one of the objective functions of the original multi-objective optimization problem is selected to be the single objective function (primordial objective function), while the others are included as constraints. These new constraints are subjected to maximum values previously chosen. Therefore the İ-constraint approach transforms the multi-objective optimization problem, Eq. (1), composed by N objective functions, into a single objective optimization problem described by Eq. (2).

^  ` >F1x, t f , F2 x, t f ,  , FN x, t f @

min F x t f , t f

­° x l x, u System constraints: ® °¯ x0 x 0

(1)

Manipulated variables constraints: h>u t @ d 0 End point constraints: g x t f d 0

>  @

min F1u x l x, u x0

(2)

x0

F j u d H j ,

j

2,3,, N

u:

3. Results and discussion A nonlinear mathematical model, representing the drilling system, was developed based on mass and momentum balances. The mass balance comprised two systems: the drill string and the annulus between the wall of the

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well and the drill string. The momentum balance was evaluated at the drill bit and at the choke valve, taking into account frictional losses and compression and hydrostatic pressures. The flow from the reservoir into the well was modelled using a simple relation named productivity index, which is a constant scalar defining the mass flow rate based on the pressure difference between the reservoir and the well. The annulus bottom hole pressure was defined as the summation of annulus compression and hydrostatic pressures, frictional losses, pressure loss over the choke and atmospheric pressure. Further details of the mathematical model may be found elsewhere [6]. The state vector for the drilling problem includes liquid, gas and solid masses inside the drill string; liquid, gas and solid masses inside the annulus; well length; mass flow of the mixture at the bit and mass flow of the mixture at the choke, Eq. (3). ª º xt «m gd , mld , m sd , m ga , mla , m sa , L, Wmix,bit , Wmix,choke » « » ¬ ¼

(3)

The set of time varying control inputs (manipulated variables: drilling rate, choke opening index, pump flow or mud density) to the process are shown in Eq. (4). Any vector satisfying the constraint equations is termed a feasible solution. The manipulated variables constraints insure that no control variable is outside a feasible region. The end point constraints are imposed on annulus bottom hole pressure. The final time is fixed at 2400 seconds, a typical time interval between pipe connection procedure, besides, sampling time equals 2 seconds. u t

>vd , zchoke, wpump @

(4)

To apply the multi objective optimization method to the oil well drilling problem, two objective functions were selected for being minimized as can be observed from Eqs. (5-6). Maximizing annulus solid mass produces the effect of maximizing the rate of penetration into the well, reducing the drilling cost. Concerning the second objective function, the aim was increasing the annulus bottom hole pressure to a desired level named Pabotd . The complex situation where narrow operational window between pore and fracture pressures occurs, mainly when lower collapse is higher than pore pressures and/or upper collapse is lower than fracture pressures, was taken into account by including this variables as nonlinear constraints into the optimization problem. F1 >xtf , tf @

>1 1  m sa @

(5)

F2 >xtf , tf @

>Pabotd  Pabot Pabotd @2

(6)

For the multi objective optimization problem, the primordial objective function was maximizing the rate of penetration. The other objective function (minimizing mud invasion into the reservoir or migration of reservoir fluids into the well annulus) is included as a nonlinear constraint. During oil well drilling, the pore pressure (minimum limit) and the fracture pressure (maximum limit) define mud density range. As a result, the drilling fluid hydrostatic pressure

Optimization Studies of an Oil Well Drilling Process

633

needs to be higher than pore pressure, in order to avoid formation fluid invasion into the well. Simultaneously, the drilling fluid hydrostatic pressure needs to be smaller than fracture pressure, for avoiding formation damage. It is well known that instability is associated with low competency of rock formations. The drilling process alters the state of stresses inside a formation over passed by a bit. The material removed by the excavation is placed by the drilling fluid, which, among other utilities, tries to restore the equilibrium before the excavation. If equilibrium is not attained, some type of rupture (fracture and collapse) is generated. Fractures are associated with the rupture of rock material (traction rupture), while collapses are produced due to the shearing produced by an unequal par of stresses around the well (compression rupture). The collapse may produce the wall tumbling down effect, increasing cuttings deposition, mainly in a highly inclined section, restricting flow area and producing pressure peaks. In addition, the pore collapse produces a flux decrease in the reservoir due to a permeability reduction and may induce sand production, degrading the well productivity. The fracture produces mud inflow into the porous formation, which may collapse uncovered superior regions. If the formation contains gas, a kick may occur as the reservoir fluids migrate into the well annulus, producing the risk of an uncontrolled blow-out situation. As can be observed from Fig. 2, two different control modes are illustrated: drilling rate vd and choke opening index zchoke versus drilling rate vd and pump flow Wpump . For the two objectives chosen the theoretical absolute minima are F1min 0 and F2min 0 . This point is termed utopia point. It can be observed that there is a trajectory (drilling rate and pump flow inputs) which gives the closes approach to utopia, an in fact, requires very little sacrifice of the objective function F2 . Fig. 3 shows dynamic simulation concerning the two optimization strategies. It can be observed that choosing drilling rate and pump flow as inputs produced a faster output response, as the time constant of this strategy is smaller. u(1)=vd; u(2)=zchoke u(1)=vd; u(2)=Wpump 1.0E-3

F2

8.0E-4 6.0E-4 4.0E-4 2.0E-4 0.0E+0

4.90E-5 5.00E-5 5.10E-5 5.20E-5 5.30E-5

F1

Figure 2 – Pareto set.

M.P. Vega et al. Dimensionless annulus bottom hole pressure

634

u(1)=vd; u(2)=zchoke u(1)=vd; u(2)=Wpump 1.0

0.9

0.8

0.7

0

400

800

Sampling time

1200

Dimensionless annulus solid mass

u(1)=vd; u(2)=zchoke u(1)=vd; u(2)=Wpump 1.2 1.0 0.8 0.6 0.4 0.2

0

400

800

Sampling time

1200

Figure 3 – Dynamic simulation. 4. Conclusions The Pareto optimization strategy unveiled that drilling rate and pump flow were the most appropriate input variables in order to maximize the rate of penetration (annulus solid concentration) and to drill under desired pressure operational window (minimize mud invasion into the formation and migration of reservoir fluids into the well annulus). 5. References [1] G. Nygaard, G. Naevdal, Journal of Process Control, 16 (2006) 719. [2] F-S. Wang, J-W. Sheu, Chem. Eng. Sci. 55 (2000) 3685. [3] H. Madsen, Journal of Hydrology 235 (2000) 276. [4] V. Chankong, Y.Y. Haimes, Multiobjective decision making – theory and methodology, Elsevier, New York, 1983. [5] A. Tsoukas, M. Tirrel, G. Stephanopoulos, Chem. Eng. Sci. 37 (1982) 1785. [6] M.P. Vega, CM. Scheid, L.A. Calçada, M.C. Mancini and A.L. Martins, In: Bertrand Braunschweig and Xavier Joulia (Org.), 18 ESCAPE - ISBN (CD): 9780444532282, Lyon, France, 2008.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Particle Swarm Optimization for Phase Stability and Equilibrium Calculations in Reactive Systems Adrián Bonilla-Petriciolet a and Juan Gabriel Segovia-Hernández b a

Departamento de Ingeniería Química, Instituto Tecnológico de Aguascalientes, Av. López Mateós 1801, Aguascalientes, 20256, México. [email protected] b Departamento de Ingeniería Química, División de Ciencias Naturales y Exactas, Universidad de Guanajuato, Campus Guanajuato, Noria Alta s/n, Guanajuato, 36050, México. [email protected]

Abstract This study reports the application of Particle Swarm Optimization (PSO) for phase stability and equilibrium calculations in reactive systems. These thermodynamic problems are formulated using transformed composition variables and PSO is used as global optimization strategy. Our results indicate that Particle Swarm Optimization is an alternative and suitable stochastic method for solving these challenging calculations in reactive systems. Keywords: Particle swarm optimization, phase equilibrium, chemical equilibrium, global optimization

1. Introduction In recent years, reactive separation processes have emerged as attractive technologies for the chemical industry because they offer various advantages over conventional separation strategies. The design and synthesis of these separation units is fundamentally based on the study and analysis of thermodynamic equilibrium. However, the modeling of phase equilibrium in reactive systems is a difficult task due to the complex interactions among components, phases and reactions. In these conditions, conventional numerical methods are not suitable for performing reactive phase equilibrium calculations. Until now, some studies have applied global solving strategies for reliably modeling the phase behavior in reactive systems; see for example McDonald and Floudas (1996) and Bonilla-Petriciolet et al. (2006). Stochastic methods have proven to be useful because they do not require assumptions about the thermodynamic problem, are reliable and efficient. However, few attempts have been performed on the application of these strategies for reactive phase equilibrium calculations. One of the most-promising stochastic methods is Particle Swarm Optimization (PSO) (Kennedy and Eberhart, 1995). It is a novel evolutionary algorithm capable of handling the challenging characteristics of global optimization problems. Furthermore, PSO is simpler, both in formulation and computer implementation, than the Genetic Algorithm and other metaheuristics. In the chemical engineering community, PSO is of great interest and has been successfully used in several applications. However, the performance of PSO in the modeling of phase behavior of reactive systems has yet to be studied. Therefore, in this study we illustrate the application of PSO for performing phase stability and equilibrium calculations in mixtures subject to chemical reactions.

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2. Formulation of reactive phase stability and equilibrium problems At constant temperature and pressure, a multicomponent and multiphase system achieves equilibrium when its total Gibbs free energy is at the global minimum. For reactive mixtures, the Gibbs free energy minimization is subject to chemical equilibrium restrictions. However, this difficult thermodynamic problem can be readily solved if the Gibbs energy function is expressed in terms of transformed composition variables (Ung and Doherty, 1995). Transformed composition variables provide a simpler thermodynamic framework for modeling reactive mixtures, restrict the solution space to the compositions that satisfy stoichiometry requirements, and reduce the problem dimensionality (Ung and Doherty, 1995; Wasylkiewicz and Ung, 2000). Thus, for a system of c components that undergoes r independent chemical reactions, the transformed mole fractions Xi are defined by selecting r reference components

xi − vi N −1 xref

Xi =

1 − vTOT N −1 xref

for i =1,…,c − r

(1)

where xi is the mole fraction of component i, xref is a column vector of mole fractions for r reference components, vi is the row vector of stoichiometric coefficients of component i for each of the r reactions, N is an invertible and square matrix formed from the stoichiometric coefficients of the reference components in the r reactions, and vTOT is a row vector where each element corresponds to the sum of stoichiometric coefficients for all components that participate in each of the r reactions. Note that transformed mole fractions (X) are related to conventional mole fractions (x) using the reaction equilibrium constants (Ung and Doherty, 1995). Using these transformed variables, the Gibbs free energy function for a multiphase system is given by

gˆ =

π

c−r

¦ ¦X Φj

j =1

i, j

μi, j

(2)

i =1

where ƣ is the transformed molar Gibbs free energy, π is the number of phases at equilibrium, μ i,j is the chemical potential of component i in phase j, Xi,j is the transformed mole fraction of component i in phase j, and Φi,j is the transformed mole fraction for phase j. Transformed composition variables are subject to the material balances

Zi −

π

¦X

i, j

= 0 for i = 1,..., c − r

j =1

c −r

¦X

i, j

= 1 for j = 1,..., π

(3)

i =1

π

¦Φ

j

=1

j =1

where Zi is the transformed mole fraction of component i in the feed. For a reactive mixture with all Xi∈(0,1), the unconstrained global optimization of Eq. (2) can be performed using the next equations

Particle Swarm Optimization for Reactive Phase Stability and Equilibrium Calculations π −1 § · nˆi , j = λi , j ¨¨ Z i − nˆi ,m ¸¸ for i = 1,..., c − r and j = 1,..., π − 1 m =1 © ¹

637

¦

nˆi ,π = Z i −

π −1

¦ nˆ

i ,m

(4)

for i = 1,..., c − r

m =1

where λi,j ∈(0, 1) for i = 1,…,c − r and j = 1,…,π − 1 are the decision variables and nˆi , j is the transformed mole number of component i in phase j. Note that

X i, j =

nˆi , j c−r

¦ nˆ

k, j

k =1

for i = 1,..., c − r and j = 1,..., π

c −r

Φj =

¦ nˆ π

(5)

k, j

k =1 c −r

¦ ¦ nˆ

k ,m

m =1 k =1

On the other hand, for a reactive mixture, the phase stability analysis can be performed via the global minimization of the reactive tangent plane distance function (RTPDF). This stability criterion is also formulated using X and, as a consequence, retains all characteristics and advantages of the classical stability test used for non-reactive mixtures. So, RTPDF is defined as (Wasylkiewicz and Ung, 2000)

RTPDF =

c−r

¦ X (μ i

i =1

i X

− μi

Z

)

(6)

where μi is the chemical potential of component i evaluated at the transformed composition X or Z. The necessary and sufficient condition for global stability is RTPDF ≥ 0 for any transformed composition X from the whole composition space. RTPDF is optimized with respect to c − r decision variables λi,1∈(0, 1) using Eq. (4) where X is obtained from Eq. (5). Finally, it is convenient to note that the chemical potentials are functions of X for both ƣ and RTPDF.

3. Optimization strategy: Particle Swarm Optimization Particle Swarm Optimization is a population based method that belongs to the class of swarm intelligence algorithms. Eberhart and Kennedy (1995) introduced this strategy for global optimization, which is inspired by the social behavior of flocking swarms of birds and fish schools. It exploits a population of potential solutions to identify promising areas for optimization. In this context, the population of potential solutions is called the swarm, and each solution is called particle. The success histories of the particles influence both their own search patterns and those of their peers. Each particle has two state variables: its current position si,j(t) and its current velocity Vi,j (t) where t is an iteration counter. In the local version of PSO, the search is focused on promising regions by biasing each particle’s velocity toward both the particle’s own remembered

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638 p

best

best position ( si , j ) and the communicated best neighborhood location ( si , j ). The relative weights of these two positions are scaled by the social (C1) and cognitive (C2) parameters. The velocity and position of each particle are updated by using: p Vi , j (t + 1) = wVi , j (t ) + C1 R1 ( sibest , j − si , j (t )) + C 2 R2 ( si , j − si , j (t ))

si , j (t + 1) = si , j (t ) + Vi , j (t + 1)

(7)

where R1, R2∈(0, 1) are random numbers, and w is the inertia weight factor. In our calculations, we have considered that w decreases linearly from 0.8 to 0.4 over the whole run; while C1 also decreases linearly from 2.0 to 0.5 where C2 = 4.0 − C1. Dynamic values for w, C1 and C2 are used to favor the global search during the early iterations and to encourage the particles to converge to global optimum at the end of the search. The velocity of each particle is restricted to a maximum value within the interval [−Vmax, Vmax], which is defined by considering the bounds on decision variables. Each particle is assigned to a neighborhood of a pre-specified number of particles (nh = 10). Thus, the best position attained by particles that comprise the neighborhood is communicated among them. It is important to note that all PSO parameters were defined by considering the results obtained from several trial calculations using benchmark problems and our numerical experience. Finally, the overall algorithm of PSO is given as follows: at the beginning, a population of np particles is initialized with random positions si,j and random velocities Vi,j for i = 1,…,nvar and j = 1,…,np where nvar is the number of decision variables. Once all particles are initialized, the positions and velocities of all particles are modified using Eq. (7). After calculating the velocities and position for the next iteration t + 1, the current iteration is completed. The best particle is only updated when a new one is found yielding a decrease in the objective function value. This process is performed for a certain number of iterations (Niter), or until a maximum number of iterations, without improvement in the best function value, is satisfied.

4. Results and Discussion The reaction for butyl acetate production at 298.15 K and 1 atm is used to illustrate the performance of PSO. This reactive system is given by: acetic acid (1) + n-butanol (2) ↔ water (3) + n-butyl acetate (4). Phase stability and equilibrium calculations are performed for a transformed feed Z (0.05, 0.2, 0.75). At these conditions, this mixture shows a liquid-liquid equilibrium, and UNIQUAC model is used to predict thermodynamic properties with the parameters reported by Wasylkiewicz and Ung (2000). Transformed fractions X are defined using n-butyl acetate as reference component

X 1 = x1 + x4 X 2 = x2 + x4

(8)

X 3 = x3 − x4 = 1 − X 1 − X 2 Both RTPDF and ƣ are minimized by considering three decision variables: λi,1∈(0, 1). Phase stability and equilibrium problems were solved 100 times using random initial values via different random number seed. For illustrative purposes, Figure 1 shows the plot of success ratio (SR) versus Niter for PSO in this system. Note that SR is defined as the number of runs out of 100 that satisfy the condition⏐fopt − fcalc⏐≤ 10-04 where the

Particle Swarm Optimization for Reactive Phase Stability and Equilibrium Calculations

639

known global optimum of the objective function is fopt, and fcalc is the value of objective function calculated by PSO. This plot was obtained using the best objective function values recorded at different values of Niter and for several swarm sizes np.

100

a) 80

60

np

40

10 15 25 50

20

0

SR

1

21

41

61

81

101

100

b) 80

60

np

40

10 15 25 50

20

0 1

201

401

601

801

1001

Niter Figure 1. Success ratio versus number of iterations of PSO for the global optimization of: (a) RTPDF and (b) ƣ. Reactive mixture: reaction for butyl acetate production at 298.15 K and 1 atm.

Results indicate that the algorithm performance (reliability and efficiency) is dependent on Niter and np. Reliability of PSO improves as these parameters increase but at the expense of a higher computational effort. In stability calculations for this example, high SR is obtained at Niter > 100 and np > 25nvar. However, for ƣ, several iterations are required to obtain an acceptable performance and the increase of np favors the reliability of PSO. As expected, reactive phase equilibrium problems are generally more difficult to solve compared to stability problems, and they involve more numerical effort. It is expected that for reactive phase equilibrium problems with more decision variables (i.e., multireactive and multicomponent mixtures), the reliability of PSO will increase with Niter and np. For this example, CPU time ranged from 0.6 to 60 s, depending on the swarm size and maximum number of iterations. Based on our numerical practice using PSO, it appears that this stochastic method is a reliable strategy for modeling the phase

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behavior in reactive systems. The comparison of PSO with other stochastic methods is under way by our research group.

5. Conclusions This paper introduces the application of Particle Swarm Optimization for performing phase stability and equilibrium calculations in reactive systems. This stochastic method appears to be robust for solving these challenging thermodynamic problems in a reasonable computational time. In future studies, we will hybridize this method with other metaheuristics to develop more efficient global optimization strategies for these calculations.

6. Acknowledgements We acknowledge the financial support provided by CONACyT, Dirección General de Educación Superior Tecnológica, Instituto Tecnológico de Aguascalientes and Universidad de Guanajuato (Mexico).

References C.M. McDonald, C.A. Floudas, 1996, GLOPEQ: A new computational tool for the phase and chemical equilibrium problem, Computers Chemical Engineering, 21, 1, 1-23. A. Bonilla-Petriciolet, R. Vazquez-Roman, G.A. Iglesias-Silva, K.R. Hall, 2006, Performance of stochastic global optimization methods in the calculation of phase stability analyses for nonreactive and reactive mixtures, Industrial Engineering Chemistry Research, 45, 13, 47644772. J. Kennedy, R.C. Eberhart, 1995, Particle Swarm Optimization, In Proceedings of the IEEE International Conference on Neural Networks, IV: 1942-1948. S. Ung, M.F. Doherty, 1995, Theory of phase equilibrium in multireaction systems, Chemical Engineering Science, 50, 20, 3201-3216. S.K. Wasylkiewicz, S. Ung, 2000, Global phase stability analysis for heterogeneous reactive mixtures and calculation of reactive liquid-liquid and vapor-liquid-liquid equilibria, Fluid Phase Equilibria, 175, 1-2, 253-272.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

641

Solution of separation network synthesis problems by the P-graph methodology István Heckl,a Ferenc Friedler,a L. T. Fanb a

Department of Computer Science, University of Pannonia, Egyetem u. 10, Veszprém, 8200, Hungary, [email protected], [email protected] b Department of Chemical Engineering, Kansas State University, Manhattan, KS 66506, USA, [email protected]

Abstract The current work demonstrates that separation-network synthesis (SNS) problems can be transformed into process-network synthesis (PNS) problems: The SNS problems constitute a particular class of PNS problems. Thus, the transformed SNS problems are solvable by resorting to the P-graph methodology originally introduced for the PNS problems. The methodology has been unequivocally proven to be inordinately effective., Keywords: separation-network synthesis, optimization, P-graphs, process-network synthesis, mathematical modeling

1. Introduction A separation network comprises separators, dividers, mixers, and streams linking them. Depending on their locations, these streams can be categorized as feed, intermediate and product streams. To yield the desired product streams from the given feed streams, a separation network performs a sequence of separation tasks [1]. A large number of different separation networks are capable of producing the same product streams. These networks differ in the numbers of separator included and the interconnections among them, as well as in their total costs. The aim of a separationnetwork synthesis (SNS) problem is to identify the most favorable, i.e., optimum, network, often in terms of cost, from a multitude of alternatives. A typical example is the refining of crude oil to yield various products. A process network creates the desired products from the specific raw materials with a given set of operating units. The objective of process-network synthesis (PNS) is also to identify the most favorable, i.e., optimum, network. The P-graph methodology is a graph theoretical approach for solving PNS problems. The P-graphs are bipartite graphs, each comprising nodes for a set of materials, a set of operating units, and arcs linking them. The materials can be the raw materials, intermediates, and products. The operating units are defined in terms of input and output materials as well as their ratios. Apparently, SNS and PNS problems are analogous. Nevertheless, there is a fundamental difference between them: In general, the number of possible streams, which are obviously materials, involved in any SNS is infinite, while that involved in any PNS is finite. For instance, even if only two components are involved in a separation network, a variety of streams, each with an arbitrary composition, can be generated from them by means of mixers. This fundamental difference implies that a separation network can not generally be transformed into a process network. The

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exceptions are separation networks in which mixers precede only the products; in any of such separation networks, the number of streams is finite.

2. P-graph-based methodology Friedler et al. [2] have proposed P-graphs (process graphs) for PNS problems and have identified five axioms underlying the combinatorially feasible process networks, i.e., solution structures. These axioms have given rise to various algorithms including the maximum structure generator, MSG [3], the solution structure generator, SSG [2], and the optimal structure generator algorithm, ABB [4], which is based on an accelerated branch-and-bound strategy. The P-graph-based methodology has demonstrated its efficiency in many areas such as emission reduction [5], optimal retrofit design for a steam-supply system [6], and downstream processes for biochemical production [7]. Our aim is to extend the P-graph-based methodology to SNS. In the P-graph-based methodology, a process network comprises two types of nodes, the nodes for materials and those for operating units. Hence, P-graphs are bipartite graphs as mentioned earlier. In the P-graph representation of a process network, the maximum available raw materials may be constrained, and the rate of manufacturing of each product must be specified. An operating unit produces its output materials if all its input materials are supplied. The input materials are consumed according to the rates given on the arcs leading to the respective operating unit. The input and output materials, and the aforementioned rates collectively define formally an operating unit. Moreover, an operating unit may have upper and lower capacities. At any material node, the sum of the outgoing flows is equal to the sum of the incoming flows, i.e., the mass balance holds.

M1

Input materials

M2

2

7

4 1

4

O1

M3 M4 M5

Output materials

Figure 1. Graphical representation of an operating unit

Figure 1 illustrates operating unit O1, which has two input materials, M1 and M2, and the three output materials, M3, M4, and M5; O1 converts 2 units of M1 and 7 units of M2 into 4 units of M3, 1 unit of M4, and 4 units of M5.

Solution of Separation Network Synthesis Problems by the P-Graph Methodology

643

M1

Raw materials

O1 M2

M3

O2

M4 O3

Products

M5

M6

Figure 2. PNS network involving three operating units and six materials

Figure 2 represents a process network featuring operating units O1, O2, and O3, and materials M1, M2, ..., and M6, where M1, M2, and M3 are the raw materials; M4, an intermediate; M5, the product; and M6, a byproduct.

3. SNS problems with pure products General SNS problems can not be transformed readily into PNS problems: A separation network often contains a mixer, depending on the ratio of its inputs, a mixer can yield a variety of streams, each with an arbitrary composition, and thus, the number of possible outlets is infinite. In contrast, a process network contains only a finite number of materials. Heckl et al. [8] and Heckl et al. [9] have proposed a solution method for SNS problems, involving simple, sharp separators with proportional cost functions by applying different separation methods. The method, termed SNS-LIN, deploys a linear mathematical model, which can be solved efficiently; moreover, it invariably generates a super-structure in which mixers precede only the products. Consequently, the number of streams, i.e., materials, is finite, thereby rendering it possible to solve this type of SNS problems with the methodology developed for PNS problems. A simplified version of SNS-LIN is addressed first where only pure products and a single separation method are considered. Initially, a material node needs to be introduced for each stream in the super-structure, which is followed by the introduction of an operating node representing each separator.

[c1, c2, 0] c1c2c3 [c1, c2, c3]

S2

30 cost: 3

c1c2|c3

18 12

[10, 8, 12] F1

cost: 90

c1c2

D0

c3

[0, 0, c3] Figure 3. Representation of a separator and the corresponding operating unit

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The symbol for a material signifies its components, e.g., material c1c2 contains components c1 and c2, and the symbol for an operating unit signifies the nature of separation, e.g., operating unit c1c2|c3 separates c1c2 from c3. The rates of flows through the arcs of the operating unit are computable from the component flow rates of the corresponding feed stream; see Fig. 3. The cost of the operating unit is calculable from the cost of the separator and the rate of the material input. Upon defining all the materials and operating units, the maximal structure, all solution structures, and the optimal structure are determined by algorithms MSG, SSG, and ABB, respectively. Algorithm SSG generates five solution structures for a threecomponent problem, and algorithm ABB determines the optimal and a finite number of near optimal structures in ranked order directly from the maximal structure. The optimum value of the PNS problem and the original SNS-LIN are identical, thus ascertaining the validity of the transformation.

4. SNS problems involving different separator families Separation induced by the difference in volatility has long been ubiquitous in practice. Nevertheless, the implementation of methods of separation induced by the differences in other properties has been steadily gaining popularity in recent years [8]: These methods are potentially capable of leading to substantial energy saving [1]. The aforementioned transformation procedure and the P-graph methodology are applicable when several separation families are available.

5. SNS problems with multi-component products The inclusion of multi-component products requires the explicit representation of the mixers in the maximal structure. A single operating unit is incapable of representing a mixer: While an operating unit needs all its inputs to function, the mixer needs just one input. Figure 4 depicts a mixer as multiple operating units, each with a single input and a single output. Note that one operating unit is needed for each inlet of the mixer, and the mixer functions as long as one of its operating units functions.

6. Example Let us consider an illustrative example involving 3 components, 1 feed, 2 mixed-component product streams; see Table 1 and 2. Figures 5 and 6 show the solution structure with PNS and SNS notation respectively. Table 1: The component flowrates of the feed and the products

F1 P1 P2

c1 (kg/s)

c2 (kg/s)

c3 (kg/s)

6 4 2

5 2 3

9 7 2

Table 2: The available separators

Components Separators Total cost coefficients ($/kg)

c1

c2 1

S 4

c3 2

S 2

Solution of Separation Network Synthesis Problems by the P-Graph Methodology

c1c2c3 c1c2|c3

c1|c2c3

c2c3

c1c2

c2|c3

c1|c2

c1 M1a

M1b M1c

c2

M1d M1e M1f

c3

M2a

M2b M2c M2d M2e

Mixer 1

M2f

Mixer 2 P1

P2 P2c1 P2c2 P2c3

P1c1 P1c2 P1c3

Figure 4. Maximal structure of the example

c1c2c3 c1c2|c3 c1c2 c1|c2 c1 M1a

c2

M1c

c3

M1f

M2b

M2f

M2e

M1

M2 P1 P1c1 P1c2 P1c3

P2 P2c1 P2c2 P2c3

Figure 5. Solution structure of the example with PNS notation

xD1,M 2 = 0.4 xD1,M1 = 0.222

[6, 5, 9]

xD2 ,M 2 = 0.111 x

D2 , S1

D2

D1 S2

F1 x

D1 , S 2

= 0.378

[4, 2, 7] P1

= 0.267

S1 cost=26.844 $/s [2, 3, 2] P2

Figure 6. Solution structure of the example with SNS notation

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7. Conclusions A procedure is introduced to transform three classes of SNS problems into the corresponding PNS problems. The first class is the SNS problems with pure products; the second, the SNS problems involving different separator families; and the third, the SNS problems with multi-component products. The resulting PNS problems are solved by resorting to algorithm MSG for the maximal structure generation, algorithm SSG for solution structure generation, and algorithm ABB for accelerated branch-and-bound search, derived for PNS problems. The transformation involves the steps for the definition of the material for each stream in the super-structure; the specification of an operating unit for each separator in the super-structure; and the determination of the cost and other parameters of the operating units. The optimal structures obtained for the transformed PNS problems are identical to those obtained by directly solving the SNS problems, thereby indicating that the transformation is indeed valid.

8. Acknowledgements The first two authors would like to acknowledge financial support provided by Faculty of Information Technology, University of Pannonia. This is also contribution No. 03-336-J, Department of Chemical Engineering, Kansas Agricultural Experiment Station, Kansas State University, Manhattan, KS 66506, U.S.A., from which the last author received financial support.

References [1] King, C. J., 1980. Separation processes. McGraw-Hill. [2] Friedler, F., K. Tarjan, Y. W. Huang, and L. T. Fan, Combinatorial Algorithms for Process Synthesis, Computers Chem. Engng, 16, (1992) S313. [3] Friedler, F., K. Tarjan, Y. W. Huang, and L. T. Fan, Graph-Theoretic Approach to Process Synthesis: Polynomial Algorithm for Maximal Structure Generation, Computers Chem. Engng, 17, (1993) 929. [4] Friedler, F., J. B. Varga, and L. T. Fan, Decision-Mapping for Design and Synthesis of Chemical Processes: Application to Reactor-Network Synthesis, AIChE Symposium Series (Eds: L. T. Biegler and M. F. Doherty), 91, (1995) 246. [5] Klemeš, F., Pierucci, S., Emission reduction by process intensification, integration, P-Graphs, micro CHP, heat pumps and advanced case studies, Applied Thermal Engineering, 28, (2008) 2005. [6] Halasz, L., A. B. Nagy, T. Ivicz, F. Friedler, L. T. Fan, Optimal Retrofit Design and Operation of the Steam-Supply System of a Chemical Complex, Applied Thermal Engineering 22, (2002) 939. [7] Liu, J., L. T. Fan, P. Seib, F. Friedler, and B. Bertok, Downstream Process Synthesis for Biochemical Production of Butanol, Ethanol, and Acetone from Grains: Generation of Optimal and Near-Optimal Flowsheets with Conventional Operating Units, Biotechnol. Prog., 20, (2004) 1518. [8] Heckl, I., Z. Kovács, F. Friedler, L. T. Fan, and J. Liu, Algorithmic Synthesis of an Optimal Separation Network Comprising Separators of Different Classes, Chemical Engineering and Processing, 46, (2007) 656. [9] Heckl, I., F. Friedler, and L.T. Fan, Reduced Super-structure for a Separation Network Comprising Separators effected by Different Methods of Separation, accepted for publication in Computers Chem. Engng. (2009).

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

647

Solving Nonlinear Problems with MILP Models Jose Barahona da Fonseca Department of Electrical Engineering, Faculty of Sciences and Technology, New University of Lisbon, Monte de Caparica, 2829-516 Caparica, Portugal, [email protected]

Abstract Although the author is an Electrical Engineer he got interested in optimization problems using the GAMS software. Rapidly he understood the limitations of the nonlinear solvers, like the necessity to have an initial feasible solution and the high probability of the solver being trapped in a local optimum and since 2004 he solved a set of complex nonlinear problems using MILP models. From the solution of the optimization of AGVs (Autonomous Guided Vehicles) Network [1] resulted techniques of implementation of logical functions over variables of the model only with algebraic expressions and the division of two model variables with the aid of auxiliary binary variables. From the solution of generation of optimal error correcting codes [2,9] resulted a first sketch of the automatic relaxation of a set of constraints, after improved in the solution of university timetabling with soft (that can be relaxed) and hard (that cannot be relaxed) constraints. We claim that our solution is the optimal solution to the well know problem of maximal constraint satisfaction. Finally from the solution of the generation of additive-multiplicative magic squares [3-5] resulted in a technique of multiplication of a set of variables of a MILP model. Obviously these latter techniques can be extended to implement any nonlinear operation over a set of variables of a MILP model. This way any nonlinear problem can be solved with a MILP model. This will guarantee that the solver reach always the global optimum even for a multimodal nonlinear problem. This way we solve an open fundamental problem in optimization theory: obtaining the global optimum for any multimodal nonlinear problem. Nevertheless the MILP model that solves the nonlinear problem can be too large and the computational resources can be not enough. Finally we propose new ways to implement nonlinear solvers based on meta-heuristics and Neural Networks, since our techniques require great computational resources for moderate size problems. Keywords: Implementing Any Nonlinear Function over a Set of Variables of a MILP Model, Automatic Relaxation of a Set of Constraints of a MILP Model.

1. Introduction In this work we try to summarize the new mathematical programming techniques that we created to solve nonlinear problems with MILP models during the last four years of intense work and that for our knowledge are original in the literature. We assume the reader knows the GAMS language syntax to simplify the formulation of constraints. Due to the limitations of nonlinear solvers we point as a possible evolution of our work the development of nonlinear solvers based on state of the art neural networks learning algorithms and metaheuristics optimization techniques.

2. Nonlinear Operations over a Variable in a MILP Model Although some previous works have implemented particular nonlinear functions over a variable in a MILP model [6], to our knowledge this is the first proposal of the implementation of a general solution to the implementation of any nonlinear function

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over a variable of a MILP model. Let’s assume we want to calculate a third degree polynomial in x in a MILP model. In the following we will assume the reader knows the GAMS syntax and we will present the constraints in a GAMS like style. First we have to create a binary variable x_bin(i_x), where the index i_x has at least as much values as the variable x, such that: constr1_x_bin.. ¦( i_x, x_bin(i_x) ) = 1 constr2_x_bin.. ¦ ( i_x, ord(i_x) x_bin(i_x) ) = x Now, since we can make nonlinear operations over an index, we can calculate the third degree polynomial with the following simple equation: calc_3d_pol.. p = ¦ ( i_x, ( w3 ord(i_x)3 + w2 ord(i_x)2 + w1 ord(i_x) + w0 ) x_bin(i_x) ) where w0..w3 are predefined scalars that define the third degree polynomial.

This approach although very simple and efficient has a major drawback: if the domain of x is very big we would have a very big MILP model. Another marginal drawback is the ‘zero problem’, i.e. if the x domain contains the value zero then it must be added a constant to x. If for example x is an integer variable then we must add 1 to x in constr2_x_bin constraint and subtract 1 to ord(i_x) in the calc_3d_pol constraint: constr2_x_bin2.. ¦ ( i_x, ord(i_x) x_bin(i_x) ) = x + 1 calc_3d_pol2.. p = ¦ ( i_x, ( w3 (ord(i_x)-1)3 + w2 (ord(i_x)-1)2 + w1 (ord(i_x)-1) + w0 ) x_bin(i_x) Nonlinear Operations over a Set of Variables in a MILP Model The first time we solve the problem of the calculation of a nonlinear function over a set of variables in a MILP model was about two years ago when we generate small multiplicative and additive-multiplicative magic squares [3-5] with a MILP model. Next we show how to calculate the product of the elements ( set of variables of the MILP model) of a line of the multiplicative magic square. qm is a binary variable in which the first two indexes correspond to the line and column and the third corresponds to the value of the element of the multiplicative or additive-multiplicative magic square. constr_l1(i).. ¦ ( (k1,k2,k3), line(i,k1,k2,k3) ) = 1 constr_l2(i,k1,k2,k3).. Order line(i,k1,k2,k3) ≤ qm(i,'e1',k1)+qm(i,'e2',k2)+qm(i,'e3',k3) constr_l3(i).. prod_line(i)= ¦ ( (k1,k2,k3), line(i, k1,k2,k3) ord(k1) ord(k2) ord(k3) ) This method can be easily extended to a greater number of variables and to more complex nonlinear functions. Note that the binary variable qm(i,j,k) means that the element of line i and column j has value ord(k). Note that in the following two constraints, the scalar Order=3: constr_l1(i).. ¦ ( (k1,k2,k3), line(i, k1,k2,k3) ) = 1; constr_l2(i,k1,k2,k3).. Order*line(i,k1,k2,k3) ≤ qm(i,'e1',k1)+qm(i,'e2',k2)+qm(i,'e3',k3) implement the logical AND of the binary variables qm(i,'e1',k1), qm(i,'e2',k2) and qm(i,'e3',k3).

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We could modify these two constraints to implement the logical OR over these binary variables: constr_l1(i).. ¦ ( (k1,k2,k3), OR(i, k1,k2,k3) ) = (Order-1) max_value (Order-1) constr_l2(i, k1,k2,k3).. OR(i, k1,k2,k3) ≤ qm(i,'e1',k1)+qm(i,'e2',k2)+qm(i,'e3',k3) assuming that each qm(i,j,k) is 1 for only one combination of the indexes (i,j,k). The (Order-1)max_value(Order-1) scalar in the first constraint results from the fact that it is enough that only one of the binary variables qm(i,'e1',k1), qm(i,'e2',k2), qm(i,'e3',k3) be 1 to result a 1 in the OR operation. The max_value scalar is the cardinal of the common domain of the k indexes. 2.1. Logical Implication Between Two Sets of Binary Variables The logical implication between two sets of binary variables, a(i) => b(i), can be implemented by an alternative simpler following set of constraints: a_implies_b(i).. a(i) ≤ b(i) since when a(i) is ‘1’ then b(i) must be ‘1’, but when a(i) is ‘0’, b(i) can be ‘0’ or ‘1’, which coincides to the logical implication function truth table. 2.2. Using Logical Implication to Obtain the Shortest Path in a Graph We did apply our solution of implementation of logical Implication to the generation of the shortest path in a given graph using a MILP model. To our knowledge this is the first published solution of the shortest path problem based on the logical implication function. In the following example, Path(i,j) is a binary variable that says that the directed arc (i,j) belongs to the shortest path. Node 1 is the origin node and 13 the destination node. The parameter dist(i,j) contains the distance between node i and j. We solve the problem of nonexistent arcs attributing to them a very high value of dist(i,j) such that when we minimize the distance d they are never considered. * any node that belongs to the Shortest Path must have a successor, except the destination node, *node 13 constr4_path(i,j) $( (ord(j) ne 13) and (ord(i) ne ord(j)) ).. Path(i,j) ≤ ¦ (k $ ( ord(k) ne ord(j)), Path(j,k) ) calc_d.. d = ¦ ( (i,j) , dist(i,j) Path(i,j) ) Next we will explain how the first set of constraints translates into a equivalent logical predicate. Saying that each node i that belong to optimal path must have a successor can be expressed in formal logic as N Path(j, i) Ÿ Node i Must Have a Successor ≡ ¦ Path(i,k) > .0 k =1, k ≠ i

The total distance will be the sum of the binary variable Path over all possible arcs (i,j) that define the graph.

3. Relaxation of a Set of Constraints by a Set of Binary Variables When we want to restrict the following set of constraints

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a_less_than_b(i).. a(i) ≤ b(i) to the instances where a another binary variable c(i) is ‘1’, we cannot write, in a linear model, a_less_than_b(i) $ (c(i) = 1).. a(i) ≤ b(i) but we can write an equivalent set of constraints a_less_than_b(i).. a(i) ≤ b(i) + ( 1-c(i) ) max_a_minus_b Note that 1-c(i) means the negation of the binary or logical variable c(i), and when c(i)=0 the scalar constant max_a_minus_b is added to b(i) which guarantees that the constraint is always true, even when a(i) > b(i). This is equivalent to restrict the constraint to the cases where c(i)=1, for which the constant is not added. If we want to restrict an equality constraint a_equal_to_b(i).. a(i) = b(i) to the cases where another binary variable c(i)=1, we can solve the problem with two sets of constraints: a_less_than_b(i).. a(i) ≤ b(i) + ( 1-c(i) ) max_a_minus_b a_greater_than_b(i).. a(i) + ( 1-c(i) ) max_a_minus_b ≥ b(i) which are equivalent to the restricted equality constraint a_equal_to_b(i) $ ( c(i) = 1 ).. a(i) = b(i) Simpler Equality Constraints Relaxation Based on the Indexes and on a Binary Variable In a work that we are just submitted to the IEEE Transactions on Information Theory [9] we impose the constraint of a constant weight w. The weight of a word is just the number of characters that are different from zero. In practical terms it is important to use constant weight codes because that implies a uniform power consumption in the coder and a uniform signal to noise ratio, and so a uniform probability of error in the transmission of all words. We only want to impose this weight constraint for words that belong to the code, i.e. for which the binary variable word(a1, .., an)=1. So the set of constraints that impose a weight w for a length 3 code is expressed in GAMS simplified syntax as Impose_w(a1,a2,a3)..word(a1,a2,a3)( (a1 ne 0)+(a2 ne 0)+(a3 ne 0) )=w word(a1,a2,a3) This is the most simple type of set of constraints relaxation by a binary variable that arises when we want to impose a set of equality constraints based on a computation over the indexes that define the set of constraints. 3.1. Automatic Relaxation of a Set of Constraints by a Set of Binary Variables

In some problems, like in university timetabling, there are sets of soft constraints with different priorities which can be relaxed, but we want to minimize the total number of relaxations. This can be done simply summing all binary variables associated to each set of soft constraints and multiplying this sum by a weight proportional to the

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relevance or priority of the set of soft constraints and finally summing these latter values to the objective variable, obj: Calc_obj1.. obj1 = ¦ (i, c1(i) ) Calc_obj2.. obj2 = ¦ (i, c2(i) ) Calc_obj.. obj_final = obj + w1 obj1 + w2 obj2

We applied these technique intensively in our work [10] where we make the university timetabling where there are hard constraints, constraints that cannot be relaxed, like a teacher cannot give two classes at the same time, a classroom cannot be occupied by two courses at the same time and soft constraints, like a teacher prefer to give classes in the afternoon. The main problem that we faced was the difficulty to make an hierarchy of soft constraints given more priority to a set than to another. We solved this problem given more weight to the sum of binary variables that control the relaxation of soft constraints with higher priority, but we recognize that this is not a satisfactory solution and in the near future we plan to apply evolutionary multiobjective algorithms to obtain the Pareto Front timetables and then apply a decision support algorithm to choose one timetable from the Pareto Front set of solutions. Next we show two hard constraints and two soft constraints. The GAMS primitive ord applied to an index gives the integer order of the value assumed by the index taking into account the set domain. * HARD CONSTR- in one room, s, d and h it can be only 1 discipline hard_constr_ocup_s(s,d,h).. ¦ ( (c,t,sg), ocupation(s,d,h,c,t,sg) )≤ ≤1 ; * Hard Constraint- 1 student Cannot Have More than 1 Class at the Same Time constr1_student(sg,d,h).. ¦ ( (s,c,t), ocupation(s,d,h,c,t,sg) Class_sg(sg,c))≤ ≤1; *Soft Constraint- IF POSSIBLE Prevent Classes in the End of the Day constr2_student(d).. ¦ ( (s,t,h,c,sg), ocupation(s,d,h,c,t,sg) Class_sg(sg,c) (ord(h)=h_max) ) ≤ 100 Relax_constr2_st(d); *Soft Constraint- IF POSSIBLE 1 Teacher Must Not Give Consecutive Classes constr7_class(c,s,s1,d,d1,h,h1,t,sg,sg1)$(ord(d)>ord(d1)).. 50Relax_dist_c(t,c,sg,sg1) + ocupation(s,d,h,c,t,sg)ord(d)-ocupation(s1,d1,h1,c,t,sg1)ord(d1)+ 50 (1-ocupation(s,d,h,c,t,sg)) + 50 (1-ocupation(s1,d1,h1,c,t,sg1))+ 50 (Teacher_hours(t,c)=0) ≥2 ; calc_obj.. obj=Flag_eq_h 100 aux_eq + ¦((c,sg),(n(c,sg)-Nhours_c(c)) ) + 5 ¦ ((t,c,p,sg),Category(t) Weights_pref(p) Relax_preference(t,c,p,sg)) + 5 aux3 + 5 aux4 + 50 aux5 + 1400 aux6 + 1350 aux61+ 1800 aux62 + 50 aux7 + 150 aux8 + 5000 aux9 + aux10 + aux11 + 1200 aux12 + 500 aux13 + 5 aux2_sg;

We claim that our automatic relaxation technique is the best solution to the very well know problem since 1990, the maximum constraint satisfaction problem, where we want to optimize one objective variable and simultaneously maximize the number of satisfied soft constraints. We also hope to show rigorously that our solution is the optimal solution to the constraint satisfaction problem.

4. Conclusions and Future Work The main conclusion of about the last four years of author’s mathematical programming experience is that mathematical programming tools have still a long way to go until we can solve real world linearized nonlinear problems with moderate computational resources using our linearization techniques. The main result of our paper is a general

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technique to solve any nonlinear problem with a MILP model. The main difficulty is that our linearization techniques turn the MILP model of a real world Nonlinear Problem too big to be solved by a PC. Nevertheless the author is very proud of having developed new techniques to linearize nonlinear problems that can be used by the mathematical programming community. The great difficulties of using nonlinear solvers, like the necessity of an initial feasible solution and the high probability of the solver being trapped in a local optimum points to the possible development of alternative nonlinear solvers based on neural networks and meta-heuristics. The great difficulty with the implementation of these solvers is to guarantee the same level of generality. For example, making solvers for meta-heuristics, in particular for Evolutionary Algorithms, implies the solution of two great problems: the automatic generation of good operators, which would only be possible using very sophisticated Artificial Intelligence techniques and the setting of the parameters, where there are already some results obtained in Fernando Lobo's PhD thesis [7]. Recently we applied our linearization techniques to the solution of the training of a hardlimit multilayer perceptron and obtained a three variable XOR with only three neurones [8]. We also made an experiment with the well known function sin(x)/x, x varying between 0 and 120π, x initialised in 120π, and in few seconds our adapted MILP model converged to the global maximum of 1 at x→0+. Based on these latter experiments we will try to improve our linearization techniques such that we can solve bigger Nonlinear Problems with MILP models.

References [1] J. Barahona da Fonseca, “From the Magic Square to the Optimization of Networks of AGVs and from MILP to an Improved GRASP like Optimization Algorithm”, in Proceedings of CIMCA 06, IEEE Conference on Computational Intelligence for Modelling, Control and Automation, 181-186, 2006, available at IEEE Xplore database. [2] J. Barahona da Fonseca, “Code Design as an Optimization Problem: from MILP to an Improved High Performance Randomized GRASP like Algorithm”, in Proceedings of Escape-17, V. Plesu and P. S. Agachi (Eds), 279-284, 2007. [3] N. N. Horner, “Addition-Multiplication Magic Squares”, Scripta Math., 18, 300-303, 1952. [4] N. N. Horner, “Addition-Multiplication Magic Squares of Order 8”, Scripta Math., 21, 23-27, 1955. [5] J. Barahona da Fonseca, “The Magic Square as a Benchmark”, International Journal of Computing Anticipatory Systems, Vol. 18, 27-33, CHAOS, 2006. [6] T. Koch, Rapid Mathematical Programming, PhD thesis, Technische Universität Berlin, 2004. [7] F. Lobo, The Parameter Less Genetic Algorithm, PhD thesis, New University of Lisbon, 2000. [8] J. Barahona da Fonseca, “Training Hardlimit Multilayer Perceptrons with a MILP Model”, paper submitted to ESANN 2009 conference. [9] J. Barahona da Fonseca, “Generating Optimal Ternary Constant Weight Codes with a MILP Model”, paper submitted to the IEEE Transactions on Information Theory. [10] J. Barahona da Fonseca, “Generating University Timetables with a MILP Model”, in Proceedings of Controlo 08, University of Tras-Os-Montes, Vila Real, Portugal, 2008.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Steady-state constrained optimisation for input/output large-scale systems Ioannis Bonis and Constantinos Theodoropoulos* School of Chemical Engineering and Analytical Science, The University of Manchester, Sackville Street, PO Box 88, Manchester M60 1QD, UK.

Abstract A model reduction-based, constrained optimisation algorithm for large-scale, steadystate systems is presented. The proposed technique belongs to the reduced Hessian class of methods and involves only low-order Jacobian and Hessian matrices. The reduced Jacobians are computed as projections onto the dominant subspace of the system and are calculated adaptively by numerical directional perturbations. The reduced Hessians are computed the same way, based on a 2-step projection scheme, firstly onto the dominant subspace of the system and secondly onto the subspace of the independent variables. The inequality constraints are handled using constraint aggregation functions. A more efficient version of the proposed algorithm is also presented. The behaviour of the proposed scheme is illustrated through two illustrative case studies including both equality and inequality constraints. Keywords: model reduction, dominant subspace, reduced Hessian, two-step projection.

1. Introduction The optimisation of complex industrial systems is based on models, typically consisting of sets of Partial Differential Equations (PDEs) which are discretized over a computational grid, leading to large-scale systems which can be solved using direct or iterative methods, the latter being more efficient as the size of the system increases. The simulator delineated may either be open source or input/output (e.g. commercial). There are two trends in process design: exploiting the existing detailed simulator for optimisation, or using a simplified process model. The former approach yields, obviously, more accurate results. Deterministic [1], or stochastic/meta-heuristic methods may be applied, the latter being more suitable for moderate-sized problems [2], as they typically include a large number of function evaluations. On the other hand, deterministic methods have increased CPU and memory requirements hence, their application to large-scale systems is often problematic/unrealistic especially in the case of black-box simulators. We have recently developed a model reduction-based framework for steady-state [3] and dynamic [4] optimisation using input/output dynamic simulators, as well as steadystate simulators [5]. Here, we further extend the latter work by considering inequality constraints and modifying the existing scheme to reduce computational cost. The performance of the proposed algorithm is demonstrated through illustrative case studies.

*

Corresponding author, e-mail: [email protected].

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2. The proposed algorithm We consider the following optimisation problem: L U min f (x) s.t. G (x) = 0 and x ≤ x ≤ x

(1)

x

Where f : ℜn + dof → ℜ is the objective function, x ∈ ℜ n + dof is the joint vector of the dependent ( u ∈ ℜn ) and independent ( z ∈ ℜdof ) variables:

x T = [u T

zT ] and

G ∈ ℜn × ℜ dof → ℜn is twice differentiable. The solution of the equality constraints is found using a black-box simulator. A well known method that handles such optimisation problems is Sequential Quadratic Programming (SQP). This is equivalent to solving the KKT conditions with the Newton – Raphson method. In every iteration, a QP subproblem is solved:

1 T T T L U min d Bd + ∇f (x k ) d, s.t. ∇G (x k ) d = −G (x k ) , (x − x) ≤ d ≤ (x − x) d 2

(2)

B ∈ ℜ( n + dof )× ( n + dof ) is the Hessian of the Lagrangian and d the search direction, d ∈ ℜn + dof . If the number of decision variables is small, reduced Hessian methods are more appropriate [6]. These methods, however, involve the construction and inversion of Jacobians, so they are expensive for large systems. Especially if the simulator at hand is a black-box, Jacobians are not available, or not even fully computed if advanced iterative linear algebra methods are employed. To address these issues, we propose a scheme using a reduced Jacobian, H. Let P be the invariant subspace of the dominant modes of the system, corresponding to the m right-most eigenvalues. In many engineering systems, m << n. A basis for this subspace Zˆ ∈ ℜnxm ,can be computed using subspace iterations, which do not require the Jacobian to be explicitly provided. The reduced Jacobian is given by:

H = Zˆ T G u Zˆ

(3)

Following reduced Hessian methods, we decompose the search direction in two subspaces: the null space of the constraints and its complement, with bases:

ª − H −1 Zˆ T ∇ z G T º ªI º Zr = « », Y = « » I ¬0¼ ¬« ¼»

(4)

Thus, a basis for the subspace of the independent variables can be computed from a 2step projection scheme:

ª − ZˆH −1 Zˆ T ∇ z G T º ª Zˆ 0 º ª −H −1 Zˆ T ∇ z G T º * Z=« »=« » ⇔ Z = Zˆext Z r »« I I «¬ »¼ «¬ 0 I »¼ «¬ »¼

(5)

Hence, the QP subproblem of Eq. 2 becomes: T 1 T T T T L U min Z ∇f + Z BYpY p z + p z Z BZ p z s.t. (x − x) ≤ YpY + Zp Z ≤ (x − x) (6) pz 2

(

)

(

)

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Z T BZ = BR ∈ ℜ dof × dof is the reduced Hessian, BR, and can be computed through numerical directional perturbations. Estimates of the Lagrange multipliers can be computed from: Y T BYpY + Y T BYp Z + Y T ∇Gλ = −Y T ∇f

(7)

The term pY is negligible if feasible points are calculated at each iteration [7]. The proposed algorithm is depicted in Table 1. Table 1. The proposed algorithm 1.

Choose initial guesses for x0 and B0

2.

Compute the steady state using the black-box simulator and evaluate x, f , ∇f , Zˆ , H

3.

ª − ZˆH −1Zˆ T ∇ z G T º Compute the basis Z : Z = « » I «¬ »¼ ˆ Calculate the reduced Hessian, B , using Z

4.

T

R

(

)

T

6.

Solve the QP subproblem: min Z T ∇f z p z + 1 2 p zT BR p z s.t. (x L − x) ≤ Zp Z ≤ (xU − x) pz Update Zˆ , H and calculate an estimate of the Lagrange multipliers: Hφ = − Zˆ T Y T ∇f

7.

Update the solution: x = x + Zp Z

8.

Check for convergence. If convergence is not achieved go to (2).

5.

3. A computationally efficient modification To compute an estimate of the Lagrange multipliers for the next iteration, one needs to update the basis Z. However, computing the dominant subspace is the most expensive step of the algorithm. To reduce the number of basis computations we make the assumption that the basis calculated after the QP step is a good approximation of the basis at the corresponding feasible point. This way Z is updated once per step and the the calculation of the Lagrange multipliers (step 6) can be moved to the next iteration, after step 2. This assumption incurs loss of accuracy. Hence, in practice we suggest the use of the modified version for the first few iterations reverting to the original version in the vicinity the optimum, where the cost for updating Z is small.

4. Handling inequality constraints We consider the optimisation problem including inequality constraints: L U min f (x) s.t. G (x) = 0 , H (x) ≤ 0 and x ≤ x ≤ x

(8)

x

Here, we adopted an approach based on a Constraint Aggregation function [8]. The KS function aggregates all inequality constraints and replaces them with a single one. The two equivalent forms of the KS function are:

KS ( H j ) =

1

(

)

J ln ª ¦ j =1 exp ρ H j º or ¬ ¼ ρ

KS ( H j ) = M +

1

(

)

J ln ª ¦ j =1 exp ρ ( H j − M ) º (9) ¬ ¼ ρ

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Where M § max(Hj). We can further eliminate all inequality constraints by modifying the objective function to incorporate the KS function. In our formulation we use a projection of the KS function onto the dominant subspace. This incurs little extra cost to the overall optimisation, as the most expensive step, the calculation of the basis, is left unmodified. It is worth mentioning that it is beneficial for the convergence of the algorithm, that the variables used in the KS function are scaled. That also simplifies the selection of the parameters ρ and M.

5. Case studies 5.1. Optimisation of a tubular reactor To illustrate the features of our proposed algorithm, we apply it to the case of a tubular reactor with axial dispersion, where an elementary first order irreversible exothermic reaction takes place: A → B [9]. The problem is described two nonlinear PDEs, which in dimensionless steady-state form, are:

§ x2 · 1 ∂ 2 x1 ∂x1 − + Da (1 − x1 ) exp ¨ ¸=0 2 Pe1 ∂y ∂y © 1 + x2 γ ¹

(10)

§ x 2 · β x2 w C 1 ∂ 2 x 2 1 ∂x 2 β x2 + − − =0 Da(1 − x1 ) exp ¨ ¸+ 2 LePe2 ∂y Le ∂y Le Le Le © 1 + x2 γ ¹

Here x1 and x2 are the concentration and temperature, Da the Damköhler number and y the dimensionless longitudinal coordinate. The boundary conditions are:

∂x1 − Pe1x1 = 0, ∂y

∂x 2 − Pe2 x 2 = 0 at ∂y

y =0,

∂x1 = 0, ∂y

∂x 2 = 0 at ∂y

y =1

(11)

The values of the parameters were Le = 1.0, Pe1 = Pe2 = 5.0, Ȗ = 20.0, ȕ = 1.50, C = 12.0, Da = 0.1. The PDEs were discretized using central Finite Differences, with 250 nodes, resulting in a system of 500 algebraic equations. We consider 3 cooling zones along the reactor, whose temperatures (x2w) can be controlled independently. The objective is to maximise the exit concentration from the reactor subject to the model being satisfied:

max x1 exit x2 wi

s.t. F1 = 0,

F2 = 0,

0 ≤ x1 k ≤ 1, 0 ≤ x1 k ≤ 8, 0 ≤ x2 w j ≤ 8 k ∈ Ω, j ∈ {1, 2,3}

(12)

where x2w ( y ) = ¦ j =1 ª¬ H ( y − y j −1 ) − H ( y − y j ) º¼x2w j , y1 = 1/3, y2 = 2/3 and y3 = 1. J

The previous optimisation problem can be augmented to include also inequality constraints. A new problem can now be formulated as: max x1 exit x2 wi

s.t. F1 = 0, and

F2 = 0, 0 ≤ x1 k ≤ 1, 0 ≤ x1 k ≤ 8, k ∈ Ω, also ( x2 k + x2

) 2 ≤ 160, k ∈ J = {125, ,130} k +1

(13)

5.2. Optimisation of a counterflow jet reactor To illustrate the efficiency of the proposed scheme in handling truly large-scale optimisation problems, we have applied it to the case of a counterflow jet reactor used

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for the decomposition studies of tertiary butyl arsine (TBA) [10]. The reaction mixture is heated with the input of hot carrier gas from the bottom and TBA is decomposed to arsine (AsH3) and AsH. A schematic of the reactor and the corresponding operating conditions can be seen in Fig.3. The system was simulated using the state-of-the-art, massively parallel CFD software MPSalsa, developed at SANDIA National Laboratories [11]. This is an implementation of the Finite Element method, employing unstructured meshes and inexact Newton methods with iterative linear solvers. MPSalsa was handled by our optimisation code as black box. The model consists of 19040 dependent variables (temperatures, pressures, velocities and concentrations). Here we consider maximization of the yield of AsH which implies maximal decomposition of TBA and at the same time minimal production of the highly toxic byproduct arsine, with respect to the velocity of the upper stream.

6. Results and discussion 6.1. Case Study I The size of the dominant subspace chosen was m=10. Convergence was achieved in 10 iterations. The corresponding convergence curve can be seen in Fig. 1. The optimal yield found was 99.87%, for x2w,1 = 2.483, x2w,2 = 0.5254, and x2w,3 = 4.000, as can be seen in Fig.2. The computational gain from implementing the improved version of the algorithm was 13.4%, which makes it 292% faster Figure 1: Convergence curve (Case I) than the conventional reduced Hessian method in this case. If we also consider the inequality constraints, convergence is achieved in 12 iterations. The optimal yield found was 99.32%, for x2w,1 = 1.7915, x2w,2 = 0.000, and x2w,3 = 0.000.

Figure 2: Solution profiles at the optimum for concentrarion (a) and temperature (b)

6.2. Case Study II In the case of the optimisation of the counter flow jet reactor, convergence was achieved in 8 iterations. The optimal yield found was 80.34%, which corresponds to an optimal velocity of 0.8193cm/s for the upper jet. Solution profiles are depicted in Fig. 3.

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Figure 3: Schematic representation of the counterflow jet reactor (a) and solution profiles at the optimum for temperature (b) and concentrations of TBA (c), arsine (d) and AsH (e).

7. Conclusions A model reduction-based constrained optimization framework for black-box steady state simulators has been presented. It can be considered as an extension of Reduced Hessian methods. Only low-order Jacobians and Hessians are needed, which are calculated with directional numerical perturbations. The proposed algorithm features a 2-step projection scheme; first onto the dominant system subspace, adaptively computed through subspace iterations, and second onto the subspace of the decision variables. Inequality constraints are handled using KS functions with minimal additional computational cost. A modified version that enhances efficiency has also been presented. Two case studies were used to illustrate the capabilities of the algorithm.

Acknowledgements: The financial contribution of the EU Programmes CONNECT COOP-2006-31638 and CAFE KBBE-2007-1-212754 is gratefully acknowledged.

References [1] T.F. Edgar, D.M. Himmelblau, 1988, Optimization of Chemical Processes, McGrawHill, NY [2] C. Blum and A Roli, 2003, Metaheuristics in Combinatorial Optimization: Overview and Conceptual Comparison, ACM Computing Surveys, 35: 268-308. [3] E. Luna-Ortiz and C. Theodoropoulos, 2005, An input/output model reduction-based optimization scheme for large-scale systems, Multiscale Modeling & Simulation 4: 691708. [4] C. Theodoropoulos and E. Luna-Ortiz, 2006, A Reduced Input/Output Dynamic Optimisation Method for Macroscopic and Microscopic Systems, in Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena, A. Gorban et al (eds) pp. 535-560. [5] I. Bonis and C. Theodoropoulos, 2008, A model reduction-based optimisation framework for large-scale simulators using iterative solvers, Computer Aided Chemical Engineering 25:545-550. [6] L.T. Biegler, J. Nocedal and C. Schmidt, 1995, A Reduced Hessian Method for LargeScale Constrained Optimization, Siam Journal on Optimization 5: 314-347 [7] J. Nocedal and M. L. Overton, 1985, Projected Hessian updating algorithms for nonlinearly constrained optimization, SIAM Journal of Numerical Analysis, 22: 821-850. [8] C.G. Raspandi, J.A. Bandoni, L.T. Biegler, 2000, New strategies for flexibility analysis and design under uncertainty, Comput. Chem. Eng. 24: 2193-2209. [9] K. F. Jensen and W. H. Ray, 1982, The Bifurcation Behavior of Tubular Reactors, Chemical Engineering Science 37: 199-222. [10] Safvi, S.A. and T.J. Mountziaris, A new reactor for purely homogeneous kinetic studies of endothermic reactions, AIChE Journal, 1994. 40: 1535-1548. [11] Shadid, J, et al, Efficient parallel computation of unstructured finite element reacting flow solutions, Parallel Computing 1997, 23: 1307-1325.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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The optimal design of heat exchanger networks considering heat exchanger types Georg Fieg a, Xi-Ru Hou b, Xing Luo a,b, Hu-Gen Ma b a

Institute of Process and Plant Engineering, Hamburg University of Technology, D21071 Hamburg, Germany, [email protected] b Institute of Thermal Engineering, University of Shanghai for Science and Technology, 200093 Shanghai, China, [email protected]

Abstract A hybrid genetic algorithm for the optimization of heat exchanger networks (HEN) considering the heat exchanger types is developed. The algorithm is based on an analytical solution of the stream temperatures. The heat capacity flow rates of hot and cold streams and the heat transfer parameter (the product of the correction factor of logarithmic mean temperature difference F, the overall heat transfer coefficient k and the heat transfer area A) of each heat exchanger in the HEN are taken as the decision variables to be optimized. With this method, the investment and utility costs can be calculated separately in a user subroutine where the specificities of heat exchangers can be easily taken into account. An example from literature is used to illustrate the procedure, and better optimization results are obtained. Keywords: heat exchanger network, heat recovery system, hybrid genetic algorithm, optimization

1. Introduction In the past three decades, extensive efforts have been made in the fields of energy integration and heat recovery technologies because of the steadily increasing energy cost and more rigorous CO2 discharge limitations. One of the most active subjects is the synthesis of heat exchanger networks (HENs). By the use of HEN in a heat recovery system, large amounts of hot and cold utilities as well as the investment costs can be reduced. The well known approaches to HEN synthesis are the pinch method [1], mathematical programming [2] and stochastic or heuristic algorithms such as genetic algorithm [3-4], genetic/simulated annealing algorithm [5] and tabu search procedure [6]. A review of the early work on the grassroot and retrofit design of HEN was given by Jezowski [7-8]. Recently, Chen et al. [9] developed a new hybrid genetic algorithm for HEN synthesis based on the explicit analytical solution of the stream temperatures in HENs, which ensures the feasibility of randomly produced individuals and enhances the search ability of the genetic algorithm in both structure and continuous parameters. This method can also be applied to the optimal design of HENs with multiple types of heat exchangers. The example given by Hall et al. [10] was used to test the present

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procedure. The calculations dealt with different types and materials of heat exchangers and for each case a better HEN configuration was found.

2. Mathematical model The HEN synthesis problem can be stated as follows: Given are Nh hot process streams, Nc cold process streams, hot utilities HU and cold utilities CU. Specified are heat capacity flow rates W and the supply and target temperatures of process streams. Given also are the temperature levels and costs of the hot and cold utilities, the types, costs and overall heat transfer coefficients of heat exchangers, heaters and coolers. Determine the configuration of the HEN and the values of heat transfer areas and heat capacity flow rates of each heat exchanger in the HEN which bring the total annual cost of the HEN to the minimum. The stage-wise superstructure HEN proposed by Yee et al. [11] is used in the HEN synthesis. However, the restriction of isothermal mixing used in their model is rescinded in the present model. To deal with different types of heat exchangers, we introduce the correction factor of the logarithmic mean temperature difference F into the analytical temperature solution of the HEN given by Chen et al. [9]. Then the analytic temperature solution is valid not only for counterflow heat exchangers but also for other exchanger types. the objective function of the optimization can be expressed as:

C = ¦ CE,m + ¦ C U ,n m

(1)

n

in which CE is the cost of an exchanger, which is usually a function of heat transfer area A:

CE,m = f E,m ( AE,m )

(2)

In the practical cases it could also depend on the type and material of the exchanger and design and operation restrictions. In such cases the cost function fE,m can be specified by the corresponding heat exchanger index m. CU represents the utility cost including the heaters and coolers. It can be determined by the

CU ,n

− − ­CHUW n (tOUT ′′ t n′′ < tOUT ,n − t n ) + f HU,n ( AHU ,n ), ,n ° − + ′′ tOUT t = ®0, < n < t OUT ,n ,n °C W (t ′′ − t + ) + f ( A ), t ′′ > t + n CU, n CU ,n OUT ,n ¯ CU n n OUT ,n

(n = 1, 2,  , N h + N c )

(3)

+ − where tOUT and tOUT are the upper and lower bounds of the target stream temperatures, and CHU and CCU the hot and cold utility costs per unit duty, respectively. The costs of heaters and coolers are calculated according to the stream index n and the required heat transfer areas AHU,n and ACU,n,

AHU ,n =

− ′′ Wn (tOUT ,n − t n )

( Fk ) HU ,n Δt m HU ,n

(4)

The Optimal Design of Heat Exchanger Networks Considering Heat Exchanger Types

ACU ,n =

+ W n (t n′′ − tOUT ,n )

( Fk ) CU ,n Δt m CU ,n

661

(5)

in which Δt m is the logarithmic mean temperature difference. The exit stream temperatures of the HEN (before the heaters and coolers) t n′′ are obtained by the analytic temperature solution. For a given stage-wise superstructure, they are function of Wh , m , Wc,m and (FkA)m of the heat exchangers in the HEN. Their optimal values are determined by the hybrid genetic algorithm which bring the total annual cost of the HEN (Eq. (2)) to the minimum. For a known value of (FkA), the correction factor F and overall heat transfer coefficient k can be calculated according the known heat capacity flow rates and stream temperatures as well as the heat exchanger types and design and operation restrictions. Then, the heat exchanger costs can be calculated. If the calculated temperature can not be reached by the given types of heat exchangers, the correction factor should be zero, i.e., an infinite large heat transfer area were required. The genetic algorithm will eliminate such designs automatically.

3. Example The example is taken from [10] and the problem data are listed in Table 1. The optimal design is carried out for 6 cases. It is assumed that the heat transfer coefficients are constant and do not depend on the exchanger type. In [10] it is implied that the cold utility cost depends only on the heat duty and therefore the outlet temperature of the cooling water is equal to its inlet value. It is not realistic. However, for comparison, this assumption is still used in the present design, as well as the assumption of counterflow type ( F = 1 ). Case 1: All heat exchangers including heaters and coolers are carbon-steel shell-andtube ones (CS). Hall et al. [10] used the Pinch method to optimise the problem and obtained a HEN with 14 units. According to the network configuration in Fig. 4a of [10], the total annual cost is 3.169 × 106 $/yr. Using the present genetic algorithm, we obtained a HEN with ten units and the total annual cost reduces to 3.117 × 106 $/yr, as is shown in Fig. 1. Case 2: Titanium shell-and-tube heat exchangers (TI) are used in the HEN. The optimization with the hybrid genetic algorithm yields the total annual cost of 5.864 × 106 $/yr ( 5.988 × 106 $/yr according to Fig. 4b of [10]). The HEN consists of six exchangers (H1C1a, H3aC1b, H3bC2, H4C4, H5C3, in which the subscripts a and b indicate stream splits.), three heaters for C2, C3 and C4, and two coolers for H1 and H2. Case 3: Titanium is selected for H4, H5, C1 and C2, and carbon-steel for other streams. The total annual cost of the present work is 4.148 × 106 $/yr ( 4.39 × 106 $/yr in [10]). The HEN consists of seven exchangers (TI: H5C1, H5C2a, H4C2b; CS: H1C4, H2C3, H3C3, H3C4), three heaters for C2 (TI/CS), C3 (CS) and C4 (CS), and three coolers for H1 (CS), H2 (CS) and H4 (TI/CS). Case 4: Only the plate-and-frame heat exchangers are used in the HEN. The total annual cost of the present work is 4.238 × 106 $/yr ( 4.25 × 106 $/yr according to Fig. 11 of [10]).

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Table 1. Problem data

Stream data tOUT (°C) h (kW/m2K) Stream t ′ (°C) W (kW/K) H1 120 65 50 0.50 H2 80 50 300 0.25 H3 135 110 290 0.30 H4 220 95 20 0.18 H5 135 105 260 0.25 C1 65 90 150 0.27 C2 75 200 140 0.25 C3 30 210 100 0.15 C4 60 140 50 0.45 HU (steam) 250 250 0.35 CU (cooling water) 15 15 * 0.20 Cost data Shell-and-tube, plant life = 6 yr, capital interest = 10% per annum Carbon-steel (CS) Cost ($) = 30,800 + 750 A0.81 (m2) Titanium (TI) Cost ($) = 30,800 + 4,470 A0.81 (m2) CS/TI or TI/CS Cost ($) = 30,800 + 3,349 A0.81 (m2) Plate-and-frame Cost ($) = 1,950 A0.78 (m2) Spiral Cost ($) = 19,687 A0.59 (m2) Plant life = 6 yr, capital interest = 16% per annum Annual cost of hot utility per unit duty = 120 ($/kWyr) Annual cost of cold utility per unit duty = 10 ($/kWyr) * Note: This value is estimated according to the design results of [10]. The HEN consists of seven exchangers (H1C1a, H5aC1b, H5bC3, H4C4a, H3aC4b, H3bC2, H2C3), two heaters for C2 and C3, and two coolers for H1 and H2. Case 5: Only the spiral heat exchangers are used in the HEN. The total annual cost of the present work is 6.788 × 106 $/yr ( 7.4 × 106 $/yr according to Fig. 12 of [10]). The HEN consists of five exchangers (H1C1a, H3aC1b, H3bC2, H4C4, H5C3), three heaters for C2, C3 and C4, and two coolers for H1 and H2. Case 6: Spiral heat exchangers should be used for H3 or C2, and plate-and-frame heat exchangers are used if the streams are not H3 or C2. The total annual cost of the present work is 5.021× 106 $/yr ( 5.20 × 106 $/yr in [10]). The HEN configuration is shown in Fig. 2.

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Fig. 1. Optimal heat exchanger network configurations with carbon-steel shell-and-tube heat exchangers (3,116,625$/yr).

Fig. 2. Optimal heat exchanger network configurations with spiral heat exchangers (SP) for H3 or C2 and plate-and-frame heat exchangers (PF) for other matches (5,020,606$/yr).

4. Conclusions A hybrid genetic algorithm is developed for the synthesis of HEN considering heat exchanger types. By taking the heat transfer parameter (FkA) and heat capacity flow rates W h and Wc as the decision variables in the analytical temperature solution, the costs of the heat exchangers can be calculated separately in a user subroutine, therefore, it is easy to deal with different kinds of heat exchangers in the optimization. An example taken from literature is used to illustrate the procedure and better design results are obtained.

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5. Acknowledgements The present research was supported by the Innovation Program of Shanghai Municipal Education Commission (No. 07ZZ89).

References [1] B. Linnhoff, D.R. Mason and I. Wardle, Comput. Chem. Eng., 3 (1979) 295. [2] I.E. Grossmann and R.W.H. Sargent, Comput. Chem. Eng., 2 (1978) 1-7. [3] D.R. Lewin, H. Wang and O. Shalev, Comput. Chem. Eng., 22 (1998) 1503. [4] D.R. Lewin, Comput. Chem. Eng., 22 (1998) 1387. [5] H.-M. Yu, H.-P. Fang, P.-J. Yao and Y. Yuan, Comput. Chem. Eng., 24 (2000) 2023. [6] B. Lin and D.C. Miller, Comput. Chem. Eng., 28 (2004) 1451. [7] J. Jezowski, Hung. J. Ind. Chem., 22 (1994) 279. [8] J. Jezowski, Hung. J. Ind. Chem., 22 (1994) 295. [9] D.-Z. Chen, S.-S. Yang, X. Luo, Q.-Y. Wen, H.-G. Ma, Chinese J. Chem. Eng. 15 (2007) 296. [10] S.G. Hall, S. Ahmad and R. Smith, Comput. Chem. Eng., 14 (1990) 319. [11] T.F. Yee, I.E. Grossmann and Z. Kravanja, Comput. Chem. Eng. 14 (1990) 1151.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Towards Dynamic Conceptual Design Roberto Granaa, Flavio Manentia and Davide Mancaa a

CMIC Department “Giulio Natta”, Politecnico di Milano Piazza Leonardo da Vinci, 32, 20133, Milano, ITALY, [email protected]

Abstract This paper deals with the definition and the application of a novel approach to process design. As it was originally conceived, the conceptual design (CD) of industrial processes [1] looks for the optimal solution among different alternatives within a given superstructure [2] once raw materials, output specifications, prices, and costs are defined. Such an approach may sometimes identify suboptimal solutions since it does not consider the time-dependency of prices and market volatility, which can strongly affect the optimal solution. Based on the market dynamics, a new approach to CD focused on the dynamic attribute is formulated. A simple application is also provided. Keywords: Superstructures, MINLP, Time-dependent design, Market volatility

1. Introduction The optimization of chemical and industrial processes is a multifaceted problem that involves several issues. Some of them are nowadays well understood and fully implemented, whereas others are still not and they deserve further attention since they are open issues for both scientific and industrial communities. For instance, process optimization is fast moving from off-line to on-line application and from steady-state product optimization to real-time dynamic optimization. Some authors [3-4] discussed how integrate the CD activity, with market uncertainties and dynamic optimization. This manuscript tries to make a further step by addressing and discussing the process design optimization in terms of conceptual design [1]. CD deals with an optimization problem where specific superstructures are chosen according to some criteria [2]. A superstructure summarizes a few process alternatives that are selected by corresponding sets of Boolean/integer variables. The CD procedure cuts off the suboptimal equipment layouts while identifying the best one according to economical, environmental, and safety criteria. Often, the problem is a multi-objective optimization where continuous variables and geometric specifications are mixed with integer and Boolean variables. Nevertheless, the classic conceptual design is a steady-state problem, based on fixed costs and prices. Conversely, this paper focuses on the dynamic evolution of the market (e.g. energy costs, raw material prices). By doing so, the process layout derived by the steady-state approach of conventional CD can strongly differ from the solution of a dynamic conceptual design (DCD).

2. Mathematical Formulation Usually, the mathematical formulation of conventional CD is a mixed-integer linear or nonlinear programming (either MILP or MINLP), where continuous process variables and geometric specifications are mixed with integer and Boolean variables. The problem can be formulated as follows:

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min Φ ( x, y ) x, y

s.t. h ( x, y ) = 0

(1)

g ( x, y ) ≤ 0

where Φ is the economic objective function, involving both investment and operating costs; x ∈

n

are the continuous (process) variables; y ∈ {0,1}

m

are the discrete

variables. Constraints h, g describe the material and energy balances, as well as the lower and upper bounds of the degrees of freedom. Some authors discussed in the literature [5-7] the influence of price fluctuations and uncertainty of markets on the objective function but at our knowledge a specific contribute on dynamic allocation of process resources and plant subsections is still missing. For this reason, we chose to introduce the dynamic attribute into the CD framework so to evaluate the economic feasibility of installing simultaneous and distinct process sections devoted to specific duties (e.g. inlet stream process-to-process preheating, electric energy production). The theoretical framework is then focused on balancing the dynamic use of distinct process subsections according to periodic cost/price fluctuations/uncertainties during the design activity. The dynamic approach to conceptual design, i.e. DCD, goes beyond the conventional CD approach. Actually, DCD is not limited to the steady-state optimum search of the best process design that allows achieving the maximum profit by considering a nominal (assigned a priori) product capacity. DCD can address the coexistence of more than a single structure (belonging to the original superstructure) so to maximize the plant profit based on a dynamically changing economic horizon. Actually, the process can account for dynamic price fluctuations by changing its operating configuration/layout (e.g. dynamically switching from a production subsection to another one). In other words, let us consider the energy market. It involves a number of fluctuations (e.g. daily, weekly, and seasonal fluctuations). Industrialized countries are characterized by high daytime prices of electric energy and low prices at night and during weekends. It often happens that a specific process layout is the best one throughout the day, whereas another one performs better at night. This solution unavoidably requires an increase in the capital investment (i.e. more coexisting plant subsections), but the breakeven point may occur earlier and the overall return on investment may be higher. In order to prove this statement, we performed a detailed non-linear simulation of the hydrodealkylation process [1], which it usually belongs to industrial sites for oil refining, and we implemented a straightforward superstructure (one Boolean variable), which produces a time-dependent MINLP problem.

3. Case Study The industrial case study focuses on the layout optimization of the toluene hydrodealkylation to benzene process [1]. It consists mainly of a reaction zone and of a separation section. Fresh hydrogen (H2) and toluene (C7H8) are preheated and fed to a plug flow reactor to produce benzene (C6H6). The reactor geometry must be optimized to improve the yield in benzene while reducing biphenyl (C12H10) which is a byproduct. The outlet flowrate from the reactor is first quenched and then fed to the distillation section to separate the incondensables, C6H6, and the low volatile components (C7H8 and C12H10). A gaseous H2 (and CH4) stream and a liquid C7H8 stream are both recycled

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to the reaction zone. A fraction of the gaseous recycle stream is purged to avoid possible holdups. 3.1. The Boolean Logic The aforementioned process simulation comprises also a discrete logic portion to describe the DCD problem. The superstructure is modeled and defined within the process simulation. This is made feasible by introducing auxiliary flow mixers and splitters while defining the following constraints:

¦

N

Y ⋅F =1

(2)

i =1 i

where Yi is a Boolean variable, Fi is a normalized process flowrate and N are the available alternatives. By doing so, only one alternative can be activated at a time, together with its corresponding flowrate, and this is the most appealing respect to the objective function, whereas the other solutions are automatically removed by the optimizing procedure. However, Boolean nodes cannot be placed everywhere within the process layout, since there could be some process limitations and the number of configurations would increase exponentially with the number of decisional variables. For the sake of brevity, it is not possible to describe exhaustively the whole case study. E-7

Compressor

Purge

H2 Toluene

FEHE Furnace

Reactor

Flash

Y=0

Products Purge

Compressor

H2 Toluene

FEHE Furnace

Reactor Steam Turbine

Y=1 Flash Products

Figure 1. Alternatives for the process layout: feed effluent heat exchanger (top) and electric production section (bottom). Dashed-dot line: night-time, dashed line: day-time.

Figure 1 shows only the reaction zone of the plant (reactor, flash drum, gas recycle compressor, heat exchangers, and surge line) and only one Boolean variable is adopted. The reader could correctly argue that the one-Boolean-variable problem can be made explicit and transformed into two distinct CD problems to be compared in terms of overall economic convenience. However, for the sake of completeness, we chose to express the question in terms Boolean variables and mixed-integer problem so to generalize the theoretical treatment. Actually, the same DCD framework can be applied

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to industrial processes that are much more complex (i.e. comprising a large number of discrete variables). The simplified superstructure of DCD (as reported in Figure 1) consists of two alternative layouts, both capable of exploiting the enthalpy content of the outlet stream from the reactor. Layout (i) preheats the flowrate entering the reactor by means of a feed effluent heat exchanger. Layout (ii) generates electric energy by means of a dedicated plant subsection. These layout alternatives are activated by the Boolean variable Y . At design time, Y allows switching dynamically between the alternative and possibly coexisting layouts. Actually, it gives the opportunity to design the process with a new additional section (i.e. electric power section). For the sake of clarity, scenario Y = 1 accounts for the time dependency of DCD where according to daytime and nighttime price fluctuations the process may switch from power generation to FEHE layouts (and vice versa). In addiction, a few continuous variables xi are introduced in the process simulation: DADI is the diameter of the adiabatic reactor; S is the purge fraction; TIR is the reactor inlet temperature; and FTol is the toluene fresh inlet flowrate. It is worth underlining that when the second alternative is active ( Y = 1 ) the original feed-effluent heat exchanger requires an external duty (utility) to preheat the inlet stream to the adiabatic reactor. 3.2. Dynamic Conceptual Design The dynamic conceptual design can be formulated as follows:

(

max Fobj ( x, Y ) = EP3steady − CI heat − CV furnace + Y Pel ( p ( Ȧ ) , Ȧ ) − CI el − CVheat ( Ȧ ) x ,Y ,ω

)

(3)

s.t. : h(x,Y) = 0; g(x,Y) ≤ 0

where EP3steady accounts for the end-product and raw material terms, as well as the equipment installation (capital investment and operating costs). CI heat summarizes the capital investment of the feed effluent heat exchanger and the furnace. CV furnace represents the operating cost of the furnace. Y is the Boolean variable that discriminates between the alternatives of Figure 1. When Y = 0 , we do not install the energy production section. Conversely, when Y = 1 we install the energy production section and we have to consider the time-dependency of some economic terms, e.g. the revenues from selling electric energy Pel ( p ( Ȧ ) , Ȧ ) , and the operating costs due to purchasing the auxiliary fuel CVheat ( Ȧ ) to preheat the raw materials. CI el quantifies the investment costs for plant expansion (i.e. installation of the electric power subsection). Finally, ω = ω ( t ) accounts for the daily fluctuations of electric energy price. Specifically, it defines the fraction of the day devoted to the production of electric energy. In this perspective, let us consider the energy price of Figure 2. This variable changes hourly i.e. 24 times in a day [8]. In addition, the optimal solution depends also on the instant (switch time) when the process-to-process operation of the FEHE is switched off and the electric power section is switched on. As aforementioned, when the electric power section is switched on, we must provide a hot utility to preheat the inlet stream to the reactor.

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Figure 2. Italian daily energy price on 14-Jul-2008 (source: www.mercatoelettrico.org).

3.3. Integration of Process Design and Boolean Logic The toluene hydrodealkylation model was simulated by PRO/II, a detailed process simulation software developed by Simsci-Esscor (Invensys). The simulator produces the input data for the evaluation of the economic objective function (3) by modeFRONTIER, which is the optimization package (Enginsoft). With reference to the optimization routine, the Multi-Membered Evolution Strategy (MMES) algorithm solved the MINLP problem of DCD.

4. Numerical Results Figure 3 shows the objective function value as a function of the daily time fraction ω of electric power production starting from 10:00am (circles). The triangles represent the cumulative mean of the energy price p (ω ) . The horizontal line is the breakeven, singling out just the profitable limit. This line is obtained by setting Y = 0 , i.e. by removing the energy production section. When circles are over the breakeven line of Figure 3, the economic revenue can be increased by power production. It is worth remarking that we would expect a profit higher than the breakeven point at the beginning of the diagram of Figure 3, since we chose to plot it starting from the first economically convenient time interval. However, we have to account for the investment costs related to the equipment for power generation. The first hours of energy production are necessary to cover the additional capital investment. Moreover, if we consider the cost of the fuel (hot utility) to preheat the inlet stream to the reactor (during the electric power production), the real economic margin is reduced further. Actually, the first derivative of the objective function respect to ω is:

dFobj dω where

= f ( p (ω ) ) − q ( c fuel )

(4)

x ,Y

f ( p (ω ) ) depends on the energy price and consequently on ω , while

q ( c fuel ) depends on the fuel cost. The net profit margin increases when the derivative of

the objective function is positive, since f ( p (ω ) ) > q ( c fuel ) . On the other hand, when the derivative becomes negative then the plant profit starts decreasing since the cost for the additional fuel required by the furnace is larger than the additional margin produced by power production (i.e. q ( c fuel ) > f ( p (ω ) ) ).

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Figure 3. Dynamic conceptual design. Plant profit is time-dependent.

This means that the energy production becomes less profitable than the previous situation up to a condition where it assumes values that are lower than the breakeven line. The solution of the DCD problem allowed quantifying that the installation of a new power generation section is economically feasible if the electric energy is produced and sold in the time interval 10:00am-06:00pm. In the remaining portion of the day, it is preferable to use the hot outlet stream from the reactor to preheat the inlet stream by means of the process-to-process FEHE.

5. Conclusions The novel approach to dynamic conceptual design is based on time-dependent economic quantities (market, demand, and volatility) within a mixed-integer optimization problem. DCD may improve the process efficiency, and consequently the net profit margin. DCD may also shorten the return on investment. In addition, DCD allows accounting for economic uncertainties within the process design study and facilitates the analysis of their influence on the short, medium, and long-term operation of the plant.

References [1] Douglas, M. J., 1988, Conceptual Design of Chemical Processes, NY, McGraw-Hill. [2] Biegler, L.T., Grossmann, I.E., and Westerberg, A.W., 1997, Systematic Methods of Chemical Process Design, New Jersey, Prentice Hall. [3] Cruse, A., Marquardt W., Allgor R. J., and Kussi, J., 2000, Integrated Conceptual Design of Stirred Tank Reactors by Periodic Dynamic Optimization, Computers & Chemical Engineering, 24: 975-981. [4] Iršiþ Bedenik, N., Ropotar M., and Kravanja Z., MINLP Synthesis of Reactor Networks in Overall Process Schemes Based on a Concept of Time Dependent Economic Regions, Computers & Chemical Engineering, 31: 657-676. [5] Cheng, L., Subrahmanian, E., and Westerberg, A.W., 2003, Design and Planning Under Uncertainty: Issues on Problem Formulation and Solution, Computers & Chemical Engineering, 27: 781-801. [6] Sahinidis, N.V., 2004, Optimization under uncertainty: state-of-the-art and opportunities, Computers & Chemical Engineering, 28: 971-983. [7] Gupta, A., and Maranas, C.D., 2003, Managing demand uncertainty in supply chain planning. Computers & Chemical Engineering, 27: 1219-1227. [8] Manenti, F., and D. Manca, 2008, Enterprise-wide Optimization under Tight Supply Contracts and Purchase Agreements, Proceedings of ESCAPE-18, ISBN978/0/444/53228/2.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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CFD Modeling of a jet-pump mixer Wojciech Ludwiga, Janusz Dziaka a

Wrocław University of Technology, Department of Chemical Engineeringj, Norwida Str. 4/6, 50-373 Wroclaw, [email protected]

Abstract CFD model of a jet-pump mixer was presented in the paper. The model was subsequently applied for optimization of the device used for crude oil desalination by means of water. The model enables determination of base parameters of system hydrodynamics i.e. phases velocity distributions and effectiveness of mixing. Keywords: computational fluid dynamics, jet-pump mixer

1. Introduction Crude oil output from the earth in Poland is significantly contaminated. The main problems are sulfur compounds and salinity. Jet-pump mixer, which is proposed for mixing two-phase system crude oil-water is characterized by simple construction (there is no movable elements) and low investment costs [1-3]. Jet-pump application for mixing in two-phase liquid systems enables creation of large interface (~2000 m2/m3) [4-5], which increases mass transfer between phases. CFD (Computational Fluid Dynamics) models, for which the basis constitutes general differential equations are characterized by their elasticity, graduation and universality. They can be used for wide range of process variables changeability [6-7]. They have been successfully applied for mixer work optimization, in case of one- and multi-phase systems [1-3]. The jet-pump that constitutes the main part of the mixer for two phase liquid system was previously examined by means of CFD methods [8-9]. As a result the set of best constructional and process parameters of the jet-pump was obtained. Those parameters are: the diameter of feed nozzle, liquid linear velocity in the feed nozzle, the distance between the feed nozzle outlet and the mixing chamber inlet, the length and diameter of mixing chamber. This jet-pump was applied by the authors of this paper for crude oil desalination in jet-pump mixer. The purpose of this work was elaboration of CFD model of the jet-pump mixer and then preliminary verification of its usefulness for optimization of an installation for crude oil desalination.

2. System, which was modeled Liquid from cylindrical tank of 0.38 m height and 0.213m diameter, possessing flat bottom was taken by the rotary pump and transported through the rotameter to the jet-pump nozzle. In the suction chamber of the jet-pump there were side openings, which enable suction of liquid from the tank. During flow of liquid through the jetpump nozzle, transport of liquid into the jet-pump through side openings took place with a mass flowrate depending on the underpressure created by the jet-pump. The jet-pump described in our earlier studies [8-9] was applied in all simulations that were proceeded. The jet-pump possessed the feed nozzle of 2 mm diameter and the outlet of the nozzle was located 4 mm distance from the inlet to the

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mixing chamber of the jet-pump. The average liquid velocity in the feed nozzle of the jet-pump was 20.09 m/s. Such established parameters enabled getting the highest value of injection coefficient equaled 4.4. The tank of the mixer was filled with water and oil (volume ratio=1:10). The jet-pump was placed in the axis of the mixer tank at different distances from the bottom of the tank, but always with the side openings inside oil phase, at the beginning of the process of mixing. Circulation of the liquid inside apparatus was continued until complete intermixing of the liquid phases was obtained.

3. CFD model CFD models of multiphase flows could be divided into two groups [7]. The first group is constituted by pseudo-homogeneous models. In those models calculations are proceeded in a way applied for one-phase system (one equation for all phases). Typical representative of pseudo-homogeneous model is volume of fluid model VOF. Heterogeneous models constitute the second group of CFD models describing multiphase flows. In those models there are separate equations that describe each phase flow. Two main types of those models are: Euler-Euler and Euler-Lagrange models. Taking into consideration the concentration of the dispersed phase (water), it was decided to choose simplified Euler-Euler approach, in which the fundamental equations are as follows [10]: - continuity equation for the mixture → ∂ρ m § · + ∇ ¨ ρ m vm ¸ = 0 ∂t © ¹

- momentum equation for the mixture → ª § → § n → ·º → → → → → → · ∂( ρ m vm ) § · + ∇ ¨ ρ m vm vm ¸ = −∇p + ∇ «η m ¨ ∇ v m + ∇vmT ¸ » + ρ m g + F + ∇ ¨ ¦ α k ρ k vdr ,k vdr ,k ¸ « ¨ ¸» ¨ k =1 ¸ ∂t © ¹ © ¹ ¹ ¼» ¬« ©

For turbulence description classical k-İ model was used.

4. Model solution The solution of the model proposed above in analytical way is impossible and it is necessary to choose appropriate tool enabling solution with the help of numerical methods. At the beginning of eighties first professional programs (grid generators and solvers) were implemented applying control volume method for CFD models solutions. One of the most commonly applied program of this type is Fluent. Its main advantages are: easy handling, high stability and trust to the code implemented in the program. Taking into account this, it was decided to apply Fluent to solve proposed model of jetpump mixer. Solver parameters, which were constant for all simulations are presented in table 1. Several attempts with numerical grids of different cell shape and density were proceeded during examinations. Finally it was decided to choose unstructured triangular grid with variable density. The dimension of the cells was between 0.0005 m (inside the jet-pump and in the region of the discharge from the jet-pump) to 0.003 m (in the region of low velocity of the flow).

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Table 1. Solver parameters (constant for all simulations)

Solver parameter Solver type

Value Two-dimensional, axisymmetric, pressure based, implicit, unsteady default proposed by program For all parameters besides vof: second order upwind, for vof first order upwind SIMPLE 0.0001-0.1 s

Under-relaxation factors Discretisation Pressure-velocity coupling Time step

The user defined function (UDF) was written by the authors for simulation of liquid circulation in the installation. UDF transferred the volume fractions values of both phases from the outlet of the tank to the outlet of jet-pump feed nozzle. The calculations were continued until the volume fractions of both phases inside the whole apparatus or in the part of it, inside which mixing took place, differ only by 5% from the value, resulted from the volume balance. The time was considered as time of mixing.

5. Calculations results

Volume fraction of the crude oil (-)

As a result of CFD calculations the values of velocity as well as volume fractions of both phases in the tank were obtained for specific time steps and for different distances of the jet-pump location from the bottom of the mixer tank (5, 10, 15 and 25 cm). As we can see in Fig. 1 and 2 the process of mixing is very intensive at the beginning. The volume fractions of oil in the specific points in the mixer go quickly to the value resulting from volume balance. After that the speed of change of volume concentration in selected points of the two-phase mixture decreases. At the bottom of the tank the regions are created, where is a circulation of the liquid with bad mixing conditions. Those zones disappear relatively slowly, making longer the time of complete intermixing. 1.2 1 0.8 Point 1

0.6

Point 2

0.4

Point 3

0.2

Full mixing

0 0

10

20

30

40

50

Time (s)

Fig. 1. The dependence between volume fraction of oil and the time for three example points in the tank for L=5 cm

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5s

10 s

40 s

55 s

75 s

81 s

Fig.2. The distribution of volume fraction of the oil depending on time for L=25 cm.

The model anticipated intermixing only in that part of the tank, which was below the upper edge of the jet-pump (Fig.3). The region above the jet-pump was not mixed at all (there was only oil phase there). Complete intermixing of liquids in the tank took place only in the case of L=25 cm i.e. when the upper part of the jet-pump was located at the upper edge of the tank. So it was impossible to determine the time of intermixing for the whole volume of liquid in the tank but only for part of liquid below the jet-pump. To take into account this phenomenon some specific quantity of time was involved, which was related to some part of the volume of liquid in the tank (Fig. 4).

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L=5 cm

L=10 cm

L=15 cm

L=25 cm

Fig. 3. Oil volume fraction distribution in steady state (there is no change in successive time steps) for several locations of the jet-pump towards the bottom of the tank. 7000 6000

t' [s/m3]

5000 4000 3000 2000 1000 0 0.15

0.2

0.25

0.3

0.35

0.4

L [m]

Fig. 4. Time of mixing, related to the volume of the liquid, which was mixed, as a function of the distance between the jet-pump and the bottom of the tank.

6. Conclusions CFD model presented in this paper enables optimization of the construction of jet-pump mixer. On the basis of model calculations one can conclude that the jet-pump

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should be placed at the highest position from the bottom in the mixer tank. The shape of the tank bottom is important taking into consideration the possibility of creation of spaces without mixing in the tank. The presented model needs experimental verification of its assumptions as well as set-up optimization. One should also verify the phenomenon of lack of mixing in the space above the jet pump. It will be the subject of our future experimental investigation. Notation →

F →

g

L p t’

body force, N gravity vector, m/s2 distance between jet-pump outlet and the bottom of the tank, m pressure, Pa time of mixing, related to liquid volume in the tank, which was mixed, s/m3

→

vdr →

vm

α ηm ρm

drift velocity, m/s mass averaged velocity vector, m/s volume fraction, dynamic viscosity of the mixture, Pa s density of the mixture, kg/m3

References [1] H.D. Zughbi, M.A. Rakib, Chem. Eng. Sci., 59, (2004), 829. [2] S. Jayanti, Chem. Eng. Sci., 56, (2001), 193. [3] A.W. Patwardhan, Chem. Eng. Sci., 57, (2002), 1307. [4] M. T Kandakure, V. G. Gaikar, A. W. Patwardhan, Chem. Eng. Sci., 60, (2005), 6391. [5] P. Havelka, V. Linek, J. Sinkule, J. Zahradnik, M. Fialova, Chem. Eng. Sci., 52, (1997), 1701. [6] J. D. Anderson, Computational fluid dynamics: the basics with application, Mc-Graw Hill, New York, 1995. [7] Z. Jaworski, Numeryczna mechanika plynow w inzynierii chemicznej i procesowej, Akademicka Oficyna Wydawnicza Exit, Warszawa, 2005. [8] W. Ludwig, J. Dziak W. Sawinski, Inzynieria i Aparatura Chemiczna, 6, (2007), 18. [9] J. Dziak, J. Kaplon Jacek, A. Koltuniewicz, XIX Ogolnopolska Konferencja Inzynierii Chemicznej i Procesowej. Materialy konferencyjne, Oficyna Wydaw. Przesz, Rzeszow, (2007),135-138. [10] FLUENT 6.3 User’s guide, Lebanon NH, Fluent Inc, (2003), 1629.

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Computational fluid dynamics applied to study the hemodynamics in sangvin vessels. Case study - the portal system. Claudiu Cristian Botar-Jid,a Paul Serban Agachi,a Simona Clichici,b a

Chemical Engineering Department, Faculty of Chemistry and Chemical Engineering, “Babes-Bolyai” University, Arany Janos Str. no. 11, Cluj Napoca RO-400028, Romani,E-mail: [email protected], [email protected] b Department of Physiology, University of Medicine and Pharmacy “Iuliu Hatieganu”, Emil Isac Str. Nr. 13, Cluj-Napoca RO-400023, Romani, E-mail: [email protected]

Abstract The blood flow under physiologic conditions is an important field of study. Detection and quantification of the normal and abnormal blood flow in vessels serve as basis for diagnosis and/or surgical planning. The blood flow complex characteristics have been investigated through simulations based on mathematical models that include constitutive equations describing the hemodymanics and its relations with the deformable vessels wall. The computational techniques applied to model the blood flow in the circulatory system investigated either the velocity field or the pressure field, but not both of them in the same time, treating the vessel walls as rigid ones or considering significantly simplified or reduced geometries for the deformable wall models. The approximation of rigid-walls was made mostly due to the difficulty of solving the coupled blood flow/vessel deformation problem and was justified by the observation that, under normal conditions, wall deformability does not significantly alter the velocity field. Modeling of the three-dimensional blood flow in compliant vessels is extremely challenging for a number of additional reasons such as: geometry acquisition, accurate constitutive description of the behavior and induced movement of the tissue, inflow and outflow boundary conditions, etc. The computational fluid dynamics (CFD) technique is applyed to describe the blood flow in a segment of portal vein system. The reconstructed model of the vessels provides geometric boundaries for the CFD blood flow model. In this respect a finite difference grid is going to be generated over the finite element model geometry. Hemodymanics parameters such as velocity magnitude, pressure and wall shear stress are going to be computed. Keywords: CFD, hemodymanics, blood flow, flow/vessel wall interaction

1. Introduction Promising applications such as disease research - where fluid mechanical conditions are correlated to regions prone to different pathologies [1], medical devices design - where the interactions between a device and the blood stream are modeled [2], surgical planning [3] and also theoretical interests represented the driving forces to study the blood flow in human circulatory system for many years. The computational techniques applied to model the blood flow in the circulatory system investigated either the velocity field or the pressure field, but not both of them in the

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same time, treating the vessel walls as rigid ones [4] or considering significantly simplified or reduced geometries for the deformable wall models [5]. The blood vessel system is characterized by its 3D geometry that involves shape in diameter, spatial bending and twisting. The tree like structure of a complex vascular structure, as the present investigated one – the portal vein, that involves branching and bifurcation – is characterized by a very complex hemodymanics and fluid-vessel wall interaction. Rheological and geometrical changes along the vessel, in a healthy organ, is an important issue that may be addressed in order to serve as a basis for comparison in case of disease or irrigated organ disease installation analysis. Therefore a complete understanding and description of the hemodymanics and associated phenomena at macroscopic level (main branches of the portal vein) could be useful means for predictive medicine, which may be implemented in a form of computational-aided diagnosis (CAD). Due to an increase in software development and computers performance the CAD paradigm may be implemented successfully.

2. Problem statement and paper approach Since many fundamental issues of the blood flow are still not fully understood the computational modeling is a challenging task. A number of special features have to be taken into consideration in order to calculate the blood flow accurately: the geometry acquisition, the accurate constitutive description of the blood flow behavior and its interaction with the vessel tissue, and the inflow and the outflow boundary conditions. The blood flow interacts mechanically with the vessel walls, giving rise to complex fluid-structure interactions whose mathematical analysis is still incomplete. Mesh representation has to be related with solving moving boundaries with velocity, pressure and stress [6]. The geometry of the portal vein has been reconstructed using the 3D computer- aided capabilities of the software Solid Edge V20 (Figure 1 a). The volume geometry has been imported in GAMBIT, a software package designed to build and mesh models for computational fluid dynamics (CFD), and smooted using the lenght-weighted Laplacian smooting algorithm. The surface and volume mesh have been applied and the boundary zone and continuous zone have been specified (Figure 1 b and c). The geometry parameters are presented in Table 1. Table 1.Portal vein model dimensions

Inlet diameter Left brancing diameter Right brancing diameter Left secondary brancing diemeter Right secondary brancing diemeter Total height of the geometry (O-Z axis) Total width of the geometry (O-Y axis) Total width of the geometry (O-X axis)

10 mm 7.47 mm 10 mm 3.8 mm 6.32 mm 71.35 mm 88.25 mm 44.39 mm

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Figure 1. The geometry of the portal vein: a) the Solid Edge reconstruction; b) boundary zone specification; c) continuous zone specification.

The thixotropic characteristics of the blood are considered because in a non-Newtonian fluid the relation between the shear stress and the strain rate is nonlinear, and can even be time-dependent. Therefore a constant coefficient of viscosity is not appropriate to be defined. A ratio between shear stress and rate of strain (or shear-dependent viscosity) can be defined, this concept being more useful for fluids without time-dependent behavior, as in the case of portal vein circulation. The computational modeling of the blood flow has been done considering the threedimensional, incompressible Navier-Stokes equations written in strong conservation form for mass and momentum. Finding the solution of the governing equations is difficult using traditional analytical techniques for such a complicated system involving 3D irregular geometry, complex flow and non-Newtonian viscosity. Numerical techniques have been required, hence the need for CFD. The CFD software used was FLUENT. The model implemented here, to describe the blood flow, is the Reynolds stress model (RSM) which is the most elaborate turbulence model that FLUENT software provides. The RSM model is abandoning the isotropic eddy-viscosity hypothesis, and closes the Reynolds-averaged Navier-Stokes equations by solving transport equations for the Reynolds stresses, together with an equation for the dissipation rate. Since the RSM accounts for the effects of streamline curvature, swirl, rotation, and rapid changes in strain rate in a more rigorous manner than one-equation and two-equation models, it has greater potential to give accurate predictions for complex flows [FLUENT 6.3.26 user guide]. The differential equations are discretized in a manner of finite element method, and the boundary conditions are specified. The vessel walls are treated as being elastic. A dynamic mesh condition has been used. The no-slip condition has been imposed, meaning that the speed of the fluid relative to the boundary is 0, but at some height from the boundary the flow speed must equal that of the fluid. The blood viscosity has been defined according to the non-Newtonian power law (Table 2). The blood mass flow rate has been considered 0.01 kg/s. Table 2. The non-Newtonian power law parameters

Power law index (n) Consistency index k (kg-s^n-2/m) Reference temperature (°K) Minimum viscosity limit ηmin (kg/m-s) Maximum viscosity limit ηmax(kg/m-s)

0.4851 0.2073 310 0.001 0.003

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3. Results The following results of the complete process of preprocessing, solving and postprocessing following the procedure discussed above enabled the visualization and quantification of the biologic phenomena taking place in the portal vein.

Figure 2. The velocity magnitude (in m/s), ( a) – rigid wall, b) – elastic wall) and the cell Reynolds number distribution ( a) – rigid wall, b) – elastic wall).

In Figure 2 the velocity magnitude and the cell Reynolds number distribution are represented. The results suggested the presence of laminar flows along the entire structure, in both rigid and elastic wall conditions. Differences appear in velocity magnitude values; higher flow rates are developed in case of elastic walls; the order of magnitude is 1.18. Figure 3 shows the distribution of velocity path lines. Their profile colored by velocity magnitude shows uniform flow in the main branching as well in its bifurcations until reaching the second bifurcations in case of rigid wall. When elastic wall conditions were imposed the path lines become smoother and their uniformity maintained along the entire geometry length.

Figure 3. The distribution of velocity path lines (in m/s), ( a) – rigid wall, b) – elastic wall)

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The influence of flow characteristics on static pressure may be observed in Figure 4. The developed contours show higher uniformity in pressure distribution along the main bracing of the portal vein in case of elastic wall conditions.

Figure 4. The contours of static pressure (in Pascal) ( a) – rigid wall, b) – elastic wall)

The wall shear stress and the skin friction coefficient contours developed at the vessel wall are represented in Figure 5. In case of elastic wall conditions their values are lower than in case of rigid wall ones (the order of magnitude is 1.62), even if the Reynolds number and the flow rates values are higher when elastic wall conditions were imposed than in case of rigid walls. These results can yield to new insights into the portal vein blood flow behavior and disease evolution, considering the flow rate or the Reynolds number influence on the shear stress distribution.

Figure 5. The contours of wall shear stress (in pascal) ( a) - rigid wall, b) - elastic wall) and the skin friction coefficient ( a) - rigid wall, b) - elastic wall)

4. Conclusions The present analysis demonstrate once more the utility of computer aided design and CFD tools to assess the distributions of blood velocity and wall stresses along circulatory segments. Understanding the normal behavior of the portal vein circulation

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may provide a link to predict the relationship hemodymanics - organ pathology, and associated with other investigations, could lead to the development of a tool for noninvasive early diagnosis of liver disease or for surgical planning.

References [1] C.A. Taylor, T.J.R. Hughes, C.K. Zarins, Finite element modeling of three-dimensional pulsatile flow in the abdominal aorta: relevance to atherosclerosis, Ann. Biomed. Engrg. 26 (6), pp. 1–14, 1998. [2] G.R. Stuhne, D.A. Steinman, Finite-element modeling of the hemodynamics of stented aneurysms, Trans. ASME J. Biomech. Engrg. 126 (3), pp. 382–387, 2004. [3] C.A. Taylor, M.T. Draney, J.P. Ku, D. Parker, B.N. Steele, K. Wang, C.K. Zarins, Predictive medicine: computational techniques in therapeutic decision-making, Comput. Aided Surg. 4 (5), pp. 231–247, 1999. [4] C.A. Taylor, T.J.R. Hughes, C.K. Zarins, Finite element modeling of blood flow in arteries, Comput. Methods Appl. Mech. Engrg. 158, pp. 155–196, 1998. [5] K. Perktold, G. Rappitsch, Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model, J. Biomech. 28 (7), pp. 845– 856, 1995. [6] Cairncross R.A., Schunk P.R., Baer T.A., Rao R.R., Sackinger P.A., A finite element method for free surface flows of incompressible fluids in three dimensions, Part I: boundary fitted mesh motion. Int. J. Numer. Meth. Fluids 33, 375–403, 2000.

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Computational Fluid Dynamics Simulation of the Water – Sugar Cane Bagasse Suspension in Pipe with Internal Static Mixer E. L. Martínez, A. González Quiroga, A. L. Jardini, R. Maciel Filho School of Chemical Engineering, University of Campinas – UNICAMP P.O. Box 6066, 13083-970, Campinas-SP, Brazil [email protected]

Abstract A comprehensive CFD model was developed to gain insight into flow characteristics of water-sugar cane bagasse suspension in pipe with and without internal static mixers. Two different modeling approaches were used: Eulerian-Eulerian and Lagragian Particle Tracking, both with the k-İ turbulence model. Local solid volume fraction distribution was studied for three mean velocity suspension; 0.10, 0.15 and 0.20 m/s. The mass volume fraction studied were 49.6 and 10 W/V of water-swollen particles. The predicted flow indicates the presence of loop flow pattern in the pipe with internal static mixers as a function of mean velocity suspension. Keywords: Biomass Suspension, Particle Volume Distribution, Static Mixer, Lagrangian Particle Tracking Model, Eulerian-Eulerian Model.

1. Introduction Enzymatic hydrolysis of lignocellulosic materials to produce reducing sugars has long been pursued for its potential to provide an alternative renewable energy source. For the practical realization of technology, the biomass must be pretreated to decrease the recalcitrance and make the cellulose in the feedstock more susceptible to digestion by cellulose enzymes and finally hydrolyzed in suspension form. While many publications have dealt with development and improvement of biomass conversion processes, relatively few authors have studied biomass suspension flow characteristics [1]. The process of enzymatic hydrolysis can be carried out in reactor of various types: batch stirred reactors [2, 3], continuous stirred tank reactors (CSTR) [2, 3], tubular reactors [4, 5], CSTRs in series [6] and tubular column reactors [2]. The tubular reactors offer advantages such as reducing required reaction volume, energy agitation requirements and enzyme inhibition by final product. In the present work, a CFD based model was used to assess the complex interactions between the suspension quality and the fluid mixing process of water-pretreated sugar cane bagasse suspension in a pipe with or without internal static mixer. Two modeling approaches are used: The Lagrangian Particle Tracking Multiphase Model and Eulerian-Eulerian Multiphase Model, along with the standard k-e turbulence model. The main advantage of using a Lagrangian framework for dispersed phase particles is that particle-level phenomena can be modeled rigorously. The Eulerian-Eulerian approach is more suitable for modeling the dispersed multiphase system with a significant volume fraction of dispersed phase (>10%) [8].

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2. Computational Model 2.1. Eulerian-Eulerian model The different phases are treated mathematically as interpreting continua, since the volume of a phase cannot be occupied by the other phases. These volume fractions are assumed to be continuous function of space and time and their sum is equal to one. Conservation equations for each phase are derived to obtain a set of equations, which have similar structure for all phases. Coupling is achieved through the pressure and inter-phase exchange co-effects. Any interaction between the interoperating phases is accounted for using closure laws [7]. Eulerian-Eulerian approach is more suitable for modeling dispersed multiphase systems with a significant volume fraction of dispersed phase (>10%) and thus allows the computation of three-phase flow fields even with high solid hold-up. The accuracy of the Eulerian-Eulerian approach heavily relies on the empirical constitutive equations used, but it does not provide information about the hydrodynamics of individual particles and thus has limitations in predicting certain discrete flow characteristics such as particle size effect, particle agglomeration [8]. 2.2. Lagrangian Particle Tracking model The fluid phase is treated as a continuum by solving the time averaged Navier-Stokes equations in the same manner as for a single-phase system, while the dispersed phase is solved by tracking a large number of particles through the calculated flow field using Newtonian equation of motion. The dispersed phase can exchange momentum, mass, and energy with the fluid phase. The particle models are combined with an Eulerian model for the continuous phase to simulate the disperse phase. The motion of fluid phase is calculated from the averaged fluid-phase governing equations, which are similar to Eulerian-Eulerian. The motion of the discrete phase particle is given by integrating the force balance on the particle, which is written in Lagrangian reference frame. The advantage of Eulerian-Lagrangian approach is that the dynamics of the individual particles can be assessed, however, in the case of turbulent flows, it is necessary to simulate a very large number of particle trajectories to obtain meaningful averages. While, with the high concentrations of particles and for the large size reactors, the tracking process becomes highly memory-intensive and this approach is, therefore, suitable for simulating multiphase flows containing a low (<10%) volume fraction of the dispersed phases [8]. ANSYS CFX employs a finite volume method to solve the general partial differential equations that describes fluid flow and mass momentum transport. The standard k-İ turbulence model is used for calculating the turbulent kinetic energy and the power rate dissipation. It is the most widely tested and the results are generally considered as reliable with a short calculation time [8]. For interface transfer multiple particle effects on the drag forces have included according to Wen Yu (1966) [9] drag model. Non-drag forces for virtual mass, lift, buoyancy, wall lubrication and turbulent dispersion have been included in the simulation.

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3. Boundary Condition and Solution Domain The system of study consists in a pipe with eight internal baffles (Fig. 1). The water retention volume (WRV), defined as the ratio of the weight of water retained per unit weight of pretreated sugar cane bagasse after centrifugation at 2000 rpm for 10 min, was measured [10]. The water-swollen particles have a WRV of 9.912 and ȡ=1112.2 kg/m3. The particle size distribution is modeled through normal distribution of Sauter diameter. Minimum, mean and maximum Sauter diameters are 5.00*10-6, 385*10-6 and 770*10-6 m respectively. Standard deviation in Sauter diameter is 128*10-6 m. The temperature was fixed at 50 ºC. The concentration of water-swollen particles used in the lagrangian-particle tracking approach was 10.0 W/V equivalents to 0.981 W/V of dry particles. The concentration of water-swollen particles used in the Eulerian-Eulerian approach was 49.6 W/V equivalents to 5.00 W/V of dry particles. The initial condition for each simulation was a parabolic solid particles and water profile with equal mean velocities (mv) of 0.10, 0.15 and 0.20 m/s inside the computational domain.

Figure 1. Pipe geometry and 3D grid details; Total length "T=2.032 m, pipe diameter d=0.152 m, mixer length "m=0.152 m, mixer angle ĭ=120°.

4. Result and Discussion 4.1. Solids volume fraction distribution For the Eulerian-Eulerian approach, the size distribution of dispersed particles was discretized into ten size groups. The same Sauter mean diameter used in the Lagrangian Particle Tracking approach was used. Each of these size groups is considered as an individual dispersed phase. The predicted solids volume fraction distribution shows higher solid particles concentration under the central axis and absence of solid particles near the top (Fig 2). The advantage of the static mixers is that they allow to avoid sedimentation of solids through modifications in geometry and/or increases in the mean velocity suspension.

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Figure 2. Predicted solids volume fraction distribution. a) Pipe with static mixers, mv’=0.1m/s; b) Pipe without static mixers, mv=0.1m/s; c) Pipe with static mixers, mv’=0.2m/s; d) Pipe without static mixers, mv=0.2m/s.

4.2. Suspension quality The criteria based on the variation of the standard deviation (Sd) of the radial solid volume fraction was used to predict the quality of suspension prevailing along the pipe (Fig 3). It can be see that the sd values along the pipes with internal static mixer are lower and more uniforms than the sd values for pipes without static mixers, that is to say, the quality of suspension is higher. However, increasing the mean velocity of the suspension diminishes the differences between the qualities of suspension for the two internal pipe configurations. It is well known that the enzymatic hydrolysis requires residence times over 24 hours to reach high conversion of substrate. The main advantage of using static mixers for the reaction system is the ability to operate at lower velocities of suspension without losing the quality of the suspension. However, one must keep in mind that the simulation corresponds to the physical situation at the entrance to the reactor and it is expected that the concentration of solid decline for long residence times (reactor length) due to the solubilization of cellulose.

Figure 3. Predicted influence of mean solid velocity (mv) [m/s] on suspension quality: Pipe with (mv’) and without (mv) static mixers.

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Figure 4. Particle flow pattern for mean velocity (mv) of: (a) 10 m/s and (b) 20 m/s.

5. Conclusions The predicted liquid flow indicates the presence of loop flow pattern in the pipe with internal static mixers unlike the pipe without mixers. The internal static mixers are capable for generation liquid circulation which consequently leads to faster mixing. The liquid-phase flow pattern allows two limiting situations with increases in liquid-phase mean velocity: piston flow, transition between piston and loop flow and finally will predominate the loop flow. The other possibility to alter the flow pattern is changing the geometry of static mixer. The Lagrangian Particle tracking was used for simulate the behavior of discrete particle in turbulent flow in the pipe with static mixers. The simulate result show that static mixer created confined mixing zones that affect the solid distribution inside of pipe. However, this approach appear gives an accurate insight to the particle behavior in the flow for the later optimization of the angle mixer with the aim of generated smaller turbulent length scales for to enhance suspension quality. The model and results presented in this work are useful for extending the application of CFD model for simulating the flow of biomass suspensions in tubular reactors. The study suggests the use of other internal static mixer configurations. In addition, the advantages of configurations presented offer insides on the novel tubular reactor for the enzymatic hydrolysis of biomass.

6. Acknowledgements The authors wish to acknowledge the financial support provide by FAPESP (The Scientific Research Foundation for the State of São Paulo).

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Nomenclature CFD WRV Sd mv mv’ "T d "m ȡ ĭ

Computational fluid dynamics Water retention volume Standard deviation Mean velocity in pipe without static mixer Mean velocity in pipe with static mixer Total length Pipe diameter Mixer length Density Mixer angle

[m/s] [m/s] [m] [m] [m] [kg/m3]

References [1]

H. Cui and J. R. Grace, 2007, Flow of pulp fibre suspension and slurries: A review, International Journal of Multiphase Flow, 33, 9, 921-934. [2] A. V. Gusakov, A. P. Sinitsyn and A. A. Klyosov, 1985, Kinetics of the enzymatic hydrolysis of cellulose: 1. A mathematical model for a batch reactor process, Enzyme and Microbial Technology, 7, 7, 346-352. [3] C. R. South, D. A. L. Hogsett and L. R. Lynd, 1995, Modeling simultaneous saccharification and fermentation of lignocellulose to ethanol in batch and continuous reactors, Enzyme and Microbial Technology, 17, 9, 797-803. [4] A. Borchert and K Buchholz, 1987, Enzymatic hydrolysis of cellulosic materials, Process Biochemistry, 22, 6, 173-180. [5] S. Yang, W. Ding and H. Chen, 2006, Enzymatic hydrolysis of rice straw in a tubular reactor coupled with UF membrane, Process Biochemistry, 41, 3, 721-725. [6] X. Shao, L. Lynd, C. Wyman and A. Bakker, 2009, Kinetic modeling of cellulosic biomass to ethanol via simultaneous saccharification and fermentation: Part I. Accommodation of intermittent feeding and analysis of staged reactors, Biotechnology and Bioengineering, 102, 1, 59-65. [7] B. G. M. Van Wachem and A. E. Almstedt, 2003, Methods for multiphase computational fluid dynamics, Chemical Engineering Journal, 96, 1-3, 81-98. [8] V.V. Ranade (ed.), 2002, Computational flow modeling for chemical reactor engineering, London, U.K. [9] C. Y Wen and Y. H. Yu. Mechanics of fludization, Chemical Engineering Progress Symposium Series, 62, 62, 100-111. [10] Y. H. Lee and L. T. Fan, 1983, Kinetic studies of enzymatic hydrolysis of insoluble cellulose: (II). Analysis of extended hydrolysis times, Biotechnology and Bioengineering, 25, 4, 939-966.

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Developing a mathematical model for the complete kinetic cycle of direct synthesis of DME from Syngas through the CFD technique Leila Vafajoo*a, Seyed Hossein Ahmadi Afsharb, Behnaz Firouzbakhtc a

Islamic Azad University Tehran South Branch,Graduate School of Engineering, Faculty of Chemical Engineering,Tehran, Iran, [email protected] b Islamic Azad University Tehran South Branch,Graduate School of Engineering, Faculty of Chemical Engineering,Tehran, Iran, [email protected] c Sharif University of Technology, Dept. of Chemical and Petroleum Engineering, Azadi Ave., P.O.Box 11365-9465, Tehran, Iran,[email protected]

Abstract It is well known that the direct synthesis of Di-Methyl Ether (DME) from the Syngas is highly exothermic; therefore, the temperature control for its production and hence a suitable heat transfer pattern is of ought most significance to the success of such process. As such, slurry bubble column reactor is recognized to be a more suitable means for this purpose than other choices including fixed bed reactor which is the usual type of system in which direct DME synthesis takes place. In other words, slurry reactors are desirable due to having suitable heat and mass transfer properties. In this research a mathematical model for direct synthesis of DME from synthesis gas in a slurry reactor for a complete kinetic cycle including; CO consumption, Water-Gas shift reaction and methanol dehydration steps has been developed and evaluated. This is done through FLUENT software incorporating k-İ model with 10% intensity (i.e.; usual industrial value) and reactor hydrodynamic diameter of 8 cm. Then, investigation of effects of various parameters such as pressure (in the range of 25 to 40 bars), temperature (between 220-280 °C), inlet feed flow rate (of 200 ml/min) and inlet feed composition (of CO:H2 = 1:1) on the performance of the reactor in terms of CO conversion and selectivity toward production of the DME in this process were undertaken. It is noteworthy, that the maximum error resulted from comparison of results obtained from current model and those of experimental data is less than 10% for conversion of CO selectivity toward DME which are reasonable considering assumptions utilized. Keywords: DME, Syngas, Kinetics, CFD, Slurry bubble column

1. Introduction Dimethyl ether (DME) is a colorless, nontoxic, and environmentally benign compound. It is currently used as a solvent and propellant in various aerosol products. Its physical properties closely resemble those of Liquefied Petroleum Gas (LPG). DME is considered as a substitute for diesel fuel. Compared with diesel fuel combustion, DME produces much less pollutants such as carbon dioxide, nitrogen oxides and particulates. DME may be manufactured in large quantities from natural gas, coal, biomass and municipal solid waste. DME traditionally produced by dehydration of methanol, which is in turn produced from Syngas. The traditional process is called a two-stage or

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indirect method of DME preparation. However, DME may also be prepared directly from Syngas (single-stage or direct method). The single stage, liquid phase DME synthesis process, incorporates the sequential reaction of methanol synthesis and methanol dehydration and a slurry phase reactor system. Preparation of DME from the Syngas can be represented by four catalytic reactions as shown below: CO+2H2ĺCH3OH

¨H=-90.29 kj/mol

(Eqn.1)

CO2+3H2ĺCH3OH+H2O

¨H=-49.43 kj/mol

(Eqn.2)

2CH3OHĺCH3OCH3+H2O

¨H=-40.96 kj/mol

(Eqn.3)

CO+H2OĺCO2+H2

¨H=-23.41 kj/mol

(Eqn.4)

In addition to the superior heat management allowed by the liquid phase operation, the synergistic effects of these reactions yield more DME than the two-stage sequential processing. Most theoretical works in creating a one-stage Di-Methyl Ether has been performed in Fixed Bed reactors. Considering equations of mass and energy balances, Fang and colleagues have carried out a theory study in the Bubble Column reactor. In this research a mathematical model for direct synthesis of DME from synthesis gas in a slurry reactor for a complete kinetic cycle is developed using CFD modeling. Ultimately, simulated results were compared with experimental ones obtained previously utilizing an optimum catalyst of modified H-Mordenite Zeolite with Alumina for the dehydration step and CuO/ZnO/Al2O3 for the CO and Water-Gas shift reactions.

2. Mathematical model The existing flow in the reactor is of an agitated type. Hence, governing equations control the momentary and medium speeds. The relationship for the fluid momentary speed in direction of i ui(xi,t) is given in equation (5). This equation may also be written for the medium speed of the flow. Equation (6) shows the mass persistence for it. In this equation nji is the medium speed of the flow in the direction of i and ȡ is the fluid density: wU w  ( Uu i ) wt wx i

0

(Eqn.5)

wU w  ( U ui ) 0 wt wxi

(Eqn.6)

The Momentum relations used are those provided by the Navier-Stokes equation in an indexical form in which P is the thermodynamic pressure and bi is the volume power (i.e.; the gravity power in this reactor)

wui wu uj i wt wx j



w 2 ui 1 wp X  bi wx j wx j U wxi

Equation (8) shows the Navier-Stokes equation in a moderate form: wu wu wp w ª § wui wu j 2 wul ·º w ( U uicucj ) U( i  u j i )     G ij «P ¨ ¸»  wt wx j wxi wx j «¬ ¨© wx j wxi 3 wxl ¸¹»¼ wx j

(Eqn.7)

(Eqn.8)

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Since the second term on the right hand side of it is actually a characteristic of the flow, it is difficult to calculate it. Therefore agitated forms are utilized. In the present work, the agitated form of k-İ is consumed for this purpose.

3. Modelling 3.1. Modelling of the reactor The Fluent 6.3.26 software has been utilized in this model. Furthermore, the Gambit 2.3.16 software has been used to create the geometry of the intended model and its mesh. Considering the grid independency, the dimension of the used mesh is 40×50. The volume of the modelled reactor is 500 ml with a height of 10 cm and a width of approximately 4 cm. The fluid input flow rate is about 200 ml/min and the working pressure is about 25-40 bar. The actual temperature of the experiments is 200-280˚C. Furthermore, due to the symmetry in the geometry of the reactor the problem is solved in 2 dimensions. The finite volume method has been utilized for the numerical modelling of the reactor. The formulation of the equations is implicit, the solver of the solution is also segregated, that is the equations are being solved separately. The high accuracy method of quick is used to segregate the momentum equation and power and volume fractions. In addition, the first order upwind method has been used to segregate other variables. In the present model whenever the residual is 10-8 for the density and 10-5 for other variables, the calculations will come to an end. The following equation is also used to calculate the consistency of agitation:

Pt

UC P

k2

(Eqn.9)

H

The flow inside the reactor includes both the gas and liquid phases. To simulate the two phase flow, the Eulerian model is utilized which is the richest form for a multi-phase calculations. The third phase of the slurry reactor is the solid particles of the catalyst which are smaller than 5 microns. Therefore the solid phase may be considered to be fully mixed in the fluid, hence assuming the flow in the reactor to be of 2 phase. The fluid inside the reactor is taken to be Kerosene (C12H23) for which the thermo-physical properties are well known. At the entrance of the reactor the boundary condition is set to be the fluid flow rate in that location. Furthermore, the ratio of entering gas particles is well defined (i.e.; the flow rate of the H2 and CO at the entrance of the reactor are equal). These quantities in addition to the dimensions of the reactor have been taken from the in vitro model. Due to the use of the k-İ agitation model, the hydraulic width of 8 cm and intensity of 10% were used at the entrance and exit points of the reactor. The outflow conditions have been utilized at the exit of the reactor. At the margins of the reactor the boundary condition and wall have been used as the no slip and the non-entry and -exit of the fluid have also been made use of. As previously mentioned, at the other margin of the reactor use of the symmetry condition is made. This means that the gradient of all the variables on the middle axis perpendicular to the main movement of the flow is zero. 3.2. Reaction rate equations All four reactions shown in equations 1 to 4 have been utilized for kinetic modeling of the process under investigation. The rate equations for modeling of direct synthesis of DME from the Syngas in regards to the optimum catalyst used for the dehydration of Methanol (i.e.; modified H-Mordenite zeolite with Alumina) and also for reactions of

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synthesis of Methanol and water-gas shift (i.e.; CuO/ZnO/Al2O3) are all selected and incorporated in present model.

4. Results and discussions In this section, a comparison between generated results of the present simulations with experimental works of others is made. Fig.1 displays a diagram of CO conversion at various temperatures for both numerical (i.e.; of this work) and experimental (i.e.; works of others) results. As indicated through the experimental results between 220 and 280˚C the ratio of the CO conversion to the product formation increases. The reason for this behavior is that rising in temperature will normally enhance the reaction rate. An important point to note is that as the temperature increases the slope of this curve decreases. This means, temperature impact becomes less pronounced which in turn is due to the equilibrium conversion of CO being reached. In other words, as the CO concentration is reduced, the probability for the reaction to take place is lowered. This satisfactory comparison between numerical and experimental results emphasizes the validity of the simulation results for present work.

Avtivity (%)

70 60 Experiment 50

Numerical

40 30 210

230

250

270

290

T ( C) Fig.1 Variation of activity in terms of CO conversion as a function of temperature

The DME selectivity in different temperatures is illustrated in Fig.2 for both numerical and experimental data. It is seen from the experimental results that an increase in reactor’s temperature does not cause a sensible change in DME selectivity. According to this trend, the DME selectivity between 220˚C and 280˚C is constant. In other words, the DME selectivity is not a function of reactor’s temperature and is about 80%. It is concluded from this Figure that the numerical results indicate the same trends. The contour for the rate of reaction producing DME thru the reactor length is presented in Fig. 3. This figure demonstrates that the rate of reaction increases as the reaction front moves toward the reactor outlet.

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DME Selectivity(%)

95 90 85 80 75 70

Experiment

65

Numerical

60 210

230

250

270

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T ( C) Fig.2 Comparing the numerical and experimental data of DME selectivity in different temperatures

Fig.3 Rate of CO+2H2ĺCH3OH reaction through reactor’s length at 240˚C, 200 ml flow rate and 35bar

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5. Conclusion In this study, a CFD model is developed to simulate the production of the DME through the direct method from the Syngas in a slurry reactor. A thorough comparison between simulated results of this work and experimental works of others has validated this model. Therefore, one may conclude that consideration of complete kinetic cycle added to the thorough CFD model provides a good tool to optimize this process.

6. References S. Lee and W. Cho, 2006, Simulation of fixed bed reactor for dimethyl ether synthesis, Korean J. Chem. Eng., 23, 4, 522-530 D. H. Liu, J. Xu, H. T. Zhang and D. Y. Fang, 2002, Direct synthesis of dimethyl ether from syngas in three phase agitated reactor, J. Chem. Ind. Eng., 53, 1, 103 K. L. Ng, D. Chedvick and T. Toseland, 1999, Kinetics and modelling of dimethyl ether synthesis from synthesis gas, Chem. Eng. Science, 45, 3587-3592 D. Fang, 2007, Mathematical Simulation and Design of Three-Phase Bubble Column Reactor for Direct Synthesis of Dimethyl Ether from Syngas, J. of Natural Gas Chemistry, 16, 193-199 N. Khandan and M. Kazemeini, 2008, Determining an optimum catalyst for liquid-phase dehydration of methanol to dimethyl ether, Applied Catalysis A., 349, 1-2, 6-12 W. Z. Lu and H. Teng, 2004, Simulation and experiment study of dimethyl ether synthesis from syngas in a fluidized-bed reactor, Chem. Eng. Science, 59, 5444-5464 S. Lee and A. Sardesai, 2005, Liquid phase methanol and dimethyl ether synthesis from syngas, Topics In Catalysis, 32, 3-4

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Multiphase CFD modeling - scale-up of FluidizedBed Crystallizer Mohsen Al-Rasheda, Janusz Wójcikb*+, Roch Plewikb, Piotr Synowiecb,c & Agata KuĞb a

Public Authority for Applied Education and Training, College of Technological Studies, Kuwait b Silesian University of Technology, Department of Chemical & Process Engng, ks.M.Strzody 7, 44-101 Gliwice, Poland c Institute of Inorganic Chemistry , ul. SowiĔskiego 11, 44-100 Gliwice, Poland * Corresponding author e-mail:[email protected] + Presenting author

Abstract The main goal of this study was to obtain a closer look to scale up problem of the Fluidized-Bed crystallizer operation, in particular for solids concentration larger than 10 vol.%. To achieve that a multi-phase CFD code was used. Such an approach to this problem has not been investigated until now. Data collected using CFD technique, impossible to obtain in any other way, especially for an industrial apparatus, provides the information about the suspension flow behaviour in such crystallizers. Keywords: scale-up, fluidized bed, crystallizer, multiphase flow, CFD

1. Introduction The fluidized-bed crystallizers (FL) were introduced to the industry in 1920’s (I. Isaachsen & F. Jeremiassen, 1925). Since then they have been used when large crystals are required (G. Hoffmann, 2005). Comprehensive research, conducted in order to better understand the performance of FLs, and a constant progress in designing of such crystallizers, results in a spectacular success of this technology (G. Hoffmann, 2005). Previously while studying FLs, the ideal classifying bed model was used (J. Wójcik, 1997). This model possess one important disadvantage, namely it is unable to predict the polydispersity of a crystal product. Particles segregation and their longitudinal mixing in the bed were taken into consideration by Francis et al. (C. Frances et al. 1994) in a series of ideal mixers connected into one multistage crystallizer. Shiau & Lu (L. D. Shiau & T. S. Lu 2001) used this concept for batch FL. To give more accurate prediction of the real situation, the axial dispersion modelling concept was applied in the investigation of FL performance (J. Wójcik, 2005; K. Toyokura et al., 1973). During the last decade, crystallization and precipitation processes were analyzed by means of the CFD techniques (M. H. Al-Rashed, & A. G. Jones, 1999). Those research however, were performed for the particle concentrations lower than 5% and for MSMPR crystallizers. Recently, one-phase and two-phase models of CFD were used while studying the performance of a conical apparatus equipped with a central tube and stator (J. Wójcik &

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R. Plewik, 2007; R. Plewik et al., 2007). Also behaviour of monodispersed fluidized bed in such crystallizer was investigated. The process parameter was the outlet velocity, and the determined one was the size of crystals held in the bed. The purpose of this article is to compare predictions of the model for small tank (0.68 m in diameter) with the large one (6 m in diameter which is a common industrial dimension) using multiphase CFD technique for the first time. Description of the FL operation, in particular for the solids concentration larger than 10 vol%. To achieve that, a multi-phase CFD code was used (J. Wójcik & R. Plewik, 2008).

2. Modeling One of the most often used fluidized-bed crystallizers is Oslo fluidized-bed crystallizer with classification leg. Fluidization of the bed is provided by circulation of fresh solution in the direction from a central tube to the overflow. The smallest crystals are washed out from the bed by streams of solution. The large crystals, having the sedimentation velocity larger than the solution velocity, pass into the classification leg. Smaller crystals are removed from it by the additional inlet stream. In a model preparation industrial data of NaCl crystallization were used (T. Messing & G. Hofmann, 1980). This paper provides information about the production rate of 3 t/h of 2-3 mm NaCl (40 mass % in suspension) crystals from 230 m3 apparatus of 6 m diameter. Ten size classes of particles are introduced to the model, i.e. 0.4; 0.6; 0.9; 1.2; 1.5; 1.8; 2.1; 2.4; 2.7 and 3 mm. The simulations were performed using commercial package designed for fluid dynamics computations Fluent 6.3.26. In case of multiphase flow, the Eulerian multiphase model with standard k-ε method was used. Calculations for an unsteady state were conducted until the normalized residuals reached the level of 10-410-7 .

3. Results and discussion Expansion of the polydispersed bed in the whole working space of apparatus is presented in fig.1. The calculation were performed in laboratory scale (volume of the crystallizer is 0.25 m3) and in industrial scale (volume of the apparatus 250 m3). Solid phase distribution as the porosity of the bed is presented for laboratory scale (fig. 1a), industrial scale with the same outlet

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Fig. 1. The porosity of the fluidal-bed for different cases: a) laboratory scale 0.038m/s b) industrial scale 0.038m/s c) industrial scale 0.114m/s

velocity as in previous case (fig. 1b) and for industrial scale in which the outlet velocity was increased (fig. 1c). When as a scale-up factor the outlet velocity is chosen (fig. 1a) and b)), compression of the bed takes place. Increase in the velocity can solve this problem (fig. 1c)). One can observe the proper choice of the inlet velocity because there are no solids present in the vicinity of the outlet of a central pipe and the upper outlet of the apparatus in fig. 1. It prevents settling and incrustation of crystals at the bottom of the tank and in the proximity of the outlet of a central pipe. Cases 1a and 1b shows increased concentration of the solid particles on the conical part of the central pipe as well as at the walls of conical part of the apparatus’ jacket. In case 1b this phenomenon does not exist. Solid accumulates at the bottom where fluid flow is the largest. Bright area near the outlet (upper part of the apparatus) indicates that the crystals are not washed out from the crystallizer or are removed in a small extent. Accumulation of grains can be seen outside the conical part of the central pipe and at the walls of the apparatus. Figure 2 shows distribution of solids volume fraction of different size classes in polydispersed bed in the working space of the apparatus. Considering laboratory scale one can observe that the particles do not enter the classification pipe. Particles of 0.4 mm in diameter are kept at the top of the apparatus (fig. 2g,h,i). Broad dark stripe in the outlet zone is observed in fig. 2h, which suggests complete retention of small particles inside the crystallizer. In fig. 2g,i a strong decrease in concentration of the smallest particles in the direction of outflow

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Fig. 2. The distribution of size volume fractions for the polidyspersed bed: a, b, c) l= 3mm; d, e, f) l= 0.9mm; g, h, i) l= 0.4mm; a, d, g) laboratory scale 0.038m/s b, e, h) industrial scale 0.038m/s c, f,i) industrial scale 0.114m/s

can be noticed. This is confirmed by a thin dark strap in the upper section of the crystallizer. Therefore crystals of the diameter of 0.4 mm can be considered as seeds, which is in good agreement with (T. Messing & G. Hofmann, 1980), but only in industrial scale. In all cases hydraulic classification can be observed: increase in the level of expansion of the bed is interconnected with the decrease in grain diameter. Figure 3 presents the liquid velocity profiles within the tank. Figure 3a), and d) show velocity distribution for small model (laboratory scale) whereas Fig. 3b), c), e) and f) demonstrate it for scale-up model (industrial scale). Figure 3 proves that both laboratory and industrial cases differ. In case of fig. 3a and 3c large circulation loops are clearly visible. In all three investigated systems small loops can be detected. They are probably only a small turbulence. In fig. 3b there are no such circulation loops that could not be considered as a turbulence only and the velocity profile is the most even among all cases.

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Fig.3. Liquid velocity profiles for two cross sections: a),d) laboratory scale (0.038m/s) b),e) industrial scale (0.038m/s) c), f) industrial scale (0.114m/s)

Comparison of fig. 1 and fig.3 shows that the largest concentration of solids is at the peak of the circulation loops. It seems that it could cause additional attrition of crystals. In addition vortex liquid flow generates energy dissipation which can cause an increase of crystals destruction and erosion of the inner jacket surface. The results confirm previous observations concerning strong polydispersed particles concentration distribution in both horizontal as well as in vertical cross section of the apparatus. These inner circulation loops affect the homogeneity of the bed. The shape of an apparatus shell, necessary for hydraulic classification of polidyspersed suspension in the industrial conditions, as well as the conical outlet from the central pipe causes adverse axial velocity distribution in the annular zone of the vessel (fig. 3).

4. Conclusions Fluidized bed crystallization can be successfully analyzed using the method of multiphase CFD. For such flow, the Eulerian multiphase model with standard k-ε method has been used, respectively. Substantial differences were found in predictions for laboratory and industrial scale. Those differences are in velocity profiles and distribution of solids in fluidized bed. We are aware that during scale up process the outlet velocity should be changed. In case of scaling up with conservation of the outlet velocity as the scaling factor, compression of bed and circulation loops disappearance takes place. This is due to decrease of the maximal axial velocity of the fluid in the absence of circulation loops. Increase of the outlet velocity results in reappearance of the circulation loops and further expansion of the bed. Data collected using CFD technique, impossible to obtain in any other way, provide the information about the suspension flow behaviour especially for the industrial apparatus.

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References M. H. Al-Rashed, & A. G. Jones, (1999). “CFD modeling of gas-liquid reactive precipitation”, (GLS4, Delft, Netherland), Chem. Engng. Sci., 54, 4779. C. Frances, B. Biscans & C. Laguerie, (1994). Modelling of a continuous fluidized-bed crystallizer Effect of mixing and segregation on crystal size distribution during the crystallization of tetrahydrate sodium perborate, Chem. Eng. Sci. 49, pp. 3269–3276. G. Hoffmann, (2005). Situation of plant construction in industrial crystallization – a process intensification, ISIC16, 759-772. I. Isaachsen & F. Jeremiassen, (1925). Ein neues industrielles Kristallisierungs-verfahren. Zeitsch. Ang. Chem., 38, 317-322. T. Messing & G. Hofmann, (1980). Industrielle Kristallisation - Moderne groβtechnische Anlagen und Fallstudien. Chem.-Ing.-Tech. 52, 11, 870-874. L. D. Shiau & T. S. Lu (2001). Interactive Effects of Particle Mixing and Segregation on the Performance Characteristics of a Fluidized Bed Crystallizer, Ind. Eng. Chem. Res. 40, 707713. R. Plewik, P. Synowiec & J. Wójcik, (2007). The simulation the two-phase CFD of hydraulic classification of deposit in cisternal apparatus from circulatory pipe. Pol. J. Chem. Tech., 10, 1, 22 — 27. K. Toyokura, H. Tanaka & J. Tanahashi, (1973). Size distribution of crystals from classified bed type crystallizer. J. Chem. Eng. Jap., 6, 4, 325-331. J. Wójcik, (2005). Modelling of crystal time distribution in the fluidized-bed crystallizer. ISIC16, 1015-1019. J. Wójcik, (1997). Population balance in a fluidized-bed crystallizer with ideal classification. InĪ. Chem. Proc., 18, 3, 411-426, (in Polish). J. Wójcik & R. Plewik, (2007). CFD modelling of a fluidized-bed crystallizer. InĪ. Chem. Proc. 28, 75–83. J. Wójcik & R. Plewik, (2008). Modeling of fluidized-bed crystallizers with the use of multi-phase CFD method. Int. J. Mult. Flow., submitted

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Optimisation of a torus reactor geometry using CFD Laura Pramparo,a Jeremy Pruvost,b Frank Stüber,a Josep Font,a Agusti Fortuny,c Azael Fabregat,a Patrick Legentilhomme,b Jack Legrand,b Christophe Bengoa,a a

Universitat Rovira i Virgili, Chemical Engineering Dpt., Av. Paisos Catalans 26, 43007 Tarragona, Spain, E-mail: [email protected] b Université de Nantes, GEPEA, UMR-CNRS 6144, CRTT, B.P. 406 ,F-44602, SaintNazaire Cédex, France c Universitat Politecnica de Catalunya, Chemical Engineering Dpt., Víctor Balaguer, 08800 Vilanova i la Geltrú, Spain

Abstract Different configurations of torus reactors were investigated, batch (close geometry) and continuous (open geometry) operating modes, different reactor geometries (square and circular sectioned) and, a scale-up of the reactor was finally conducted (100 to 300ml). The torus reactor was simulated using the commercial code Fluent® (Fluent Inc.). In batch conditions, a linear evolution of the mean circulation velocities with respect to the impeller rotation speed was obtained. A circular-sectioned torus reactor of 100 ml was next tested to compare the performance with a square-sectioned one. Negligible differences were found due to the small volume of the reactor and the high turbulence generated inside it. A 300 ml square-sectioned reactor was also studied. This reactor seemed to be more effective than the 100 ml one because it allowed higher bulk velocities for same impeller rotation speed. Reynolds number and Reynolds mixing number were also calculated for the 300 ml reactor. A linear relation between those two numbers was obtained. In continuous mode, only a slight difference in mixing times was observed for small values of impeller rotation speeds (200 rpm). For higher velocities of rotation, differences were found negligible. Keywords: Optimisation, CFD, Geometry, Torus reactor

1. Introduction Despite experimental studies have confirmed efficiency of the torus geometry, the optimal conception of torus reactors and their utilisation in industrial scale production require still theoretical research. Little information about hydrodynamic characteristics involved in torus shape reactors is known. Khalid et al. [1,2] emphasized the main features of the flow, and especially the high degree of mixing and the decay of the swirling motion when moving far from the impeller zone. Other studies were mainly restricted to global measurements, like the circulation time as a function of the impeller rotation speed [3], or a general overview of the flow structure using tracer methods [4]. This is mainly explained by the difficulties encountered to conduct an experimental investigation of the complex flow obtained in torus geometries. But the hydrodynamics resulting of its complexity also explains the reactor efficiency, and for this reason such kind of investigations is of primary interest.

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Moreover, Belleville and Legrand [5] have showed that torus reactors are characterised by an efficient radial mixing and the absence of dead volume allows an easy scale-up. They studied the influence of the viscosity of the solution and the geometry of the impeller on the mean velocity of circulation in a torus reactor. The study by Nasrallah et al. [6] showed that an efficient mixing is obtained in the toroidal geometry and found that the only parameters influencing the flow and the mixing are the rotating speed, diameter and type of the impeller. The torus reactor can be operated in continuous regime. In this mode, mixing performance can be modified [7], due to the effect of the flows on the flow structure inside the reactor. In this context, Computational Fluid Dynamics appears as an interesting tool to conduct a further analysis of flow structures. In Pruvost et al. [8], the numerical investigation was applied for torus reactor geometry with straight parts fitted with a marine impeller. The particular behaviour of the flow in torus reactor was analysed, and specially its evolution along the distance from the marine impeller. Results achieved with the commercial code Fluent being satisfactory, same authors [9] have also applied CFD to the particular case of a square-sectioned photobioreactor of torus geometry, but only for batch configuration. The aim of this study is the comparison of performance of different torus reactor configurations, batch (close geometry) and continuous (open geometry) operating modes, different reactor geometries (square and circular sectioned). Finally, a scale-up of the reactor was conducted (100 to 300ml).

2. Methodology The hydrodynamic characterization for the different geometries of the torus reactor in both batch and continuous conditions was carried out with numerical simulation using the commercial code Fluent® (Fluent Inc.). The torus reactor geometry was three-dimensionally meshed using Gambit Software (Fluent Inc.). Due to the impeller, a regular mesh is difficult to apply in the entire geometry. So, the reactor was divided in two different zones. The first one, in the marine impeller vicinity, has been meshed using tetrahedral volumes and prisms. A regular mesh with elementary hexahedral volumes has been used in the remaining part of the torus. To mesh the region near the impeller, a refinement function (size function) was applied to control the cells density in boundary layers. A second order interpolation scheme was applied for all discretized transport equations. These equations were numerically solved using a segregated method. The computations were performed until the convergence of all residual criteria with no variation of the values. The k-ω model was used as turbulence model. In the torus reactor, the flow, results from the impeller rotation, is the only driving mechanism in the reactor working in batch. In continuous, the driving force is the impeller rotation and the inlet-outlet flow rate. The moving part (impeller) in the geometry was modelled using a Multiple Reference Frames (MRF) resolution.

3. Results The circulation velocity U0 is one of the most important values in the study of the influence of the impeller rotation speed on the hydrodynamic of the torus reactor. The figure 1 presents the values of U0 in batch mode for impeller rotation velocities varying from 200 rpm to 2000 rpm for a square-sectioned torus reactor of 100 ml. As it can be seen in the figure, the circulation velocity obtained with Fluent increased with the

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impeller rotation speed in a linear proportion. The solid line represents the empirical equation obtained by Belleville et al. [5]. Those authors used a torus reactor consisting of four flanged smooth bends without straight lengths of pipes with a total volume of 2 L. They have proposed a model whereby the mean circulation velocity is calculated as a function of the velocity related to the volumetric rate of discharged flow from the impeller. It must be noticed that the relation between the circulation velocity and the impeller rotation speed is strictly linear, that is in agreement with the correlation presented by Belleville et al. [5]. However, the mean bulk velocity obtained for a fixed impeller rotation speed is even lower in the case of a square-sectioned reactor. As it was described by Pruvost et al. [8], the use of a square-sectioned geometry reduces the induced flow rate in the torus geometry, because the swirling flow is better maintained in circular-sectioned pipes. It is interesting to introduce the Reynolds number in order to characterise the flow. In a mixing tank, where there is no bulk velocity, the Reynolds number is given as the mixing Reynolds number Rem = ρ ⋅ N ⋅ D 2 μ . In the torus reactor, the Reynolds number can be calculated by the equation Re = ρ ⋅ U 0 ⋅ D μ with the values of U0 obtained in previous results. In the case of batch torus reactor, the relation between Re and Rem is given by [10] Re = 0.1109•Rem1.16 for Rem between 4500 and 5500; and Re = 0.0027•Rem1.59 for Rem under 4500. These equations were obtained for a square-sectioned torus reactor of 0.1 L. Figure 2 shows the correlations of Reynolds number as a function of the mixing Reynolds number for a torus reactor and also the results obtained by numerical prediction. The results are in agreement with the predicted correlations, especially for Reynolds numbers higher than 1000. However, for lower values of the mixing Reynolds number, numerical results were slightly higher than the predicted ones. In the same way, it was possible to obtain a correlation between the mixing Reynolds number and the Reynolds number. The relationship is given by Re = 0.0695·Re 1m.2 . Due to the presence of inlet and outlet flow, the continuous regime can lead to different hydrodynamics with respect to the batch one. The relation between N and U0 could be modified due to the effect of the entering flow rate through the inlet. This entering flow rate can modify the U0 due to a possible effect in the circulation. It was found that the inlet flow rate has a small influence on the mean velocity except for small agitation speeds. With the higher inlet flow rates the mean velocities are slightly smaller, may be due to the perturbation of the flow inside the reactor. Finally, for all flow rates, the results are mainly dependent on the impeller rotation speed as it was observed in batch conditions. In a next step, a new geometry and grid were created for the torus reactor but using a circular-sectioned reactor. The same methodology was kept. In this case, the regular part of the reactor was created using the default toroidal geometry available in Gambit. However, in order to include the impeller, the irregular part had to be modified and rebuilt to be compatible with the rest of the geometry. Once the geometry was finished, the mesh was created resulting in a regular mesh in ¾ of the reactor and an irregular mesh for the quarter that contained the impeller. As can be seen in figure 1, the mean velocities in the circular-sectioned reactor showed the same trend than the square-sectioned torus reactor and negligible differences were observed. This fact can be due to the small volume of the reactor and the high turbulence generated inside it.

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Finally, a scale-up to 300 ml of the square-sectioned torus reactor was realised. The geometry and mesh for this new torus reactor were made in the same way described above. To compare the performance of the 300 ml reactor, the mean bulk velocities were calculated. The mean velocities inside the reactor are shown in figure 3 and, as it can be seen, they presented also a linear relation between U0 and the impeller rotation speed. These mean velocities were higher compared with the ones obtained for the 100 ml square-sectioned reactor.

Figure 1. Mean bulk velocity for 100 ml reactor. Figure 2. Variation of the Reynolds numbers.

Figure 3. Mean bulk velocities in the 300 ml Figure 4. Reynolds vs. Reynolds mixing number in the 300 ml torus reactor. square-sectioned torus reactor.

A higher volume of the reactor, with a bigger impeller, could be the reason for this behaviour. The impeller for this case had an external diameter of 25 mm and an internal diameter of 7 mm, keeping the same pitch angle. In comparison with the empirical equation obtained by Belleville et al. for a torus reactor with circular section, the mean velocities obtained in this case were slightly smaller. It is possible that the flow in the model used by Belleville et al. that consisted of four flanged smooth bends without straight lengths of pipes with a total volume of 2 L, behaves in a similar way than in this 300 ml square-sectioned torus reactor. This might be possible supposing that large diameter reactors behaves in a similar way. This fact is also confirmed by other simulations [9] made in a torus photobioreactor of 1.3 L. On the other hand, the Reynolds and the Reynolds mixing numbers for the 300 ml reactor were also calculated and are presented in figure 4. A linear relation between the Reynolds numbers was obtained and it is comparable to the one obtained for the 100 ml

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torus reactor. Thus, the same approximation was used. As in can be observed in figures 2 and 4, a good approach is obtained between experimental and numerical results, where the correlations were obtained from experimental data.

4. Conclusions The characterization of the flow-field in a torus reactor of 100 ml was carried out for two different configurations. It was obtained that the hydrodynamic is mainly a function of the impeller rotation speed. Negligible influence on the hydrodynamic was observed for flow inlets located perpendicular to the flow circulation. No differences were found using a circular-sectioned reactor due to the small volume and the high turbulence generated inside it. A 300 ml square-sectioned reactor seemed to be more effective than the 100 ml one because it presents higher bulk velocities similar to those predicted for a torus reactor with circular section. The main practical interest of this work is that it is possible to have the same hydrodynamic behaviour for a 0.3 L torus reactor as for several litres torus reactors. This is an important result for scaling-up the performance obtained in lab-scale torus reactor.

5. Acknowledgements Laura Pramparo is indebted to the Universitat Rovira i Virgili and the Agència de Gestió d’Ajuts Universitaris i de Recerca (AGAUR) of Catalan Government for the predoctoral scholarships. Financial support was provided by the European Community, project REMOVALS, FP6-018525.

References [1] Khalid A., Legrand J., Rosant J.M., 1996. Turbulent flow induced by an impeller in a closed toroidal loop. J. Fluids Eng. 118(4): 677-684. [2] Khalid A., Legrand J., 2001. Energy dissipation distribution and mixing in a torus reactor. Chem. Eng. Com. 185: 141-164. [3] Sato Y., 1979. Flow pattern, circulation velocity and pressure loss in loop reactor. J. Chem. Eng. Japan 12: 448-453. [4] Legrand J., Belleville P., 2002. Flow characteristics and transport phenomena in toroidal loop reactors. Chem. Eng. Technol. 25(6): 667-670. [5] Belleville P., Nouri L., Legrand J., 1992. Mixing characteristics in the torus reactor. Chem. Eng. Technol. 15: 282-289. [6] Nasrallah N., Legrand J., Bensmaili A., Nouri L., 2008. Effect of impeller type on the mixing in torus reactors. Chemical Engineering and Processing 47(12):2175-2183. [7] Benkhelifa H., Legrand J., Legentilhomme P., Montillet A., 2000. Study of the hydrodynamic behaviour of the batch and continuous torus reactors in laminar and turbulent flow regimes by means of tracer methods. Chem. Eng. Sci. 55: 1871-1882. [8] Pruvost J., Legrand J., Legentilhomme P., Rosant J.M., 2004. Numerical investigation of bend and torus flows. Part II: Flow simulation in torus reactor. Chemical Engineering Science 59(16): 3359-3370. [9] Pruvost J., Pottier L., Legrand J., 2006. Numerical investigation of hydrodynamic and mixing conditions in a torus photobioreactor. Chem. Eng. Sci. 61: 4476-4489. [10] Legrand J., Guéguen J., Bérot S., Popineau Y., Nouri L., 1997. Acetylation of pea isolate in a torus microreactor. Biotech. Bioeng. 53: 409-414.

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.

Robust and efficient numerical methods for the prediction of pollutants using detailed kinetics and fluid dynamics Alessio Frassoldati, Alberto Cuoci, Tiziano Faravelli, Eliseo Ranzi, Guido Buzzi Ferraris Dipartimento di Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20133 Milano, Italy, [email protected]

Abstract The design of combustion devices demands the fulfillment of always more stringent limitations concerning pollutant emissions. Turbulent flows are characterized by complex interactions between turbulence and chemistry. However, even with the increase of computer power and speed, it is not currently feasible to directly couple CFD models and large kinetic schemes which are necessary to predict pollutants. A two-step approach can be adopted: CFD results obtained with simple combustion schemes are post-processed using detailed kinetics. The proposed Kinetic Post Processor (KPP) operates by assuming the temperature and flow fields to be those predicted by the CFD code and solves the overall system of balance equations in a complex network of reactors. With proper attention to the numerical procedures, this approach is able to couple and handle CFD and detailed kinetics. A specifically conceived hybrid numerical method, based on a modified Newton and successive substitution methods, was developed to solve such large and extremely non-linear systems [1]. In this paper the attention is focused on new improvements in the numerical method obtained by using the age of the fluid to accelerate the convergence of the iterative solver and by calculating the Jacobian matrix analytically rather than numerically. In the application example, these numerical approaches reduced the computational time by a factor of ~8.

Keywords: Detailed kinetics, CFD, Large systems, Combustion, Pollutants

1. Introduction Pollutant formation is one of the main focuses of new burner designs: this explains the increasing demand for computational tools capable of characterizing the combustion systems in terms of pollutant species also. The direct coupling of detailed kinetics and complex CFD is a very difficult task, especially when considering the typical dimensions of the computational grids used for complex geometries and industrial applications. Pollutant species only marginally affect the main combustion process and consequently do not significantly influence the overall temperature and flow fields. Consequently it is feasible to evaluate the structure of the flame with reduced kinetic schemes first and then post-process the CFD results with this newly-conceived numerical tool, the Kinetic Post-Processor (KPP) [1]. This KPP model, which has already been applied to evaluating the performance industrial furnaces [2], is able to accurately predict the formation of different pollutants, such as NOx, CO and unburned hydrocarbons. The KPP is based on the general concept of “reactor network analysis”

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which has already been employed by various authors to post-process CFD results and evaluate the formation of pollutants, using detailed kinetic mechanisms for various applications by utilizing a different level of description and various numerical methodologies [3-6]. In this paper we briefly describe the numerical method used to solve the large system defined by the conservation equations of the chemical species (molecules and radicals) contained in a detailed kinetic mechanism. Then, the attention is focused on new improvements of the numerical method.

2. Mass balance equations and numerical method As already mentioned, the KPP uses the temperature field as obtained by the CFD computations. A fixed average temperature is assumed in each equivalent reactor and the rates of all the reactions involved in the kinetic scheme are evaluated. In turbulent combustion conditions, these reaction rates cannot simply be calculated as a function of the mean temperature and composition, mainly due to the highly non-linear dependence of reaction rates on temperature. A proper correction is applied to take into account the effects of temperature fluctuations [1]. These corrections are mainly relevant for thermal NOx formation reactions, where high activation energies are involved. CFD results are also used to define the overall system by describing the mass balance equations of all the chemical species involved in the detailed kinetic scheme as well as providing the initial composition guess. For all the equivalent reactors, the steady mass balance of each species (Ȧi) accounts for convection, diffusion and chemical reaction terms: NF NR G * ª º W p ˜ Z inp ,i  W p ˜ Z out J S V M Q ij ˜ rp , j  ˜  ˜ ¦ ¦ p ,i p i ¬ p , n ,i p , n ¼ n 1

0

i 1...N SP , p 1...N P

(1)

j 1

where WP is the total convective flow pertaining to the reactor, Nsp the number of species, NP the number of reactors (cells), NF the number of faces with surface area S of the cell, NR the number of reactions, VP the volume of the cell, M is the molecular weight and r the reaction rate. The mass diffusion term is the sum of all the contributions pertaining to the adjacent reactors and is computed in the following form: G P (2) J i  t ˜’Zi Sct where Sct is the turbulent Schmidt number and Pt the turbulent viscosity. The global Newton or the modified Newton methods are not robust enough to solve this system simply using CFD results as a first-guess. It is therefore convenient to approach a better estimate of the solution by iteratively solving the sequence of individual reactors with successive substitutions. Each reactor is solved using a local Newton method with the possible use of a ‘false transient’ method (time stepping) to improve the initial guess or to approach the solution. Only when the residuals of all the equations reach sufficiently low values, a modified global Newton method is applied to the whole system. The bottleneck of this very large system is both in memory allocation and in CPU time when a Gauss factorization method is applied to the whole system. Therefore, Gauss factorization is applied only to the main diagonal blocks, while an iterative method is applied to the other terms [1]. This approach allows to save the memory allocation and makes viable the solution of this overall system. Also in this case, if the global Newton method does not converge, a ‘false transient’ method is applied to better approach the solution of the whole system.

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The global Newton method not only increases the efficiency but mainly assures the complete convergence to the solution. Additional details on the Kinetic Post-Processor and its numerical method are reported in [1,7].

3. Improvements of the numerical method and solution strategies The attention is here focused on the new improvements developed to enhance the overall efficiency of the numerical method. 1) The first upgrade can be obtained by taking into account the relevant physical phenomena, i.e. solving the individual reactors according to their fluid age (FA). The age on an element of fluid is the time elapsed since it entered the computational domain [8]. This has a relevant impact on the iterative solution which is accelerated because of the higher convergence speed. FA is a scalar variable which can be easily calculated by CFD codes and describes how the fluid flows through the computational domain. FA is zero at all inlets, it increases along the flow streamlines and increases further in recirculating flows and stagnation points. The idea beneath this approach is that a lower number of iterations is necessary to transport the information along the computational domain when the solver takes advantage of the fluid flow streamlines. Since FA is not given implicitly by the CFD code it must be calculated in an additional transport equation. In this work, FA is defined as a new user-defined (conserved) Scalar. FA easily converges in a restarted CFD simulation and, since the calculation of the fluid age relies only on information from the flow field but it does not affect it, only the scalar equation needs to be solved. 2) The second improvement is related to the Jacabian matrix. In fact, the numerical solution of large scale nonlinear problems involves computing Jacobian matrices several times, making the computation of derivatives a central and time-consuming part of the solution process. In order to increase the computational efficiency, the derivatives of kinetic rate equations are evaluated analytically rather than numerically. The MATLAB differentiation toolbox is used to read the kinetic scheme and calculate the analytical derivatives, which are then directly included and compiled in the C++ routines of the KPP code. This calculation, which is needed only one time for each mechanism, takes about 1 h on a PC in the case of a scheme with ~100 species and 1500 reactions.

4. Application example: FLOX burner A semi-detailed kinetic scheme able to describe the oxidation of heavy hydrocarbon fuels, up to diesel and jet fuels, has been developed and its main features have been already discussed in the literature [9]. The chemistry of nitrogen compounds is also discussed elsewhere [10]. The thermodynamic properties are taken from CHEMKIN Thermodynamic Database [11]. The overall mechanism is available at (www.chem.polimi.it/CRECKModeling). The burner was investigated in different flameless operating conditions (see Table 1) and is placed at Enel Ricerca Laboratories in Livorno [12]. Figure 1 (left) shows the Temperature, Velocity and FA in the combustor chamber. Moreover, a comparison between measured NO emissions and the corresponding predictions of the KPP NO is also shown in Figure 1. The agreement is satisfactory and confirm the possibility to use this computational tool also for the simulation of flameless combustion.

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710 Table 1. Burner operating conditions.

Case 1 2 3 4 5 6 7

Q [kW] 8.23 9.13 9.31 9.90 10.53 10.70 10.42

T exhaust [K] 1479 1535 1651 1687 1710 1722 1702

T [K]

FA [s]

T max [K] 1815 1920 2034 2065 2066 2096 2049

NO exp [ppm] 5.8 18.9 40.7 52.9 52.8 61.8 48.6

|V| [m/s] 80

NO [ppm] - Num.

70 60 50 40 30 20

20

30

40

50

60

70

80

NO [ppm] - Exp.

0

0

2000

2000

4000

4000

Cell index

Cell index

Figure 1. Left: contour plots of Fluid Age (s), Temperature (K) and velocity magnitude (m/s) for Case 2. Right: Comparison between calculated and measured NO for several cases (Table 1)

6000

6000

8000

8000

0

2000

4000 6000 Cell index

8000

0

2000

4000 6000 Cell index

8000

Figure 2: Boolean structure of the Jacobian matrix of the non-linear system for a structured 2D computational mesh. Left (CFD): mesh is ordered according to the reverse Cuthill-McKee method. Right (KPP): mesh is ordered according to the fluid age (FA) of each cell.

The flameless combustion technology is based on an enhanced recirculation of exhaust gases into the reaction zone which allows the dilution of the flame, thus reducing the reactivity and avoiding temperature peaks. The system is then well mixed and for this reason in this particular case the effect of the use of FA is expected to play a minor role.

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It is important to notice that this effect is expected to be significantly dependent on the case studied. As already mentioned, the dimension of the overall system is NSPuNCELLS. Figure 2 shows a typical Boolean structure of the whole matrix system for the 2D structured grid with a9500 cells. In the CFD simulation the structure is regular because the reordering of the domain was performed to reduce the bandwidth: cells are reordered so that neighboring cells are near each other in the zone and in the computer memory. This increases the CFD code (FLUENT 6.23) computational performance because it increases memory access efficiency. On the other hand, when the cells are ordered according to their FA, the structure of the matrix becomes less regular and the sparsity is increased. Nevertheless, as already discussed, this structure allows to increase the convergence speed of the iterative solver of the KPP by a factor of ~1.3. In this application example the use of both FA an analytical Jacobian matrix allowed to improve the numerical efficiency by a factor of ~8. On a 3 GHz workstation, the amount of time required for this calculation is reduced from ~9 hours to ~1 hour. It is important to notice that the improvement in the efficiency of the numerical method makes viable the post-processing of CFD simulations obtained using large computational grids, as those typically used for 3D simulation and complex geometries [2,6].

5. Acknowledgements The authors acknowledge the financial support of Technip BV and wish to thank Chiara Galletti, Alessandro Parente and Leonardo Tognotti for the details on the flameless burner.

6. References [1]

A. Cuoci, A. Frassoldati, G. Buzzi Ferraris, T. Faravelli, E. Ranzi, Int. J. Hydrogen Energy, 32:3486(2007) [2] S. Barendregt, M. van Goethem, I. Risseeuw, A. Frassoldati, T. Faravelli, A. Cuoci, X. J. Li, The Design Of Ultra-Low NOx Critical Furnaces, Proceedings of the 8th european conference on industrial furnaces and boilers, Vilamoura Portugal, 25-28 March 2008. [3] M. Falcitelli, S. Pasini, and L. Tognotti, Comb. Sci. Tech., vol. 174, pp. 22, 2002. [4] M. S. Skjøth-Rasmussen, O. Holm-Christensen, M. Østberg, T. S. Christensen, T. Johannessen, A. Jensen, and P. Glarborg, Comp. Chem. Eng. 28:2351-2361 (2004). [5] I. V. Novosselov, P. C. Malte, S. Yuan, R. Srinivasan, and J. C. Y. Lee, Proceedings of GT2006 ASME Turbo Expo: Power for Land, Sea and Air, Barcelona, Spain, 2006. [6] A. Frassoldati, A. Cuoci, T. Faravelli, E. Ranzi, S. Colantuoni, P. Di Martino, G. Cinque, Comb. Sci. Tech., in press. [7] D. Manca and G. Buzzi Ferraris, ESCAPE 18 (2008). [8] Himmelblau D.M. and Bischoff K.B, Process analysis and simulation, Wiley (1968). [9] E. Ranzi, M. Dente, A. Goldaniga, G. Bozzano, T. Faravelli, Prog. Energy Combust. Sci., 27:99(2001). [10] A. Frassoldati, T. Faravelli and E. Ranzi, Combust. Flame 135, (2003), 97-112. [11] R.J. Kee, F. Rupley, J.A. Miller, The Chemkin Thermodynamic Data Base, Sandia 1989 [12] C. Galletti, A. Parente, L. Tognotti, Comb. Flame 151:649-664 (4) (2007)

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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An Approach to the Representation of Gradual Uncertainty Resolution in Stochastic Multiperiod Planning Vicente Rico-Ramireza, Ignacio E. Grossmannb, Bora Tarhanb, Salvador Hernández-Castroc and Juan G. Segovia-Hernándezc a

Instituto Tecnologico de Celaya, Av. Tecnologico y Garcia Cubas S/N, Celaya,Gto., 38060, Mexico, [email protected] b Carnegie Mellon Uiniversity, Pittsburgh, PA, 15213, USA c Universidad de Guanajuato, Facultad de Quimica, Guanajuato, Gto., 36050, Mexico

Abstract This work focuses on the modeling of multistage stochastic problems with endogenous (decision dependent) uncertainties. We assume that the probability distributions of the uncertain parameters are discrete, so that a scenario tree representation can be used. As the main contribution, the paper describes an approach to represent the gradual resolution of endogenous uncertainties after an investment in information is made; partial resolution of uncertainty through time is defined in terms of a percentage of variance reduction. The approach is based on the concepts of posterior and revelation distributions and on the practical propositions of the theory of conditional expectations. A mining production planning problem with endogenous uncertainty in ore quality is used as a case-study to show the scope of the proposed representation as well as to evaluate the effect of the gradual resolution of uncertainties on the optimal solution. Keywords: Multiperiod stochastic planning, uncertainty resolution

1. Introduction Typical engineering applications are decision problems subject to the combination of inherent, modeling and statistical uncertainties. Uncertainty in planning problems can be divided into two classes: exogenous (or market) uncertainty and endogenous (or technical) uncertainty [1]. Problems where stochastic processes are independent of decisions are said to have exogenous uncertainty, whereas problems where stochastic processes are affected by decisions are said to possess endogenous uncertainty. For example, in a multiperiod oilfield development project, the actual size and the initial deliverability of a reserve is generally uncertain [2]; however once a capital investment decision is made (interpreted as an investment in information) regarding exploration and/or production, the uncertainty will eventually be resolved (after a “learning time”). Hence, uncertainties in actual size and initial deliverability are endogenous and their resolution through time is influenced by the decisions made in a given time period. Literature reports some previous approaches to handle decision dependent uncertainties. Jonsbraten et al. [3] assume that decisions affecting uncertainty resolution occurs at the first time period. Similarly, Goel and Grossmann [1,2] consider immediate resolution of endogenous uncertainties after an investment in information is made, and apply their approach to gas field development problems. More recently, Tarhan and Grossmann [4] analyze the synthesis of process networks with time-varying uncertain yields in which investment in pilot plants can be considered to reduce uncertainty of the yields.

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The problem is formulated as a multistage stochastic program with decision dependent elements where investment strategies are considered to reduce uncertainty, and timevarying distributions are used to describe uncertainty. Nevertheless, it is assumed that full resolution of the uncertainty is achieved after one time step (period). In this work we describe an approach to represent the gradual resolution of endogenous uncertainties after an investment in information is made; our resolution strategy allows partial resolution of uncertainty through several time periods, so that the resolution at each time period is defined in terms of a percentage of variance reduction. The approach has been incorporated into a multistage stochastic program with application to mining production planning. The model includes gradual resolution of ore quality (uncertain parameter) and the concept of indistinguishability. The following sections describe the gradual resolution of uncertainty approach and the multiperiod stochastic model. Further, a case-study is used to show the scope of the proposed representation as well as to evaluate the effect of the gradual resolution of uncertainties on the optimal solution.

2. Gradual Resolution of Endogenous Uncertainty Dias [5] developed a strategy to model uncertainty reduction as the result of an investment in information. The mathematical representation is based on four propositions from the theory of conditional expectation. Also, the resolution process involves three different probability distributions; namely, prior distribution, posterior distribution and revelation distribution. The author applied his approach by assuming continuous probability distributions and expressed the reduction of uncertainty as a percentage of variance reduction. Our approach to resolve endogenous uncertainty Here we have extended the approach described by Dias [5] to cases where the probability distributions are discrete, so that we can apply a scenario tree representation to multiperiod stochastic planning problems. The uncertainty resolution process is as follows. We assume that a prior (original) discrete distribution of the endogenous parameter is known, so that the probabilities πi of n probable values (zi) are given (i=1…n). Then, after an investment in information is made at any time period, the resolution process for the parameter starts and it will continue for a learning time involving r resolution steps, with a reduction of variance at each resolution step (the variance reduction is expressed in terms of a fraction V). We also assume that, at each resolution step, we may receive m messages (each with probability θj, j=1…m) so that the original distribution changes, resulting in m posterior distributions. The time varying profile for the endogenous parameter is finally given by using the revelation distribution at each resolution step. The revelation distribution is defined by the mean values (each with probability θj) of the posterior distributions. Figure 1 shows a representation of the three different probability distributions for the case of three messages. In the practical implementation of the approach, our main assumptions are: i) the number of messages is equal to the number of probable values (m=n), ii) all of the messages are equally probable (θj =1/m) and iii) each of the posterior distributions shows a high probability (pz) for one of the probable values. We derived a general expression to calculate the probability pz of each posterior distribution which results in a reduction of variance V. The derivation is not presented here, but it is based on the theoretical proposition which states that the reduction of variance of the prior distribution is equal to the (expected) mean variance of the posterior distributions.

An Approach to the Representation of Gradual Uncertainty Resolution in Stochastic Multiperiod Planning

3 Messages

Good News

Prior Distribution πi ---------

zi ---------

Investment on information

θ1 Neutral

715

3 Posterior Distributions Value ---------

pi ---------

z1

Value ---------

pi ---------

z2

Value ---------

pi ---------

z3

θ1

θ2

1 Posterior Distribution

θ2 Bad News

θ3

θ3

Figure 1. Prior, posterior and revelation distributions

After applying the assumptions enlisted above, the general expression reduces to Eq. 1.

¦ (z n

i =1

i

2 2ª n 2 (1 − p z ) º (1 − p z ) n n (z i − z j )2 − z «(1 − V ) + »= ¦ ¦ 2 (n − 1) »¼ n − 1 j =1 i =1,i ≠ j «¬

)

(1)

where z is the mean of the prior distribution. Also, in Figure 1, z i is the mean of each posterior distribution. Eq. 1 can be solve to obtain pz.

3. Multiperiod Model for Mining Production Planning This section describes the case-study and the multiperiod model which incorporates the gradual resolution of endogenous uncertainty. Seeking simplicity due to space limitations, only one example and the main elements of the model are described. Case-study and gradual resolution profiles The case-study consists of a mining production planning problem involving three mines (adapted from Williams [6]). The mineral produced by each of the mines is mixed in order to satisfy the demand and ore quality at each time period. Royalties are paid if a mine is open for production. Optimal decisions includes the mines production profiles and, previous to that, whether a mine should be open (and royalties paid) or not. The ore quality of one of the mines is known (equal to 1), but it is uncertain for the other two. Regarding the mines with uncertain ore quality, it is also assumed that, after a mine starts operation (an investment in information is made through the payment of royalties) the ore quality will resolve gradually for one mine, but it will immediately be resolved for the other one (either 0.8 or 0.9). The prior distribution for the endogenous ore quality consists of two equally probable values (n=m=2; π1=π2=0.5; z1=0.6; z2=0.7) and the learning time includes three resolution steps (the variance reduction is of 33% at each step). Table 1 shows the mean values of the posterior distributions (revelation distribution) at each resolution step calculated by using Eq. 1; the investment in information is at time t. It can be observed that there is a successive reduction at the expected value of variance until full resolution is achieved.

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Table 1. Revelation distribution for the endogenous ore quality

Time step t t+1 t+2 t+3

Posterior Distributions Low quality High quality 0.65 0.65 0.62127 0.67872 0.60938 0.69062 0.6 0.7

E(variance) 0.00253 0.00167 0.00083 0.00000

Variance reduction 0 33% 66% 100%

As theoretically anticipated, the revelation distribution at full resolution is equal to the prior distribution. Both of the posterior distributions are assumed as equally probable. Notice that, due to the number of resolution steps, 16 combinations of values for the uncertain parameters result (8x2=16; 23=8 for the endogenous parameter and 2 for the immediately resolved uncertain parameter). Hence, if both of the mines with stochastic ore quality are operated, 16 different scenarios should be considered. Stochastic Multiperiod Model The MILP stochastic multiperiod model is defined by Eqs. 2 through 6. The time horizon is divided in N time periods. T is the set of time periods (1…N), I is the set of mines (1…M), S represents the set of scenarios, J is the set of mines with endogenous uncertain parameters, K is the set of mines without exogenous uncertainties and R is the number of resolution steps. Binary variables y represent decisions about opening and operation of a mine at time t and scenario s. M N M N ªN º − ¦¦η i xis,t » f = ¦ p s «¦ α t qt − ¦¦ ρ i y iopen ,t s∈S i =1 t =1 i =1 t =1 ¬ t =1 ¼

,s xis,t ≤ U i y ioper ,t ,s ,s yioper ≤ y iopen ,t ,t ,s open , s yiopen ,t +1 ≤ y i ,t M

¦P

s i ,t

≥ C t q ts

(2)

∀i ∈ I , ∀t ∈ T , ∀s ∈ S ∀i ∈ I , ∀t ∈ T , ∀s ∈ S ∀i ∈ I , ∀t ∈ T , ∀s ∈ S ∀t ∈ T , ∀s ∈ S

i =1 s k ,t

P = Qks x ks ,t ∀k ∈ K , ∀t ∈ T , ∀s ∈ S t −1 § · ,s w sj ,t = ¨ ¦ y oper = 0 ¸ ∀j ∈ J , ∀t ∈ T , ∀s ∈ S j ,τ © τ =1 ¹ s oper , s s xp j ,t ⇔ y j ,t ∧ w j ,t ∀j ∈ J , ∀t ∈ T , ∀s ∈ S M

¦x

s i ,t

= q ts

i =1 M

¦y i =1

open , s i ,1

=M

∀t ∈ T , ∀s ∈ S ∀s ∈ S

(3)

An Approach to the Representation of Gradual Uncertainty Resolution in Stochastic Multiperiod Planning

717

º ª§ t oper , s · ªt ,s º Z ts , s′ ⇔ «∧ ¬y ioper ∨ ,τ » r =1...R ( j ) «¨ ¦ y j ,τ = r + 1¸ ∧ ( j , s, s ′) ∈ M r ( j , s, s ′)» (4) ¬τ =1 ¼ ¹ ¼ ¬© τ =1 ∀(s, s ′), s < s ′, ∀t ∈ T

(

)

ª º Z ts , s′ « » s s′ « xi ,t = xi ,t » ∨ ¬Z s , s′ t ,s oper , s ′ » « y ioper ,t +1 = y i ,t +1 « open ,s open , s′ » ¬« y i ,t +1 = y i ,t +1 ¼» xis,1 = xis,1′ ,s , s′ yioper = y ioper ,1 ,1 ,s , s′ yiopen = y iopen ,1 ,1

[

]

∀(s, s ′), s < s ′∀t ∈ T (5)

∀i ∈ I , ∀t ∈ T , ∀s ∈ S ∀i ∈ I , ∀t ∈ T , ∀s ∈ S ∀i ∈ I , ∀t ∈ T , ∀s ∈ S

ª º xp sj ,t « s » s s s « Pj ,t + r −1 = x j ,t + r −1Qr , j ∀r = 1 R ( j ) + 1 » ∨ ¬xp j ,t « Pjs,t + r = x sj ,t + r QRs ( j ), j ∀r = R( j ) + 1T − t » ¬ ¼ ∀j ∈ J , ∀t ∈ T , ∀s ∈ S

[

]

(6)

x represents the ore production of a mine and q is the total ore production. Q is the endogenous parameter (ore quality), P is the mine production of the valued mineral, U is the maximum achievable ore production of a mine and C is the minimum required quality of the produced material. Very important, Z is a binary variable representing indistinguishability of scenarios s and s’. Finally, xp and w are binary variables used just to represent the logical relationships among decisions. The objective function (Eq. 2) includes three terms; the profit, the royalty cost and the operation cost. Results and discussion For time horizon involving 8 time periods, the model contains 2881continuous variables and 1984 binary variables, which shows the combinatorial complexity of the approach. As per the results, the difference between the deterministic and stochastic objectives (value of the stochastic solution, VSS) is almost 48% for the example, which shows the significance of incorporating uncertainties in the model parameters. Interestingly, the optimal decisions for all the scenarios and the deterministic case include the opening and operation of the mine with endogenous uncertainty since the first time period. However, because of poor ore quality, the deterministic case suggested stopping operation after 2 time periods. As an example of the numerical results, Table 2 shows the ore production (106 ton/year) in 4 time periods of the mine with immediate resolution of ore quality in scenarios 1 through 8.

4. Conclusions and Future Work This paper describes an approach to model the gradual resolution of endogenous uncertainties represented by discrete probability distributions on the context of MILP multiperiod planning problems.

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Table 2. Numerical results (x) for mine with immediate resolution of uncertainty

Time period 1 2 3 4

s1 2.5000 1.0000 2.5000 0.8080

s2 2.5000 1.0000 2.5000 0.8080

s3 2.5000 1.0000 1.0000 0.8080

s4 2.5000 2.5000 1.0000 0.8080

s5 2.5000 1.0000 2.5000 0.8080

s6 2.5000 1.0000 1.0000 0.8080

s7 2.5000 2.5000 2.5000 0.8080

s8 2.5000 0.0000 1.0000 0.8080

The derivation is based on the theoretical proposition which states that the reduction of variance of the prior distribution is equal to the (expected) mean variance of the posterior distributions. In fact, partial resolution of uncertainty through time is defined in terms of a percentage of variance reduction. Due to combinatorial complexity, the number of scenarios rapidly increases with both the number of resolutions steps and the number of probable values of the uncertain parameters. Hence, the resulting MILP models can only be solved through an LP-based branch and bound for smaller instances. The difference between the deterministic and stochastic objectives (value of the stochastic solution, VSS) is almost 48% for the case study, which shows the significance of incorporating uncertainties in the model parameters. Duality-based branch and bound algorithms for solving larger (linear and nonlinear) problems are currently being developed and tested. Furthermore, a paper describing a generalized approach to model the time varying profiles of gradually resolved endogenous parameters is also in preparation.

5. Acknowledgements V. Rico-Ramirez thanks the financial support provided by the Fulbright Scholarship program and by CONACYT, Mexico.

References [1] Goel, V. and I. E. Grossmann. A class of stochastic programs with decision dependent uncertainty. Mathematical Programming - Series B, 108, 355-394, 2006. [2] Goel, V. and I. E. Grossmann. A stochastic programming approach to planning of offshore gas field developments under uncertainty in reserves. Computers & Chemical Engineering 28, 8, 1409–1429, 2004 [3] Jonsbraten, T.W., R. J. B. Wets and D. L Woodruff, A class of stochastic programs with decision dependent random elements. Annals of Operations Research, 82, 83-106, 1998. [4] Tarhan, B. and I. E. Grossman. A multistage Stochastic Programming Approach with Strategies for Uncertainty Reduction in the Synthesis of Process Networks with Uncertain Yieldss, Computers & Chemical Engineering 32, 4-5, 766-788, 2008. [5] Dias, M. A. G. Investment in information in petroleum: Real options and revelation, In the proceedings of the 6th Annual International Conference on Real Options, Cyprus, 1-47, 2002 [6] Williams, H.P. Model building in mathematical programming, 4th Edition John Wiley and sons, London, 2002.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

719

Axial dispersion/population balance model of heat transfer in turbulent fluidization Zoltán Sülea, Béla G. Lakatosb, Csaba Mihálykóc a

Department of Computer Science, [email protected] Department of Process Engineering, [email protected] c Department of Mathematics and Computing, [email protected] University of Pannonia, Egyetem u. 10, Veszprém, H-8200, Hungary b

Abstract An axial dispersion/population balance model is presented for describing heat transfer processes in gas-solid turbulent fluidized beds. In the model, the gas and particle transport is described by the axial dispersion model, while the particle-particle and particle-wall heat transfers are modeled as collisional random events, characterized by the collision frequencies and random variables with probability density functions determined on interval [0,1]. An infinite hierarchy of moment equations is derived from the population balance equations, which can be closed from the first order of moments. The properties of the model and the effects of process parameters are examined by numerical experimentation.

Keywords: Turbulent fluidization, Heat transfer, Axial dispersion/population balance model, Moment equations hierarchy, Simulation 1. Introduction Turbulent fluidization is characterized by low amplitudes of pressure fluctuations and favorable gas-solids contacting. In gas-solid turbulent fluidized beds the solids hold-ups are also high, typically 25-35 % by volume [1], thus, because of intensive motion of particles, particle-particle and particle-surface collisions appear to play significant role in controlling the thermal characteristics of the bed. For modeling and simulation of collisional heat transfer processes in gas-solid systems, an Eulerian-Lagrangian approach, with Lagrangian tracking for the particle phase [2-5], and a recently developed population balance model [6-9] have been applied. The population balance equation is a widely used tool in modeling the disperse systems of process engineering [10], describing a number of fluid-particle and particle-particle interactions. This equation was extended by Lakatos et al. [7] with terms to describe also direct exchange processes of extensive quantities, such as mass and heat between the disperse elements as well as between the disperse elements and solid surfaces by collisional interactions [8,9]. The aim of the present paper is to develop an axial dispersion/population balance (ADPB) model for describing also the spatial distributions of the gas and particle temperatures in turbulent fluidized beds.

2. Preliminary The axial dispersion model is often applied to describe mixing of gas and solids in turbulent fluidised bed reactors when using two-phase modelling approach [1,11,12]. In these models both phases are treated as intermittent continua so that collisional pro-

Z. Süle et al.

720

cesses inside the particulate phase can not be taken into consideration. When, however, applying a population balance model for describing the heat transfer behaviour of particles [6-9] both the particle-particle and particle-wall interactions can be modelled separately taking into account in this way also the possible temperature inhomogeneities in the particle population. In a two-phase model, the continuity equations for gas and solids take the forms:

∂ (ει ρι ) ∂ (ει ρι jν ) + = 0, t > 0, x ∈ (0, X ) (1) ∂t ∂x where İȚjȚ, Ț=g,s denote the flux densities of gas and solid phases in the axial direction x. Gas may be treated as continuum, but in gas-solid turbulent fluidisation particles move with random motion due to turbulent motion of gas, as well as to particle-particle and particle-wall collisions. Let n x, T p , t dT p denote the number of particles in a unit volume of fluidised bed res-

(

)

(

)

iding in the intervals of temperature T p , T p + dT p and axial coordinate (x, x + dx ) at time t. By using this form, we can write

ε s ( x, t )ρ s ( x, t ) = m p N ( x, t )

(2)

where N denotes the total number of particles in the interval (x, x + dx ) at time t:

N ( x, t ) =

T p ,max

³ n( x, Tp , t )dTp

(3)

T p ,min

Similarly, for the enthalpy hι of phases we have

hι = ε ι ρι cι Tι , ι = g , s, w, ε w = 1

(4)

where c and T denote, respectively, the heat capacities and temperatures of phases. However, taking into consideration Eq.(2), the total enthalpy of the particulate phase is expressed as hs (x, t ) = c p m p N (x, t ) T p (x, t ) = c p m p

T p , max

³ T p n( x, T p , t )dT p

(5)

T p , min

where T p (x, t ) denotes the mean temperature of particles in the interval (x, x + dx ) at time t: T

p ,max 1 T p ( x, t ) = Tp n( x, T p , t )dTp . N ( x, t ) T p³,min

(6)

In this model, because of intensive motion of particles, the particle-particle and particlewall heat transfers occur through interparticle and particle-wall collisions [6-9] so that five thermal processes should be considered: fluid-particle, fluid-wall, particle-particle, particle-wall and wall-environment. As a consequence, the main assumptions concerning the system are as follows: 1) Particles are of constant size and are not changed during the process. 2) The system is operated under steady state hydrodynamic conditions. 3) Heat transfer between the gas and particles, wall and gas, as well as the wall and environment are continuous pro-

Axial Dispersion/Population Balance Model of Heat Transfer in Turbulent Fluidization

721

cesses, characterised by the heat transfer coefficients hgp, hgw and hwe respectively. 4) Interparticle heat transfer occurs by collisions, and is described by the random variable ω pp ∈ [0,1] with probability density function fpp. 5) The particle-wall heat transfer also occurs by collisions that are characterised by the random variable ω pw ∈ [0,1] with probability density function fpw. 6) There is no heat source inside the particles. 7) Heat transfer by radiation is negligible. 8) The axial dispersion model can describe the transport of enthalpy of gas and particles in the physical space of bed:

∂ (.) , ι = g, s ∂x

jι (.) = vι (.) − Dι

(7)

where v denotes the linear velocity, and D is the axial dispersion coefficient. 9) Heat transport in the wall occurs by conduction. 10) The environment is of homogeneous temperature with infinite capacity.

3. Axial dispersion/population balance model Under the conditions formulated in the previous section, the balance equations for the particles, gas, and wall are as follows. Gas phase:

∂Tg

= Dg

∂t

∂ 2Tg ∂x

2

− vg

∂Tg ∂x

+

1

ε g ρ g c pg

H gp +

1

ε g ρ g c pg

hgw , t > 0, x ∈ (0, X )

(8)

Particulate phase:

∂n( x, T p , t ) ∂t

= Dp

∂ 2 n ( x, T p , t ) ∂x

2

− vp

∂n( x, T p , t ) ∂x

+

H gp cpmp

+

H pw cpmp

+

H pp cpmp

(9)

t > 0, x ∈ (0, X ) Wall:

∂Tw ( x, t ) k ∂ 2Tw ( x, t ) 1 1 1 hgw + H pw + h = w + 2 ∂t ρ w cw ρ w cw ρ w cw ρ wcw we ∂x t > 0, x ∈ (0, X )

(10)

where kw denotes the thermal conductivity of the wall. Boundary conditions:

v g ,in T g ,in (t ) = v g T g (0+, t ) − D g

(

)

(

∂Tg (0+, t )

)

v p ,in nin T p , t = v p n 0+, T p , t − D p ∂Tw (0+, t ) = 0, ∂x

∂Tw ( X −, t ) =0 ∂x

∂x ∂n 0+, T p , t

(

∂x

∂Tg ( X −, t )

,

)

=0 ∂x ∂n X −, Tp , t , =0 ∂x

(

)

(11a) (11b) (11c)

In Eqs (7)-(9) the constitutive relations describing the heat transfer rates between the phases are expressed in the following way. Gas-particle and gas-wall:

Z. Süle et al.

722 T p max

³ hgp (Tg ( x, t ) − Tp )n( x, Tp , t )dTp

H gp = a gp

T p min

(

hgw = ε g a gw hgw Tg ( x, t ) − Tw ( x, t )

(12)

)

(13)

Particle-gas, particle-particle and particle-wall:

h pg = a gp

(

)

∂hgp Tg ( x, t ) − T p n( x, T p , t ) ∂T p

[

]

H pp n( x, T p , t ) = − S pp n( x, T p , t ) +

³

Ω pp

(

2S pp

1

ω pp 1 ( x, t )

× (14)

)

ª § 2 Tp − y · º × ³ n « x, ¨ + y ¸, t » n( x, y , t )dyFω pp (dω pp ) ¨ ω pp ¸ » T p ,min « ¹ ¼ ¬ © H pw n( x, T p , t ), Tw ( x, t ) = − S pw n( x, Tp , t ) + T p ,max

[

]

§ T p − pwω pwTw ( x, t ) · 1 n¨ ,t ¸ F dω pw ¸ ¨ 1 − pwω pw Ω pw T p ,min © ¹ 1 − pwω pw T p ,max

+ S pw

(

³ ³

)

(15)

Wall-gas, wall-particle and wall-environment:

(

hwg = ε g a gw hgw Tg ( x, t ) − Tw ( x, t )

)

(16)

T p ,max

H wp = S pw

³ ³ p pω pw (T p − Tw ( x, t ))n( x,T p , t )dT p Fω

wp

(dω pw )

(17)

Ω pw T p ,min

hwe = awe hwe (Tw ( x, t ) − Te )

(18)

where Te = const = 20oC. Note that in this case only the gas-wall and wall-gas heat transfer rates are symmetrically equal.

4. Simulation results and discussion The set of boundary value problems (7)-(11) was solved by means of the moment method using a second order moment equation reduction of the population balance equation (9), written for the first three leading moments of the temperature of particle population [8,9]. The moment equations induced by Eq.(9) can be closed at any order of moments [9], defined as T p , max

M k (ξ ,τ ) =

³ T p n(ξ , T p ,τ )dT p , k = 0,1,2,3... k

(19)

T p , min

which are necessary for a basic characterization of the temperature distribution of particles. The zero order moment M0(ξ,τ)=N(ξ,τ) provides the total number of particles, by means of which the solids concentration can also be computed. The mean temperature and the variance of temperature of particles are expressed, respectively, as

Axial Dispersion/Population Balance Model of Heat Transfer in Turbulent Fluidization

T p (ξ ,τ ) =

723

M1 (ξ ,τ ) M (ξ ,τ ) ª M1 (ξ , τ ) º and σ 2 (ξ ,τ ) = 2 −« » . M 0 (ξ ,τ ) M 0 (ξ ,τ ) ¬ M 0 (ξ ,τ ) ¼ 2

(20)

The program for solving the set of 5 partial differential equations of the second order moment equation reduction, written by the dimensionless variables and parameters

ξ=

vg X vp X x X X t ,τ = , Peg = , tg = , Pe p = , tp = tp Dg vg Dp vp X

for variables (M0, M1, M2, Tg, Tw), was developed in MATLAB environment applying the pdepe-solver. The results presented here were obtained using the same constitutive parameters and expressions as given in [9]. The gas inlet temperature was 540oC, the inlet feed temperature of particles was 20oC, while the initial temperature of the whole system was 20oC. The frequencies of collisions were chosen: Spp=20 s-1, Spw=1 s-1. For illustrating the efficiency of the model, the influence of the mean value of random variable Ȧpp is presented in Fig.1 for particles of size 10-4 m. When the collisional heat transfer efficiency between the particles is small, i.e. the mean value m1,ω pp is equal to 0.02 then the temperature of particles does not become homogeneous even at the end of the bed, while the mean temperature of the particle population does change signifycantly. Development of the axial distribution of the mean temperature of particles is presented in Fig.2 as a function of time. Similar processes were obtained for all values of the expectation of random variable Ȧpp illustrating that the heat transfer between the particles does not affect the mean value of the temperature of population. Development of the axial distribution of variance of particles temperature as a function of time is shown in Fig.3 for the same parameter values. 800

T p (ξ ,τ )

m1,ω pp

ı2(ȟ)

0.02 0.05 0.1 0.2 0.5

600 400 200

τ 0 0

0.5

ȟ

ξ

1

Fig.1. Influence of the mean value of random variable Ȧpp on the steady state variance of temperature of particles

Fig. 2. Variation of the axial distribution of the mean temperature of particles as a function of time

Effects of the particle size on the variance of steady state temperature of particle population are shown in Fig.4. These diagrams show clearly that under the same process conditions the final values of the variance are practically are equal close to zero but

Z. Süle et al.

724

increasing particle size causes rather strong decrease of variance already in the input region of the bed. The results obtained by simulation allow concluding that the axial dispersion/population balance model appears to be an efficient tool for analysis of heat transfer processes in gas-solid turbulent fluidization. It makes possible to detect the inhomogeneities in the temperature distribution of particles population, and, because in the present model each moment can be computed exactly, computing also some higher order moments, it allows predicting an approximate population density function from the knowledge of a finite sequence of moments. 500 ı 2( ȟ ) 400

ı 2( ȟ , IJ )

dp 1.0Â10-4 2.0Â10-4 3.0Â10-4 4.0Â10-4

300 200 100

ξ

τ

Fig.3. Variation of the axial distribution of the temperature variance of particles as a function of time

0 0

0.5

1 ȟ Fig. 4. Influence of the particle size on the steady state axial distribution of the variance of temperature of particles

5. Acknowledgements Zoltán Süle wishes to thank the Hungarian Ministry of Education and Culture for supporting this research under Ferenc Deák scholarship.

6. References [1] H.T. Bi, N. Ellis, A. Abba and J.R. Grace, Chem. Eng. Sci., 55 (2000) 4789. [2] P. Boulet, S. Moissette, R. Andreaux, B. Osterlé, Int. J. Heat Fluid Flow, 21 (2000) 381. [3] Z. Mansoori, M. Saffar-Avval, H. Basirat-Tabrizi, G. Ahmadi, S. Lain, Int. J. Heat Fluid Flow Transfer, 23 (2002) 792. [4] V. Chagras, B. Osterlé, P. Boulet, Int. J. Heat Mass Transfer, 48 (2005) 1649. [5] Z. Mansoori, M. Saffar-Avval, H. Basirat-Tabrizi, B. Dabir, G. Ahmadi, Powder Technology 159 (2005) 35. [6] Cs. Mihálykó, B.G. Lakatos, A. Matejdesz, T. Blickle, Int. J. Heat Mass Transfer, 47 (2004) 1325. [7] B.G. Lakatos, Cs. Mihálykó, T. Blickle, Chem. Eng. Sci., 61 (2006) 54. [8] Z. Süle, Cs. Mihálykó, B.G. Lakatos, Computer-Aided Chem. Eng., 21A, Elsevier, Amsterdam, 2006, pp. 589-594. [9] B.G. Lakatos, Z. Süle, Cs. Mihálykó, Int. J. Heat Mass Trans., 51 (2008) 1633-1645. [10] D. Ramkrishna, Population Balances. Theory and Applications to Particulate Systems in Engineering. Academic Press, San Diego, 2000. [11] M. Foka, J. Chaouki, C. Guy, D. Klvana, Chem. Eng. Sci., 51 (1996) 713-723. [12] M.L. Thompson, H. Bi, J.R. Grace, Chem. Eng. Sci., 54 (1999) 2175-2185.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

725

Dealing with Uncertainty in Polymer Manufacturing by Using Linear Regression Metrics and Sensitivity Analysis Aarón David Bojarskia, Carlos Rodrigo Álvareza, Luis Puigjanera a

Universitat Politecnica de Catalunya, Chemical Engineering, ETSEIB, Pavello G-2, Av. Diagonal 647, E-08028 Barcelona, Spain; [email protected]

Abstract In the polymers industry, models are heavily parameterizised, and the effect of each parameter on model outputs has not been extensively studied. A wide range of values for most of model’s parameters can be found in literature [1], a thorough analysis regarding the model’s sensitivity to the parameters’ values is needed to find the set of parameters that have the most impact in the output results and consequently deserve an extra effort and care during their estimation. In this work, a global sensibility analysis of a styrene emulsion polymerization reactor model is carried out in order to determine the set of critical parameters. Keywords: polymer production modelling, sensitivity analysis, regression analysis, uncertainty, Monte Carlo sampling

1. Introduction In the case of the chemical industry uncertainty sources are found due to the model which includes all kinds of information arising from experimental and pilot plant data (kinetic constants, physical properties and transfer coefficients) and the process including information regarding stream quality, (variations in flow rate, pressure and temperature). Other uncertainty sources are external uncertainty including variability regarding information that is outside the system boundary and finally discrete uncertainty which is related to equipment availability and other random events [2]. During the last decades, polymerization processes have played a central part in petrochemical industry for the production of plastics, rubbers, paints and other many kinds of products. The many possible phases present inside some types of polymerization reactors and transfer phenomena occurring between them make emulsion polymerization systems very difficult to model. In addition to the common difficulties of modelling mass transfer phenomena and equilibrium conditions between several phases, the lack of reliable values for parameters makes the modelling task even more complex. The big disparity between parameters values used in those models, either, related to reaction kinetics or used within transfer and equilibrium equations, causes serious problems when one attempts to validate the model. Some of these parameters like preexponential constants or activation energies for the different polymerization reactions involved (propagation, termination, chain transfer etc) may differ in more than one order of magnitude in similar conditions [1]. This big disparity can also be found in other parameters like diffusion coefficients or phase surface tension values [3, 4].

A.D. Bojarski et al.

726

Due to this big parameter uncertainty ranges, it is important to estimate the actual effect of each one of these uncertain parameters on the final model outcomes, aiming at determining which are the most influential ones. The knowledge of this set of critical parameters can focus attention on them for more accurately estimation via physical experiments or for further model enhancements. Moreover, it also allows for the modeller to know which parameters are the least influential to model outcomes, to ease the modelling of such model parts, by assuming model simplifications. A sensibility analysis (SA) [5] is the study of how the variation in the output of a model can be apportioned, qualitatively or quantitatively, to different sources of variation and of how this model depends on information fed into it. Various methods have been proposed to make uncertainty operational due to parameter uncertainty, such as the use of analytical uncertainty propagation methods; calculations based on intervals; applied fuzzy logic computations; and stochastic modelling describing parameters as uncertainty distributions [6]. The usage of analytical propagation methods suffers from complexity in algebra that increases rapidly with the complexity of the model, the method produces moments of distributions (mean and variance) making hard to obtain reliable estimates for the tails of the output distribution. It is basically a local approach and will not be accurate if the uncertainties are large; if the model is not smooth or if important covariance terms are omitted. In this respect Saltelli [5] points out that the usage of error propagation methods (derivative methods) provide only of a local glimpse at model factors effect on model outputs. The usage of sampling methods which explore the full space of possible model parameters values is recommended.

2. Problem statement Several metrics can be calculated based on sampling results, such as standard statistics (mean, standard deviations and confidence intervals) or regression analysis metrics. Regression metrics are based on a linear correlation resulting from input variables (x) and model output results (y). Standardization of input variables and output results is performed by subtracting the mean value and normalizing the standard deviation. SRCs are obtained from a fit to a minimum square difference optimization. A value of any SRC close to zero indicates that the output variable is not correlated to that input variable. The sign of SRC also indicates the relationship between input and output variables.

yl − yl

σl

M

= ¦ SRClh l =1

xh − xh

σh

∀l = 1: N

(1)

Another commonly used metrics are Partial Correlation Coefficients (PCCs); which are calculated by performing several regressions including or not the variable under study. In this case a PCC tries to show how much each input variable affects the behaviour of the output variables. This can be obtained by performing two separate regressions one where all input variables are used (ylfxh) and one with the subject input variable ignored (ylf~xh) [5].

Dealing with Uncertainty in Polymer Manufacturing by Using Linear Regression Metrics and Sensitivity Analysis M

PCChl2 =

¦(

ylf − ylf xh

f =1

)

2

M

¦( y

lf

M

(

− ¦ ylf − ylfxh f =1

− ylf

f =1

xh

)

2

)

727

2

∀l = 1: N ; h = 1: M

(2)

PCCs have only positive values; the values that are closer to one represent more important variables.

3. Paper approach In this work we adopt a stochastic sampling approach, which varies input data (model and process parameters) according to given probability distributions. The model is run for a given set of input values realizations and stores its output results. This procedure is repeated until the appropriate uncertainty ranges are obtained for the output variables. Methodology and Case Study An isothermal batch reactor model for styrene emulsion polymerization is considered. The model includes the mass balances for initiator, surfactant, monomer, radical and polymer species. Both, micellar and homogeneous nucleation are considered and the radical flow into particles and micelles and also its desorption from particles are included following a similar approach as in Gao et al. [3]. The model also includes polymer molecular weight calculations by using the moments approach. The model renders a detailed description of the physical phenomena and chemical reactions that take place in the aqueous and polymer phases. Model results have been able to reproduce experimental data provided in the literature [1,3,4]. Sampling methodology A Monte Carlo sampling (MCS) methodology was used. Variable input probability distribution functions (pdfs) can be seen in table 1. In order to set these pdfs data from literature was used. Uniform distribution functions were used for parameters for which no information except a range was found, while normal distributions were used in the case of parameter for which more information was available (process operating conditions).

A.D. Bojarski et al.

728 Table 1. Input parameter tested distributions

Variable Name

Unit

Distribution shape

Distribution parameters Mean / Lower Bound

STD / Upper Bound

Variable Remark

Akt

[l/mol·min]

Uniform

3.33E+15

4.50E+15

A

Ekt

[kJ/mol·K]

Uniform

7.54E+03

1.02E+04

A

Aktw

[l/mol·min]

Uniform

3.33E+15

4.50E+15

A

Ektw

[kJ/mol·K]

Uniform

7.54E+03

1.02E+04

A

Akp

[l/mol·min]

Uniform

9.64E+10

1.30E+11

A

Ekp

[kJ/mol·K]

Uniform

8.84E+03

1.20E+04

A

[l/mol·min]

Uniform

9.64E+10

1.30E+11

A

Akpw Ekp

w

[kJ/mol·K]

Uniform

8.84E+03

1.20E+04

A

alfaTerDes

[1]

Uniform

0.00E+00

1.00E+00

A

Akfm

[l/mol·min]

Uniform

4.69E+03

6.34E+03

B

Ekfm

[kJ/mol·K]

Uniform

2.86E+04

3.86E+04

B

Chi

[1]

Uniform

4.00E-01

7.00E-01

C

Dw

[dm2/min]

Uniform

1.20E-07

1.76E-09

D

2

Dp

[dm /min]

Uniform

1.20E-08

1.76E-12

D

mmd

[1]

Uniform

8.50E+11

1.15E+12

D

Jcr

[1]

Uniform

5.00E+00

8.00E+00

D

DMM

[dm2/min]

Uniform

8.72E-12

1.18E-11

D

F

[1]

Uniform

5.00E-01

7.00E-01

E

Akd

[l/mol·min]

Uniform

1.30E+18

1.75E+18

E

Ekd

[kJ/mol·K]

Uniform

2.83E+04

3.83E+04

E

rmic

[dm]

Uniform

2.00E-08

5.00E-08

F

Surfactant

[g]

Normal

1.43E+01

2.00E+00

G

Monomer

[g]

Normal

3.00E+02

1.67E+01

G

Initiator

[g]

Normal

7.07E+00

1.00E+00

G

Reactor Temp.

[K]

Normal

3.23E+02

6.67E+00

H

Reactor Vol.

[l]

Normal

7.00E-01

3.33E-02

H

Variables marked as A, represent values associated to the propagation-termination reaction system, B related to inhibition and chain transfer mechanisms, C, D, E and F are related to monomer, radical, initiator and surfactant physical properties respectively. G and H refer to initial charge and reactor working conditions. In the case of kinetic related parameters the superscript refers to the phase where reaction occurs. Each scenario was created by sampling all variables from their respective distributions, these variables realizations were used to run the model. Output variables were calculated at three different time intervals namely: 0-10, 45-55 and 90-100 minutes. These three time regions were defined due to expected different model behaviour. Random variable value generation and SRC and PCC calculation were performed using Matlab®. The number of scenarios used to compute SRCs and PCCs was gradually increased until the obtained values did not change appreciably. The total number of simulation runs performed was 5000.

Dealing with Uncertainty in Polymer Manufacturing by Using Linear Regression Metrics and Sensitivity Analysis

729

Results and discussion The model output results studied were monomer conversion (X), polymer molecular weight (MW) and polydispersion (PD). These variables allow for a global interpretation of model results. Table 2. Calculated time average SRCs and PCCs

Variable Metric Akt

X SRC 0,003

PCC 0,005

MW SRC PCC -0,012

0,016

PD SRC 0,024

PCC 0,026

Ekt

-0,011

0,048

0,064

0,082

-0,110

0,115

Aktw

-0,002

0,004

-0,001

0,001

-0,010

0,010

Ektw

-0,015

0,065

0,024

0,031

0,006

0,007

Akp

0,020

0,042

0,020

0,026

-0,005

0,008

Ekp

-0,306

0,521

-0,215

0,268

0,014

0,017

Akpw

-0,009

0,020

0,005

0,007

0,008

0,008

Ekpw

0,000

0,005

0,000

0,003

-0,006

0,006

alfaTerDes

-0,005

0,029

0,021

0,028

0,085

0,089

Akfm

-0,011

0,022

-0,003

0,004

0,002

0,002

Ekfm

0,147

0,295

0,114

0,146

0,056

0,058

Chi

-0,006

0,017

-0,003

0,004

-0,009

0,010

Dw

0,003

0,011

-0,008

0,010

0,004

0,005

Dp

-0,076

0,159

0,073

0,095

0,011

0,012

0,009

0,022

0,001

0,001

-0,010

0,011 0,005

mmd Jcr

0,000

0,003

0,013

0,017

-0,005

-0,002

0,022

-0,004

0,005

-0,021

0,022

0,018

0,038

0,003

0,004

0,010

0,011

Akd

0,019

0,039

-0,018

0,023

-0,004

0,004

Ekd

-0,757

0,839

0,629

0,625

0,295

0,292

rmic

0,037

0,079

-0,041

0,053

-0,066

0,069

DMM F

Surfactant

-0,015

0,039

0,025

0,033

-0,010

0,014

Monomer

-0,009

0,029

0,008

0,010

0,017

0,018

Initiator

0,029

0,061

-0,012

0,016

0,001

0,004

Reactor Temp.

0,217

0,414

-0,111

0,142

-0,041

0,043

-0,005

0,011

-0,002

0,003

0,017

0,018

Reactor Vol.

The values were calculated for each variable at three different time intervals, the reported value is the arithmetic average (see table 2). It is found that each input parameter affects in different ways to the selected output variables results. In all cases a high value for PCC is also associated to a value significantly different than zero for SRC. The most influencing input variables found were: reactor temperature (T) and the activation energies for the initiator decomposition (Ekd), inhibition (Ekfm) and polymer phase polymerization (Ekp) reactions. It can be seen from SRCs values that increments in reactor temperature for this system will impact increasing conversion while decreasing polymer molecular weight. The other parameters found to be influential are the activation energies for the polymer phase, while all other reactions are mostly non influential. The only input parameter influencing polydispersion was found to be the activation energy for the initiator decomposition reaction.

A.D. Bojarski et al.

730

Table 3. Calculated SRCs for different time intervals for the four most significant variables

Variable Time Interval

[0-10]

Ekp

-0.456

Ekfm Ekd Reactor Temp.

X

MW

[45-55] [90-100] -0.248

-0.214

[0-10] -0.231

PD

[45-55] [90-100] -0.206

-0.207

[0-10] 0.040

[45-55] [90-100] 0.005

-0.003

0.143

0.152

0.144

0.110

0.117

0.115

0.052

0.058

0.056

-0.666 0.210

-0.795 0.222

-0.808 0.220

0.640 -0.105

0.625 -0.115

0.621 -0.113

0.309 -0.055

0.298 -0.036

0.279 -0.031

From table 3, it can be seen that some input variables that show an appreciable change over time in its influence over and output variable is Ekp and Ekd over X. At the reaction start their SRCs values are different than at reaction end. In the first case Ekp influence is higher at reaction start, while lower at the end, the opposite behaviour is found for Ekd. For the remaining variables their influences over output variables remain similar over the whole time interval, no changes in the SRCs values are found. A similar trend is found when analysing the PCCs results.

4. Conclusions It has been shown that the usage of SRCs and PCCs eases the selection procedure for variables that influence the most on model outputs. It also enables the study of how the input parameter behaviour affects model output. The current procedure enables to focus attention only on four parameters for further studying, instead of the original set of 26. The most influencing parameters found were related to kinetic reaction constants.

5. Acknowledgements Financial support received from the Agencia de Gestio d'Ajuts Universitaris i de Recerca (AGAUR) from Generalitat de Catalunya and Fons Social Europeu (EU), through FI grants and PRISM-MRTNCT-2004-512233 and ToleranT (DPI2006-05673) projects is gratefully acknowledged.

References [1] J. Brandrup, E. H. Immergut, E. A. Grulke, Eric A. Grulke, D. Bloch (eds); Polymer Handbook, Wiley (2003). [2] Pistikopoulos, E., Computers and Chemical Engineering No. 19 S553 (1995). [3] Gao, J. and A. Penlidis, Prog. Polym. Sci., No. 27 403 (2002). [4] M. Rajabi-Hamane, S. Engell; Chemical Engineering Science No. 62 5282 (2007). [5] Saltelli, A., Chan, K., Scott, E. M. Sensitivity Analysis, Ch 6, Wiley , (2002). [6] Huijbregts, M., International Journal of Life Cycle Assessment, No 3, 5, 273 (1998).

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

731

Detailed mathematical model for pollutants transport in a natural stream Elisabeta C. Ani,a,b Steve Wallis,c Andrzej Kraslawski,a Serban P. Agachib a

Department of Chemical Technology, Lappeenranta University of Technology, P.O.Box 20, FIN-53851, Lappeenranta, Finland, E-mail: [email protected] and [email protected] b Faculty of Chemistry and Chemical Engineering, "Babes-Bolyai" University, 11, Arany Janos, 400028, Cluj-Napoca, Cluj, Romania, E-mail: [email protected] c School of the Built Environment, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, Scotland, UK, E-mail: [email protected]

Abstract This paper concerns the simulation of pollutant transport in a small river, using a dynamic model. The aims of the study are (1) to describe the features of the developed concentration model; (2) to compare two approaches of parameterising the study site; (3) to propose a model for the evaluation of the velocity and dispersion coefficients, and (4) to present the results of the concentration model calibration and validation. Keywords: pollutant transport modelling, analytical model, tracer experiments, dispersion coefficient.

1. Introduction The need to satisfy the growing expectations regarding the availability of acceptable quality water requires the development of specific simulation tools and decision support systems for a responsible management of the environment. Such tools are offered by water quality modelling workers, who have developed analytical models based on the fundamental advection-dispersion equation (ADE) for pollutant transport in rivers. Despite the large quantity of existing results (Socolofsky and Jirka, 2005; MarsiliLibelli and Giusti, 2008; Boxall and Guymer, 2007; Jirka and Weitbrecht, 2005; Rowinski et al., 2007) there are still difficulties related to the evaluation of the parameters characterising mass transport in rivers (e.g. the dispersion coefficients). The present paper contributes to the above field by proposing (1) a mathematical model for pollutant transport in a stream, (2) a novel approach to describe the river length, and (3) a model for parameter evaluation. The pollutant transport model is calibrated and validated for the Murray Burn stream. The methodology as well as the level of detail in representing the river features bring added value to our research, compared to previous work on the Murray Burn (Piotrowski et al., 2007; Wallis and Manson, 2005).

E.C. Ani et al.

732

2. The mathematical model background The model uses the analytical solution of the ADE for an instantaneous injection of a mass of conservative tracer (Jirka and Weitbrecht, 2005):

c ( x, t ) =

§ (x − (x 0 + V x t ))2 exp¨ − ¨ 4 Dx t A 4πtD x © M

· ¸ ¸ ¹

(1)

where x is the distance along the river [m]; t is the time from the tracer release [s]; M is the mass of released tracer [g]; A is the cross-sectional wetted area of the channel [m2], Dx is the dispersion coefficient [m2/s], Vx is the velocity of the water [m/s], and x0 is the location of the source. Most of the existing analytical models for pollutant transport use a classical approach to describe a study site. This implies splitting the river into independent reaches characterised by constant average parameter values. Each reach starts at the source and ends at a certain downstream monitoring site (as shown in Table 1). The present paper is proposing a novel technique to describe the study area, with the purpose of improving the concentration prediction.

3. Comparison of the two approaches for parameter evaluation 3.1. Study area and experimental data The studied river stretch of the Murray Burn is 540m long and flows through HeriotWatt University’s campus in Edinburgh. The experiments were conducted at different water flow rates, between 14 l/s and 2931 l/s. In each case a known quantity of Rhodamine WT was injected in the middle of the stream, and the evolution of the concentration in time was measured at 4 sampling sites. More information about the study area and the experimental arrangements are provided in Piotrowski et al. (2007) and Wallis and Manson (2005). The experimental data consisting of concentration versus time curves at the monitoring sites were organized in two parts: a calibration data set (14 experiments) and a validation data set (3 experiments). 3.2. The calibration and validation methodology The calibration set was used to develop and calibrate the model. The parameters of the model were estimated from the concentration versus time curves using the method of moments (Piotrowski et al., 2007; Chin, 2006). Then these predictions were used as initial values in a non-linear optimization algorithm along with the experimental data from the calibration set, the purpose being to obtain the optimal values of Dx and Vx. Using the optimal values, models for parameter estimation were developed. For Vx a simple non-linear dependence on the water flow rate was proposed (eq. 2), while for Dx a modified form of the well known Fischer formula (Fischer et al., 1979) was used (eq. 3):

Vx = C1Q C2

(2)

Detailed Mathematical Model for Pollutants Transport in a Natural Stream

733

B 2v 2 Dx = C u* H

(3)

where Q is the water flow rate [m3/s]; B is the river width [m]; H is the water depth [m]; u* is the friction velocity with the river bed [m/s]; C, C1 and C2 are coefficients. The values of all these parameters are different for the two approaches used to describe the study site. Hence the models for parameter estimation have the same form for each approach, but different coefficient values. And the calibration and validation were made separately. The models for parameter estimation were used to make predictions of Dx and Vx for the experiments in the validation data set. The validation was made by comparing the predicted against the measured concentration profiles. The prediction accuracy was measured by calculating R-squared for each concentration profile. 3.3. The approaches used to describe the study site The river channel is hydraulically non-uniform between the source and the last monitoring site. In the present model the variation of the parameters along the channel is expressed in two ways. First by using the classical approach of considering the study site using four independent reaches, presented in Table 1. Each reach is characterised by constant average parameters. And second by using a novel approach which considers the study site as one single reach with variable parameters along it. Table 1. The reaches of Murray Burn in the classical approach Reach number Boundaries (up-downstream) Length [m]

1

2

3

4

source- site 1

source - site 2

source - site 3

source - site 4

120

257

356

540

In the novel approach the upstream boundary is the source and the downstream boundary is site 4. During the computation this length is discretized into spatial steps, and the parameters are calculated according to this arrangement. All model parameters (B, H, S, Q, A, Dx, Vx) are re-evaluated at each spatial step such that the parameter values corresponding to a certain point along the river are equal to weighted averages of the upstream values.

4. Results and discussion In the calibration runs, when the optimum values of Vx and Dx were used the model was able to give quite accurate prediction of the concentration at all sites, for both of the approaches. The values of R-squared are above 0.93, as shown in Table 2. In the validation runs R-squared values are lower (as would be expected), but apart from site 4 they are above 0.91.

E.C. Ani et al.

734

Table 2. The average values of R-squared at calibration and validation R-squared/Site Classical approach Novel approach

1

2

3

4

calibration

0.98

0.98

0.98

0.98

validation

0.91

0.94

0.94

0.60

calibration

0.98

0.98

0.98

0.93

validation

0.94

0.97

0.97

0.86

During calibration and validation the best correlations are at sites 2 and 3, the results at the first site are within acceptable limits in all cases, and the poorest correlations are at site 4, where the peak is sometimes under-predicted. Even though the calibration results for the novel approach at the fourth site are the poorest the results of the validation show improvements at site 4 when using the novel approach compared with the classical one (note the larger R-squared values for the novel approach in the last column of Table 2). Interestingly, in the validation runs the novel approach of describing the study site brings improvements in the concentration prediction at all the monitoring sites.

Figure 1. Validation results for a low flow experiment (62.1 l/s)

Some comparative results of the model validation when using the two approaches are presented in Figure 1 (for a low flow experiment) and Figure 2 (for a high flow experiment). The peak arrival time is well predicted for most of the concentration curves, showing a good estimation of the velocity made with the simple non-linear model. The only site with poor Vx prediction is the last one, although the novel approach performs well for the high flow experiment.

Detailed Mathematical Model for Pollutants Transport in a Natural Stream

735

For the low flow experiment at the first site Dx is under-estimated with the novel approach and at the third site it is over-estimated with both approaches. Dx is estimated well at all sites for the high flow experiment. The poor validation results at site 4 compared to the other sites could be caused by the relatively small number of experiments that had measurements at the last monitoring site (Piotrowski et al., 2007), which leads to a less accurate estimation of velocity and dispersion coefficients.

Figure 2. Validation results for a high flow experiment (535.4 l/s)

The overall results show that the model is efficient for the simulation of pollutant transport in the Murray Burn. Clearly, such prediction tools are very important in the field of environmental modelling, and their prediction accuracy depends very much on the ability to make good estimations of Vx and Dx.

5. Conclusions The paper proposes a mathematical model for pollutant transport in small rivers; compares two different approaches of parameterising the river and proposes models for the evaluation of the velocity and the dispersion coefficient. The concentration model was calibrated and validated with satisfactory results. The interest was not just to have the best prediction tool for pollutant transport, but also to use reliable parameters. In this regard, the novel approach of describing the study site brings improvements in the concentration prediction at all the monitoring sites.

736

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References Boxall, J.B., Guymer, I., 2007. Longitudinal mixing in meandering channels: New experimental data set and verification of a predictive technique. Water Res., 41, 341–354. Chin, D. A., 2006. Water-quality engineering in natural systems. John Wiley & Sons, Inc. Chapter 3 and 4, 91-145. Fischer, H.B., Liet, E., Koh, C., Imberger, J. and Brooks, N., 1979. Mixing in Inland and Coastal Waters. (Chapters 5) Academic Press, New York, 104-147. Jirka, G.H., Weitbrecht, V., 2005. Mixing models for water quality management in rivers: continuous and instantaneous pollutant releases. In: Czernuszenko, W. and Rowinski, P.M. (Eds.), Water Quality Hazards and Dispersion of Pollutants, Springer, New York, USA, 1-34. Marsili-Libelli, S., Giusti, E., 2008. Water quality modelling for small river basins. Environmental Modelling & Software, 23, 451-463. Piotrowski, A., Wallis, S. G., Napiorkowski, J. J., Rowinski, P. M., 2007. Evaluation of 1-D tracer concentration profile in a small river by means of Multi-Layer Perceptron Neural Networks. Hydrol. Earth Syst. Sci., 11, 1883–1896. Rowinski, P. M., Guymer, I., Bielonko, A., Napiorkowski, J. J., Pearson, J., Piotrowski, A., 2007. Large scale tracer study of mixing in a natural lowland river. Proceedings of the 32nd IAHR Congress, 2007, Venice, Italy, paper 297. Socolofsky, S.A., Jirka, G.H., 2005. Special Topics in Mixing and Transport Processes in the Environment. Engineering – Lectures. 5th Edition. Texas A&M University, USA. Wallis, S.G., Manson, J.R., 2005. Modelling solute transport in a small stream using DISCUS. Acta Geophysica Polonica, 53(4), 501-515.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

737

.

Developing a mathematical model for Ibuprofen’s controlled release accounting for solubility and diffusion effects Leila Vafajoo*a, Mohammad Kazemeinib and Payam Baroodia a

Islamic Azad University, Tehran South Branch, Graduate School of Engineering, Faculty of Chemical Engineering, Tehran, Iran, [email protected] b Sharif University of Technology, Dept. of Chemical and Petroleum Engineering, Azadi Ave., P.O. Box 11365-9465, Tehran, Iran, [email protected]

Abstract In this research a mathematical model for controlled drug delivery of Ibuprofen has been developed which accounts for physical kinetics based upon variations of the drug concentration, size and release time for a spherical drug pill. Through this model, the drug release for three sizes of the active ingredient including; 213nm (representing existence of only diffusion limitations), 515nm (representing existence of only solubility limitations) and 367nm (representing both diffusion and solubility limitations) was calculated. Theoretical amounts of the drug after two hours of release are calculated to be 95.3, 99.5 and 95.5 percent, respectively. Comparison of theoretical and experimental data enables one to conclude that when considering nano scale particle sizes for the active ingredient both solubility and diffusion mechanisms control the rate of the drug delivery. In other words, for small active ingredient particles corresponding to small drug pill diameters, the diffusion mechanism and for the drugs with bigger diameters the solubility mechanism is the rate controlling for the release of the Ibuprofen drug. On the other hand, for drugs with middle size diameters (i.e.; those between these two limits) both these are drug release rate controlling steps. Keywords: Controlled release, Modelling, Solubility, Diffusion

1. Introduction In the modern drug delivery systems main goals include; limited repetition of drug dosages, reduction of blood concentration tolerance, decreasing of side effects and controlled release of active materials. In this research a mathematical model for controlled drug delivery of Ibuprofen has been developed which accounts for physical kinetics based upon variations of the drug concentration, size and release time for a spherical drug pill. As such, assumptions utilized in this model are; (i) the initial concentration of the drug in the matrix is much higher than the solubility of it, (ii) diffusion takes place only in radial direction, (iii) the mono-dispersed, nano sized particles of the drug’s active ingredient (i.e.; ibuprofen) are much smaller than the surrendering matrix system diameter, (iv) swelling and solubility of the matrix is negligible compared to the embedded active ingredient and finally (v) the system is taken to be isothermal at human body temperature of 37°C. The current mathematical approach is distinguished from previous works due to its accounting for two limiting mechanisms including; solubility and diffusion for the Ibuprofen while the experimental data obtained are based upon drug release from coated Ibuprofen-Cholestryamine (i.e.;

L. Vafajoo et al.

738

an anionic resin) complex embedded into a polymer mixture of Polyethylene glycol (PEG) 4000 and Ethyl cellulose. The aforementioned diffusion limitation is determined through the Fick’s second law and the solubility limitation is accounted for through mass balance calculations for the Ibuprofen. Furthermore, effects of the drug initial concentration changing on the amounts and times of its release have been investigated.

2. Theoretical background 2.1. Solubility mechanism (for larger particle size) The solubility mechanism is imposed when the rate of the drug adsorption is considerably higher than its dissolution. Furthermore, this mechanism occurs when a small particle is going under dissolution. The drug concentration upon imposing the mass balance and related equations and replacement into the following equation:  dC rd k (C  K P C L ) (Eqn. 1) dt In which rd is the rate of the drug dissolution, k is the dissolution coefficient and Kp is the ratio of the drug concentration inside the particle to that of the bulk of liquid under thermodynamic equilibrium condition; will lead to the following concentration time dependent relation: C0 1D º ª 1  exp( CL t )» (Eqn. 2) K P (D  1) «¬ D ¼ In which C0 is the initial drug concentration and Į is a coefficient between 0 and 1 depending on whether the drug release system is controlled by the diffusion or solubility mechanism. 2.2. Diffusion mechanism (for smaller particle size) Under this mechanism the drug release takes place by three steps including 1) drug dissolution in the polymer layer, 2) drug molecular diffusion taking place due to concentration gradient and 3) and desorption into the external environment of the drug adsorbed on the polymer layer. In order to make easier to work with mass transfer equations, following assumptions are incorporated: 1) diffusion is one dimensional, 2) diffusion proceeds under constant rate, 3) particles are spheres of uniform size, 4) no interaction is foreseen between drug particles, 5) initial drug concentration is considerably higher than that of dissolution and 6) under this mechanism no drug dissolution is accounted for. Therefore, utilizing the thin film theory and overall mass transfer within this layer one may obtain partial differential equations the solution of which will lead to the drug concentration profiles inside the aforementioned sphere. In other words, the overall drug release equation based upon the diffusion mechanism may be written for A being the diffusing substance as follows:

m 10  m 20

dm

(Eqn. 3)

dt

In which:

dm dt m

M . 4 S r 2 .' r . ( M .V 0 C )

dC dt

(Eqn. 4)

(Eqn. 5)

Developing a Mathematical Model for Ibuprofen’s Controlled Release Accounting for Solubility and Diffusion Effects

739

Therefore, the flux equation neglecting the bulk movement will ultimately be given by: n wC N r J r  X ¦ N ir  D (Eqn. 6) wr i 1 Next, if one logically assumes that initially there are no drugs in the bulk, the following relation is obtained:

wC wt

D(

w 2C 2 wC )  wr 2 r wr

(Eqn. 7)

Which is the Fick's second law in which, C is the local drug concentration and D is the drug diffusion coefficient in the polymer matrix. Kp also may be obtained from the overall mass balance equation on the drug. Ultimately, after solving these equations, the ratio for the Ibuprofen's concentration to that of its equilibrium value in the environment is determined in an analytical manner to be: f ª º CL 6 (D  1 )D  q n2 1 ¦ exp( Dt ) » (Eqn. 8) 2 2 2 « C 1f R n 1 ( 9  3D  q n D ) ¬ ¼ For which the diffusion equation is solved implicitly through programming in MATLAB6.2 Software. Furthermore, the needed physiochemical parameters are those determined by palazzo and co-workers. In current research, experiments are done on 3 particles indicated by T1 to T3. Table 1 demonstrates experimental parameters needed to solve the equation leading to the concentration of the drug released into the stomach at a given time which then may be compared to that of the initial amount (i.e.; ClVr /C0) as a function of time. Table 1. Experimental Parameters

Particle T1 T2 T3

Particle Diameter(nm) 213 367 515

Vr

C0(g/l)

Cl0(g/l)

KP

412 132.2 57.3

13.24 39.7 42.55

0.0321 0.1476 0.1387

41 134 276

D(m2/s) *10-9 4.1 7.1 17.2

K(s-1) *10-9 6.2 12.2 18.4

3. Results and discussions Results of this model are presented in figures 1 to 3 where the drug release rate versus time are displayed due to both diffusion and solubility mechanisms from this study and compared with those of experimental values. These comparisons are done for three different particle sizes of 213, 367 and 515 nm. It is seen that there will be a change of controlling release rate mechanism from diffusion to solubility as the Ibuprofen’s particle size is increased. In figure 1 it is shown that for smaller particle size of 213 nm there exists a very good comparison between the experimental data and the model due to diffusion mechanism, hence, the controlling mass transfer mechanism is that of diffusion limitations. However, in figure 3 for particle size of 515 nm results are reversed in terms of good comparison between experimental data and those generated for solubility mechanism by this model. This latter behavior is indicative of solubility mechanism control for this particle size drug release. On the other hand, for intermediate drug size of 367 nm a combination of both controlling mechanisms are

740

L. Vafajoo et al.

present since a hybrid of them produces results satisfactorily comparing with experimental results. It is noteworthy that the drug release rate for the hybrid model of the aforementioned mechanisms is calculated from the following relation: Result= Į diffusion+ (1-Į) dissolution (Eqn. 9) In which the goal is to determine an optimum value for the coefficient Į. A very good method to achieve this is to perform a least square fit of the experimental data as follows: N result i  exp i 2 ( ) SSE ¦ (Eqn. 10) exp i i 1 Where N is the number of experimental points and SSE is the least square error, resulti is a point from hybrid model generated data in this work and expi is the corresponding (i.e.; in regards to time) experimental data. Figure 4 shows the drug release rate as time goes by as a function of initial drug concentration for the 213 nm drug particle sizes. It is seen that increase of the initial concentration results in higher released rate as time proceeds. Furthermore, as this C0 is increased, there is a shift in time where the maximum released rate is obtained, indicating that diffusion limitations causes steady state release rate to be delayed.

Developing a Mathematical Model for Ibuprofen’s Controlled Release Accounting for Solubility and Diffusion Effects

741

Ultimately, figure 5 shows that theoretical amounts of the drug released after two hours are 95.3, 99.9 and 95.5 % for 213, 367 and 515 nm particle sizes. This enables one to conclude that when considering nano sized particles for the active ingredient, both solubility and diffusion mechanisms control the rate of the drug delivery.

Figure 5. Comparison of release percentage of T1, T2 and T3 nano particles

4. Conclusions In this research, it has been tried to determine the extent of release of the Ibuprofen’s drug through three different holding polymer matrixes with variety of sizes proportional with appropriate release rate models. Results of this type of investigations are very helpful in precise prediction of the medicine extent of release during the rehabilitation period of patients in such a way to improve the preparation and effectiveness of such medicines. In this study, it is shown that the release rate of the drug for smaller size particles is more dependent on the molecular diffusion mechanism within the nano-particles. However, for larger size particles, the effect of dissolution mechanism is also observed. The reason for this latter behavior is the smaller resistance due to dissolution in smaller size material which in turn is due to larger specific surface area of them giving rise to a diffusion limited phenomena. In this direction a parameter called Į was introduced into the model which acts as a statistical weight displaying the share of the diffusion and solubility limitations in the drug release issue. Results show that by increasing the size of the nano particles, this parameter decreases which emphasizes an increase for the share of the solubility limitation mechanism. Ultimately, this research provides an important piece of information for tailor making this drug for a particular patient when studied limitations are added to other patient factors.

5. References J. Siepmann and A. Göpferich, 2000, Mathematical modeling of bioerodible, polymeric drug delivery systems, Advanced Drug Delivery Reviews B. Palazzo, M. C. Sidoti, N. Roveri, A. Tampieri, M. Sandri, L. Bertolazzi, F. Galbusera, G. Dubini, P. Vena and R. Contro, 2005, Controlled drug delivery from porous hydroxyapatite grafts: An experimental and theoretical approach, Materials Science and Engineering, 25, 207–213

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L. Tamaddon, 2006, The study of drug release from coated Cholestryamine-Ibuprofen complexes with Ethylcelluose and polyethylene glycol 4000, PhD thesis, Faculty of Medical Sciences, Ahwaz Jondi Shapour University (in Farsi). M. Polakovi, T. Görner, R. Gref and E. Dellacherie, 1999, Lidocaine loaded biodegradable nanospheres: II. Modelling of drug release, J. of Controled release, 60, 169 J. SDuk, K. Yun, M. Kim, M. Kim, K. Do, Ch. Kim, J. Young- Ke., K. Kim, M. Ma, 2004, Modelling on the controlled release of drugs-encapsulated poly (lactic acid- co- ethylene oxide) nanoparticles, Institute of physics publishing- Nanoparticles B. Palazzo, M.C. Sidoti, N. Roveri, A. Tampieri, M. Sandri, L. Bertolazzi, F. Galbusera, G. Dubini, P. Vena, R. Contro, 2005, Controlled drug delivery from porous Hydroxyapatite grafts: An experimental and theoretical approach, Material Science and Engineering, 25, 207213 N. Khanmirzaei, 2006, Mathematical Modeling on the Controlled release of Indomethacin, M.Sc. thesis, Chemical Engineering (biotechnology), Azad University, Research and Science branch (in Farsi). J. Pan, Y. Qian, L. Zhang and Y. Jiang, 2005, A Novel Dissolution-Diffusion Model for Investigation of Drug Release from Polymeric Microspheres, European Symposium on Computer Aided Process Engineering.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

743

Development of a Computational Tool for Simulating Falling Film Molecular Design Evandro S. Mallmann, Caliane B. B. Costa, Maria Regina Wolf Maciel and Rubens Maciel Filho School of Chemical Engineering, University of Campinas, UNICAMP, P.O. Box 6066, 13083-970, Campinas – SP, Brazil, [email protected], [email protected]

Abstract In a previous work, a software named DISMOL was developed in order to simulate molecular distillation (MD). However, due to the restricted access to this tool, and to the importance of having a computational tool available for future investigations of operational policies in oil refinery, in the present work, it is proposed the development of a general procedure for this highly specific process in the commercial simulator Aspen Plus®. Since no single unit operation is available in the commercial simulator that can appropriately simulate a falling film distillator, the proposal, in a preliminary approach, makes use of a sequence of flash vessels corrected with process efficiency, in order to accomplish the task of MD simulation. Experimental data of a binary system distillated in a falling film molecular distillator are used for the validation of the developed procedure. The results indicate the potential of the proposed procedure to represent a MD equipment for the system evaluated, making possible the study of different operational policies in conducting this high vacuum distillation operation for high-value products, such as the derived from oil refining. Keywords: Molecular Distillation, Aspen Plus®, Model Validation, Flash, Petroleum

1. Introduction The petroleum obtained in several reservoirs around the world is of heavy and ultraheavy types, presenting high viscosities which make difficult its exploration (oil removal from submarine reservoirs) and also the refining operations for fuel and production of other derivatives. The refining processes currently in activity in refineries usually do not allow the heavy and ultra-heavy oil processing, so that they are mixed with light oils (of the Arab type) for their refining. In this context, an alternative to the initial heavy and ultra-heavy oil operation is the use of molecular distillation, a process conducted at high vacuum. Molecular distillation technology, also known as short-path distillation, is an operation for effective separation or purification of products of high molecular weight. It is a special vaporization operation at very low pressures and, consequently, relatively low temperatures, which make this operation also suitable for thermally sensitive products [1]. Besides that, no external component needs to be introduced into the system in order to perform the operation. Previous experiments [2, 3-4] showed the viability of the molecular distillation (MD) operation also for heavy and ultra-heavy oil refining. Nevertheless, a deep knowledge of the process is required in order to obtain the desired product streams: small process variations may result in product streams with completely different characteristics [5]. A wide investigation for the development of operational polices that lead to high

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performance of the molecular distillation (MD) operation for oil refining is necessary. For this purpose, the development of simulators that allow an extensive study covering the possible operational ranges, that are functions of the characteristics of the oil, is very much welcome. In this context, it is interesting to develop a simulation tool based on commercial simulator since components data bank and facilities to integrate with other unit operation are available. Basically, two pieces of equipment are available for MD operations: the falling film and the centrifugal ones. Rigorous modeling and simulation are necessary in order to establish the viability as well as the operational conditions so as to improve the final product yield and purity and to establish the process flexibility level. Bearing all these in mind, the main objective of this work is the development of a simulator of a falling film MD piece of equipment in Aspen Plus® for heavy and ultraheavy oil processing. The developed tool turns possible an evaluation of the process variables impact on process behavior and characteristics of obtained product streams (residue and distillate). As Aspen Plus ® does not include a MD piece of equipment, it is necessary to choose, among the available unit operations, the one that better suits to the MD parameters. A sequence of flash vessels coupled with process efficiency is selected to represent the process and experimental data are used to validate the model. This is a preliminary approach used to develop a MD simulation procedure in the Aspen simulator, since it is easier to start the procedure development with flash operation than use straight way the mass transfer models, as a rate base system.

2. Methodology, Simulator Development and Results Initially, data from the binary system Dibutyl phthalate – DBP (278.35 g/mol) and Dibutyl sebacate – DBS (314.14 g/mol) were used for MD process simulation [5]. This binary system was chosen due to its simplicity when compared to the petroleum (multicomponent system), to its high molecular weight and to the availability of published experimental data. Since Aspen Plus® does not possess a MD operation tool, a sequence of flash vessels, operating at equilibrium, were proposed to emulate the molecular distillation. As MD process is ruled by mass transfer rates [6] (nonequilibrium) [7], efficiency considerations must be done in the developed tool in order to fit the simulator outputs to the experimental data. The idea to use a sequence of flashes corrected with process efficiency is a preliminary approach since relatively well established mass-transfer models could be used into Aspen environment to develop the simulator. However, the proposed approach has the advantage to be simpler and be dependent upon only the efficiency values rather than the uncertainties of the mass transfer models and the need to identify which could be the more suitable one. This is an important issue to develop the whole simulation methodology and, once it has been considered suitable, the next step should be the use of rate-based approach. The parameters used for the efficiency and simulator validation were distillation mass ratio (distillate mass/inlet mass) and the molar compositions of distillate and residue. The operation temperature was the analyzed parameter, since it is the limiting factor for the great majority of MD applications [8]. 2.1. Simulator Development In the simulations performed, 50 kg/h of an equimolar mixture were fed to the system, operated at 0.001 mmHg. For the MD operation, this process conditions lead to temperature operation of 95.85°C and a distillation mass ratio of 21.2% (i.e., 21.2% of the mass fed to the falling film molecular distillation unit is obtained as distillate), with molar fraction of DBP equal to 0.775 in distillate and 0.429 in residue streams

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(DISMOL results). The MD simulation first built in Aspen Plus® is shown in Fig. 1, in which, three flash vessels are connected. The condensed vapor streams obtained with the simulated process depicted in Fig. 1 have, together, a mass rate greater than that obtained with DISMOL simulation. Also, the molar fraction of DBP in “Distill” stream (Fig. 1) is higher than the real MD one (simulated with DISMOL).

Figure 1: Sequence of flash vessels for DM process simulation in Aspen Plus® Environment

Furthermore, the operation temperatures of each flash vessel (61.5 °C, 63.0 °C and 64 °C for FLASH-01, FLASH-02 and FLASH-03 respectively) were lower than the real MD temperature for the defined operation pressure. These results are presented in Table 1. The differences in simulation results are due to the fundamental differences with the two unit operations: while a MD process is governed by mass transfer limitations, an ideal flash vessel, as the ones illustrated in Fig. 1, is an equilibrium stage and with an efficiency of 100%. Table 1. Simulation results for DISMOL and the developed Aspen Plus® tool

Distillation mass ratio Distillate DBP molar fraction Residue DBP molar fraction Operation temperature (°C)

DISMOL 0.2120 0.7750 0.4290 95.85

ASPEN PLUS® 0.2854 0.8700 0.3420 FLASH-01 61.50 FLASH-02 63.00 FLASH-03 64.00

The flash sequence leads to a better separation of components since it is an equilibrium operation. However, since MD process is a mass transfer ruled process, it is expected that just one flash vessel may be used (since the more number of flash vessels, the greater the distance of simulation results from non-equilibrium processes results) coupled to an adjusting equation, used to translate flash simulation results to MD process results. Therefore, the final MD tool built in Aspen Plus® possesses just one flash vessel and an adjustment equation to take into consideration that a rate-based process is been emulated by an equilibrium approach. 2.2. Adjustment of the Tool Using just one flash vessel, with the selected operation pressure, operation temperature was manipulated in order to evaluate in which operation temperature a distillation mass

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ratio equals to the one of a real MD process was obtained. Figs. 2 and 3 show the vapor (which emulates MD distillate) mole fractions and mass flows both for DBP and DBS as a function of temperature. Fig 2 represents the mass flow of the DBP and DBS components on the vapor stream as a function of flash temperature, while Fig. 3 shows the molar fraction variation of DBP and DBS on the vapor stream when the flash temperature is changed. From these Figures it is possible to observe that the better separation of system components occurs when flash temperature is 61.5° C. If the flash temperature gets higher, the DBS molar fraction increases and the DBP molar fraction decreases, lowering the vapor purity grade. The condenser turns into liquid all the vapor stream coming from the flash vessel. However, in order to obtain the same distillation mass ratio of the DISMOL (21.2 %), the flash equipment has to operate at temperature of 63.1° C. This temperature, nevertheless, results in a higher molar fraction of DBP in the distillate (0.875) and a lower molar fraction of DBP in the residue (0.329).

Figure 2. Mass flow of distilled stream as a function of flash vessel operation temperature.

Figure 3. Mole fractions of distilled stream as a function of flash vessel operation temperature.

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An adjusting equation, which quantifies an efficiency measurement, is then formulated in order to convert flash results into MD ones, that means to correct the fact that a ratebased process is represent by an equilibrium operation unit. This equation correlates the MD unit operation temperature (given by DISMOL) to the flash operation temperature, so as to provide the same emergent flows composition. The efficiency is calculated, then, dividing flash by DISMOL operation absolute temperatures (Kelvin scale), as depicted in Eq. (1).

η=

T flash ( K ) TDISMOL ( K )

=

336,26 = 0,91 = 91% 369

(1)

The adjusted molar fraction is then calculated multiplying the efficiency factor ‘Ș’ to the DBP molar fraction of flash exit vapor stream. The new (corrected) DBP molar fraction in residue is found by mass balance. Table 2 brings DISMOL results compared to the results generated by the developed tool (one flash vessel coupled to an efficiency factor calculated by Eq. (1). In principle, the proposed procedure is general and may be used to any system including multicomponent ones. Table 2. DISMOL and corrected simulated data (by Eq. 1) for the binary mixture molecular distillation

Distillation mass ratio Distillate DBP molar fraction Residue DBP molar fraction

DISMOL 0.2120 0.7750 0.4290

ASPEN PLUS® 0.2120 0.7900 0.4090

3. Conclusions A new tool was developed with the software Aspen Plus® available unit operations to represent MD. As a preliminary approach it is proposed the use of flash operation corrected with process efficiency since MD is a mass transfer limited process. This tool simulates with a good prediction capability literature data for a binary system. The best tool structure was found with the use of one flash vessel coupled to an efficiency factor. The results generated with the developed tool indicated it can be applied to more complex systems, like heavy and ultra-heavy petroleum.

4. Acknowledgements The authors are grateful to FAPESP (2007/06833-3 and 2006/55177-9) for the financial support.

References [1] A.T. Erciyes, H. Ishikawa, M. Inuzuka, S. Hiraoka, H. Mori and I. Yamada, I. Chem. E. Symposium Series, 1 (1987) A359 [2] J. A. B. Hernández, L. Z. Linan, A. Jardin, M. R. W. Maciel, R. M. Filho and L. C. M. Oliveira, Rio Oil & Gás Expo and Conference, Rio de Janeiro, Brazil, IBP2712_08 (2008) [3] E. R. L. Rocha, M. R. W. Maciel, R. M. Filho, C. B. Batistella and L. C. M. Oliveira, Rio Oil & Gás Expo and Conference, Rio de Janeiro, Brazil, IBP2724_08 (2008) [4] R. S. Rocha, M. R. W. Maciel, R. M. Filho, C. B. Batistella and L. C. M. Oliveira, Rio Oil & Gás Expo and Conference, Rio de Janeiro, Brazil, IBP2730_08 (2008) [5] C. B. Batistella and M. R. W. Maciel, Computers Chem. Engng., 20 (1996) S19.

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[6] J. Lutisan, J. Cvengros, M. Micoslav, Chemical Engeneering Journal, 85 (2002) 225 [7] K.C.D. Hickman, A Review. Chem. Rev., 34 (1943) 51 [8] J. Lutisan, J. Cvengros, M. Micoslav, Chemical Engeneering Journal, 78 (2000) 61

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Dynamic analysis of oscillating flames Alberto Cuoci, Alessio Frassoldati, Tiziano Faravelli, Eliseo Ranzi Dipartimento di Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20133 Milano, Italy, [email protected]

Abstract Turbulent diffusion flames are inherently complex due to the coupling of highly nonlinear chemical kinetics and turbulence. In order to understand this interdependency of transport and kinetic mechanisms, acoustically forced flames are useful because they exhibit a larger range of combustion conditions than those observed in steady flames. A mathematical model was developed to simulate oscillating, counter flow diffusion flames. This model solves the unsteady conservation equations of mass, momentum, energy and species which are discretized using a non uniform grid. The structure of the resulting large DAE system is a tridiagonal block, because of spatial discretization. Most of the equations are devoted to the chemical species involved in the detailed kinetic scheme. The overall number of DAEs ranges between ~20,000 and ~30,000, depending on the number of grid points. The possibility of exploiting the tridiagonal block structure is of crucial importance in drastically reducing CPU time. The solution of the whole system of equations requires specific attention because of the numerical complexity, mainly related to the stiff nature of the kinetic mechanisms and to the high temperature gradients. The flame behavior at extinction resulted more complex under unsteady conditions.

Keywords: Combustion, Dynamic analysis, Flame extinction, DAE systems, Stiffness.

1. Introduction Effects of unsteadiness on the characteristics of strained flames are today well recognized as a relevant tool for understanding unsteady phenomena occurring in turbulent combustion. In a real combustion device the strain rate can fluctuate around its main value (which is established by the large scale eddies) due to the smaller eddies with characteristic turnover times comparable to the characteristic diffusion time (especially at high Reynolds numbers). From a numerical point of view the introduction of unsteadiness in combustion is a challenge due the strong coupling between the time and spatial scales of convection, diffusion and reaction. As a first step, many authors suggested to perform this kind of investigations by exposing the counterflow flames to far-field harmonic oscillations, using a large range of frequencies, from very low to very high values [1-5]. From both experimental and numerical results [1-7], it is evident that the strain rate responds quasi instantaneously to the oscillations imposed on the velocities of inlet streams, both at low and large frequencies. However, the response of temperature and concentrations of main species is quasi-steady only if the frequencies are sufficiently low. At high frequencies a non negligible phase lag between the oscillations and the response of the flame arises. As a consequence the chemical reactions do not respond immediately to the oscillations

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in the strain rate and the chemistry and flow field become uncoupled. At intermediate values of oscillation frequency the behavior of the flame response is even more complex [8]. This paper describes the effects of unsteadiness on flame extinction, in order to better understand how the extinction limits are modified by flow oscillations.

2. Mathematical model The counter flow configuration consists of two nozzles which produce an axisymmetric flow field with a stagnation plane between the nozzles. The two-dimensional flow is reduced mathematically to one dimension by assuming that the radial velocity varies linearly in the radial direction [8]. The numerical solution of these counter flow flames is obtained by solving the unsteady conservation equations of mass, momentum, energy and species concentrations [8]. Initially the problem for the steady flame is solved: the corresponding solution is assumed to be the starting point for the application of the harmonic oscillations [2]. It is assumed that the oscillations of the inlet velocities have a sinusoidal form (eq. 1), where usteady is the inlet velocity and Au the dimensionless semiamplitude of the oscillations of frequency f.

u (t ) usteady >1  Au ˜ sin(2S f ˜ t ) @

(1)

The overall model consists of a differential system of the conservation equations with boundary and initial conditions. The resulting system of algebraic and partial differential equations are discretized by means of a non uniform grid using conventional finite differencing techniques for non-uniform mesh spacing. Diffusive terms use central differences; for better convergence, convective terms use upwind differencing, based on the sign of the axial convective velocity u. The numerical problem corresponds to a large system of differential-algebraic equations (DAE). The complexity of this problem, coupled to the intrinsic stiffness of the DAE systems [9], means that specific attention must be paid to the numerical methods and solver routines [10,11]. The DAE system is tridiagonal, due to spatial discretization; The possibility of exploiting the tridiagonal block structure is of crucial importance in drastically reducing CPU time [11,12]. The simulations were carried out using detailed kinetic scheme involving a1100 reactions with a70 species [13].

3. Extinction of premixed flames in steady-state and oscillating conditions The flames studied in this work are obtained by impinging two identical premixed mixtures of CH4, H2 and air against each other [14]. Table 1 summarizes the composition corresponding to the flames studied in this work. The inlet streams are preheated at the temperature of 573K. The strain rate is largely used to parameterize the behavior of counterflow flames, because it is a measure of characteristic diffusive time scales. In this work a global strain rate KG and local strain rate KL are used. KG

4 ˜ uO ; L

KL



du dx

(2) max

KG accounts only for boundary conditions and represents an imposed stretch rate while KL, defined as the negative maximum of the local axial velocity gradient ahead of the thermal mixing layer, is more appropriate for dynamic analyses of counterflow flames as it represents the interaction between the hydrodynamic flow field and the flame.

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Figure 1 (left) shows the structure of Flame II when KG~5400 1/s. Since for the flames investigated in this work the inlet streams are always balanced, the global strain rate is here simply defined as KG=4VIN/L, where VIN is the inlet velocity and L is the separation distance between the two nozzles. Figure 1 (right) shows the effect of hydrogen on the maximum flame temperature and the extinction strain rate. As expected, the flame temperature tends to decrease when strain rate increases, since the residence time becomes smaller. As evident, the extinction strain rate becomes larger for higher amounts of hydrogen in the fuel mixture. Periodic oscillations of identical frequency and amplitude fraction (Au) were imposed with time varying velocities at the two nozzle exits, given by Equation (1). The steadystate flames presented in the previous section were used as the initial state upon which oscillation was subsequently applied with given Table 1. Inlet compositions (mass fractions) of investigated flames.

Flame I Flame II Flame III

CH4 0.04196 0.03990 0.03784

H2 0 0.001 0.002

O2 0.2232 0.2234 0.2236

N2 0.7349 0.7356 0.7364

Figure 1. Left: Temperature and mole fraction profiles of CH4, H2, CO2 and CO along the axial coordinate for Flame II in steady-state conditions (KG~5400 1/s). Right: Flame temperature (in steady-state conditions) versus the local strain rate at different amount of added H2.

frequency and amplitude. The initial condition for the application of the dynamic analyses corresponds to a strain rate sufficiently close to the steady-state extinction strain rate Kext. In particular two reference initial conditions were chosen, corresponding to Kin/Kext=0.76 and Kin/Kext=0.85. Figure 2 shows the numerical results obtain in unsteady conditions for Flame I. The initial conditions corresponded to Kin/Kext=0.85, while the frequency of imposed oscillations was 400 Hz. The amplitude of oscillations was gradually increased, up to the extinction of the flame. The flame temperature and CH4 mole fraction at the stagnation plane are reported against the dimensionless time. It is evident that the maximum velocity (or equivalently the maximum strain rate) corresponds to a minimum in the temperature and a maximum in the CH4 at the stagnation plane. When the strain rate increases the flame temperature decreases without following the steady state solution. When K increases from the initial condition, the flame temperature begins to decrease, due to the reduction of the residence time, without following the curve obtained in

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steady-state conditions. If K decreases, the flame temperature begins to rise, reaching values above the steady state curve. It is evident that the flame survives even with strain rates larger than the steady-state extinction value. Moreover the temperature can reach values well below the steady-state extinction temperature, without causing the extinction of the flame. While the initial steady flame has no CH4 at the stagnation plane, when the oscillations are imposed some unburned CH4 can be observed. This is a clear indication of an incomplete combustion especially close to the extinction limit.

Figure 2. Calculated flame temperature and CH4 mole fraction Flame I (f=400Hz, KGin=4000 1/s) versus the local strain rate. The oscillation amplitude is gradually increased from 20% up to the extinction. Bold line represents the envelope of the steady-state solutions, grey line represents the dynamic analysis which starts as Kin=4000 1/s as indicated by the circle.

Figure 3. Left: Effects of oscillation frequency on the response of Flame I (Kin=3500Hz,Au=35%). Right: Calculated extinction semiamplitudes versus the dimensionless frequency.

Figure 3 (left) compares the response of Flame I at different oscillation frequencies. Deviation from the steady state solution is larger at higher frequencies because the time available to the flame for adjusting its properties to the time-varying velocities is less and therefore the flame tends to conserve its initial properties. On the contrary, if the frequency of oscillations is small, the flame has more time to respond to the fluctuating velocities and therefore the deviation from the steady-state curve becomes smaller. In fact Figure 3 (right) compares the numerical results with the corresponding experimental measurements obtained by Plaia et al. [14]. As reported by the same author, due to some issues with the experimental ring, the measured Kext resulted larger than the real extinction strain rates and therefore it is

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suggested to compare the numerical results corresponding to Kin/Kext=0.85 with the experimental measurements corresponding to the Kin/Kext=0.60 case. Even if the numerical results tend to slightly overpredict the experimental data, the overall agreement can be considered satisfactory. In particular the trend of oscillation amplitude for the extinction seems to be correctly predicted as a function of the dimensionless frequency.

4. Conclusions The frequency response to externally imposed strain rate harmonic oscillations of counter-flow flames was investigated solving the transport equations governing the dynamic behavior of the flame. A detailed kinetic scheme and accurate description of the transport properties were used. The numerical investigations showed that the strained flames can survive to instantaneous strain rates much larger than the steadystate extinction strain rate, especially when the frequency of flow field oscillation is large. In such conditions a phase-lag develops between the imposed oscillations and the response of the flame. The most important parameter to explain the response of the is the ratio between the frequency of imposed oscillations and the flame strain rate, i.e. the ratio of the characteristic times of flame and imposed disturbances, respectively. The approach proposed in the present work is only a first step for a deeper analysis of the effects of unsteadiness on the behavior of strained flames.

5. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

Im, H. G., C. K. Law and F. A. Williams (1995), Combustion and Flame, 100, 21-30. Egolfopoulos, F. N. and C. S. Campbell (1996), Journal of Fluid Mechanics, 318, 1-29. Xiao, J., E. Austin and W. L. Roberts (2005), Comb. Sci. Tech. 177, 691-713. Decroix, M. E. and W. L. Roberts (1999), Comb. Sci. Tech., 146, 57-84 Decroix, M. E. and W. L. Roberts (2000), Comb. Sci. Tech., 160, 165-189. Welle E.J., Roberts W.L., Decroix M.E., Campbell C.S., Donbar J.M., Proc. Comb. Inst. 28:2021(2000). Welle E.J., Roberts W.L., Campbell C.S., Donbar J.M., Comb. Flame, 135:285(2003) Cuoci, A., Frassoldati A., Faravelli T., Ranzi E. (2008), Comb. Sci. Tech. 180(5):767. Shampine, L. F. (1985). Numerical solution of ordinary differential equations in Stiff Computation, Ed. by R. C. Aiken. New York, Oxford University Press. Buzzi-Ferraris, G. (1993). Building numerical libraries the object-oriented way, Addison Wesley-Longman, New York. Buzzi-Ferraris, G. (2007), C++ Numerical Libraries, www.chem.polimi.it/homes/gbuzzi Manca, D. and G. Buzzi-Ferraris (2005). BzzMath: an Object Oriented Numerical Project, Proceedings of ICheaP-7, Taormina (Italy). Ranzi (2007). C1C30704 Kinetic Scheme www.chem.polimi.it/CRECKModeling. Plaia, J. M. (2005), PhD Thesis, University of Maryland.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

Eliminating the Effect of Multivariate Outliers in PLS-Based Models for Inferring Process Quality D.Wanga, R. Srinivasana, b a b

Institute of Chemical and Engineering Sciences, [email protected] National University of Sungapore, [email protected]

Abstract Outliers in multivariate data demand special attention in data-driven process modeling. Their extremeness usually gives them an excessively high influence in the calculation, which may result in a less precise model. It is challenging to detect them using existing univariate approaches. A novel robust modeling method is presented; this PLS based modeling procedure not only alleviates the harmful effect of multivariate outliers, but also retains the information necessary for building a robust model from the training data. The performance of the proposed approach is compared with conventional strategies using an actual industrial case study.

Keywords: PLS, outlier detection, inferential model, quality prediction. 1. Introduction Data-driven process modelling has been widely used in chemical industries for the purpose of process monitoring, optimization, control and prediction. The treatment of data takes an important role in the model development, since most of modelling techniques are based on a certain assumption of data such as that they are normal distributed. Practical examination tells us that the real plant data collected seldom satisfy this crucial assumption. The data are usually unpredictable, having different distribution characteristics, especially when they contain anomalous outliers. The Outliers can be defined as ‘any observation that does not fit a pattern’[1], or simply regarded as the data that are not consistent with the bulk of data. They demand special attention in data-driven process modelling for several reasons. Their extremeness usually gives them an excessively high influence in the calculation of the model. Therefore, if they represent erroneous readings, then they will add disproportionately more error to the model. On the other hand, it is very important to note that the term ‘outlier’ does not imply ‘incorrect’; it could just as easily be caused by a real phenomenon that is relevant to the problem. Simple removal may result in loss of information and a less precise model. Outlier treatment has therefore been challenging in practical data-driven modelling, making itself as one of most important processes in model development. Even through several outlier detection methods have been developed, e.g. visual detection, filtering methods, and median absolute deviation, they are either time-

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consuming or applicable only to univariate data, rather than to the multivariate data. Data from chemical processes are usually not independent from each other (due to variable-wise correlation as well as sample-wise correlation in data set), it is more appropriate to examine the outliers status with the consideration of all variables rather than inspect individually. The univariate outliers’ detection may not be effective and could result in masking and swamping effects. These effects may result in that outliers are incorrectly identified as normal samples, or the normal samples are classified as outliers. It is quite possible to encounter outliers (regarded as multivariate outliers) that are not easily visible through plotting the raw data, or detected by univariate approaches. These outliers, if they represent unwanted or erroneous phenomena, can have a negative impact on the model. In this paper, a model-based outliers replacement approach is presented with the aim to eliminate their effect while retaining the information. It is noted that the discussion here focuses on the multivariate outliers, assuming that certain data pretreatment has been undertaken before PLS is applied. This pretreatment includes that, for example, some obvious outliers have been removed by visual or univariate approaches. The next section discuses the proposed approach. In section 3, the proposed approach is implemented to an industrial refining process where a model which relates process variables to final quality characteristics is sought[2].

2. PLS model based on winsorization 2.1. Partial least square regression(PLS) Given predictor sample X and response sample Y, PLS can be represented as

X = TA PA' + E Y = U A Q 'A + F , TA = XWA , U A = Q 'A Y

(1)

where X and Y can be used to present process measurement matrices and quality variables; TA and U A are score matrices of X and Y; PA and Q A are the corresponding loading matrices; WA is weighting matrix to ensure orthogonality of

TA ; E and F are the residual matrices. The regression coefficient matrix, B PLS , in a form of standard least square regression, is given by

(

B PLS = WA PA' WA

)

−1

Q 'A

(2)

2.2. Winsorization Consider the regression problem

Y = f (X, B) + E

(3)

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where f is non-linear function. An estimation of model parameter B can be obtained by ˆ , the prediction of least square regression method. With the parameter B estimated as B the dependent variable Y is given by

( )

( )

ˆ = f X, B ˆ , or yˆ = f X, B ˆ Y i i

(4)

and the residual is given by e i = y i − yˆ i

(5)

where y i and yˆ i are the original data and the predicted data, respectively. In the winsorization process, the regression is undertaken where the value y i is replaced using pseudo observation yˆ iw obtained by transformation according to specified M-estimates, such as Huber’s[1], which characterizes the residual distribution as a contaminated normal, with one normal distribution representing bulk of data and the other representing the abnormal data:

yˆ iw

­ yˆ i + bs i ° = ®y i ° ¯ yˆ i − bs i

e i > bs i e i ≤ bs i

(6)

e i < −bs i

here the parameter b is the degree of freedom representing the contamination degree, which can be used to regulate the amount of robustness, and s i is the estimation of scale associated with e i .

The above approach is similar to trimming but instead of throwing away the extreme values, the extreme values are replaced by pseudo values toward the centre of the distribution, making it less sensitive to outliers in the calibration data set. 2.3. PLS model based on winsorization Considering the multivariate outliers will manifest themselves in residual spaces produced in PLS calibration, the proposed approach integrates winsorization with PLS with the aim of eliminating the effect of outliers. Given a set of calibration data (Xsample along with its Y-sample), a preliminary model is established using partial least squares method. A winsorization is applied to the data in the spaces, where the extreme values are replaced by pseudo values making them toward the centre of the distribution[3]. The training data are reconstructed from the transformed data and then they are used to build a PLS model. This procedure can be repeated until a criterion, such as small enough difference between loadings, or an improved model calibration or prediction, is satisfied. The procedure for integrating both approaches is as follows:

(1) Given a reasonable number of latent variables, compute score and loading matrices in preliminary PLS model using training data X i and y i . (2) Reconstruct training data X i and y i according to Eqn. (1) (3) Compute the residual matrices

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ˆ w and yˆ w . (4) Winsorize training data X i and y i to obtain X i i ˆ w and yˆ w . (5) Build a PLS model using X i i (6) Stop with the model if a criterion is satisfied, otherwise, set i = i + 1 , go to step (1).

3. Case study 3.1. Process description The developed modeling approach is applied to an industrial refining process, which is briefly described as follows. Crude is preheated to the desired temperature and is desalted to remove salt and impurities before it enters the crude tower. In the crude tower - crude distillation unit (CDU), fractionation occurs on the trays, separating the crude oil into desired fractions according to their boiling points, from lighter to heavier. Wet gas and unstabilized naphtha pass overhead, and the low pressure wet gas is sent to the gas compression section. Light kerosene, heavy kerosene, light diesel and heavy diesel are trapped out of the crude tower and then steam stripped to remove light hydrocarbon. The light kerosene and heavy kerosene are then combined and sent to the Kerosene Merox unit after cooling. Some undesulphrised heavy kerosene is used for cutter stock for atmospheric residue. The light diesel is sent to the Diesel Hydrofiner. The heavy diesel is fed to a unit for processing (Fig. 1). The plant is equipped with a DCS and a powerful Plant Information Management System, which is able to record and store all the meaningful process data[2],[4].

The 90% point temperatures of the distilated streams are the quality indexes of the products. These quality varaibles need to be predicted by an inferential sensor in order to provide operators real-time information thus allowing them to make timely adjustment to keep the control variables within control limits. Crude overhead system Naphtha Stabilizer

Heavy Kerosene

Strippers

&UXGH 7RZHU

Light Diesel

M e a s u re d v a lu e

Light Kerosene

Heavy Diesel

Pairs from Model A Pairs from Model B diagonal line

Feed $WPRVSKHULF5HVLGXH Steam

+LJK6XOIXU)XHO2LO

Fig. 1. Crude distillation unit

Predicted value

Fig. 2. Prediction results

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3.2. Data selection, pretreatment and prediction results Only one of quality predictions using the proposed approach is reported in the case study. Three months’ data of 78 process condition variables and 1 quality variable are collected from the process histrorian, the aligment and pretreatment were made to exclude the missing and obvious error data. A preliminary PLS analysis was done to the data set and the most relavent process varibles to the quality were sellected. These procedures end up with 11 process variables which are most significant to the quality y . Considering the serial correlation in the data, a dynamic version of PLS is used. Nonlinear relationship is also considered in the model by including higher-order and cross terms of the variables.

Two PLS models are created based on the above training data and model format. Model A is from the standard PLS procedure, and Model B is from the proposed approach. Examination shows that 5 out of 147 samples in the training set are transformed by the proposed approach, with 3 samples being from the same variable. It was found that all of these samples were taken during crude switch, when product quality is known to change quickly making it prone to large errors. Table 1 shows that given the same number of latent variable held in the models, Model B gives more percentage variance captured by the model, which means it has better fitting performance than the other. Table 1. Comparison of percentage variance captured by Model A and Model B Latent Variable

1 2 3 20

LV 26.95 33.82 21.39 0.01

Model A X Cum 26.95 60.77 82.16 99.99

y LV 23.80 16.22 11.95 0.88

Cum 23.80 40.02 51.97 88.14

LV 28.47 32.97 20.55 0.00

Model B X y Cum LV Cum 28.47 27.39 27.39 61.45 20.56 47.96 82.00 14.41 62.37 99.98 1.68 92.88

Fig. 2 show the predicted vs the measured plots which are used to illustrate the prediction performance of the two models for the testing data. It can be seen that the data pairs from Model B are closer to the diagonal line than that from Model A, which means that Model B has better prediction ability than model A.

4. Conclusions Few multivariate outliers treatment has been developed for data-driven process modeling. One model-based approach on this is to plot residual versus leverage and then detect the potential outliers via visual inspection[4]. However, one must be prudent to conform their outliers status by observing and investigating their individual samples, as simply removing such detected outliers may have the risk of information loss. The fact that not all ‘outliers’ are erroneous leads one to develop a new multivariate modeling approach which not only resists the effects of outliers, but also retain the information provided in the data as much as possible, so that the model can accommodate the variety of process phenomena while being robust to outliers. The proposed approach provides a promising way to solve the issue.

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5. References [1] Huber, P, Robust Statistics, Wiley, 1981. [2] Jun Liu, R. Srinivasan, P. N. Selva Guru, "Practical Challenges in Development Datadriven Soft Sensors for Quality Prediction", ESCAPE-18, 961-966. [3] D. Wang and J. A. Romagnoli, “Robust Multi-Scale Principal Components Analysis with Applications to Process Monitoring”, J. Process Control, 15 (8), 869-882 [4] D. Wang, R. Srinivasan, J. Liu, P. N. S. Guru and K. M. Leong, “Data-driven Soft Sensor Approach For Quality Prediction in a Refinery Process”, INDIN’06, 4th international IEEE conference on industrial informatics, Singapore, 16-18 Aug., 2006.

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Feasible Separation Regions for Ternary Mixtures with S-shaped Distillation Lines Lechoslaw J. Krolikowski Wroclaw University of Technology, Norwida 4/6 Street, Wroclaw 50-373, Poland, [email protected]

Abstract The article proposes a new construction method of feasible separation regions for nonideal ternary homogenous mixtures. The method is based on an analysis of structure of feasible separation regions. The location of characteristic points and curves of the region border related to feed discrete distillation line is described. Two separate regions for rectifying and stripping sections are found. Joining them gives feasible separation region containing new areas which were not found until now.

Keywords: system synthesis, distillation column 1. Introduction A synthesis of the separation systems for azeotropic mixtures involves the successive selection of entrainers, the choice of a system structure, the design of individual columns, and the selection of suitable operating parameters. In the course of the synthesis, a necessity of quick identification of feasible separations arises. A feasible separation region is a set of possible composition points of distillate and bottoms to obtain for a given feed composition and quality. Several researchers have attempted to determine attainable regions for azeotropic homogenous mixtures but a complete solution has not been found, yet. Fidkowski et al. [1] proposed an approximate solution for ternary azeotropic mixtures for regions with C-shaped distillation lines. Jobson et al. [2] showed that the separation boundaries depend on the equipment used. Krolikowski [3] proved that feasible separation regions should be enlarged by some areas from common part of two distillation regions. It allows to determine feasible separation regions more accurately. Nevertheless, observations suggest that for cases with Sshaped distillation lines some areas (lying inside distillation region) are still missing. The present article addresses this matter.

2. Border structure of fixed distribution set Kiva and Krolikowski [4] studied continuous distillation in staged columns modelled by theoretical stages. The following assumptions were done: constant molar overflow (CMO) in each section of the column, constant pressure along the column, the products in the form of saturated liquids, and feed enters the column between stages. They considered distillation process as a function

( z D , z B ) = δ ( z F , qL , N , m| n , r , s )

(1)

which transforms feed composition zF and molar fraction of the feed that is liquid qL into distillate and bottom compositions zD and zB respectively. The function also depends on column parameters: N – number of theoretical stages, m|n –distribution of

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stages between rectifying and stripping sections (m and n stages respectively), and operating parameters: r= R/(R+1) and s = S/(S+1). Explicit representation of function δ is not known, of course. The function is represented by a system of nonlinear equations which contains material and energy balances, and vapor – liquid equilibrium relationships. Fortunately, it is not an obstacle in further considerations. An image of the feed composition zF with respect to function δ for fixed qL, N and m|n while r and s vary in [0, 1] is called a fixed distribution set. This set is a key element for construction of feasible separation regions. In order to determine a border structure of the set, it is necessary to consider limiting operation modes, in which at least one operating parameter r or s takes an extreme value 0 or 1. Some of these operation modes are not important or useless from practical point of view, or even unrealistic and considered only as an unattainable limit. The border structure of fixed distribution set for saturated liquid feed is presented in Fig. 1. Characteristic elements of the border are labelled by a pair of parameters rs, among which at least one has a value 0 or 1. Usually two digits’ labels indicate point, and one digit’s labels indicate curves. There is one exception. Label 11 shows a point when a superscript d (which is a ratio of distillate molar flow and feed molar flow) has a value 0 or 1. In another case, with the superscript

Fig. 1. Structure of fixed distribution set.

Fig. 2. Influence of stages distribution.

d, label 11 indicates a curve. Subscripts refer to bottom and distillate. Areas limited by enclosed curves represent sets of possible products compositions. The area surrounded by curves with a subscript D corresponds to distillate compositions. The second area enclosed by curves with subscripts B corresponds to bottom compositions.

3. Location of border elements Graphical methods for designing distillation columns for three component mixtures have been known for a long time (see e.g. [5]). They are useful to present steady state of distillation column, too. Considerations in the article are based on geometric model of distillation columns. Positions of vapor – liquid equilibrium vectors for column stages were studied for boundary operation conditions. It allows to draw a conclusion that characteristic points of border of fixed distribution set belong to distillation line which goes through feed composition point (see Fig. 1). Such distillation line will be called feed distillation line (FDL). Furthermore, relative location of characteristic curves to FDL is also established, although some of these curves may be found bellow or above

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FDL. For example, two curves 0s may lie on the same side of FDL or not. It depends on feed composition, shape of FDL, and number of stages in section. In order to restrict such behaviour and facilitate farther consideration, feed composition point is placed in point of inflection of FDL. This additional assumption will be removed later.

4. Transformations of fixed distribution set When distribution of stages m|n between column sections is changed (for constant number stages in the column), points 10D and 01B move along FDL. Increasing number of stages from m1 to m2 in rectifying section shifts point 10D in the direction of point

110D . The distillate compositions area expands and includes distillate composition areas for smaller number of stages (see Fig. 2). At the same time, point 01B moves towards the feed composition point zF. and bottom composition area decreases. Similarly when a number of stages in stripping section rises, point 01B moves toward the point 111B . The bottom compositions area extends and includes bottom compositions areas for smaller number of stages. Simultaneously point 10D approaches 00D and area of distillate composition decreases. Owing to such behaviour of fixed distribution set, it is enough considering columns which consist of rectifying or stripping section only. Fixed distribution sets for rectifier (N|0) and stripper (0|N) are presented in Fig. 3 and 4. Further expanding area of distillate compositions and area of bottom compositions is not possible for a fixed number of column stages. Fortunately, one may increase number of column stages from N1 to N2. Then, in rectifier case, distillate compositions area determined for N2 stages contains distillate compositions area defined for N1 stages (N2 > N1). Similarly, in stripper case, bottom compositions area for N2 stages contains bottom compositions area for N1 stages. When the number of column stages goes to infinity, fixed distribution sets for rectifier and striper are shown in Fig. 5 and 6 respectively.

Fig. 3. Fixed distribution set for rectifier with finite number of stages.

Fig. 4. Fixed distribution set for stripper with finite number of stages.

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Fig. 5. Fixed distribution set for rectifier with infinite number of stages.

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Fig. 6. Fixed distribution set for stripper with infinite number of stages.

5. Feasible separation region Joining two last fixed distribution sets gives feasible separation region as shown in Fig. 7. Segments 11dD and 11dB represent product regions for total reflux and infinite number of stages [6]. Curves 0sD (between points zF and 00D) and 1sD constitute a vapor pinch point curve, which passes through the feed composition point zF. This pinch point curve is a part of distillation limit described by Fidkowski et al. [1]. Segments r0D and 0sB correspond to a split which is called transitional [1] or preferable [7]. Invisible curves r1B and 0sB in Fig. 7 make liquid distillation limit.

Fig. 7. Feasible separation region. Curve 1sD does not cross FDL.

Fig. 8. Feasible separation region. Curve 1sD crosses FDL.

Curve 1sD may cross FDL (especially when the feed composition point lies far from the point of inflection of FDL) what has been confirmed by observations. In this case, feasible separation regions look like in Fig. 8. Segments F1 and F2 lie on a straight line,

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which passes through the feed composition point zF and is tangent to curve 1sD. A real example of feasible separation region for a mixture methyl ethyl ketone – benzene – toluene is given in Fig. 9.

Fig. 9. Feasible separation region for methyl ethyl ketone – benzene – toluene mixture.

6. Conclusions A new construction method of feasible separation regions has been proposed. The method applied to distillation regions with S-shaped distillation lines gives a larger feasible separation region with some new areas which have not been found until now.

References [1] Z.T. Fidkowski, M.F. Doherty, M.F. Malone, Feasibility of separation for distillation of nonideal ternary mixtures., AIChE J, 39 (1993) 1303–1321. [2] M. Jobson, D. Hildebrandt, D. Glasser, Attainable products for the vapor–liquid separation of homogenous ternary mixtures.. Chem Eng J, 59 (1995) 51–70. [3] L.J. Krolikowski, Determination of distillation regions for non-ideal ternary mixtures., AIChE J., 52 (2006) 532–544. [4] V.N. Kiva, L.J. Krolikowski, Product composition region in multicomponent distillation., InĪ. Chem. i Proc., 22(3C) (2001) 723–728. [5] C.F. Bonilla, Graphical design of continuous distillation columns for ternary mixtures., Trans. A.I.Ch.E., 37 (1941) 669-684. [6] F.B. Petlyuk, L.A. Serafimov, Multicomponent Distillation. Theory and Design., Chemistry Publish. Co., Moscow, 1983 (in Russian). J. Stichlmair, H. Offers, R.W. Potthoff, Minimum Reflux and Minimum Reboil in [7] Ternary Distillation., Ind. Eng. Chem. Res., 32 (1993) 2483–2345.

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Graph theory and model simplification. Case study: distillation column Ivan Dones, Heinz A. Preisig Dept. of Chemical Engineering – NTNU, Sem Sælandsvei 4, 7491 Trondheim, Norway [email protected], [email protected].

Abstract A generic system can be seen as a set of capacities exchanging extensive quantities through connecting streams. This kind of vision can be applied with different levels of detail, focusing on smaller or bigger control volumes according on how well the dynamics of the process must be. In this way the studied system can be represented as a graph, each node standing for a control volume connected to the others and to the external of the modelled system by arcs standing for the connecting streams. In this paper we discuss the simplification of a detailed distillation model, which describes each tray as a dynamic flash. A simplification, which combines lumping and eventassumptions for sub-networks is being investigated. The procedure applies singular perturbation to sub-networks thereby assuming steady-state, equilibrium or even merge together different capacities. Keywords: model reduction, distillation, DAE system.

1. From non-equilibrium to equilibrium flash: horizontal folding Flash and distillation is an old research subject. Just to quote some references, we remember [1-9]. This article is meant to provide an overview to help the reader to better grasp the assumptions and the descriptions that different forms of model reduction can bring to a distillation model. The starting point of our approach is a non-equilibrium distillation model, such as that one proposed in our previous contribution [10]: each stage of the column is considered as a dynamic flash containment, where the liquid phase and gas phase are two uniform lumps exchanging extensive quantities (mass and energy) through a discontinuity surface, the boundary. Let us call this stage model as MODEL 0 (see Figure 1). Starting from MODEL 0, a cascade of assumptions and simplifications based on the time scales of the dynamics and size of the capacities are made, evolving our model from a full dynamic to a more simplified one. All the assumption are traced back to those ones schematised in [11].

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Figure 1. MODEL 0.

MODEL 0 This model is represented by a system of differential and algebraic equations (DAE system) to calculate the extensive and intensive properties of each stage; basically the equations are conservation laws of mass and energy (dynamic part, eq. 1 and 2) and variable transformations (algebraic part). For the notations, please refer to the appendix. ­ nL = − nˆL|B + nˆIN |L − nˆL|OUT ° (1) ® nB = nˆL|B − nˆB|G ° ¯ nG = nˆB|G + nˆIN |G − nˆG|OUT

­U L = − Hˆ L|B − qˆ L|B − wˆ L|B + Hˆ IN |L − Hˆ L|OUT °° (2) ®U B = Hˆ L|B + qˆ L| B + wˆ L| B + wˆ G| B − Hˆ B|G − qˆ B|G ° ˆ ˆ ˆ °¯U G = H B|G + qˆ B|G − wˆ G| B + H IN |G − H G|OUT

Formally, the dynamic part can be written in a more compact form [11] merging eq. 1 and 2 into x = Fxˆ , where x is a vector of integration states, F maps into a matrix the directions of the flows and xˆ is a stack of the network’s flows. Recalling [11], simplifications on this generic form are made. The dynamic order of the model is reduced, but not the state space. Using the nomenclature reported in [11], assumption 1 (small and large capacities) is applied to the mass and energy balances of the boundary, since this entity is considered like a zero capacity surface, with negligible holdup. As consequence, the mass and energy balances at the boundary become algebraic equations, easing temperature and chemical potential computations at the boundary thanks to the singular perturbation assumption. 0 = nˆL|B − nˆB|G Ÿ nˆB|G = nˆL|G = nˆL|G (3)

0 = qˆ L| B − qˆ B|G − Hˆ B|G + Hˆ L| B

(4)

Then, since pressure waves propagate with the speed of sound, their velocity is orders of magnitude higher than the other transfer laws. Assumption 2 (fast and slow transfer) will in this case imply mechanical equilibrium (pL = pB = pG = p). Considerations are made even concerning the volumes, since the single distillation stage can be considered a rigid container. For each stage one can assume constant volume which has implications on the relative change and the volume work being exchanged. This is equivalent to apply assumption on assemblies of secondary states (assumption 5).

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MODEL 1 The conductive heat is, as first guess, thought as the product of a temperature difference and a coefficient of heat transfer. This coefficient is proportional to the density of the medium, thus is larger in the liquid phase. One can then imagine that the conductive heat is much faster through the liquid phase than in the gas phase, and assumption 2 will imply thermal equilibrium between liquid and boundary. The value of qˆ L|B can be reconstructed from the energy balance about the boundary. We call MODEL 1 the result of MODEL 0 plus the hypothesis of fast heat transfer in the liquid phase. MODEL 2 On a larger time scale, one may assume fast overall heat transfer between the two phases. In this case, the dynamic energy balances of liquid, boundary and gas phase are lumped together, and the set of equations (2) reduces to one dynamic equation plus two algebraic equations. U = Hˆ IN |L − Hˆ L|OUT + Hˆ IN |G − Hˆ G|OUT ; TL = TB ; TB = TG

(5)

Again, the size of the DAE system does not change, just its morphology. The values of the conductive heats in the liquid and gas phase are reconstructed from the equilibrium relations and from the energy balances at liquid phase and gas phase. MODEL 2 is MODEL 1 plus the assumption of thermal equilibrium in the flash tank, traced back to assumption 2 applied to the overall conductive heat transfer. MODEL 3 For even longer time scales, the mass transfer, normally slower than the heat transfer, can be considered of event dynamics. The implication concerns the chemical equilibrium: each species will show now the same chemical potential in the liquid phase, the boundary and the gas phase. Equations (1) are substituted by: n = nˆIN | L − nˆL|OUT + nˆIN |G − nˆG|OUT ; μ L = μ B ; μ B = μG

(6)

MODEL 3 comes from MODEL 2 plus the chemical equilibrium assumption between liquid phase and gas phase. Again, an equilibrium relation results from assumption 2. MODEL 4 In the end, MODEL 4 is the conclusion of this cascade of reduction of the models. MODEL 4 is obtained from MODEL 3 assuming that the gas phase has negligible holdup (assumption 1). Table 1 and Figure 2 summarise the procedure leading from MODEL 0 to MODEL 4. Table 1. Summary of the assumptions brought by the cascade of model reductions. MODEL 0

MODEL 1

MODEL 2

MODEL 3

MODEL 4

Mech. equilib. in flash tank

As MODEL 0

As MODEL 1

As MODEL 2

As MODEL 3

Singular perturbation at B

Thermal equilib. between L and B

Thermal equilib. in flash tank

Chem. equilib. in flash tank

Negligible gas holdup

Fix tot. volume

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Figure 2. Onion representation of the model reductions of the flash tank.

2. Vertical folding Applied to a distillation tower, the abovementioned procedure leads from MODEL 0 to models with lower level of details, and it is like folding up horizontally the distillation trays. If the required level of details is even lower, one can imagine to lump together a group of trays, obtaining a vertical lumping of the column. This approach can be done adding all the dynamic equations of the same type together. Next, one system is chosen to represent all the ones being lumped. The set of equations is completed by choosing all the others and applying a singular perturbation assumption to each. This conserves the dominating constant and locates it in the chosen system, which is kind of suspended in the stationary system of the remaining systems. The procedure can be easily shown with a picture (Figure 3), where one can even see the graph approach of the model reduction.

Figure 3. Horizontal and vertical folding in sequence.

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3. Conclusions The folding operation is a "summation" of the respective capacities, useful to reduce (when one needs) the resolution of his/her model. Here the horizontal folding implies assuming fast heat and mass transfer, whilst folding in the along vertical axis lumps the capacity effects into one lump whilst retaining a network of stationary transfers between the rest. The singular perturbation is thereby always one of the main operations. The horizontal folding eliminates the internal flows assuming fast transfers, whilst the vertical folding does not make that assumption. In both cases the dynamic order is being reduced. In both cases the state space does not reduce. Important to remember, such approaches guarantee closure of the balances under reduction.

4. Appendix Table 2. Notation. NOMENCLATURE SUBSCRIPTS

SYMBOLS

n: mass.

X :

U: internal energy.

L: liquid phase.

T: temperature. V: volume.

G: gas phase.

p: pressure. w: volumetric work. B: boundary between liquid q: heat. and gas phase. H: enthalpy.

derivative quantity X.

time of

Yˆa|b

: stream flowing from a to b.

5. Acknowledgements This work is supported by the StatoilHydro Mongstad Pilot Project. We thank also Bjørn Tore Løvfall [12], Tore Haug-Warberg, Flavio Manenti and Guido Buzzi-Ferraris [13-14].

References [1] Chung, C. B.; Riggs, J. B., Dynamic Simulation and Nonlinear-Model-Based Product Quality-Control of a Crude Tower. Aiche Journal 1995, 41, (1), 122-134. [2] Goncalves, F. M.; Castier, M.; Araujo, O. Q. F., Dynamic simulation of flash drums using rigorous physical property calculations. Brazilian Journal of Chemical Engineering 2007, 24, (2), 277-286. [3]. Kakhu, A. I.; Pantelides, C. C., Dynamic modelling of aqueous electrolyte systems. Computers & Chemical Engineering 2003, 27, (6), 869-882. [4] Krishnamurthy, R.; Taylor, R., NONEQUILIBRIUM STAGE MODEL OF MULTICOMPONENT SEPARATION PROCESSES. AIChE Journal 1985, 31, (12), 1973-1985. [5] Mazzotti, M.; Rosso, M.; Beltramini, A.; Morbidelli, M., Dynamic modeling of multistage flash desalination plants. Desalination 2000, 127, (3), 207-218. [6] Powers, M. F.; Vickeryt, D. J.; Arehole, A.; Taylor, R., A nonequilibrium stage model of multicomponent separation processes--V. Computational methods for solving the model equations. Computers & Chemical Engineering 1988, 12, (12), 1229-1241. [7] Taylor, R.; Krishna, R., Modelling reactive distillation. Chemical Engineering Science 2000, 55, (22), 5183-5229.

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I. Dones and H.A. Preisig [8] Thery, R.; Llovell, F.; Meyer, X.; Gerbaud, V.; Joulia, X., Modelling of a dynamic multiphase flash: the positive flash Application to the calculation of ternary diagrams. Computers & Chemical Engineering 2004, 28, (12), 2469-2480. [9] Tu, H.; Rinard, I. H., ForeSee - A hierarchical dynamic modeling and simulation system of complex processes. Computers & Chemical Engineering 2006, 30, (9), 1324-1345. [10] Dones, I.; Preisig, H. A., Dynamic modelling and simulation to overcome the initialization problem in steady state simulations of distillation columns. 2008; Vol. 8. [11] Preisig, H. A. In Three principle model reductions based on time-scale considerations, ESCAPE 18, Lyon, France, 2008; Lyon, France, 2008. [12] Løvfall, B. T. Computer realisation of thermodynamic models using algebraic objects. NTNU, Trondheim, Norway, 2008. [13] Buzzi-Ferraris, G., BzzMath: Numerical libraries in C++. Politecnico di Milano, http://chem.polimi.it/homes/gbuzzi. 2008. [14] Buzzi-Ferraris, G.; Manca, D., BzzOde: a new C++ class for the solution of stiff and non-stiff ordinary differential equation systems. Computers & Chemical Enginnering 1998, 22, (11), 1595-1621.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Lactic Acid Recovery in Electro-Enhanced Dialysis: Modelling and Validation Oscar A. Prado Rubio, Sten B. Jørgensen, Gunnar E. Jonsson CAPEC, Depertment of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark, [email protected], [email protected], [email protected]

Abstract A dynamic model is derived for simultaneous transport of multiple ions through anion exchange membranes based on an irreversible thermodynamics approach. This model accounts for the convective transport of the dissociated and undissociated species in the module channels, and the diffusion and migration across the boundary layers and membranes. The model is validated for Donnan dialysis recovery of different monoprotic carboxylic acids. Simulations are used to evaluate the potential enhancement of lactate fluxes under current load conditions, referred as ElectroEnhanced Dialysis operation. This model is a useful tool to understand the transport mechanism in such electrochemical system. Keywords: Electro-Enhanced Dialysis (EED), Donnan Dialysis (DD), lactate recovery, ions transport modelling

1. Introduction Lactic acid is an interesting product since it is widely used in the food industry. A significant industrial potential is for Polylactic acid (PLA) production. PLA is a sustainable polymer, which can substitute petrochemical derived polymers in several applications. It will definitely reduce our dependency on fossil feedstock. Lactic acid is mostly produced in fermentation of carbohydrates by Lactic Acid Bacteria (LAB). LAB are normally impaired by product inhibition. The inhibitory effect of lactates and low pH can be diminished by continuous removal of lactate from the fermentation broth and pH control, this will result in a higher productivity and product yield. The present contribution is focused on modelling and investigation of Electro-Enhanced Dialysis (EED) as a method for lactate recovery from fermentation broth.

2. Modelling of Electro-Enhanced Dialysis In 1980’s, electrically driven membrane separation processes were suggested as a potential in situ separation method, since lactate can be selectively removed by ion exchange membranes (Hongo et al., 1986). Donnan dialysis (DD) is a promising process. However, its main drawback is a rather low lactate flux since the driving force behind the lactate transport is the OH- concentration gradient (Strathmann, 2004). EED emerges as a potential method to enhance the lactate fluxes in conventional Donnan dialysis operation, this is done by imposing an external electrical field. The transport of ions across anion exchange membranes in an EED stack cell is modelled (fig. 1). A dynamic model is derived for transport of multiple ions through anion exchange

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membranes and Nernst diffusion layers. The model is based on first principles for dissociation, diffusion, convection and migration of species.

Figure 1: sketch of a cell in the EED module. BL: boundary layer, AEM: anion exchange membrane 2.1. Model Assumptions •

•

•

General: electroneutrality at any location in the system, the current is carried by ions and ideal solution. Species included in the model are: lactate, hydroxyl, sodium, dissociated protein, lactic acid and undissociated protein. Membrane: convective transport is not investigated, transport of water by osmosis and electro-osmosis is neglected, there is no transport of uncharged or big molecules through the membrane, equilibrium at the membrane surface and constant membrane dimensions. Boundary layer: convective transport is neglected and the thickness of the boundary layers are constant for a given flow condition.

2.2. Transport in boundary layer and membranes As a general notation, the substances and the phases are denoted by the subscripts k and p, respectively. A mass balance is formulated:

∂Ck , p ∂t

+ ∇J k , p − ΔRk , p = 0

(1 )

The reaction term (ǻRk,p) is used to introduce the acid dissociation into the model. The flux Jk,p is estimated using Nernst-Planck equation for ideal solutions, neglecting convective transport (Strathmann, 2004):

z FC ∂ψ · § ∂C J k , p = − Dk , p ¨ k , p + k k , p ¸ RT ∂x ¹ © ∂x

(2 )

Where Dk,p is the diffusion coefficient, zk the valence, F is the Faraday number, R is the ideal gas constant, T is temperature and ȥ is the electrical potential. The potential gradient is calculated using the assumption that the current Id is carried by ions.

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I d = ¦ zk FJ k , p

(3 )

k

2.3. Bulk channels model The models for bulk channels are formulated using a tank in series approach. In each tank there is mass exchange with the adjacent boundary layers, and the dissociation reactions are present as well. The mass balance for each tank in the feed channel is depicted in eq. (4).

(

q feed dCkfeed 1 = Ckfeed ,in − Ckfeed ) + Jk ( dt h feed LW h feed

x = x7

− Jk

x = xo

) + ΔR

k,p

(4 )

Where q is the flow rate and h, L, W are the height, length and width of the channel, respectively. The dialysate channel model is completely analogous. 2.4. Boundary conditions at the interfaces For sorption in equilibrium at the membrane surface, the electrochemical potential in the ionic solution and the membrane surface must be the same. Then the following expression arises for an ideal solution (Strathmann, 2004):

Δψ Don

RT § Cks · = ln ¨ ¸ zk F © Ckm ¹

(5 )

Where ǻȥDon is the Donnan potential and the superscripts s and m correspond to solution and membrane, respectively. Besides, fluxes at the interfaces membranesolution are continuous, that means there is no accumulation. Points xj- and xj+ correspond to the left and right side of the interface located at xj, respectively.

Jk

x = x −j

= Jk

(6 )

x = x +j

Finally, the electroneutrality condition affects the concentration distribution in both the membrane and the solution. On the solution and membrane sides:

¦z C k

s k

=0

and

k

¦z C k

m k

+ z fix C mfix = 0

(7 )

k

Where the subscript fix is related to the fixed charge in the membrane. Finally, the assumption that all current is carried by ions remains. The dynamic model depicted above consists of a system of multiregion partial differential equations (PDEs). Method of lines is used, where the spatial dimension is discretized using sixth order Taylor expansion with asymmetric centered differences.

3. Results and discussion 3.1. Model validation The model is validated agaist experimental data taken from Zheleznov (1998). In that publication, the dialytic transport of carboxylic acids, through Neosepta-AMH, is

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investigated as function of the inlet base concentration in the dialysate channel. The derived model was simplified in order to reproduce the experimental conditions. First of all, a sensitivity analysis was performed to evaluate the influence of several unknown parameters on carboxylic ion fluxes. Those parameters are: anion exchange capacity of the membrane, the boundary layers thickness and the water content of the membrane. From there, the thickness of boundary layers and the anion exchange capacity of the membrane were fixed. The membrane water content has a big influence on the fluxes, since the diffusion coefficients within the membrane are related to their value in solution by a steric factor, which is a function of the membrane water content. The Mackie and Meares equation is used (cited by Jonsson, 1980). It has been evidenced experimentally that the membrane water content increases by increasing the average pH. However, if pH is very high membrane dehydration could happen (Izák et al., 2007). In this study, a black box model is proposed for water absorption as function of the concentration of hydroxyl ions at the inlet of dialysate channel (eq. 8). dia ,in WC = α ( COH )

β

(8 )

The methodology used for parameter estimation is the interior reflective Newton method for non linear minimization subject to bounds (Coleman and Li, 1994). The unknown parameters in the swelling model were estimated for three different monoprotic carboxylic acids: acetate, lactate and propionate. The results are shown in fig. 2. From the fitted simulation results, the agreement between experimental data and the predicted fluxes is clear. The developed model can be employed to understand the phenomena behind the anion transport through anion exchange membranes.

Figure 2: experimental and fitted simulated fluxes for acetate, lactate and propionate as a function of the inlet base concentration in the dialysate channel 3.2. Ions transport under current conditions As mentioned above, a disadvantage of Donnan dialysis operation is the rather low fluxes through the membrane. Consequently, EED design proposes to enhance ion fluxes by applying an external potential gradient. Using the fluxes calculated for Donnan dialysis operation as reference point, lactate flux is calculated for a range of

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current densities up to 260 A/m2. In fig. 3, the relative lactate flux enhancement is depicted.

Figure 3: relative lactate flux enhancement as function of the current density and hydroxyl inlet concentration in the dialysate channel, 0% enhancement correspond to the Donnan Dialysis flux Higher enhancements are evidenced at low inlet base concentration in dialysate channel. The reason is related to the transport mechanism. During Donnan dialysis counter ion exchange-diffusion takes place. However, a competitive anion transport is enforced under current load conditions. The imposed potential gradient compites with the concentration and the induced potential gradient, where the latter is generated by OHflux. At low base concentration, it is easier for ion migration to overcome diffusive transport. An interesting behaviour is evidenced by increasing the strenght of the electric field, the fluxes gradually turns in the opposite direction. The influence of the fluxes enhancement is represented in the total fluxes which are plotted in fig. 4.

Figure 4: total lactate flux as function of the current density and hydroxyl inlet concentration in the dialysate channel

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As expected, higher flux enhancement at low base concentrations in the dialysate channel, implies that the fluxes at high current densities are almost independent of the base concentration. These results are very promising since high fluxes can be achieved at low base concentrations, which diminishes the base requirements in the operation and will reduce the membrane damage due to the less aggressive pH of the environment.

4. Conclusions A dynamic model was derived from first principles for simultaneous transport of multiple ions across ion exchange membranes. The solution was approximated numerically by discretization of the PDE’s using high order Taylor expansion. The parameters in the model have been estimated based on experimental data for dialytic recovery of monoprotic carboxylic ions. The predictive power of the model is limited to each ion and the investigated membrane. The model was used to evaluate the potential flux enhancement by imposing an electrical field. Lactate fluxes were increased up to 230% compared to Donnan dialysis operation. It remains to verify this improvement experimentally. Furthermore, this model can be used to understand the transport phenomena under current load conditions.

Acknowledgements This project is carried out in CAPEC within the Bioproduction project which is financed by the 6th Framework Programme, EU.

References Coleman, T. and Li, Y. (1994). On the Convergence of Interior-Reflective Newton Methods for Nonlinear Minimization Subject to Bounds. Mathematical Programming, 67, 189–224. Fila, V. and Bouzek, K. (2003). A Mathematical Model of Multiple Ion Transport Across an IonSelective Membrane under Current Load Conditions. Journal of Applied Electrochemistry, 33, 675–684. Hongo, M.; Nomura, Y. and Iwahara, M. (1986). Novel Method of Lactic Acid Production by Electrodialysis Fermentation. Applied and Environmental Microbiology, 52(2), 314–319. Izák, P.; Hovorka, S.; Bartovská, L. and Crespo, J. (2007). Swelling of Polymeric Membranes in Room Temperature Ionic Liquids. Journal of Membranes Science, 296, 131–138. Jonsson, G. (1980). The influence of the Porous Sublayer on the Salt Rejection and Reflection Coefficient of Asymmetric CA Membranes. Desalination, 34, 141–157. Møllerhøj, M. (2006). Modeling the REED Process. Master’s thesis, Technical University of Denmark. Rype, J. (2003). Modelling of Electrically Driven Processes. Ph.D. thesis, Technical University of Denmark. Strathmann, H. (2004). Ion-Exchange Membrane Separation Processes. Membrane Science and Technology Series, 9. Elsevier. Zheleznov, A. (1998). Dialytic Transport of Carboxylic Acids through an Anion Exchange Membrane. Journal of Membrane Science, 139, 137–143.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

779

Maxwell-Stefan in mass fractions for numerical simulation of the pervaporation process Adrian Verhoef,a Emmanuel De Ridder,a Ben Bettens,a Jan Degrève,a Bart Van der Bruggena a

Katholieke Universiteit Leuven, Department of Chemical Engineering, Applied Physical Chemistry and Environmental Technology Section, W. de Croylaan 46, B-3001 Heverlee, Belgium, [email protected]

Abstract Membrane processes are becoming more and more important in industry. Therefore, modelling of these processes is also gaining interest, as this offers opportunities to predict process performance, membrane properties, efficiencies and economical aspects. With this information, industry can be helped to improve existing separation processes, or switch to more profitable alternatives. The choice of the transport model is important to describe membrane transport correctly. For processes with a solution-diffusion transport mechanism, like pervaporation, the Maxwell-Stefan equations have proven to be capable of describing multicomponent transport. In this model, the membrane is considered to be part of the system, and interactions between all system components are accounted for. Because for the generalized Maxwell-Stefan equations unknown information about the membrane is necessary, like the molar mass, a conversion to mass fractions is performed in this paper. This conversion has consequences for several parameters and these are discussed in this paper. From an economical point of view, pervaporation is a possible alternative to energy consuming processes, like distillation. If executed solely or in a hybrid process, it can reduce the process energy consumption. As an example of the capabilities of the conversion, a pervaporation case study is simulated. The structure of this simulation program is briefly discussed, and an example is elaborated that shows the applicability of the conversion. Keywords: Numerical techniques, Maxwell-Stefan, mass fractions, pervaporation

1. Introduction Membrane processes offer good alternatives in process engineering for separations that are hard to establish with traditional processes. For instance energy consuming processes like distillation can be replaced by pervaporation from an economical point of view (Van Hoof et al., 2004)). Either executed as a single process, or in a hybrid process, an energy reduction can be achieved. As membrane processes become more and more important, transport mechanisms are increasingly researched. With the use of a good transport model, calculations can be performed to estimate process performance, necessary membrane properties, efficiencies or economical aspects (Verhoef et al., 2008). This will help industry to decide which membrane processes and membranes best to use for certain applications.

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To describe membrane transport correctly, the choice of a good model is important. Depending on the characteristics of a separation method, different transport mechanisms are possible. In pervaporation mostly dense membranes are used, and the solutiondiffusion mechanism is applicable. Also, transport is driven by a gradient in chemical potential. Formulation of the transport equations with this driving force therefore provides a logical and thermodynamically consistent model. In most cases the MaxwellStefan equations have proven to be capable of describing the multicomponent mass transport through pervaporation membranes (Nagy, 2004). The Maxwell-Stefan model considers the membrane to be part of the system, thereby making it possible to describe multicomponent systems correctly and accounting for interactions between all components. Not only the interaction between permeating components and membrane are considered, but also between the different permeating components, like drag effects. This ensures a correct description of the multicomponent mass transfer (Bettens et al., 2007). In this paper, a brief outline of previous studies of the Maxwell-Stefan model is given. Here, a conversion to mass fractions is made, to overcome the problem of unknown membrane data. This conversion has consequences for parameters used, and these are stressed too. After obtaining the Maxwell-Stefan in mass fractions, the model is tested on a pervaporation case study. Therefore, a simple simulation program is written, which structure will be briefly explained. After that, an example is calculated, to show the accuracy of the conversion.

2. Molar generalized Maxwell-Stefan and variations The generalized Maxwell-Stefan (GMS) equation is derived from the thermodynamics of irreversible processes and is given by (Taylor and Krishna, 1993):



xi  ’Pi T , P RT

n

¦ j 1 j zi

x N j

i

 xi N j

ct Ðij

i=1,2,...,n

(1)

In this equation i and j are the diffusing species in the mixture, xi is the molar fraction, ’Pi is the gradient in the chemical potential, Ni is the molar flux, Ðij is the binary Maxwell-Stefan diffusivity, ct is the total molar concentration, and the subscripts T,P in the gradient operator indicate constant temperature and pressure. The binary Maxwell-Stefan diffusivity has the physical meaning of the inverse of an intermolecular friction coefficient (Taylor and Krishna, 1993). These diffusivities are symmetric with respect to components i and j, obeying Onsager's reciprocity relations. For ideal systems they are independent of concentration, but, in general, they depend on composition (Kuiken, 1994). The GMS model has been successfully applied to describe multicomponent diffusion in simple fluid mixtures (Taylor and Krishna, 1993). Recently, it has also been used to describe transport through polymeric (Bausa and Marquardt, 2001; Cunha et al., 2002; Fornasiero et al., 2005; Ghoreysi et al., 2002 and 2004; Heintz and Stephan, 1994; Izak et al., 2003a and 2003b; Paul, 2004), or ceramic membranes (Nagy, 2004; Krishna and Baur, 2004; Loos et al., 1992; Van den Broeke and Krishna, 1995). However, application of the GMS equations to a solvent-membrane system presents a problem: the molar concentration of the membrane is ill-defined because the molar mass of a

Maxwell-Stefan in Mass Fractions for Numerical Simulation of the Pervaporation Process

781

membrane is unknown. Therefore, different researchers have tried to find a variation to the GMS equations that overcomes this problem. Some considered an isothermal and isobaric binary membrane/solvent system, and assumed that the membrane molar concentration was negligible compared to that of the solvent (Hoch et al., 2003). Others tried to arbitrarily define segments as a measure of macromolecular concentration in GMS (Wesselingh and Bollen, 1997), or, in electrochemical literature, arbitrarily choose the molar mass of the membrane, most often the so-called equivalent weight (Hogendoorn et al., 2005). However, these alternatives invoke new parameters that cannot be independently ascertained from experimental data, or are not applicable to other systems then described in the paper. Another often seen modification is the conversion to volume fractions for a multicomponent, isothermal, isobaric system (Cunha et al., 2002; Heintz and Stephan, 1994; Izak et al., 2003a and 2003b). However, the resulting equation is inconsistent with the Gibbs-Duhem equation and Onsager's reciprocity relation. In this paper a conversion to mass fractions will be used to overcome the problem of the unknown membrane molar mass.

3. Paper approach Converting the Maxwell-Stefan equation to mass fractions seems a logical approach from a practical point of view. Normally, fluxes are measured by weighing the permeate samples. Also, the weight of the membrane can easily be measured. In previous research a similar approach has been used for reverse osmosis (Paul, 2004), or for transport through polymeric pervaporation membranes (Bausa and Marquardt, 2001). However, whereas the latter research takes strong swelling phenomena into account and presents a detailed model, this paper tries to formulate a general approach, applicable to both polymeric and ceramic membranes. Also, the conversion influences parameters used in the model, what seems to be overlooked in the former research, and will be shown in this paper. 3.1. Conversion to mass fractions Starting from Eq. (1), the Maxwell-Stefan equations can be converted to mass fractions, using the correlation between molar and mass fractions. Only the final equations will be shown here, not the entire conversion process. If desired, this can be obtained from the author. For non-ideal systems, the result is:

dwi * dz ' i

*i'

n

¦ j 1 j zi

w J j

' i

 wi J 'j ' ij

Ut Ð



i=1,2,...,n

' · § · § ¨ G ij  wi ¨ G ln J i ¸ ¸ ¨ G wj ¸ ¸ ¨ © ¹T , P ¹ ©

§ n w · Ðij' Ðij M j ¨ ¦ k ¸ © k 1 Mk ¹

(2)

(3)

i=1,2,...,n

(4)

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782

with ī'i the i-th row of a matrix with elements ī'ij (Eq.(3)), įij the Kronecker delta, wi the mass fraction, Ȗ'i the activity coefficient on mass base, z the place coordinate in the membrane, J'i the mass diffusive flux, ȡt the total mixture density, and Ð'ij the new diffusion coefficients defined by Eq.(4), with Mi the molar mass and Ðij the binary Maxwell-Stefan diffusivity. As can be seen in Eq.(4), the newly determined diffusion coefficients are concentration dependent. Also, the diffusion coefficients are no longer symmetric. The values can be independently obtained by fitting experimental data. Another important consequence is that the used activity coefficients need to be calculated on a mass base. Using molar-based activity coefficients will give incorrect results. Consequently, also the elements of matrix [ī'] will not simplify to the unity matrix for the ideal case. Testing the found equations was done by calculating multicomponent diffusion in a Stefan tube. The result (not given) showed good agreement with literature data (Carty and Schrodt, 1975). 3.2. Case study on multicomponent diffusion Now, Eq. (2) can be used to simulate a pervaporation process. Therefore a simple, iterative numerical simulation program is developed. The algorithm to describe the transport of components through the selective layer of the membrane is based on the film model, resulting in the continuity equation that the flux of every component is invariant over the path of diffusion (as is the concentration). Since the membrane flux and the sum of all fluxes are equal to zero (the coordinate system moves along with the total flux), N equations can be used to solve the Maxwell-Stefan equations. Often, N-1 equations are used, but this can be tricky. Since the importance of the different components is unknown, it is difficult to decide which component equation can be safely removed from the calculations without influencing the result. Dimensionless Maxwell-Stefan equations are rewritten in matrix-vector notation, and during the simulation in every grid point the diffusion coefficients, fluxes and composition are determined. Activity coefficients are calculated using the UNIQUAC model based on mass fractions. Also sorption into and desorption from the membrane are calculated using the UNIQUAC model. With this program, the diffusion of a benzene-cyclohexane mixture through a polyurethane membrane is simulated, at a temperature of 25 °C, and a permeate pressure of 300 Pa. The results are given in Table 1. Table 1. Simulation of a benzene-cyclohexane mixture through a polyurethane membrane Concentration benzene

Flux -4

(wt%)

(10 kg/m²s)

feed

permeate

benzene

cyclohexane

total

0.20

0.67

0.25

0.064

0.32

0.50

0.80

1.02

0.072

1.09

0.70

0.87

1.83

0.069

1.90

The diffusion behavior of the components can also be observed by looking at the different fluxes in function of the feed benzene concentration. The found result shows

Maxwell-Stefan in Mass Fractions for Numerical Simulation of the Pervaporation Process

783

that the total flux increases with increasing feed benzene concentration. The flux of cyclohexane shows a maximum, probably because of couple and drag effects. The membrane appears to have a greater affinity with benzene, which agrees with sorption data (Enneking et al., 1996; not shown). In literature, no experimental data was found for the above mentioned system. However, experimental data could be found of a benzene-n-hexane mixture through the same membrane under the same conditions (Cunha et al., 2002). Since both mixtures consist of an aromatic and aliphatic component, the results of experiment and simulation be qualitatively compared. In Table 2, the result of the comparison is shown. For both mixtures similar trends can be observed. This shows that the converted Maxwell-Stefan equations are useful for these calculations. Table 2. Comparison of simulation and literature Concentration benzene

Total flux

(wt%)

(10-4 kg/m²s)

feed

permeate

benzene-cyclohexane

benzene-n-hexane

0.20

0.67

0.32

0.17

0.50

0.80

1.09

1.16

0.70

0.87

1.90

2.53

4. Conclusions and recommendations In this paper the Maxwell-Stefan equations are converted to mass fractions to overcome the problem of unknown necessary membrane data. The diffusion and activity coefficients are influenced by this conversion. Simulation of a pervaporation case study shows good agreement with literature data, proving the accuracy of the conversion. Future research should focus on ways to obtain the necessary input parameters, and extension of the simulation program for industrial use. If the pervaporation process can be correctly simulated, the process performance can be predicted.

5. Acknowledgements The Research Council of the K.U. Leuven is gratefully acknowledged for financial support (OT/2006/37).

6. References J. Bausa and W. Marquardt, 2001, Detailed modeling of stationary and transient mass transfer across pervaporation membranes, AIChE Journal, 47, 6, 1318-1332 B. Bettens, J. Degrève, B. Van der Bruggen and C. Vandecasteele, 2007, Transport of binary mixtures in pervaporation through a microporous silica membrane: Shortcomings of Fickian models, Separation Science and Technology, 42, 1, 1-23 R. Carty and T. Schrodt, 1975, Concentration profiles in ternary gaseous diffusion, Industrial and Engineering Chemistry Fundamentals, 14, 3, 276-278

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V.S. Cunha, M.L.L. Paredes, C.P. Borges, A.C. Habert and R.J. Nobrega, 2002, Removal of aromatics from multicomponent organic mixtures by pervaporation using polyurethane membranes: experimental and modeling, Journal of Membrane Science, 206, 1-2, 277-290 L. Enneking, A. Heintz and R. Lichenthaler, 1996, Sorption equilibria of the ternary mixture benzene/cyclohexene/cyclohexane in polyurethane- and PEBA-membrane polymers, Journal of Membrane Science, 115, 2, 161-170 F. Fornasiero, J.M. Prausnitz and C.J. Radke, 2005, Multicomponent diffusion in highly asymmetric systems. An extended Maxwell-Stefan model for starkly different-sized, segmentaccessible chain molecules, Macromolecules, 38, 4, 1364-1370 S.A.A. Ghoreysi, F.A. Farhadpour and M. Soltanieh, 2002, Multicomponent transport across nonporous polymeric membranes, Desalination, 144, 1-3, 93-101 A.A. Ghoreysi, F.A. Farhadpour and M. Soltanieh, 2004, A general model for multicomponent transport in nonporous membranes based on Maxwell-Stefan formulation, Chemical Engineering Communications, 191, 4, 460-499 A. Heintz and W.J. Stephan, 1994, A generalized solution-diffusion model of the pervaporation process through composite membranes Part II. Concentration polarization, coupled diffusion and the influence of the porous support layer, Journal of Membrane Science, 89, 1-2, 153-169 G. Hoch, A. Chauhan and C.J. Radke, 2003, Permeability and diffusivity for water transport through hydrogel membranes, Journal of Membrane Science, 214, 2, 199-209 J.A. Hogendoorn, A.J. van der Veen, J.H.G. van der Stegen, J.A.M. Kuipers and G.F.Versteeg, 2005, Application of the Maxwell-Stefan theory to the membrane electrolysis process: Model development and simulations, Computers and Chemical Engineering, 25, 9-10, 1251-1265 P. Izak, L. Bartovska, K. Friess, M. Sipek and P. Uchytil, 2003a, Description of binary liquid mixtures transport through non-porous membrane by modified Maxwell-Stefan equations, Journal of Membrane Science, 214, 2, 293-309 P. Izak, L. Bartovska, K. Friess, M. Sipek and P. Uchytil, 2003b, Comparison of various models for transport of binary mixtures through dense polymer membrane, Polymer, 44, 9, 2679-2687 R. Krishna and R. Baur, 2004, Analytic solution of the Maxwell-Stefan equations for multicomponent permeation across a zeolite membrane, Chemical Engineering Journal, 97, 1, 37-45 G.D.C. Kuiken, 1994, Thermodynamics of Irreversible Processes: Applications to Diffusion and Rheology, John Wiley & Sons, New York J.-B.W.P. Loos, P.J.T. Verheijen and J.A. Moulijn, 1992, Numerical-simulation of the generalized Maxwell-Stefan model for multicomponent diffusion in microporous sorbents, Collection of Czechoslovak Chemical Communications, 57, 4, 687-697 E. Nagy, 2004, Nonlinear, coupled mass transfer through a dense membrane, Desalination, 163, 1-3, 345-354 D.R.J. Paul, 2004, Reformulation of the solution-diffusion theory of reverse osmosis, Journal of Membrane Science, 241,2, 371-386 R. Taylor and R. Krishna, 1993, Multicomponent Mass Transfer, John Wiley & Sons, New York L.J.P. Van den Broeke and R. Krishna, 1995, Experimental verification of the Maxwell-Stefan theory for micropore diffusion, Chemical Engineering Science, 50, 16, 2507-2522 V. Van Hoof, L. Van den Abeele, A. Buekenhoudt, C. Dotremont and R. Leysen, 2004, Economic comparison between azeotropic distillation and different hybrid systems combining distillation with pervaporation for the dehydration of isopropanol, Separation and Purification Technology, 37, 1, 33-49 A. Verhoef, J. Degrève, B. Huybrechs, H. van Veen, P. Pex and B. Van der Bruggen, 2008, Simulation of a hybrid pervaporation-distillation process, Computers and Chemical Engineering, 32, 6, 1135-1146 J.A. Wesselingh and A.M. Bollen, 1997, Multicomponent diffusivities from the free volume theory, Chemical Engineering Research and Design, 75, 6, 590-602

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

785

Modeling of hydrodynamic, mass-exchange and chemical processes in open cell ceramic catalyst Anton Shaymardanov, Eleonora Koltsova, Andrey Zhensa Mendeleyev University of Chemical Technology of RUSSIA (MUCTR), Information Computer Technology, 125047, Moscow, Miusskaya sq., 9, Russian Federation, [email protected]

Abstract On the basis of equations of Navier-Stokes using the method of final elements, the hydrodynamic processes in open cell ceramic material are considered. Also conversion of CO with increasing temperature in catalytic converter is simulated. Calculation is executed on the commercially available CFD-code FLUENT Keywords: porous media, ceramic catalyst, mathematical modeling, TWC

1. Introduction Open cell ceramic materials are a special class of porous permeable materials with a specific structure (Fig. 1a) characterized by such parameters as macro-porosity, cell window diameter, and equivalent diameter of a cell. (a)

(b)

Fig.1. (a) Real and (b) modeled structure.

Open cell foams have a good collection of physicochemical and performance characteristics: high porosity, gas permeability, thermal stability, dust capacity, filtering ability, corrosion resistance, low hydraulic resistance, high (at a given porosity) structural strength, and rigidity. Therefore it’s so interesting to use this material as a support for three way catalysts (TWC), which are applied to reduce the emission of combustion engines. The design of such a catalytic converter is a complex process involving the optimization of different physical and chemical parameters (in the simplest case, e.g., length, cell densities or metal coverage of the catalyst). Numerical simulation can be used as an effective tool for the investigation of the catalytic

A. Shaymardanov et al.

786

properties of a catalytic converter and for the prediction of the performance of the catalyst.

2. Structure Open cell foams are produced by duplication of a cellular lattice polymer matrix with subsequent removal of the polymer matrix by thermal destruction. As a structureforming matrix open-cell foamed polyurethane is used. The spatial arrangement of nodes is nonrandom and ordered to an extent; therefore, the free space within a highly porous cellular material can be regarded as a set of unit cells the shape of each of which is quite close to a regular dodecahedron. This cell (Fig.2) is characterized by the diameter of its forming sphere (dc) and the degree of overlapping (p). To compare the model structure of the cellular material with the real one, a relationship between one of the geometric parameters of the model (degree p of overlapping) and a parameter of the real structure (porosity) was determined (see Table 1). Table 1. Porosity ɉ vs degree of overlapping p.

Fig. 2.Unit cell.

p

ɉ

0,434

0,963

0,44

0,951

0,45

0,927

0,46

0,898

0,47

0,863

0,48

0,825

0,49

0,784

0,499

0,745

0,4999

0,741

3. Hydrodynamic A steady-state flow induced by an applied constant pressure drop is considered. For an incompressible liquid ( ρ = const ) of constant viscosity ( μ = const ), the continuity (incompressibility) equation has the form: div v ≡

∂v x ∂v y ∂ v z + + =0 ∂x ∂y ∂z

The system of Navier–Stokes equations:

(1)

Modeling of Hydrodynamic, Mass-Exchange and Chemical Processes in Open Cell Ceramic Catalyst

∂v x ∂v ∂v ∂v 1 ∂p + vx x + v y x + vz x = − + υ∇ 2 v x ∂t ∂x ∂y ∂z ρ ∂x ∂v y ∂v y ∂v y ∂v y 1 ∂p + vx + vy + vz =− + υ∇ 2 v y ∂t ∂x ∂y ∂z ρ ∂y ∂v z ∂v ∂v ∂v 1 ∂p + vx z + v y z + vz z = − + υ∇ 2 v z , ∂t ∂x ∂y ∂z ρ ∂z

787

(2)

2 2 2 is the Laplace operator and υ = μ / ρ is the kinematic where ∇ 2 ≡ ∂ + ∂ + ∂ ∂x 2 ∂y 2 ∂z 2 viscosity. This model was enhanced with standard k-ε turbulence model with typical values of variables. The turbulent kinetic energy equation has the form:

∂ρk ∂ ( ρv x k ) ∂ ( ρv y k ) ∂ ( ρv z k ) + = + + ∂y ∂z ∂x ∂t =

(3)

∂ § μ t ∂k · ∂ § μ t ∂k · ∂ § μ t ∂k · ¸ + μ t Φ − ρε ; ¸+ ¨ ¸+ ¨ ¨ ∂x ¨© σ k ∂x ¸¹ ∂y ¨© σ k ∂y ¸¹ ∂z ¨© σ k ∂z ¸¹

and the dissipation rate equation is written as: ∂ρε ∂ ( ρv x ε ) ∂ ( ρv y ε ) ∂ ( ρv z ε ) + + + = ∂t ∂x ∂y ∂z

(4)

∂ § μ ∂ε · ∂ § μ t ∂ε · ∂ § μ t ∂ε · ε ε2 ¸¸ + ¨¨ ¸¸ + ¨¨ ¸¸ + C1 μ t Φ − C 2 ρ , = ¨¨ t ∂x © σ ε ∂x ¹ ∂y © σ ε ∂y ¹ ∂z © σ ε ∂z ¹ k k

where k - turbulent kinetic energy; İ —kinematic viscosity of the flow; ȝt - turbulent viscosity; Ɏ - viscous dissipation (kinetic energy dissipation into heat); σk, σİ - diffusion factors in the k-İ turbulence model; C1 and C2 - constants. The solution of the turbulence equations is used for calculating the effective viscosity:

μe = μ + C ρ

k2

ε

,

(5)

where C is a constant. The flow-field simulation is based on the commercially available CFD-code FLUENT. The air flow through the layer of open-cell catalyst is shown on Fig.3

A. Shaymardanov et al.

788

Fig. 3. Experimental [1] (1) and modeled (2, 3) pressure drop vs velocity of the turbulent (2) and laminar (3) air flow. Porosity ɉ = 0.9, length L = 70 mm and dc = 2.1 mm.

4. Kinetics The conversion reactions of the harmful exhaust gases into harmless components inside an open-cell three-way catalyst were simplified: k CO + 1 2O2 ⎯ ⎯→ CO2

(6)

The conversion rate and therefore the performance of the three-way catalyst were taken either from the literature [2, 3]. Pre-exponential factor was 2,89Â1015 and the activation energy for the reaction was 1,57Â106 J/mol. The concentration in the CO2 inlet exhaust gas mixture was zero due to experimental reasons (composition of the simulated exhaust gas see on Table 2). Temperaturedependent uniform axial inlet velocity of the artificial exhaust gas was 1,35 m/s, surface site density was 2,72·10-9 mol/cm2, cell diameter was 1 mm, porosity of catalyst was 0,9. Table 2. Composition of the simulated exhaust gas and concentration of the gas species used for the simulations at stoichiometric mixture

Species CO O2 N2

Concentration (vol.%) 1,42 0,77 97,81

The basic conservation equations for turbulent flow fields are 3-dimensional formulations of conservation of total mass, momentum, the species conservation equation, and thermal energy. The density is computed via the ideal gas law. The mixture viscosity and thermal conductivity as well as the diffusion coefficient Di,M of species i in the mixture depend on the local composition and on the temperature: they

Modeling of Hydrodynamic, Mass-Exchange and Chemical Processes in Open Cell Ceramic Catalyst

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are calculated using the kinetic gas theory. The specific heat at constant pressure of Cp, i species i is modeled as a polynomial function of temperature. In Fig. 3 the resulting conversion of CO in open-cell ceramic catalyst with increasing temperature can be seen. The conversion starts at 500 K and increases up to 100% for CO at 750 K. Some deviations exist between the predicted conversion and the experimental conversion of CO data. These deviations can be explained by the fact that the kinetic model is too simplified.

Fig. 4. Conversion of CO with increasing temperature The simulation presented in this paper is carried out in open-cell ceramic catalyst. In the ongoing research, several extensions will be made for a more accurate model for the real catalytic converter. The next step in using numerical simulation is to expand the kinetic model and to study conversion of CO in rich and lean mixture. The final goal is the simulation of the behavior of catalytic converter during a whole test cycle including the light-off behavior of the converter.

References [1] S.V.Tishchenko, A.I.Kozlov, V.N Grunskii, and A.V. Bespalov. Hydraulic Resistance of Slip Highly Porous Cellular Material, Khim. Prom–st. Segodnya, 2005, no. 2, pp. 42–51. [2] J. Braun, T. Hauber, H. Tobben, P. Zacke, D. Chatterjee, O. Deutschmann and J. Warnatz, Influence of Physical and Chemical Parameters on the Conversion Rate of a Catalytic Converter : A Numerical Simulation Study, SAE 2000-01-0211. SAE, Warrendale, PA, USA. [3] J. Warnatz, U. Mass and R. W. Dibble, Combustion, Springer, Heidelberg, 1996; 2nd edn., 1999; 3rd edn.,2001.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

791

Modeling of thermal oxidation of silicon: stochastic approach L. T. Fan,a Y. Y. Chiu,a A. Argoti,a S. T. Chou,b B. C. Shen,a J. R. Schlupa a

Department of Chemical Engineering, Kansas State University, Manhattan, KS 66506 U. S. A., [email protected] b Department of Finance and Banking, Kun Shan University, Yung-Kang City, Tainan Hsien, 71003, Taiwan, [email protected]

Abstract It is essential that native oxide films be formed on silicon surface in manufacturing integrated circuits (ICs). Such films serve as protective masks against the diffusion of impurities, and thus, they are important components of photolithography. The formation of native oxide films is destined to proceed stochastically, especially in any nano-scale, i.e., mesoscopic, region. Herein, a stochastic model is developed for the dry oxidation of silicon containing both linear and non-linear intensity functions, which reflect the rates of diffusion and reaction encountered in various deterministic treatments of the thermal oxidation of silicon. The model gives rise to the non-linear master equation of the process, which is solved by means of a rational approximation method, system-size expansion. The solution of the process’ master equation via the system-size expansion results in the means and higher moments about the means, e.g., variances, of the random variables characterizing the process. The results are compared with the available experimental data. The model is in sufficiently good accord with these data.

Keywords: Formation kinetics, silicon, silicon oxide, stochastic modeling, thermal oxidation 1. Introduction The current effort aims at developing a stochastic model for the dry oxidation of silicon and verifying the resultant model with the available experimental data as well as via Monte Carlo simulation: In the manufacture of integrated circuits (ICs), the formation of native oxide films of silicon, SiO2, might be the most important processing step [1]. Such films provide the surface passivity, electrical insulation, and dielectric properties necessary for the fabrication and operation of semiconductor devices. Several techniques have been developed for generating the oxide layers; these techniques include thermal oxidation, wet anodization, vapor-phase deposition, and plasma anodization or oxidation. Among them, thermal oxidation with dry or wet oxygen is mainly deployed in IC processing [2]; naturally, various aspects of this technique have been extensively studied [3, 4]. Whether silicon oxidation is controlled by diffusion of charged species or neutral species have been intensely debated. Deal and Grove [5] have proposed a simple model comprising diffusive transport of molecular oxygen through the growing amorphous layers of SiO2 followed by reaction of silicon with the oxidizing species at the advancing interface. Singh and collaborators [6] have developed a onedimensional model for dry oxidation of silicon by molecular oxygen, which takes into account simultaneous heat and mass transfer. Blanc [7] has proposed a mechanism in

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which atomic oxygen was the oxidizing species, which are presumably transported as charged species as indicated by Tiller [3, 4]. The analysis of the growth of the oxide layer during thermal oxidation of silicon has conventionally resorted to the deterministic steady-state diffusion model of Deal and Grove [5, 8-10]. An alternative model for the dry oxidation of silicon based on a stochastic approach is presented herein. Solved numerically, the model yields the rate of oxide film growth as well as its fluctuations.

2. System Description Figure 1 depicts the system under consideration comprising a thin wafer of silicon (Si) of unit area inserted in a dry oxidation chamber maintained at specific temperature and pressure. The oxidizing species is gaseous molecular oxygen (O2), which reacts with silicon to form silicon oxide (SiO2). According to the available experimental evidence, see e.g., Deal and Grove [5], the SiO2-Si interface moves into the silicon wafer during the course of oxidation. The silicon surface has a high affinity for oxygen, and thus, a layer of SiO2 is formed almost instantaneously when the silicon surface is exposed to the oxidizing atmosphere. It is difficult, therefore, to initiate the oxidation process with a pristine silicon surface; consequently, the silicon wafer is considered to be covered initially by a layer of SiO2 whose thickness is x0 as illustrated in Figure 1. Hence, it is assumed that the oxidizing species, i.e., oxygen, undergoes three transitions as time progresses [5]. Specifically, the irreversible transport of oxygen from the bulk gas phase to the gas-SiO2 interface, the irreversible transport of oxygen through the layer of SiO2 towards the silicon surface, and the irreversible reaction with silicon at the SiO2-Si interface.

O2

SiO2 0

x0

Si xt

Figure 1. Conceptual framework of the present model: The terms, x0 and xt, signify the positions of the SiO2-Si interface corresponding to the thickness of the SiO2 layer at the initial time of the process and at any subsequent time t, respectively.

3. Model Formulation The system described earlier gives rise to a multi-state stochastic model comprising the following random variables, which can be defined based on the unit cross-sectional area of the reaction section perpendicular to the direction of oxygen transport at time t. Nf(t), the number concentration of molecules of oxygen in the bulk gas phase; Nb(t), the number concentration of molecules of oxygen at the gas-SiO2 interface; Ni(t), the

Modeling of Thermal Oxidation of Silicon: Stochastic Approach

793

number concentration of molecules of oxygen at the Si-SiO2 interface; and Ns(t), the number concentration of molecules of oxygen that have already reacted with silicon to form SiO2, thereby enlarging the layer of SiO2. The realizations of Nf(t), Nb(t), Ni(t), and Ns(t) are designated as nf, nb, ni, and no, respectively. 3.1. Master equation For the process under consideration, a probability balance around state (n f , n b , n i , n s ) leads to [11]

d p(n f , n b , n i , n s ; t) dt O nf 1p(n f  1, n b  1, n i , n s ; t)  O n b 1p(n f , n b  1, n i  1, n s ; t)  O ni 1p(n f , n b , n i  1, n s  1; t)  (O n f  O n b  O ni )p(n f , n b , n i , n o ; t)

(1)

This is the master equation of the process. In the above expression, p(n f , n b , n i , n o ; t) signifies the joint probability that exactly (n f , n b , n i , n s ) molecules of oxygen are present in the system at time t. Moreover, the terms, O n , O n , and O n , denote the i f b intensity functions whose nature is discussed in what follows. 3.2. Definition of intensity functions and system parameters The three intensity functions, O n , O n , and O n are associated with the transitions that f

b

i

the oxidizing species undergoes as indicated earlier. First, O n is the intensity function f for the transition of oxygen from the gas phase to the gas-SiO2 interface given by [5]

O nf

h n (D:  n b )

(2)

where hn is the number-transfer coefficient for the gas phase, D is a proportionality constant, and ȍ is the maximum capacity of oxygen on the SiO2 surface [5]. Second, O n is the intensity function for the transition of oxygen from the gas-SiO2 interface to b

the SiO2-Si interface expressed as [12]

O nb

ª (n  n i ) º Dn « b » ¬ xt ¼

(3)

where Dn is the diffusivity of molecular oxygen in SiO2 and xt is the total thickness of the SiO2 layer as presented in Figure 1; it is given by

L.T. Fan et al.

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xt

§ n · x0  ¨ s ¸ © Mv ¹

(4)

where x0 is the thickness of the initial layer of SiO2 as indicated earlier, (ns/Mv) is the additional thickness due to the growth of the SiO2 layer and Mv is the number of oxygen molecules incorporated into a unit volume of the SiO2 layer. Inserting Eq. (4) into Eq. (3) yields

Onb

ª (n b  n i ) º Dn « » ¬ x 0  (n s M v ) ¼

(5)

Third, O n is the intensity function for the transition of free oxygen at the SiO2-Si i interface to reacted oxygen in the SiO2 layer given by

O ni

k1n i

(6)

where k1 is the rate constant for the reaction between free oxygen and silicon [13]. Note that Eqs. (2) and (6) are linear whereas Eq. (5) is non-linear, thereby rendering the master equation, Eq. (1), non-linear.

4. Results and Discussion The complexity in solving the master equation, Eq. (1), is circumvented via a rational approximation method, the system-size expansion [11], thereby resulting in the governing equations for the means and variances of the random variables characterizing the process. For validation, the means are compared with the available experimental data [5] in Figure 2. These data represent the growth of SiO2 on the silicon surface with a thickness of up to approximately 4000 Å under atmospheric pressure and with the temperature ranging from 973K to 1273K. Note that means are in good accord with the experimental data. Moreover, the master equation of the process has been simulated via the Monte Carlo method at the early stage of the process for which no experimental data are available. The results of simulation are presented in Figure 3; the fluctuations of the process in terms of the standard deviation can be clearly visualized about the mean value.

5. Concluding Remarks A stochastic model for the thermal oxidation of silicon has been derived based on linear and non-linear intensity functions. The model has been validated by comparing it with the available experimental data. The model is in sufficiently good accord with these data. Moreover, the model’s master equation has been simulated via the Monte Carlo method at the early stage of the process. The results of simulation clearly exhibit the fluctuations of the process about the mean value.

Modeling of Thermal Oxidation of Silicon: Stochastic Approach

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Oxide thickness, Å

10000

1000

Time, s

Figure 2. Growth of the SiO2 layer: Comparison between the model (ņņ) with the experimental data [5] at 973K (½), 1073K (), 1193K (y), and 1273K (+).

6

Oxide thickness, Å

5 4 3 2 1 0 0.00

0.02

0.04

0.06

0.08

0.10

Time, s

Figure 3. Growth of the SiO2 layer: Mean (y) and standard deviation envelope (¯) estimated via Monte Carlo simulation of the master equation of the model at the early stage of the process.

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6. References [1] S. K. Ghandi, VLSI fabrication principles: Silicon and Gallium arsenide, WileyInterscience, New York, 1983. pp. 372-400 [2] S. M. Sze, VLSI technology, McGraw-Hill, New York, 1988. pp. 131-167 [3] W. A. Tiller, J. Electrochem. Soc., 127 (1980) 619 [4] [4] W. A. Tiller, J. Electrochem. Soc., 128 (1981) 689 [5] B. E. Deal and A. S. Grove, J. Appl. Phys., 36 (1965) 3770 [6] S. K. Singh, J. R. Schlup, L. T. Fan, and B. Sur, Ind. Eng. Chem. Res., 27 (1988) 1707 [7] J. Blanc, Appl Phys Lett, 33 (1978) 424 [8] S. Dimitrijev, H. B. Harrison, and D. Sweatman, IEEE Trans. Electron. Dev., 43 (1996) 267 [9] de Almeida, R. M. C., S. Goncalves, Baumvol, I. J. R., and F. C. Stedile, Phys. Rev. B, 61 (2000) 12992 [10] T. Watanabe and I. Ohdomari, J. Electrochem. Soc., 154 (2007) G270 [11] N. G. vanKampen, Stochastic processes in physics and chemistry, North-Holland, Amsterdam, 1992. pp. 55-58, 96-97, 134-136, 139, 163 [12] R. Ghez, A primer of diffusion problems, Wiley-Interscience, New York, 1988. pp. 140 [13] E. A. Irene and R. Ghez, Appl. Surf. Sci., 30 (1987) 1

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

797

Modelling biomass gasifiers Sauro Pierucci, Eliseo Ranzi CMIC, Politecnico di Milano, Piazza L. da Vinci 32, I 20133, Milano, Italy. [email protected], [email protected]

Abstract This work analyzes and discusses the general features of biomass gasifiers modeling. The particle model is described both by proposing a detailed kinetic scheme for the devolatilization and combustion of biomasses and by the basic mass and transport equations governing the phenomenological aspects. Volatile components released by the solid particles are involved in gas phase pyrolysis/combustion reactions described with a detailed kinetic scheme. Experimental data from a drop tube reactor has been used for evaluating the model predictions. A sensitivity analysis to inter- and intra-phase thermal resistance shows the great importance of the overall external heat transfer coefficient. The satisfactory agreement with experimental data makes the model capable to contribute to a better design and understanding of industrial gasifiers. Keywords: Biomass; pyrolysis; modeling; devolatilization; gas phase kinetics

1. Introduction The key to understanding the complex phenomena occurring inside the process units lies in the characterization of the initial biomasses, in describing the primary devolatilization phase, the released products, the gasification phase and the secondary or successive gas phase reactions. Therefore models need an appropriate description in relation both to a mechanistic kinetic model of biomass gasification and pyrolysis and to transport phenomena. Designing the transports along the reactor requires the solution of mass, energy and momentum equations both inside each particle and in the continuous surrounding gas phase. Phase changes should be properly taken into account as well as pressure contribution to mass and energy transfers. The whole system is described by a large set of partial differential equations in time and space length. The use of the discretization approach on space coordinate reduces the system to an ordinary differential equation in the time domain which still maintains a huge complexity due to its size and to the degree of stiffness. The paper will describe a model that aims to cover the above items. A set of comparisons with experimental data will also be included.

2. Kinetic model The devolatilization of the biomass is considered a straightforward combination of the pyrolysis of three reference components: cellulose, hemicellulose and lignin. Although extractives, either soluble in water or in organic solvents, usually account for less than 10% of the total biomass, they are ignored as participating to its characterization. Predictions from these models reproduce correctly the experimental thermo gravimetric (TG) curves during the pyrolysis of several biomasses. [Manya et al., 2003; Becidan et al., 2007; Miranda et al., 2007]. A more complete picture of biomass pyrolysis by taking into account the total devolatilization and gas evolution has been recently proposed by [Radmanesh et al., 2006; Yanik et al., 2007; de Jong et al., 2007]. Table 1 reports a

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novel revision of the kinetic model adopted for the devolatilization of the biomass through the three different constituents, cellulose (CELL) hemicellulose (HEC) and Lignin (LIG-C, LIG-H, LIG-O). The secondary gas phase reactions of the released gas and tar species are mainly pyrolysis type reactions in conjunction with combustions when oxygenated components are present. Several authors have extensively studied the kinetic equations related to this phenomena. The scheme proposed by Ranzi et alt. (2001) is strongly suggested and here adopted. Char combustion, i.e. the overall set of heterogeneous reactions of oxygen with the solid residue are responsible for the autothermic behaviour of the whole gasification process. They are summarized in Table 2.

3. Particle model A simplified scheme of the elemental gas-particle module indicating the gas-solid interactions and the release of tar components is reported in Figure 1. The biomass particle, which consists of a mixture of reference components and ash, is assumed as a homogeneous sphere with NS internal sectors that account for possible heat and mass transfer resistances. Gases are released by the particle to the surrounding gas phase while surrounding gases diffuse into the solid particle. Gas phase is considered as a perfectly stirred reactor inside the cell module. Convective fluxes or flowrates entering and exiting the module are allowed, both for gas and solid phase. This elemental module is flexible and suitable for simulating different process alternatives, such as fixed or moving bed gasifiers and combustors, updraft or downdraft configurations and also the entrained (drop tube) flow reactor. The ODE system is solved by using BzzMath library, available on the Internet and is downloadable as freeware software for non-commercial use from www.chem.polimi.it/homes/gbuzzi/. Physical and mathematical details on the overall complexity of this problem are described by Pierucci and Ranzi 2008.

TARS

Gases

Figure 1. Scheme of the elemental gas-particle module

Gas Phase

V-L equilibria

Modelling Biomass Gasifiers

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Table 1: Kinetics of Cellulose, Hemicellulose and Lignin devolatilization k [s-1], kmol, m3, K CELL > CELLA

8u1011exp(-46000/RT)

CELLA > 0 .95 C2H4O2 + 0.25 C2H2O2 + 0 .2 CH3CHO + 0.25 C6H6O3 +0 .2 C3H6O +0 .16 CO2 + 0.23 CO + 0.1 CH4 +0.9 H2O + 0.61 CHAR

109exp(-30000/RT)

CELLA > C6H10O5

4uTuexp(-10000/RT)

CELL

> 5.0 H2O + 6.0 CHAR

8u107exp (-32000/RT)

HEC

> 0.4 HCE1+ 0.6 HCE2

1010exp(-31000/RT)

HCE1

> 0.75 GH2+ 0.125 H2O +0.8 CO2 + 1.4 CO +0.5 CH2O + 0.125 C2H5OH + 0.25 CH3OH+ 0.625 CH4+0.25 C2H4+ 0.675 CHAR

3u109exp(-27000/RT)

HCE1

> C5H8O4

3uTuexp(-11000/RT)

HCE2

>0.125 H2O+0.2 CO2 + 0.5 CH4+ 0.25 C2H4+ 0.7 CH2O+ 0.125 C2H5OH+ 0.25 CH3OH+ 0.8 GCO2+ 0.8 GCOH2 + CHAR

1010exp(-33000/RT)

LIG-C

> 0.35 LIGCC + 0.1 C9H10O2 + 0.08 C6H6O +0.41 C2H4+ H2O + GCOH2+ 0.495 CH4 + 0.32 CO + 5.735 CHAR

4u1015 exp(-48500/RT)

LIG-H

> LIGOH + C3H6O

2u1013exp(-37500/RT)

LIG-O

> LIGOH + CO2

109exp(-25500/RT)

LIGCC

> 0.3 C9H10O2 + 0.2 C6H6O +0.35 C3H4O2 +0.7 H2O + 0.65 CH4+0.6 C2H4 + GCOH2 +0.8 GCO+6.4 CHAR

5u106exp(-31500/RT)

LIGOH

> LIG + 0.1 GH2+ H2O + CH3OH + 1.4 GCO +0.6 GCOH2 +0.45 CH4+ 0.2 C2H4 +4.15CHAR

1013exp(-49500/RT) 105 exp(-20500/RT)

LIG

> C11H12O4

LIG

> H2O + 0.2 CH2O +0.2 CH3CHO + 0.4 CH3OH + 0.5 CO + 80uTuexp(-12000/RT) 0 .2 C3H6O + 0.6 CH4 + 0.65 C2H4 +GCO +0.5 GCOH2 +5.5 CHAR

GCO2

> CO2

105exp (-24000/ RT)

GCO

> CO

1013exp (-50000/ RT)

GCOH2 > CO + H2

5u1011exp (-65000/ RT)

GH2

5u1011exp (-75000/ RT)

> H2 Table 2: Char combustion kmole, m3 , K, s CHAR+ O2

> CO2

5.7u109 exp (-38200/ RT) [O2] 0.78

CHAR+0.5 O2 > CO

5.7u1011 exp (-55000/ RT) [O2] 0.78

CHAR+ H2O > CO + H2

7.9u109 exp (-52000/ RT) [H2O] 0.7

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4. Comparison with experiments A drop tube reactor of 0.075 m internal diameter and 1-meter length is heated by an electric oven that can reach a maximum temperature of 1300 K. The reactor is fed with pure N2 that is injected at the top and then passes through an electric preheater. A constant flow rate of solid is injected at the top of the reactor by pneumatic transport. Under the explored conditions, the gas flow is highly laminar (Re<2000). The experiments were conducted by Dupont C., CEA, Grenoble, DTN/SE2T/LPTM. Figure 2 and 3 report some comparisons between experiments and predictions at different temperatures and for different particle siz: The resultse clearly show the role of secondary pyrolysis reactions: acetylene is only a product of the secondary gas phase dehydrogenation of ethylene and it is favoured by high temperatures. In agreement with experimental results, char yields reach values of 14-16 wt% of the initial dry biomass. The initial composition of the biomass C6H8.8O3.9 significantly changes at the reactor outlet and becomes C6H2.9O1.1 at 1073K. At higher temperature, the charification process is further completed and the composition of the solid residue becomes C6H1.4O0.5. These results are in agreement with the experimental measurements indicating a composition of C6H2.7O0.8 at 1073 K and C6H1.5O0.4 at higher temperatures. No comparisons with the experimental measurements are available for tar species, since these species are not measured in the gas phase. Since the transport processes have a strong influence on the devolatilization of large particles, a simple sensitivity analysis to the overall heat transfer coefficient and to the effective thermal conductivity of the biomass particle is shown in Figure 4. The reference value of the overall external heat transfer coefficient was increased of 50% (dashed lines) and decreased of 50% (dotted lines). The same variations were applied to biomass thermal conductivity. The overall external heat transfer coefficient significantly affect the heating and the devolatilization process. Thermal conductivity plays a minor role. This analysis supports and confirms the conclusions of Janse et al. 2000 that extensive description of internal mass transport phenomena in flash pyrolysis modelling is not necessary, while accurate knowledge of reaction kinetics and heat transfer parameters is crucial.

0.0025

0.012 CO

0.01

0.006

0.0015 HO 2 CO2

0.002 0

0.2

0.4 0.6 0.8 Length [m]

1

C 2H2

0.001

0.004

0

CH 4

0.002 mole fraction

0.008

C2 H4

0.0005 1.2

0

0

0.2

0.4

0.6

0.8

1

1.2

Length [m]

Figure 2: Comparisons with experiments (points) and predictions (lines) for beech wood particles of 0.20 mm at 1273 K

Modelling Biomass Gasifiers 0.012

801

0.0025

mole fraction

CH4

CO

0.01

0.002

0.008

0.0015 H2O

0.006

C2H4 0.001

0.004 0.002

C2H2

0.0005

CO2

0 0

0.2

0.4

0.6 0.8 Length [m]

1

0

1.2

0

0.2

0.4

0.6

0.8

1

1.2

Length [m]

Figure 3: Comparisons with experiments (points) and predictions (lines) for beech wood particles of 0.67 mm at 1073 K

0.012

0.012 d p =.850 mm T=1223 K

dp =.850 mm T=1223 K CO

0.010

0.010

0.008 0.006

H2O

0.004

Mole fractions

Mole fractions

CO 0.008 0.006

H2O

0.004

0.002

0.002

0 0

0.2

0.4

0.6

0.8

Reactor length [m]

1.

0 0

0.2 0.4 0.6 0.8 Reactor length [m]

1.

Figure 4: CO and H2O vs. reactor length for 0.850 mm Beech wood particles at 1223 K.Sensitivity to heat transfer coefficient (left) and solid thermal conductivity (right)

802

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5. Conclusions A novel detailed kinetic scheme for the devolatilization and combustion of biomasses has been presented and tested with experiments. The adopted particle model is described by the basic mass and transport equations governing the phenomenological aspects. Experiments have been performed at high temperatures (1073-1273 K) and fast heating rates (> 500 K s-1) in an entrained flow reactor with different wood particles of different sizes. These results have been used to further validate a semi detailed kinetic model of biomass pyrolysis. These comparisons show that the main experimental trends are well-reproduced by the model. The crucial influence of the particle size can be seen under these conditions. For small particles, the decomposition of the biomass components is completed after about 0.3 s and leads to total gas yields higher than 70 wt% at the reactor outlet, and a char yield of about 10 to 15 wt%. The major gas is largely CO, followed by H2. CH4 and CO2 are present in smaller amounts. There is a clear effect of temperature on the C2 species behaviour. For large particles, the decomposition still proceeds at the end of the reactor after about 0.5 s, due to internal heat transfer limitations. The satisfactory agreement with experimental data makes the model capable to contribute to a better design and understanding of industrial gasifiers

6. Acknowledgements Authors wish to thank Capucine Dupont and her staff for their technical support.

References M. Becidan, G. Varhegyi, J. E. Hustad and Ø. Skreiberg, 2007,‘Thermal Decomposition of Biomass Wastes. A Kinetic Study’ Ind. Eng. Chem. Res., 46, 2428-2437 A. Cuoci, T. Faravelli, A. Frassoldati, S. Granata, G. Migliavacca, E. Ranzi, S. Sommariva, 2007 ,‘A General Mathematical Model of Biomass Devolatilization’, 30th Meeting of the Italian Section of the Combustion Institute W. de Jong, G. Di Nola, B.C.H. Venneker, H. Spliethoff and M.A. Wojtowicz, 2007, ‘TG-FTIR pyrolysis of coal and secondary biomass fuels: Determination of pyrolysis kinetic parameters for main species and NOx precursors’ Fuel 86, 2367–2376 A.M.C Janse., R.W.J. Westerhout, and W. Prins, 2000.,'Modelling of flash pyrolysis of a single wood particle' Chemical Engineering and Processing, 39, 239-252. J. J. Manya, E. Velo, and L. Puigjaner, 2003, ‘Kinetics of Biomass Pyrolysis: a Reformulated Three-Parallel-Reactions Model’ Ind. Eng. Chem. Res., 42, 434-444 R. Miranda. C. Sosa_Blanco , D. Bustos-Martınez and C. Vasile, 2007, ‘Pyrolysis of textile wastes Note I. Kinetics and yields’ J. Anal. Appl. Pyrolysis 80 489–495 S. Pierucci, E. Ranzi, 2008, 'A general mathematical model for moving bed gasifier', ESCAPE18, Lyon, 1-4 June, 2008 R. Radmanesh, Y. Courbariaux, J. Chaouki and C. Guy , 2006, ‘A unified lumped approach in kinetic modeling of biomass pyrolysis’ Fuel 85, 1211–1220 E Ranzi., M. Dente , G. Bozzano, A. Goldaniga, T. Faravelli, 2001, 'Lumping Procedures in Detailed Kinetic Models of Gasification, Pyrolysis, Partial Oxidation and Combustion of Hydrocarbon Mixtures', Progr. Energy Comb. Science, 27, 99-139 J. Yanik, C. Kornmayer, M. Saglam and M. Yüksel, 2007, ‘Fast pyrolysis of agricultural wastes: Characterization of pyrolysis products’,Fuel Processing Technology, 88, (10) 942-947

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

803

Modelling of wall-flow filters for diesel particulate removal Matyáš Schejbala, Petr Koþía, Miloš Mareka, Milan Kubíþekb a

Institute of Chemical Technology, Dept. of Chemical Engineering, Technická 5, Prague 6, CZ-166 28, Czech Republic, [email protected] b Institute of Chemical Technology, Dept. of Mathematics, Studentská 6, Prague 6, CZ166 28, Czech Republic

Abstract Diesel particulate filter (DPF) is regarded as the most useful technology to reduce particulate matter from exhaust gas of a diesel engine. Exhaust gas entering the channel is forced to flow through the ceramic porous walls into the adjoining cells and thus leaving the particulates behind. The collected particulate matter inside the trap has to be periodically oxidized to DPF regeneration. We have developed a nonstationary spatially 2D model of the filter, soot deposition and its regeneration with detailed kinetics of soot combustion. Optimized numerical methods and software for the solution of the models are described and results for various catalyst distributions along washcoat layer are presented and discussed.

Keywords: DPF, soot oxidation, modelling, filtration, FVM 1. Introduction Over half the new cars sold in Europe are powered by diesel engines; however, diesel engine produces particles of carbonaceous soot, which also consists of unburned organic compounds and other solid and liquid material. Promising and widely used technology for diesel soot particle removal is diesel particulate filter. Soot particles trapped in cake layer and in the wall are oxidized by O2 or NO2. Effective and fast solution of the model is usable for kinetic parameters evaluation and for optimization and design simulations. DPF continual regeneration - soot combustion - by NO2/O2 could be also optimized by means of nonuniform distribution of catalyst within the washcoat layer - zoned coating. Distribution of catalyst in axial direction of the washcoat and the wall can be simulated to determine most effective filter design.

2. Mathematical model of single pair of channels The model has been developed on the similar basis as the single-channel model (Yong 2006, Haralampous et al. 2004, Shende et al. 2005) derived from Bissett model (Bissett 1984). Model equations for computation of mass flux ĭ, pressure p, temperature T, gas fractions yj or soot weigh mp are summarized in Tab 1. Pressure drop within the wall, soot layer and washcoat layer is computed according Forchheimer equation.

M. Schejbal et al.

804 Fig 1. Front (a) and side (b) scheme of single pair of channels

a) b) Main part of the model is represented by the following reaction-convection-diffusion equation describing component balance within the solid phase in the radial direction:

Φw

§ ∂ 2 yS , j · ¸ = M j ¦ Rk − D j ρ w ¨¨ 2 ¸ ∂x ∂ x k © ¹

∂yS , j

(1)

where ĭw is mass flux, yS,j is mass fraction of component j, D is diffusivity coefficient, Rk are reaction rates and ȡw is gas density. It is computed for every gas component in soot cake, washcoat and wall in x and z direction (cf. Fig. 1). Distribution of soot particles trapped in the washcoat and wall is given by deep-filtration model based on the single fiber efficiency (Konstandopoulos et al. 1989). Two independent collection mechanisms are assumed – Brown diffusion and interception. Deep-filtration model predicts distribution of deposited particles, DPF filtration efficiency and local porosity and permeability in the wall and the washcoat. Tab 1. Mathematical model equations Description

Equation

∂T ∂T S Enthalpy AS Cp, S S = AS λS , z 2S + sF f x Rk ΔHk dx + − w ∂t ∂z balance of solid k phase: + 4dΦwCp, g (T1 − TS ) + 4d1h1sF (T1 − TS ) + 4d2h2 sF (T2 − TS ) 2

(

³

)

w

¦

Mass balance in the inlet and the outlet channel:

∂ di2Φ i i = (− 1) 4dΦ w ∂z

Momentum balance in the inlet and the outlet channel:

∂ d i2Φ i2 / ρi ∂ d i2 pi + = − FμΦ i /ρi ∂z ∂z

Enthalpy balance in the inlet and the outlet channels:

∂ d12 Φ1C p , gT1 = 4dh1 (TS − T1 ) − 4dΦ wC p , gT1 ∂z ∂ d 22Φ 2C p , gT2 = 4dh2 (TS − T2 ) + 4dΦ wC p , gTS ∂z

(

) (

(

)

(

)

i = 1, 2

)

i = 1, 2

Modelling of Wall-Flow Filters for Diesel Particulate Removal

Component (j) balance in the inlet and the outlet channels: Conservation of mass of soot:

805

( (

)

∂ 2 d1 Φ1 y1, j = −4dΦ w y1, j + 4dk1, j yS 1 , j − y1, j ∂z ∂ 2 d 2 Φ 2 y2 , j = 4dΦ w yS 2 , j − 4dk2, j y2 , j − yS 2 , j ∂z ∂m p ( x, z ) = VFVM ( x )M SOOT ¦ Rk + e f (m p )m p ∂t k

(

)

(

)

)

We have developed original software for the numerical solution of the above described set of channel scale model equations. The software is written in Fortran 77 and its main advantage is short computation time following from extensive development of proper numerical methods and problem decomposition. The model software can thus be used also as a subroutine in kinetic data evaluation from soot combustion experiments. Numerical solution of PDE system is based on discretization of x, z and t coordinates by the finite volume method (FVM) and the resulting system of nonlinear equations has been solved by the modified Newton method. System of linear equations with Jacobi matrix is solved by special solver for sparse matrix with diagonal band. We have used second-order accurate interpolation for representing interface values. Parabolic equation for computing temperature profile of the solid has been discretized into volumes by the Crank–Nicolson scheme. Time integration of differential equations gives solution of local and transient variables in each axial and radial node. Mass flow, temperature, pressure and species concentrations profiles in both channels are obtained. Deep– filtration model of layers is solved simultaneously with channel model and also initial conditions for the regeneration simulations are obtained by the use of deep–filtration model only. Arbitrary strategy of alternating between soot loading and channel simulation can be chosen. This can reduce the computation time. Time step for integration of the DPF model is adaptively controlled in dependence on temperature, concentration and soot mass changes in chosen finite volumes. Soot particles are oxidized by O2 and NO2. Reaction C-O2 is ignited at temperature approx. equal to 600°C or 450°C in the presence of catalyst. Soot oxidation by NO2 occurs at typical exhaust temperatures of diesel engines (300 – 400°C) and it is promoted by Pt-doped or other noble group metal catalyst. NO2 reacts with soot directly or cooperatively with O2. C-NO2 reactions may be written as follows (Jeguirim et al. 2005, Tschamber et al. 2007): C + 2 NO2 ĺ 2 NO + CO2

(2)

C + NO2 ĺ NO + CO

(3)

C + NO2 + ½ O2 ĺ NO2 + CO

(4)

C + NO2 + ½ O2 ĺ NO + CO2

(5)

Produced and entering NO is catalytically transformed to NO2 by reaction in the washcoat layer. NO + ½ O2 ļ NO2

(6)

Regenerated NO2 is transported by convection and diffusion to the wall and cake layer, where it reacts with soot particles. This process is shown in Fig. 2.

M. Schejbal et al.

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Fig 2. Solid part section of DPF with reaction processes. Soot is oxidized in cake, washcoat layer and wall, produced NO is transformed back to NO2 in washcoat layer or catalyzed wall.

3. Results DPFs walls can be equipped by washcoat layer with Pt-doped catalyst which is distributed uniformly or non-uniformly (zoned coating technology). Non-uniform content of Pt in washcoat layer can strongly affect overall soot conversion. Various distributions of Pt along z-direction in the washcoat are depicted in Fig. 3, we have assumed value of var – 100 %. All setups have the same integral total amount of Pt catalyst. The DPF with diameter 144 mm, length 152 mm, 150 cpsi and 40 g/LDPF of coating has been considered. Concentration profiles of NO2 and NO are shown in Fig 4 for distribution of type a). Fig 3. Considered model types of Pt distribution in washcoat layer along the inlet channel

We have computed two types of simulations – cold start of the DPF and temperature ramp. Results for the first type are depicted in Fig. 5a. Pt-distribution a) has significantly better conversion then other distributions; e) has intermediate efficiency of soot combustion. The worst conversion was observed with distribution b). Temperature ramps (cf. Fig. 5b) have very similar results, but differences are smaller. Regeneration of the DPF by NO2 is continuous process and thus small difference (in 1500 s simulation) could be very important in long-time behaviour of soot contents in the DPF.

4. Conclusions We have developed spatially detailed 2D model and its fast and efficient solver for simulation of the DPF. One type of DPF design simulations has been studied. It has

Modelling of Wall-Flow Filters for Diesel Particulate Removal

807

been shown that the distribution of catalyst can affect soot combustion and cause an increase of conversion and could be also used for faster ignition after a cold start.

5. Acknowledgements The work was supported by the Czech Grant Agency (grant No. 104/08/H055) and the Czech Ministry of Education (project MSM 6046137306). Fig 4. Profiles of NO2 (a) and NO (b) molar fractions in the wall, washcoat, soot cake and both channels for Pt-distribution type a) at temperature 300°C.

a)

b)

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Fig 5. “Cold start” (a) and temperature ramp 1°C/5 s (b) of the filter for different Pt-distributions.

a)

b)

References Y. Yong, 2006, Simulating the Soot Loading in Wall-flow DPF Using a Three-Dimensional Macroscopic Model, SAE Technical paper 2006-01-0264 O. A. Haralampous, G. C. Koltsakis, 2004, Oxygen diffusion modeling in diesel particulate filter regeneration, AIChE Journal 50, 2008 – 2019 A. S. Shende, J. H. Johnson, S. L.Yang, S. T. Bagley, A. M. Thalagavara, 2005, The filtration and particulate matter oxidation characteristics of a catalyzed wall-flow diesel particulate filter: experimental and 1-D 2-layer model results, SAE Technical Paper 2005-01-0949 E. J. Bissett, 1984, Mathematical model of the thermal regeneration of a wall-flow monolith diesel particulate filter, Chemical Engineering Science 39, 1233-1244 A. G. Konstandopoulos, J. H. Johnson, 1989, Wall-Flow Diesel Particulate Filters-Their Pressure Drop and Collection Efficiency, SAE Technical Paper 890405 M. Jeguirim, V. Tschamber, J.-F. Brilhac, P. Ehrburger, 2005, Kinetics and mechanism of the oxidation of carbon by NO2 in the presence of water vapor, Fuel 84, Issues 14-15, 1949-1956 V. Tschamber, M. Jeguirim, K. Villani, J. Martens, P. Ehrburger, 2007, Comparison of the activity of Ru and Pt catalysts for the oxidation of carbon by NO2, Applied Catalysis B: Environmental 72, Issues 3-4, 299-303 Ch. K. Dardiotis, O. A. Haralampous, G. C. Koltsakis, 2008, Catalytic oxidation in wall-flow reactors with zoned coating, Chemical Engineering Science 63, Issue 4, 1142-115

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

809

Numerical verification of the statistical moments method used to simplify the reactive adsorption models Eugeniusz Molga,a Leszek Rudniaka a

Warsaw University of Technology, Chemical and Process Engineering Department, ul. Warynskiego , 00-645 Warszawa, Poland, [email protected], [email protected]

Abstract Numerical simulations of the adsorptive reaction process have been carried out. A homogeneous reaction taking place in the liquid and simultaneous adsorption of the reactant, which is a case met often in chromatographic reactors, have been considered. The obtained results fully confirm predictions obtained from a preliminary analysis employing statistical moments. These predictions can indicate a reasonable method to simplify a general model of the process. Keywords: Simulation, Reactive adsorption, Statistical moments

1. Introduction The reactive adsorption processes, in which the chemical reaction is integrated with a simultaneous separation of products by adsorption, are widely investigated and applied as typical examples of integrated processes. The reactive adsorption processes can be carried out in two types of reactors: in the adsorptive reactors as well as in the chromatographic reactors. Models for adsorptive and chromatographic reactors are very similar, because in both types of reactors the same stage processes are involved – in fact they consist of the same set of mass balance equations [1]. Significant differences in process description appear, when for each type of the considered reactor a characteristic way of its operation is taken into account. This is specified with a set of the appropriate initial and boundary conditions. For practical use general models of the reactive adsorption processes (taking account all stage processes) are usually significantly simplified to create an efficient working version of the reactor model. The statistical moments method can be among others used to indicate a controlling stage process and simplify the reactor model [1]. In this paper a numerical verification of predictions obtained with the statistical moments has been carried out and discussed.

2. Process model A general model of the reactive adsorption processes, which consists with a set of mass balance equations, has been formulated for each of reacting species in the moving and the stationary phase, respectively. The first order reaction, catalyzed with the homogeneous catalyst (e.g. the acid solution), has been taken as a testing reaction. In

E. Molga and L. Rudniak

810

this case the active packing of the reactor consists of the adsorbent particles. The following stage processes have been taken in to account in model formulation: - convective and dispersed flows of the moving phase in the interparticle voids, external (convective) mass transfer, - internal (diffusive) mass transfer, - adsorption at the pores surface, - reaction carried out in the moving phase flowing in the interparticle voids as well as in the liquid penetrating in the adsorbent pores. The set of the appropriate mass balance equations reads as follows: - for the component A in the interparticle voids

DL

6 (1 − ε ) ∂ 2c A ∂c ∂c − u A − k cA − NW , A = A 2 ∂x ε dp ∂t ∂x

(1)

where the mass flux at the particle surface NW,A can be estimated as:

[ ( ) ]

§∂c · NW , A = De , A ¨¨ p , A ¸¸ = k c c A - c p , A © ∂ r ¹r =R

(2)

r=R

- for the component A in the intraparticle voids (pores of the adsorbent)

∂c De , A § 2 ∂c p , A ∂ 2 c p , A · ¨ ¸ − S P, A − k c p, A = p, A + 2 ∂r ¸¹ ε p ¨© r ∂r ∂t

(3)

Eq. 3 is adequate for a pseudo-homogeneous model and the term SP,A describes the adsorption rate as:

(

)

S P , A = k a , A c p , A − cs , A =

∂q A ∂t

while the linear adsorption equilibrium is expressed as:

(4)

q A = K A cs , A

(5)

In this model the following parameters describes the appropriate stage processes: axial dispersion coefficient – DL, effective diffusion coefficient in pores – De,A, adsorption rate constant – ka,A, reaction rate constant – k, adsorption equilibrium constant – KA. A significance of each process parameters, so also their influence on the process efficiency, can be estimated with use of the statistical moments method [1]. Estimation of the a significance of the process parameters indicates acceptable simplifications of a general model.

3. Moments method to estimate a significance of the stage processes It has been found that the method employing statistical moments may supply useful information on significance of each stage process, so also on its influence on the efficiency of the whole reactive adsorption process [1]. This method is based on the observation that in a wide range of the kinetic rate constant values the chemical reaction practically does not influence the second central moment estimated for the general model of the process. In this situation, a simplified method has been proposed [1],

Numerical Verification of the Statistical Moments Method

811

where a significance of each stage process is estimated as a contribution of each stage process to the values of the second central moment μ’2,A:

μ 2' , A −

(

td2 L = δ d , A + δ a , A + δ p , A + δ e, A 12 u

)

(6)

where the terms δj,A describe the appropriate contribution: δd,A – dispersion, δa,A – adsorption, δp,A – internal diffusion in pores and δe,A – external mass transfer, respectively. Each term δj,A has been expressed depending on the appropriate parameter characterizing the considered stage process. For a case study investigated in this paper – i.e. for the homogeneous reaction carried out in the fluid phase so, for processes carried out in chromatographic reactors, the most useful simplifications of a general model arising from the moments analysis are listed in Table 1. Depending on the range of operating conditions, these simplifications indicate modifications of the model equations as it is listed in Table 1. Table 1. Simplifications considered for the homogeneous reaction carried out in the moving phase

Case

A B

C

Kind of simplification adsorption rate neglected external and internal mass transfer resistances neglected axial dispersion neglected, mass transfer represented with the effective coefficient Kz

Operating conditions full range of operating variables dp < 50 [μm] and u < 2 10-4 [m/s] e.g. at dp = 100 [μm] and u = 2 10-2 [m/s]

Modified model equations Eqs. 1÷3, 6÷8 Eq. 9

Eqs. 10÷12

The following modified model equations can be used for each case, respectively: - for case A

S P, A =

∂q A ∂t

and

q A = K A c p, A

(7, 8)

- for case B

DL

∂ 2c A ∂c (1 − ε ) ε § k c + K ∂c A + ∂c A · −u A = ¸ p¨ A A ε ∂x ∂t ∂t ¹ ∂x 2 ©

(9)

- for case C

−u

∂c A ∂c 6 (1 − ε ) − k cA − NW , A = A ∂x ε dp ∂t

(

NW , A = K z c A − c p , A

)

(10) (11)

E. Molga and L. Rudniak

812

∂c p , A · § ∂c p , A 6 ¸ N W , A = ε p ¨¨ + k c p, A + K A dp ∂t ¸¹ © ∂t

(12)

In this study an exact numerical verification of predictions obtained with preliminary moments method has been carried out, to check if this methods is sufficiently accurate. particle grain

A A 3

pore

2

1

4

Figure 1. Schematic diagram of the flow cell. Stage processes contributing to the entire reactive chromatography process: 1- external mass transfer, 2 – internal mass transfer in pores (diffusion), 3 – adsorption at the pore surface, 4 – homogeneous reaction taking place in the intraparticle pores.

4. Exact model solution To verify the predictions obtained from moment analysis a general model has been solved for a single grain of the adsorbent. To this end, the porous grain of the adsorbent has been placed inside the flow cell, where the concentration outside the grain has been changed in time – see figure 1 for details. An impulse input of the component A into the cell has been used. The set of model equations (Eqs. 2-5) has been solved, using the appropriate values of process parameters (ka,A, KA, k, De,A) typical for reactive chromatography process [2]. A FLUENT 6.3 package and a finite volume approach have been used. The simulations have been carried out for different values of the reaction rate constant - k and the adsorbent particle diameter – dp, determining the concentrations inside the adsorbent grain - cs,A(r, t), cp,A(r, t) expressed as a function of time – t and radial position – r. It has been found that, in the considered systems for values of the adsorption rate constant typical for liquid chromatographic systems, i.e. for ka,A > 5 104 s-1, concentrations cs,A(r, t) are practically the same as concentrations cp,A(r, t), so a local equilibrium can be assumed. This fully confirms predictions obtained previously from moment analysis – see Case A in Table 1. Concentration profiles of the reactant A inside the pores strongly depends on the particle diameter – dp. Typical results obtained for different particle sizes are shown in figure 2. It is clear from the diagram, that for adsorbent particle diameter dp < 50 μm, the concentration profiles inside the grain can be assumed as the uniform one and equal to the concentration on the grain surface. It also fully confirm the preliminary indications obtained with the moments method – see Case B in Table 1.

Numerical Verification of the Statistical Moments Method

1.0

dp = 10 μm

0.8

cp,A/(cp,A)r=R [-]

813

dp = 50 μm

0.6

0.4

0.2

dp = 300 μm 0.0 0.0

0.2

0.4

0.6

0.8

1.0

r/R [-]

Figure 2. Radial concentration profiles in pores obtained for different particle sizes. Simulations carried out with: k = 10-2 s-1, De,A = 2.1 10-10 m2 s-1, KA = 0.3 -, kc = 7.6 10-9/dp m s-1. Data displayed at the time moment t = 4 10-2 s.

5. Summary and Conclusions Simulations carried out for the flow cell containing a single adsorbent grain – which represents a behavior of the adsorbent particle placed in a packed bed of the chromatographic reactor – have been carried out. A general model including all stage processes taking place inside the adsorbent particle has been used. A set of model equations has been solved with a FLUENT 6.3 package, applying the finite volume method. The obtained results fully confirm the preliminary predictions supplied with use of the statistical moment analysis. In these predictions particularly significant are indications stated that in chromatographic reactors the adsorption rate in fast enough to assume the local equilibrium in pores as well as indications describing the maximal particle diameters for which the internal mass transfer resistances in pores can be neglected.

6. Acknowledgements This work has been supported by the Ministry of Science and Higher Education (Poland) within a frame of the scientific grant No. 1 T09C 023 30.

7. References [1] [2]

E. Molga, Chem.Proc. Eng., 29, (2008) 683 E. Molga, Processes of reactive adsorption – adsorptive and chromatographic reactors (in Polish), WNT, Warszawa, 2008

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

815

Rate Based Modelling and Simulation Studies of Hybrid Processes consisting of Distillation, Vapour Permeation and Adsorption for the dehydration of ethanol Tim Rotha and Peter Kreisa a

Technische Universität Dortmund, Department of Biochemical- and Chemical Engineering, Laboratory of Fluid Separations, Emil-Figge-Str. 70, 44227 Dortmund, Germany, Phone: +49-231-755 2342, [email protected]

Abstract Detailed simulation studies with rigorous models for different hybrid processes consisting of distillation, vapour permeation and adsorption are presented in this paper. The application focuses on the separation of the non-ideal binary mixture ethanol/water. Membrane processes can be a promising alternative to conventional process technologies, due to its independence from the vapour liquid equilibrium. Two polymeric membranes with hydrophilic properties have been investigated and modelled with (semi-) empirical approaches. First analysis of a hybrid process consisting of distillation and vapour permeation demonstrates the high potential to cause an improvement for the ethanol production concerning yield and capacity. A process analysis illustrates the influence of operating and structure parameters on relevant target variables. The results should become the basis for a simultaneous optimization of a complete hybrid process. Keywords: Vapour Permeation, Hybrid Process, Dehydration Ethanol, Rate Based Modelling, Simulation studies

1. Introduction During the last years membrane technology has become more relevant in the chemical and petrochemical industry. Especially a hybrid process, consisting of membrane process and another unit operation (e.g. distillation) could become a promising alternative to conventional processes and leads to an improvement in yield and product capacity. But for a further establishment of membrane technology in industry, a continuous enhancement of membrane materials concerning to flux, selectivity and lifetime is essential. At the same time mathematical methods for a better process know-how and optimization must be developed. Different process configurations consisting of the unit operations distillation, adsorption and vapour permeation (VP) for the dehydration of ethanol from 45wt.-% to 99.6 / 99.95wt.-% are investigated. 99.6wt.-% is the specification to use ethanol as a fuel and the purity 99.95wt.-% is necessary for application in the pharmaceutical or chemical industry. In addition to the heteroazeotropic distillation process, pressure swing adsorption (PSA) is the common technology used in industry to purify ethanol. Before the PSA a distillation column separates the ethanol water mixture close to the azeotrop (92-94wt.-% of ethanol). Thus the column has high energy consumption and a high number of theoretical stages. For further investigations this process should become the benchmark. The most promising option to use or integrate the VP into the

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816

Adsorption

Ethanol 99,6/ 99,95wt.-%

2

Recycle Ethanol 45wt.-%

Recycle

Retentate Ethanol 99,6/ 99,95wt.-% Ethanol/ Water Distillation

Ethanol 45wt.-%

VP Distillation

1

Regeneration

dehydration process is the subsequent connection to the distillation column so that the distillate concentration can be reduced and the disadvantage of VP, to evaporate the feed, is eliminated. In this paper hydrophilic polymer membranes placed in a hollow fibre module are investigated. The following four process configurations are compared with the benchmark and the schematic flow sheets are illustrated in figure 1.1: 1. Integration of VP into the benchmark process between distillation and adsorption. 2. Replacement of PSA with VP (combination between distillation and membrane process). 3. Replacement of distillation with VP (combination between membrane process and PSA) 4. VP as a stand alone process (replacement of distillation and PSA) For modelling and simulation of the unit operations, rigorous models will be used, which are explained in Chapter 2. The equations are implemented in the commercial simulation environment Aspen Custom Modeler™ (ACM). Additionally peripherals (reboiler, condenser, heat exchanger, pumps) are also modelled. Lipnitzki et al. [1] gives an overview of hybrid processes combining pervaporation/ vapour permeation with other unit operations.

Recycle

Water

Regeneration

Water

Adsorption

3

VP

Ethanol 99,6/ 99,95wt.-%

4

VP

Ethanol 99,6/ 99,95wt.-%

Ethanol 45wt.-%

Ethanol 45wt.-%

VP

VP

Permeate

Permeate

Permeate Recycle

Figure 1.1: hybrid process configurations distillation, VP and PSA

2. Modelling and Validation Vapour permeation Vapour permeation separates volatile components by a dense membrane due to different sorption and diffusion properties of each component of the mixture within the membrane matrix. Thus the mechanism is not limited by the vapour liquid equilibrium, which is the main advantage compared to a conventional distillation column. The vaporous feed sorbs from the bulk phase on the membrane surface, diffuses through the membrane layer and desorbs into the permeate bulk phase. The gradient between

Rate Based Modelling and Simulation Studies of Hybrid Processes Consisting of Distillation, Vapour Permeation and Adsorption for the Dehydration of Ethanol

817

retentate and permeate of the chemical potential forms the driving force, which is mainly engendered by a pressure difference (Eq. 2.1).

§ yi,F ⋅ p F ΔμiVP = RTF ⋅ ln ¨ ¨ y ⋅p © i,P P

· ¸¸ ¹

(2.1)

Two main parameters characterize a membrane process: permeance and selectivity (Eq. 2.2 and 2.3). Whereas the flux J of a component i is equal to the permeance Qi multiplied by the driving force DFi, which can be seen simplified as the difference of partial pressures or fugacities in the case of real mixtures:

J i = Qi ⋅ DFi

(2.2)

The selectivity αi,j for a binary mixture is defined as the ratio of permeances and shows the ability of a membrane to separate two components i and j [2].

αi, j =

Qi

(2.3)

Qj

Based on the solution-diffusion-mechanism [3], the simulation of the vapour permeation is performed by a detailed and flexible model. Several model approaches with empirical and physical background for calculating the permeance are implemented and applied in the previous thesis. The model can also be used for simulating the pervaporation (PV) and gas permeation (GP). For further details, refer to Kreis et al. [4]. In this paper two polymeric hollow fibre membranes with hydrophilic properties have been investigated. A polyimide membrane produced by WhiteFox Technologies Ltd., which has been applied in industry since 2001 and a PVA membrane. For the polyimide membrane the use of the Arrhenius equation shows a good agreement of the simulated and experimental results (figure 2.1). 14

2,0

12

H2O

-10%

H2O

-10%

1,6

EtOH

EtOH

1,2 1,0 0,8

0 PEtOH =0,74 mol m²hbar

0,6

E A,EtOH =45,99 kJ mol

0,4

P

0,2

E A,H2O =-4,12

0 H2O

=172,13

mol

kJ

m²hbar

JH2O,sim [kg/hm²]

10

1,4 JP,exp [kg/hm²]

+10%

+10%

1,8

8 6 4

0 PEtOH =0,002 mol m²hbar

2

0 PH2O =54,45 mol m²hbar

EA,EtOH =-149,21kJ mol

E A,H2O =-15,05 kJ mol

BEtOH =9,29

BH2O =3,51

A EtOH =-3,05

A H2O =0,0091

mol

0

0,0 0,0 0,2

0,4

0,6

0,8 1,0 1,2 1,4 JP,sim [kg/hm²]

1,6

1,8 2,0

0

2

4

6 8 10 JH2O,exp [kg/hm²]

12

14

Figure 2.1: parity plots for Arrhenius (polyimide) and empirical correlation (PVA)

Because of the amorphous structure and glassy behaviour (high glass transition temperature) the permeance is only dependent on the temperature. The activation energy EA,i and Pi0(T0) are the model parameters. In contrast the PVA membrane has elastic behaviour and is consequently strongly influenced by swelling of the polymer. It is an

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818

anisotropic phenomena since the feed side of the membrane is in contact with saturated or superheated vapour while the permeate side is nearly dry due to the vaporization of the permeate [5] For description of the separation performance an empirical correlation (Eq. 2.4) is implemented, which takes the effect of temperature T, saturation ϕ and mass fraction w on permeance into account. Beside the EA,i and Pi0(T0) two more parameters Ai and Bi have to be considered.

§ E A,i Qi = Qi0 ⋅ exp ¨ © R

§1 1 ¨ − 0 ©T T

·· Ai ¸ ¸ ⋅ w F,i ⋅ exp ( Bi ϕF ) ¹¹

(2.4)

Distillation and adsorption For the simulation of the distillation a rate-based model is applied, which was developed by Kloecker [6]. The dynamic adsorption process is modelled by a linear driving force (LDF) approach and the adsorption equilibrium is described with the Langmuir isotherm. Transport limitations, e.g. pressure drop are also taken into account.

3. Simulation studies In first simulation studies the hybrid process consisting of distillation and VP (Configuration 2 in figure 1.1) has been investigated. A detailed flowsheet with all relevant parameters is presented in figure 3.1. Capacity: 250,000 m³/a Ethanol purity: 99.6 wt.-%

1

94 wt.-% ethanol 2

Column (hiflow rings) h: 45 m d: 3 m reflux ratio: 3 heat duty: 24 MW distillate pressure: 4 bar

Polyimid membrane: n: 39 A: 132 m² countercurrent permeate pressure: 100 mbar Feed pressure: 4 bar

n

45 wt.-% ethanol

1 wt.-% ethanol

Recycle

Figure 3.1: hybrid process consisting of distillation and VP

The distillation column separates the binary ethanol/ water mixture near the azeotrop and 39 in parallel connected modules (132 m²) dehydrate ethanol up to the desired specification of 99.6 wt.-%. The capacity is 250.000 m³/a, which is related to actual planned ethanol processes in Germany. The process analysis showed a strong influence of distillate concentration, which is a so called hand over variable, on reboiler heat duty and on number of modules. The distillate concentration compared to the benchmark can be reduced and causes a reduction in operating costs. In the first investigations the distillate concentration has been changed from 94wt.-% to 80wt.-% ethanol. This results

Rate Based Modelling and Simulation Studies of Hybrid Processes Consisting of Distillation, Vapour Permeation and Adsorption for the Dehydration of Ethanol

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in a reduction of operating costs by 36% and investment costs by 7%. The detailed cost functions base on the model of Guthrie and Hirschberg.

4. Conclusion and Outlook In this work different hybrid process configurations consisting of distillation, adsorption and vapour permeation for the dehydration of ethanol in industrial scale have been investigated. For the simulation studies rigorous models will be used. The transmembrane flux for a polyimide membrane is described with the Arrhenius approach and for a PVA membrane with an empirical correlation. The determined parameters, based on experiments show a satisfactory agreement between experiment and simulation. First simulation studies of a combination between VP and distillation demonstrate the high potential of VP to cause an improvement in yield and capacity. Overall VP can be a promising alternative to the conventional PSA. In further investigations all process configurations have to be optimized concerning relevant target variables (yield, capacity, energy consumption, costs) and compared with each other and with the benchmark process.

References [1] F. Lipnitzki, R.W. Field, P. Ten, Pervaporation-based hybrid processes: a review of process design, applications and economics, J. Membr. Sci. 153 (1999) 183–210. [2] Wijmans, J.G., Process PERFORMANCE = membrane properties + operating conditions—Letter to the editor, J Membr Sci, 220 (2003) 1–3. [3] R. Rautenbach, Membranverfahren- Grundlagen der Modul- und Anlagenauslegung, 1st ed., Springer-Verlag, Berlin, Heidelberg, 1997. [4] Kreis, P.; Górak, A. Process Analysis of Hybrid Separation Processes - Combination of Distillation and Pervaporation Chem. Eng. Res. Des. 84 (2006) p. 595-600. [5] Müller-Plathe, F. Diffusion of water in swollen poly(vinyl alcohol) membranes studied by molecular dynamics simulation. In: J. Memb. Sci. 141. 1998. S. 147–154. [6] Klöker, M., Kenig, E.Y, Hoffmann, A., Kreis, P. and Go´rak, A., 2005, Rate-based modelling and simulation of reactive separations in gas/vapour-liquid systems, Chem Eng Process, 44: 617–629.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Simulating the change in shape factor for solid particles used in flue gas desulfurization and reacting in stirred batch systems. A mathematical model. Cataldo De Blasio,a Ermei Mäkilä,b Tapio Westerlunda a

Åbo Akademi University, Faculty of Technology, Process Design & Systems Engineering Laboratory, Biskopsgatan 8, FI-20500 Turku, Finland, [email protected] b Turku University, Department of Physics, Industrial Physics Laboratory, Vasilinnantie 5, FI-20014 Turku, Finland, [email protected]

Abstract Carbonates are widely used in flue gas desulfurization (FGD) processes because of their ability to form sulfur-carbonate compounds [1]. It is well established that particle size and shape substantially influence the bulk properties of powdered materials, although these characteristics are closely interrelated [2]. In order to evaluate accurately the dissolution rate the shape factor for any particle cannot be considered to be constant during the dissolution event, against what is commonly assumed. In the present study a simulation for the evaluation of the shape factor is presented and tested. Furthermore the shape factor variation as a function of dissolution time was estimated by a modification of the Hixson-Crowell cube root law method. The model emphasizes the meaning of the shape factor in the manifestation of the dissolution behavior. Keywords: Modeling, Desulfurization, Shape factor, Dissolution

1. Introduction The crystal category related to the raw material is really important when the dissolution aspects of the carbonate rocks are taken into consideration. There are seven main crystal systems in nature: regular, tetragonal, orthorombic, monoclinic, triclinic, trigonal and hexagonal; for this reason is somehow approximated the spherical assumption for solid particles. Another factor has to be taken into account: the shape factor. The sphericity factor, ȥw, defined by Wadell H. (1933) is one way to describe the degree of irregularity of solid particles. In this work, volume-weighted median diameters (d50) of the particle distribution were used in the calculations. A more fundamental equation describing the shape factor Įs,v is exposed below. [3]

D s ,v

Sw ˜ U ˜

S 6

˜

¦n d ¦n d i

3 vi

i

2 vi

(1)

Where Sw is the specific surface area per unit volume of the powder, while ni and dvi are respectively the number and the equivalent volume diameter of particles in size class i evaluated for the spherical model and ȡ is the particle density. The powder surface area was measured by gas adsorption.

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2. The modified cube root dissolution rate model. In order to describe the mass transfer phenomena involved between solid particle and liquid solution we can consider the Noyes-Whitney equation also called the Levich equation [4]:

dm dt

k ˜ A ˜ (C sat  C )

(2)

Where Csat is the concentration of the dissolving element at saturation, C is the concentration into the bulk solution, A is the reaction surface and k is the intrinsic dissolution rate constant (dm/sec). For our system and without chemical reaction the C concentration of the dissolving solid into solution is really small compared to the value of Csat. For this reason is common not to consider the term C [5] differently from what we have done in this work. In our case the system of reactions is described by the following table: Table 1. Main reactions involved in limestone-acid systems

Phenomena Dissolution of limestone Reaction with hydronium ions Carbonic ions reaction Final products

Reactions CaCO3(s)ĺCa2+ + CO32H3O+ + CO32- ĺ HCO3-+ H2O HCO3- + H3O+ ĺ H2CO3 + H2O H2CO3 ĺ CO2(g) + H2O

The concentration C in the above mentioned Levich formula indicates the concentration in moles of Ca2+ ions and it can be determined experimentally. The surface of reaction is a function of the shape factor * [6]: 2

A

§ m ·3 * ˜ ¨¨ ¸¸ ©U¹

(3)

Combining the Eq.(2) with Eq.(3) and integrating from a time t0 and a mass M0 to a generic time and mass, we obtain the relation:

§ M 1  ¨¨ © M0

1

·3 ¸¸ ¹

1

k ˜ C sat ˜ * ˜ N 3 ˜ t 1 3 0

3˜ M ˜ U

2 3

(4)

1

§ M ·3 ¸¸ 1  ¨¨ © M0 ¹

K

K ˜t

k ˜ C sat ˜ * ˜ N 1 / 3 3( M 0 )1 / 3 U 2 / 3

(5)

(6)

K is the so called cube root dissolution rate constant and N is the number of particles considered in a mono-disperse system. The Eq.(5) is the mathematical statement for the Hixson-Crowell cube root law for a mono-disperse particulate system. For a poly-disperse system the sum of the particles fractions can be studied considering the sum of all the fractions involved in the system. It is only when a particle is isometric that the shape factor is constant and independent of dimensions. The intrinsic

Simulating the Change in Shape Factor for Solid Particles Used in Flue Gas Desulfurization and Reacting in Stirred Batch Systems. A Mathematical Model. 823

dissolution rate constant was evaluated as an average over time. As a particle dissolves its dimensions change and a change of shape factors occurs. In this work it has been considered a system in which the particles are supposed to be developed along three orthogonal axes. The volume V of the particle is a composite function of l, b and h; for this reason the variation of the volume as a function of time can be rewritten as:

§ dl · § db · § dh · bh¨ ¸  lh¨ ¸  lb¨ ¸ © dt ¹ © dt ¹ © dt ¹

dV dt

(7)

The concentration of Ca++ ions can be determined experimentally and the mathematical description of it is:

a ˜ Log (t )  b

C (t )

(8)

Where the numerical coefficients a and b are experimentally determined. The surface and the volume of the particles are a function of l, b, h. We consider the constant K1 as: K1 = -2k/ȡ

(9)

Eq.(2) becomes then:

1 § dl · 1 § db · 1 § dh · ¨ ¸ ¨ ¸ ¨ ¸ l © dt ¹ b © dt ¹ h © dt ¹

§1 1 1 · K1 ¨   ¸>C sat  aLog (t )  b@ ©l b h¹

(10)

From Eq.(10) appear clear that the terms dl/dt, db/dt and dh/dt are all equal. For this reason it is sufficient to solve the following differential equation for the l dimension and the same result will be obtained for the other coordinates:

l0  l

 K1t >a  b  C sat  a ˜ Log (t )@

(11)

We nominate the quantity (1-l/l0) as a “reduced time” or as “reduced length” [5], it follows that:

u

 K1t >a  b  C sat  aLog (t )@ h0

(12)

Substituting into Eq.(11) we obtain:

l

l 0  uh0

(13)

Similarly with the other dimensions: b=b0-uh0 and h=h0-uh0. The fraction of sample not dissolved F can be determined experimentally as a function of time. The ratios p and q are defined as p=l0/b0 and q=l0/h0. The mathematical description of F in terms of u becomes then:

F

§ u ·§ p ˜u · ¸ (1  u )¨¨1  ¸¸¨¨1  q ¸¹ © q ¹©

(14)

In our system imposing k2=k/h0 considering Eq.(12) utilizing Eq.(14) and rearranging in terms of p and q, the expression for the shape factor, Eq.(3), versus time for a determinate range of particle’s size is obtained:

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*

1 1 ­ ½ §q ·º 3 ª §q ·º 3 °ª ° 1 «1  u ¨¨  u ¸¸» ° «q  u ¨¨ p  u ¸¸» >q  u 1  u @3 °° © ¹¼ ©p ° ¹¼ ¬ 2˜ ®¬  ¾ qu 1 u · §q ° ° ¨¨  u ¸¸ ° ° p ¹ © °¯ °¿

(15)

3. Experimental 3.1. Materials The origin of carbonates is from the Parainen quarry in south west Finland. The carbonate rock is a 1900 million-year-old limestone metamorphosed to marble during the Svecofennian orogeny 1830 million years ago (metamorphosed limestone). Mineralogically it is almost pure calcite and texturally an even grained marble. In the following figure we can find an image obtained from Scanning Electron Microscope at the Department of Physics in the University of Turku, Finland.

Fig. 1. Image of limestone obtained with Scanning Electron Microscope.

It is possible to see that the sample belongs to a triclinic pinacoidal crystal system Fig.1. 3.2. Equipments Particle size distributions were obtained from the distribution of the scattered light energy by using the Fraunhofer diffraction theory and the spherical model [7]. The theory is considered valid for opaque particles having a radius large compared with the laser wavelength. In our case the optical properties of the particles did not affect the results for the size range considered. The equipment includes a batch stirred tank reactor (BSTR), a laser-beam diffractometer (Malvern 2600 model), where the sample particles were analyzed in order to get a particle size distribution, and a pH meter. For each size range, the limestone fraction in volume was given. The procedure expected synchronized pH and particle size measurements. The specific surface per unit volume of the particles has been evaluated by a fully automated gas adsorption method providing high-quality surface area and porosity measurements. The data treatment and the testing of the mathematical model were performed by computer software.

Simulating the Change in Shape Factor for Solid Particles Used in Flue Gas Desulfurization and Reacting in Stirred Batch Systems. A Mathematical Model. 825

The experimental setting adopted at the Process Design and Systems Engineering laboratory is described by the following figure:

Figure 2. The schematic shows the laboratory setup used for mineral reactivity measurement.

4. Results and discussion The concentration in moles of dissolved calcium carbonate has been evaluated experimentally; the experimental values are well fitted by a logarithmic curve Eq.(8): Concentration + moless m^3 / 2.5 2.0 1.5 1.0 0.5 50 100 150 200 250 300

Time + sec /

Fig. 3. Dissolved calcium carbonate as a function of time.

The solid volume fraction as a function of time was evaluated experimentally; the following figures report a description of the volume fraction and the reduced time with experiments (dots): Volume fraction 1.0

Reduced Time 0.05

0.8

0.04

0.6

0.03

0.4

Time+ s/

0.2 0.0

0

50

100

150

200

Fig. 4. Volume fraction versus time.

250

0.02

Time+ s/

0.01 50

100

150

200

250

Fig. 5. Reduced time versus Time.

The volume fraction data reflect the non homogeneity of the BSTR mixing, other than the decrease in volume with time. This is shown in Fig. 4. The reduced time data are derived from Eq.(12) taking into account the experimental values, C(t), of the dissolved concentrations Eq.(8).

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Estimated values for the shape factor were derived from Eq.(15) considering the experimental values for the reduced time; we distinguish a linear behavior of the shape factor in the first minutes, Fig. 6. The Shape Factor simulation and the experiments are reported in Fig. 7.

Shape Factor

Shape factor 8

8

6

6

4

4

2

2

Time+ s/ 500 1000 1500 2000 2500 3000 3500

Fig. 6. Simulated shape factor vs time.

0

¯

0

50

Tim e + s/ 100 150 200 250 300

Fig. 7. (§) Eq.(1) with experimental results and spherical approximation. (*) Shape factor simulation with experiments Eq.(15).

The specific surface evaluation (gas adsorption) together with spherical approximation of particles (diffractometry) leads to a shape factor greater than the simulation, which is completely in agreement with our expectations.

5. Conclusions In the present work the mathematical simulation has been done taking into account the dissolving solid into the bulk solution. Furthermore the experimental data obtained from laser diffractometry and fully automated gas adsorption are in agreement with the model. For the case presented, the modified Hixson Crowell cube root law method was proved to be more suitable for dissolving particles in presence of reaction. The present work confirms the suitability of the method for particles related to triclinic pinacoidal systems.

6. Acknowledgements The authors would like to thank the Fortum Foundation for the financial support. The Heat Engineering and the Process Design & Systems Engineering Laboratory, Faculty of Technology, Åbo Akademi University, Åbo. The Department of Geology at University of Turku for the samples provided. Professor Heikki Ruskeepää, Department of Mathematics, University of Turku.

7. References [1] [2] [3] [4] [5] [6]

Toprac, A.J. G.T. Rochelle (1982), Environ. Prog.1, p 52. A. W. Hixson, Crowell. (1931). Ind. And Eng. Chemistry. Vol. 23, No. 8. 923-931. Fatima M. Barreiros, Ferreira, Figueiredo. (1996). Part. Syst. Charact. 13. 368-373. V. G. Levich. (1962) “Physicochemical Hydrodynamics” vol. 1. Prentice Hall, Mandar V.Dali, J. T. Carstensen (1996). Pharm. Res. Vol.13, No. 1. Wadell, 1932. H. Wadell, “Shape and roundness of rock particles”. J. Geol. 40 (1932), pp. 443–451. [7] B. B. Weiner (1984). “Principle and Droplet Sizing Using Fraunhofer Doffraction” In “Modern Methods of particle size Analysis” Wiley, New York.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Simulation and optimization of the continuous vacuum extractive fermentation for bioethanol production and evaluation of the influence on distillation process Tassia L. Junqueira, a Marina O. S. Dias, a Maria R. W. Maciel, a Rubens Maciel Filho, a Carlos E. V. Rossell, b Daniel I. P. Atalac a

School of Chemical Engineering, State University of Campinas, UNICAMP, P.O. Box 6066, 13083-970, Campinas – SP, Brazil, [email protected] b Interdisciplinary Center for Energy Planning, State University of Campinas, UNICAMP, P.O. Box 6192, 13400-970, Campinas – SP, Brazil c Sugar Cane Technology Center, Fazenda Santo Antônio, 13400-970, Piracicaba-SP, Brazil

Abstract In this work, the use of a vacuum extractive fermentation reactor, which allows the production of wine with higher ethanol concentration, as well as its effects on the distillation stage, were studied for bioethanol production. Energy consumption was evaluated and compared to the conventional process, showing that the proposed configuration provides a significant reduction in energy consumption, so it seems an interesting option for process intensification. Keywords: simulation, bioethanol, vacuum extractive fermentation, distillation

1. Introduction Bioethanol has been produced in Brazil on a large scale since the 1970s by fermentation of sugars obtained from sugarcane. A typical large-scale plant is able to produce around 1 million liters of bioethanol per day and a significant concern is devoted to find ways to increase the production and decrease energy consumption so that cheaper bioethanol may be obtained. Two types of fermentation are commonly employed in Brazilian refineries: feed-batch and continuous, both with cells recycle. These processes use low concentration of substrate, resulting in a low ethanol concentration in the wine. These conditions are necessary since the conventional alcoholic fermentation is a typical inhibitory process, with cells growth rate affected by cellular, substrate and product concentration [1]. Medium with high concentration of substrate is aimed in the fermentation process, since it provides a significant reduction of fermentor and residue volumes, when compared with conventional processes. In addition, higher concentrations of ethanol in the wine are achieved, thus leading to decreased energy consumption in the further distillation stage. In order to reduce ethanol effects on the fermentation efficiency, studies focusing on ethanol removal have been developed. A possible solution proposed is the vacuum

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extractive fermentation reactor, which allows ethanol produced in the fermentation to be simultaneously removed from the fermentor [2]. Ethanol produced from fermentation of sugars must be concentrated to about 93 wt% ethanol in order to be used as a fuel in ethanol driven engines (hydrated ethanol). To be used as an additive, hydrated ethanol must be dehydrated (at least 99.3 wt% ethanol), which requires further operations, given that ethanol forms an azeotrope with water at a concentration of about 95.6 wt% at 1 atm. In this work, simulations of the vacuum extractive fermentative process were carried out using software Aspen Plus, in order to define optimal operational conditions of the vacuum flash tank. Experimental data and restriction operation information from a pilot plant scale fermentor were used to describe the process. Distillation stage was also simulated, considering two different situations: concentration of the mixture produced on the flash tank and of the wine obtained in a conventional fermentor.

2. Vacuum extractive fermentative process The vacuum extractive fermentative process consists on a continuous fermentation reactor coupled to a vacuum flash evaporator, which allows ethanol produced to be simultaneously removed from the fermentor. The way in which it is projected and operated guarantees a relatively low concentration of ethanol in the fermentor, thus reducing its inhibitory effect on yeast cells. Besides, this configuration provides a wine concentration higher than 40 ºGL as well as a lower volume of wine, which leads to decreased consumption of energy on distillation stage. Values between 7 and 10 °GL are usually obtained on the wine in the conventional process. Process simulations were carried out using software Aspen Plus and NRTL model was used to calculate the activity coefficient on liquid phase. The reactor was modeled assuming the same reactions and fixed conversions adopted by Franceschin et al. [3]. In their work, it was supposed that sucrose is almost completely hydrolyzed (99%) into glucose, which is converted into ethanol, carbon dioxide and secondary products (glycerol and acetic acid). Reaction (1) converts 99.5% of glucose, whereas in the reaction (2) the remaining glucose is consumed. The heat of reaction was set to 1200 kJ/kg of ethanol [4]. C6H12O6 → 2C2H5OH + 2CO2

(1)

2C6H12O6 + H2O → C2H4O2 + 2C3H8O3 + C2H5OH +2CO2

(2)

Usual fermentation temperature in Brazilian refineries is around 33 ºC, since higher temperatures disable yeast cells, decreasing fermentation yields [1]. In addition, ethanol content in fermentation reactors must be maintained between 7 and 10 °GL to prevent inhibitory effects. Thus, the main objective is to obtain high concentration of ethanol in the wine, which is desirable to the distillation stage, but taking into account the restrictions in the fermentation conditions. Different fermentor-flash dispositions were evaluated in order to determine the best configuration, regarding temperature ranges, concentrations of ethanol in the fermentor as well as in the wine sent to distillation stage. It was assumed that the fermentor feed has about 450 g/L of sucrose, which is considered a highly concentrated substrate. The liquid flow that leaves the flash vat and feeds the fermentor maintains the reactor temperature in 33 ºC. Vacuum flash temperature and pressure were analyzed, since these variables affect significantly the vapor-liquid equilibrium and subsequently the separation

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accomplished. It was verified that higher temperatures and lower pressures are required to achieve a satisfactory separation, which corresponds to a larger ethanol recovery in the vapor phase that is fed into the distillation stage. So, a heater was placed before the vacuum flash heating the product proceeding from the fermentation reactor. It was assumed that heating takes place just before the flash vat, so yeast cells are not disabled. Resulting optimal conditions in the vacuum flash were 39.9 ºC and 50 mmHg (approximately 0.07 bar). The proposed vacuum extractive fermentative configuration is shown in Figure 1.

Figure 1. Configuration of the vacuum extractive fermentative process. As can be seen on Figure 1, a small amount of the fermentor output was purged to remove glycerol, preventing its accumulation, and a large recirculation flow was adopted, which enhances ethanol recovery and keeps the fermentor temperature at 33 ºC. As a result, a wine concentration of 44.5 ºGL was achieved as well as a reactor concentration of 8 ºGL. Both wine and purge are sent to a distillation stage. Simulation of a conventional fermentation reactor was also carried out. Reactions, conversions and heats of reactions described previously were considered, since conditions on the conventional fermentation reactor were equal. Concentration of substrate, though, was lower (115 g/L) to provide similar ethanol concentration in the fermentor (8 ºGL). Feed flow was defined in a way that identical amounts of ethanol are fed to distillation in both cases.

3. Distillation process In typical industrial scale Brazilian sugar mills, columns configuration consists of distillation and rectification sections as depicted in Figure 2. The distillation section is comprised by three columns, in the top of each other: A (18 stages), A1 (8 stages) and D (6 stages). In column A, less volatile components are recovered in the bottom (vinasse). In column D, more volatile components are extracted at the top. Column D bottom, known as phlegm, is fed to the rectification section. This section consists in concentration of the phlegm to about 93 wt% ethanol in the column B-B1 (45 stages). This configuration was employed in the simulations for both processes. As mentioned before, purge and wine streams proceeding from vacuum extractive fermentation are fed in the distillation column; wine is sent to column D, because it has a large amount of dioxide carbon, whereas purge is heated until 81 ºC prior to being fed into column A1. In the conventional process, the fermentation product is also heated and sent to column

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A1. Feed positions and column operation conditions were optimized for each case in relation to energy consumption and product specification.

Figure 2. Configuration of the distillation process.

Since the amount of water in the conventional process is quite higher than that of the extractive fermentor, the resultant vinasse volume is ten times superior. For this reason, in the conventional process an evaporator was employed to obtain the same vinasse volume. Main streams results of both cases are shown in Table 1. Table 1. Comparison of main streams results.

Vacuum Extractive Fermentation Stream Temperature (°C) Pressure (bar) Mass flow (kg/h) Mass fraction Water Ethanol Glucose Acetic acid Sucrose Glycerol CO2

Conventional Process

ETHANOL VINASSE PHLEGMASSE ETHANOL VINASSE PHLEGMASSE

81.6 1.16 35.9

111.9 1.52 41.5

108.4 1.36 53.7

81.5 1.16 35.1

111.9 1.52 41.5

108.4 1.36 66.5

0.067 0.932 0 0 0 0 0.001

0.995 0 0 0 0 0.004 0

0.999 0 0 0.001 0 0 0

0.061 0.932 0 0 0 0 0.007

0.979 0 0 0 0.016 0.004 0

1 0 0 0 0 0 0

Table 1 points up that hydrated ethanol has the same ethanol mass fraction (0.932) and vinasse and phlegmasse streams do not contain ethanol in both cases. However, product flow and streams compositions are slightly different when both simulations are compared. Energy consumption in both cases was evaluated and this information is given in Table 2.

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Table 2. Comparison of energy consumptions.

Vacuum extractive fermentation

Conventional process

Equipment Heater2 Column A reboiler Column B reboiler Heater1 Total

Equipment Heater2 Column A reboiler Column B Reboiler Evaporator Total

Energy (MJ/h) 10.0 22.7 120.4 117.0 270.1

Energy (MJ/h) 128.1 236.2 149.0 907.8 1421.1

It was verified that the proposed configuration provides a significant reduction on energy consumption when compared to the conventional process, as presented in Table 2. This fact was expected, since the vacuum extractive fermentative process allows the production of a more concentrated wine, thus smaller flows are involved. Total energy demand per kg of hydrous ethanol (HE) produced and ethanol recovery in both cases are displayed in Table 3. Analyzing this information, it was observed that the proposed configuration provides a reduction in energy consumption of about 80%. Besides, even if the concentration of vinasse was not taken into consideration, the reduction would be of approximately 50%. It was also verified that vacuum extractive process allows a greater ethanol recovery in the hydrated ethanol. Table 2. Energy demand and ethanol recovery for both processes.

Vacuum extractive Conventional process fermentation Ethanol recovery (%) 92.5 90.3 Total energy demand (kJ/kg HE) 7525 40515 Evaporator energy (kJ/kg HE)* 25288 *Evaporator used for vinasse concentration in the conventional process. Compressor and pump were used in the vacuum extractive fermentative process and their electricity requirements were 0.422 and 0.014 kW/kJ of HE produced, respectively.

4. Conclusions Vacuum extractive fermentative process is a potential alternative to reduce energy consumption, ethanol losses and residues volumes on bioethanol production. The amount of vinasse generated is equivalent to 10% of that produced in the conventional process; in addition, energy savings are about 80%. These improvements make bioethanol production more viable either on terms of costs or environmental aspects when a vacuum extractive fermentative process is used.

5. Acknowledgements The authors acknowledge CNPq and FAPESP for financial support.

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6. References [1] E.C. Rivera, A.C. Costa, D.I.P. Atala, F. Maugeri, M.R.W. Maciel, R. Maciel Filho. Evaluation of optimization techniques for parameter estimation: Application to ethanol fermentation considering the effect of temperature. Process Biochemistry, 41:1682-1687, 2006. [2] F.L.H. Silva, M.I. Rodrigues, F. Maugeri. Dynamic modelling, simulation and optimization of an extractive continuous alcoholic fermentation process, Journal of Chemical Technology and Biotechnology, 74:176-182, 1999. [3] G. Franceschin, A. Zamboni, F. Bezzo, A. Bertucco. Ethanol from corn: a technical and economical assessment based on different scenarios. Chemical engineering research and design, 86: 488–498, 2008. [4] J. R Kwiatkowski, A. J. McAloon, F. Taylor, D. B. Johnston. Modeling the process and costs of the production of fuel ethanol by the corn dry-grind process. Ind Crops Prod, 23: 288–296, 2006.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

833

Strategy for Validating a Population Balance Model of a Batch Crystallization Process Using Particle Size Distribution from Image-based Sensor Debasis Sarkara, Zhou Yinga, Lakshminarayanan Samavedhamb, Rajagopalan Srinivasana,b a

Institute of Chemical and Engineering Sciences, 1 Pesek Road Jurong Island, Singapore 627833 b Department of Chemical and Biomolecular Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 117576

Abstract The modeling of the transient behavior of the crystal size distribution is essential to predict and effectively control the quality of the end product. The population balance approach provides an appropriate mathematical framework for the modeling of crystal size. For most batch crystallization processes, it is often difficult to obtain on-line relevant information about the crystal size distribution and the dissolved solid concentration in the liquid phase. We have recently developed an automated image analysis strategy that yields real-time measurements of both particle length and width with acceptable accuracy. In this contribution, we present an approach for validation of a population balance model for batch crystallization of monosodium glutamate by using on-line information about the state of the crystallization process provided by our image analysis strategy and other in-situ process analytical tools such ATR-FTIR. Keywords: Crystallization, Population balance modeling, Image analysis, Parameter estimation, Model validation

1. Introduction Crystallization from solution is a widely practiced unit operation in specialty chemical, pharmaceutical, and agrochemical industries for solid-liquid separation, purification, and production of solid crystals with desired shape and size distribution. The crystal size distribution (CSD) and shape or polymorphic form are the most important product quality variables for any crystallization process as these variables strongly influence the effectiveness of the end-use properties of the crystal products (bioavailability, compressibility, stability, dissolution rate) as well as the efficiency of downstream operations (filtration, drying, storage, handling). Therefore, the modeling of the transient behavior of the CSD is essential to predict and effectively control the quality of the end product. The population balance approach provides an appropriate mathematical framework for the modeling of CSD and has been widely studied in the literature [1-3]. However, the traditional one-dimensional population balance modeling where the size of a crystal is represented as volume equivalent diameter of a sphere is inadequate for many organic crystals that present anisotropic morphology. Thus, multidimensional population balance modeling of such systems has recently attracted the growing interest as it provides a means for incorporating crystal shape into the simulation [4-6].

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D. Sarkar et al.

For most batch crystallization processes, it is often difficult to obtain on-line relevant information about the crystal size distribution and the dissolved solid concentration in the liquid phase. We have recently developed an automated image analysis strategy that combines classical image analysis techniques with multivariate statistics for online analysis of in-situ images from crystallization process [7, 8]. The strategy introduces a novel image segmentation step based on information extracted from multivariate statistical models. Experimental results have shown that the strategy effectively extracts crystal size and shape information from in-situ images and can be used to reliably investigate crystallization kinetics, especially for high-aspect ratio systems. Since the image analysis strategy yields real-time measurements of both particle length and width, it is useful for validating both one-dimensional and multi-dimensional population balance models for crystallization processes. In this contribution, we present an approach for validation of a population balance model for batch crystallization of monosodium glutamate (MSG) by using on-line information about the state of the crystallization process provided by our image analysis strategy and other in-situ process analytical tools such as ATR-FTIR. The real-time measurements provided by these insitu process analytical tools are expected to allow improved understanding and control of crystallization processes.

2. Image analysis based estimation of particle size distribution A major challenge in online automated image analysis is that in situ images from process equipment are very noisy, therefore segmentation, i.e., separating the particles from the background, is nontrivial. Traditionally, image analysis based approaches have relied on edge detection techniques for particle segmentation; however this requires the specification of suitable thresholds. Specification of robust thresholds is difficult given the high noise and other imperfections in the images. We have recently developed a new method to segment images by combining classical image analysis technique with multivariate statistics. The method takes an alternative approach to segmentation by characterizing the image background instead of the particle. A pseudo-image is first created by extracting suitable features from each in situ image, performing Principal Component Analysis, and formulating the Hotelling T2 statistic as an image. This pseudo-image has fewer imperfections compared to the in situ image given the noise elimination obtained by ignoring the smaller Principal Components. It can therefore be segmented robustly using a global threshold. The proposed image analysis strategy uses the background image (without any particle) for estimating this threshold value. The obtained particle outline is further refined through a discrete Fourier transform and signature curve analysis and particle size and shape information extracted. The accuracy, robustness and efficiency of the strategy have been established by comparing its performance with those obtained by manual image segmentation. Experimental results for batch cooling crystallization of MSG show that the method yields reasonably good estimates of the particles length with about 5% median error.

3. Modeling of MSG batch crystallization The crystals of MSG exhibit a rod-like habit. Such high aspect ratio crystals can be modeled as a rectangular body as shown in Fig. 1. Thus, two characteristic sizes, the length (L) and the width (W), are required for the formulation of the population balance model. Let us describe the population of crystal by the number population density

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function ȥ(L,W,t) such that N(L,W,t), the number of crystals with length between L and L+dL and width between W and W+dW is

N ( L, W , t ) = ³

L + dL

L

³

W + dW

W

ψ ( L,W , t )dLdW

(1)

Assuming that the population density does not depend on the spatial coordinate, the two-dimensional population balance for a constant volume (V) crystallizer can be written as

Fig. 1: Two dimensional approximation of a MSG particle

∂ψ ∂ ∂ + ( G Lψ ) + ( GWψ ) = R N + R A − RB ∂t ∂L ∂W

(2)

where RN, RA, and RB indicate the nucleation rate, the agglomeration rate, and the breakage rate, respectively. The growth rate along the length is GL and that along the width is GW. The nucleation rate and the growth rates are functions of supersaturation ı(t) and often expressed as empirical power law models. The supersaturation depends on the concentration of solute in solution C(t) and the equilibrium solubility C*(t). The solute concentration and hence the supersaturation can be measured online by ATRFTIR. The agglomeration rate and the breakage rate are expressed as differences between a birth term (B) and a death term (D). The growth rates (GL and GW) can be directly determined with our image-processing strategy (Fig. 2). As seen from Fig. 2, the width of the crystals remains almost constant after a certain period of time and thus the population density can be described by a single characteristic length, ȥ(L,t). In absence of any significant breakage, the MSG crystallization can thus be described by the following one dimensional population balance equation along with mass balance and other kinetic models.

D. Sarkar et al.

836 300

) m μ( ht g n e L

200

100

0

0

5

10

15

20

15

20

Time (h) 20 15 ) m μ( ht di W

10 5 0

0

5

10 Time (h)

Fig. 2: Time evolution of particle length and width

∂ψ ∂ (GLψ ) + = RN + RA ∂t ∂L

ψ ( L, t = 0) = ψ seed ( L)

RN = kbσ b μ3

GL = k gσ g

∞

μi = ³ Lψ ( L, t )dL i

dC 0 = −3ρ c kv GL μ2 dt

C (t ) − C * (t ) σ (t ) = C * (t )

(3)

RA = Baggl − Daggl

Baggl =

L2 2

β [( L3 − λ 3 )1/3 , λ ] ⋅ψ [( L3 − λ 3 )1/3 , t ] ⋅ψ (λ , t )d λ ³0 ( L3 − λ 3 ) 2/3 L

∞

Daggl = ψ ( L, t ) ³ β ( L, λ ) ⋅ψ (λ , t )d λ 0

kb, b, kg, g are rate constants and ȝi is the i-th moment of the CSD. ȡc is the density of the crystal and kv the volumetric shape factor. The bitth and death terms for agglomeration are expressed in terms of characteristic particle length where the

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agglomeration kernel ȕ(L,Ȝ) is a measure of the frequency at which crystals of size L and Ȝ collide to form an agglomerate [2]. The identification of an appropriate kernel is a major challenge in agglomeration modeling.

4. Validation strategy The population balance model presented in Eq. (3) can be solved numerically by discretizing the length coordinate, which results in a set of ordinary differential equations. The solution of Eq. (3) for a given operating condition will yield the number of particles, N(L,t) and the solute concentration, C(t). The number of particles, N(L,t) can be determined directly form our image analysis strategy. The solute concentration in the crystallizer can be measured online by ATR-FTIR. Thus the time evolution of CSD and solute concentration can be used to estimate the model parameters (ș) through the minimization of an objective function, ij(ș), which is a measure of the deviation between the model and experiment. The weighted least-square form is often a common choice for the objective function [9].

ϕ (θ ) = α1ε [C (θ )] + α 2ε [ψ m (θ )]

(4)

The İ[C(ș)] is the quadratic error between the measured and model-predicted solute concentration. Similarly, İ[ȥm(ș)] is the error between the measured CSD and simulated CSD. Į1, Į2 are scalars to balance the respective weights of the two quadratic criteria.

5. Concluding remarks The modeling of the transient behavior of crystal size distribution is essential to predict and effectively control the quality of the end product. This work proposes a methodology for development and validation of a population balance model for batch crystallization of MSG that exhibits rod-like habit. The strategy involves direct on-line measurement of all key variables that influence CSD, including the on-line measurement of CSD by our recently developed multivariate image analysis technique. Currently, we are applying this validation strategy to the MSG batch cooling crystallization system described above and the results from this study will be reported in future communications.

References [1] [2] [3] [4]

A. D. Randolph and M. A. Larson, Theory of Particulate Processes, second ed. Academic Press, New York, 1988 M. J. Hounslow et al., AIChE Journal 34 (1988) 1821-1832. D. Ramkrishna, Population Balances: Theory and Applications to Particulate Systems in Engineering, Academic Press, New York, 2000. [5] D. L. Ma et al., Industrial Engineering Chemistry and Research 41 (2002) 6217-6223. [6] F. Puel et al., Chemical Engineering Science 58 (2003) 3715-3727. [7] C. Y. Ma et al., Advanced Powder Technology 18 (2007) 707-723. [8] D. Sarkar et al., accepted in Chemical Engineering Science (2008). [9] Z. Ying et al., accpted in Computers & Chemical Engineering (2008). [10] A. Caillet et al., Crystal Growth and Design 7 (2007) 2088-2095.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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A New Model-Based Methodology for Simultaneous Design and Control of Reaction-Separation System with Recycle Mohd. Kamaruddin Abd. Hamid, Gürkan Sin, Rafiqul Gani Computer Aided Process-Product Engineering Center (CAPEC), Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800, Kgs. Lyngby, Denmark. [email protected]

Abstract This paper presents a new systematic model-based methodology for integrated process design and control (IPDC) for chemical processes. The novelty of this methodology is to use the decomposition method in solving IPDC problems. The idea is to decompose the complexity of IPDC problems by following four hierarchical stages: (1) preanalysis, (2) steady state analysis, (3) dynamic analysis, and (4) evaluation stage. Starting from an initially large design space, the methodology aims at reducing the dimension of the search space in each of the successive stages. To this end, the methodology makes use of the attainable region and driving force concepts as well as employs several process models with differing level of complexity (simple, steady-state, dynamic). In this paper, the potential use of the decomposition method in solving IPDC problems, particularly its ability to reduce the dimension of the design space is presented using a case study for synthesis of ethylene glycol. Keywords: Model-based methodology, integrated process design and control, decomposition method, attainable region, ethylene glycol.

1. Introduction Historically, which is still common today, process design and process control are two separate problems that are performed sequentially. The process is designed first to achieve the design objectives, and then, the operability and control aspects are analyzed and resolved. This traditional-sequential approach has some limitations such as dynamic constraint violations, process overdesign or under performance, and does not guarantee robust performance (Seferlis and Georgiadis, 2004). Another drawback has to do with how process design decisions influence the control performance of the system. To assure that design decisions give the optimum economic and best control performance, the control aspects should be considered at the design step. The importance of an integrated process design approach, considering control aspects together with the economic issues, has been widely recognized (Seferlis and Georgiadis, 2004). A number of methodologies and tools have been proposed for addressing the interactions between process design and control, and they range from optimization-based approach to modelbased methods. An optimization-based approach for the integrated process design and control (IPDC) aims at simultaneously determining the flowsheet configuration, design parameters, plantwide control structures, and the controller tuning parameters (Luyben and Floudas, 1994; Seferlis and Grievink, 2001). In the work done by Luyben and Floudas (1994), they propose a methodology that considers economic and open loop controllability

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objectives within the multi-objective optimization framework, whereas Seferlis and Grievink (2001) consider the economic and static controllability criteria. The solution of the complete optimization problem can be extremely challenging in terms of problem complexity such as huge dimension of the design space, which may be too costly with respect to computational demand. In model-based methods, a first-principles model is used to analyze the IPDC problems without involving rigorous modeling or optimization. Kiss et al. (2007) use dimensionless simplified models to analyze the nonlinear behavior of recycle systems to quickly screen and select the feasible integrated designs. In a model-based analysis proposed by Ramirez and Gani (2007), key design and control variables, limiting conditions, and feasible regions of operation are identified using appropriate models. However, few important issues have not been yet considered in the previous methods such as criteria/tool of selecting the optimal design, economic aspects and the controller structure selection. In this paper, a new model-based methodology of IPDC for chemical process which covers the above issues is presented and the potential use of the decomposition method in solving IPDC problem, particularly its ability to reduce the huge dimension of the design space using process knowledge embedded in successive models (simple, steady state and dynamic) using reverse design algorithm, is highlighted through a case study. Integrated Process Design and Control (IPDC) Problem

Stage 1: Pre-analysis Stage. Pre-analysis includes defining the design -control targets and identifiying the operating windows based on simple analysis within which feasible solutions related to design -control of the system would be located. Targets are identified by locating the maximum values of the AR /DF.

Stage 2: Steady-state Analysis. Validate the established design-control targets in stage 1 by finding/designing the acceptable values (candidates) of the design-control variables that match the target. Then candidates are analyzed using steady -state sensitivity analysis and from this, controller structure is selected . A steady-state economic analysis is also performed on the selected candidates and ranked according to their capital cost.

Stage 3: Dynamic Analysis. The selected candidates from Stage 2 are represented by their corresponding dynamic models. Their dynamic performances are analyzed using open-loop analysis . The remaining selected candidates are further refined and tested in closed-loop analysis and from this, a final set of candidates are identified.

Stage 4: Evaluation Stage. The best candidate in terms of closed -loop performance and economic is verified first through rigorous simulation (steady-state and/or dynamic) using process simulator .

Figure 1. Decomposition method for IPDC problems (Hamid and Gani, 2008)

2. Overview of Methodology For the most of the IPDC problems, the conventional way to find the solution is by using a forward solution approach. Due to obvious limitations in the use of this solution approach such as being computationally expensive and iterative in nature, a new reverse design approach is proposed. The reverse solution approach (reverse design algorithm) decomposes the IPDC problem into four stages, as shown in Figure 1 (Hamid and Gani, 2008). Accordingly, the problem is decomposed into four sequential hierarchical stages: (1) pre-analysis, (2) steady-state analysis, (3) dynamic analysis, and (4) evaluation stage. In most of IPDC problems, the feasible region can be very small compared to the search space due to the large number of constraints involved. All the feasible solutions may lie in a relatively small portion of the search space. The ability of the method to solve such problems depends on how quick one can identify and avoid the infeasible portion of the search space. By solving the pre-analysis sub-problem first, one reduces

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the search space to those satisfy some operating constraints. The search space is further reduced to satisfy the design (steady state) and control (dynamic) constraints in stage 2 and stage 3, respectively; until in the final stage only candidates that satisfy the economic constraints are evaluated. Therefore, while the problem complexity increases with every subsequent stage, the dimension and size of the problem is reduced. Within this model-based methodology, concepts from attainable region (AR) and driving force (DF) techniques are used, although differently than their original purpose, in order to assist in selection of the optimal design. The AR concept is used for dimensioning reaction units, while DF concept is applied for separation units in chemical systems. For the reactor design problem, the idea is to locate the maximum value of AR (as a target) for design feasibility, and from there the operating conditions in terms of residence time, temperature, volume, etc. are identified to match the target by using reverse design algorithm. The same idea is used to solve separator design problem using DF technique. According to Gani and Bek-Pedersen (2000), DF is a measure of the relative ease of separation. When DF is zero, no separation is possible. When DF is large, separation becomes easy. By employing this concept, one can determine optimal values of design variables for separation systems at the largest value of DF. For control problem, the value of the derivative of AR/DF with respect to manipulative variables will determine process sensitivity and flexibility as well as the controller structure selection. According to Russel et al. (2002), derivative of the constitutive variables (e.g. reaction rate) with respect to manipulative variables influences the process operation and controller structure selection. Basically, reaction rate is used to determine the value AR. If values of the derivative are small, the process sensitivity is low and process flexibility is high. Therefore, by using AR/DF technique to solve the design and control problem, insights can be gained in terms of controllability and resiliency, and IPDC problems can be solved in an integrated manner. This is demonstrated below.

3. Application The model-based methodology is generic in character and therefore can be applied at every level of chemical process design and analysis. The methodology covers chemical processes with reactor (R), separator (S) and/or reactor-separator-recycle (RSR) systems. A reaction (R) system has been selected to evaluate the capability of the new methodology. For S and RSR systems, the procedure would be exactly the same. In this case study, the IPDC problem of a single reactor for ethylene glycol (EG) production is presented. 3.1. Case Study: Reaction (R) System The objective is to determine the optimal design (with respect to controllability and economic) that gives the highest yield of the desired product at given feed flowrate and concentrations. The process reactions are given as:

EO +W ⎯ ⎯r → EG

(1)

EO + EG ⎯⎯→ DEG

(2)

1

r2

EO + DEG ⎯⎯→ TEG (3) In Eq. (1), ethylene oxide (EO) and water (W) react to produce ethylene glycol. Eqs. (2)-(3) are side reactions where the excess EO reacts with EG and DEG to produce diethylene glycol (DEG) and triethylene glycol (TEG), respectively. The reaction rates for the above reacting system are: r3

M.K.A. Hamid et al.

842

r1 = k1C EO CW , r2 = k 2C EO C EG , r3 = k 3C EO C DEG with kinetic parameters; k1 = 5.238exp30.163-10583/T [m3/kmol-h], k2 = 2.1k1and k3 = 2.2k1 are taken from Parker and Prados, 1964. 3.2. Stage 1: Pre-analysis Stage In this stage, the operational windows within which all feasible solutions related to design-control would be located are determined. The starting range for temperature is defined between the minimum melting point and maximum boiling point of components (161
dC EG R EG r1 − r2 = = dCW RW r1

(4)

Since CEG is the concentration that we wish to optimize and CW is the limiting reactant, a state-space (AR) diagram as shown in Figure 2(left) can be created showing the autonomous relation between CEG and CW. Then, the design-control target is selected at the maximum value of the AR (point A). It can easily be seen from Figure 2(left) that a maximum of 0.16671 kmol/m3 of CEG can be achieved using a CSTR with effluent of 0.59 kmol/m3 of CW.

Figure 2. Left: AR diagram for concentration of EG and W; Right: Corresponding derivatives of the AR with respect to W and Fc.

3.3. Stage 2: Steady-State Analysis In this stage, the search space defined in stage 1 is further reduced using steady state analysis. The established target (point A) is now validated by finding the feasible values (candidates) of the design-control variables (temperature, residence time, volume, etc.) that match the target. If feasible values cannot be obtained, a new target is selected and variables are recalculated until satisfactory matching is found. At point A, the allowable operating temperature is calculated using Eq. (5). (5) ¦ xiTi m < T ( K ) < ¦ xiTib i

i

where, xi is the mole fraction, and Ti m and Ti b are the melting and boiling point, respectively. The search space for temperature is now reduced to (251 x 406) from (161 x 562). With this range, the range of the residence time (0.017< τ (h)<108,199) and the

A New Model-Based Methodology for Simultaneous Design and Control

843

volume (11.78
·§ dCW ¸¸¨ ¹© dT

·§ dT ¸¨¨ ¹© dFc

· ¸¸ = 0 ¹

(6)

From Figure 2(right), value of dCEG/dFc of all candidates are zero, since they are at the maximum value of AR (point A). According to Russel et al. (2002), at the minimum value of derivatives, the process sensitivity is low and process flexibility is high. Therefore, by designing a reactor at the maximum value of AR leads to process with higher flexibility and lower sensitivity. Since, dCEG/dFc=0, it also indicates that composition of EG can be controlled by manipulating Fc. Table 1. Candidates of design-control variables for stage 2. Candidates CW (kmol/m3) CEG (kmol/m3) 1 2 3 4

0.59 0.59 0.59 0.59

0.16671 0.16671 0.16671 0.16671

T (K)

τr

(h)

V (m3)

Da

Fc (m3/h)

TAC ($)

406 402 398 394

0.0107 0.0143 0.0187 0.0244

11.78 15.76 20.53 26.89

3.48 3.48 3.48 3.48

1388.31 1388.22 1388.26 1388.34

53,300 59,700 67,000 83,700

3.4. Stage 3: Dynamic Analysis Here, the search space is further refined using dynamic analysis. Candidates from stage 2 are now represented by their corresponding dynamic models. Transfer function-based models are then developed for every candidates and from that, the controller tuning parameters are calculated. The closed loop performance are then analyzed and the results are shown in Figure 3 for all candidates. Since all candidates are designed at the maximum value of AR, the control cost (controller action to maintain its setpoint in the presence of disturbance) are the same. Therefore, in this case, only closed loop performances are considered. Candidate with the best closed loop performances and the lowest cost is verified through rigorous simulation using an appropriate simulator in the final stage. 3.5. Stage 4: Evaluation Stage As shown in Figure 3, candidate 1 shows the best closed loop performances (rise time, decay ratio, settling time) and also has the lowest cost (Table 1). Therefore, candidate 1 is the optimal design that gives the best cost and control performances.

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Figure 3. Closed loop dynamic analysis – response of CEG to its set point change.

4. Conclusion A new model-based methodology for IPDC of chemical processes has been successfully evaluated for the design of reaction system for the synthesis of ethylene glycol. The results demonstrates the potential use of the decomposition method in solving IPDC problems particularly its ability to reduce the huge dimension of the design space. It was confirmed that in each subsequent stage the search space for temperature and volume are reduced until in the final stage only a small number of the remaining feasible candidates are evaluated. As future perspective, this promising methodology will be further applied to solve IPDC problems for separation and reactor-separator-recycle systems

5. Acknowledgement The financial support from the Ministry of Higher Education (MoHE) of Malaysia and Universiti Teknologi Malaysia (UTM) is gratefully acknowledged.

References R. Gani, E. Bek-Pedersen (2000). A simple new algorithm for distillation column design. AIChE J., 46(6), 1271-1274. M. K. A. Hamid, R. Gani (2008). A model-based methodology for simultaneous process design and control for chemical processes. In Proceedings of the FOCAPO 2008, Massachusetts, USA, 205-208. A. A. Kiss, C. S. Bildea, A. C. Dimian (2007). Design and control of recycle systems by nonlinear analysis. Comput. Chem. Eng., 31, 601-611. M. L. Luyben, C. A. Floudas (1994). Analyzing the interaction of design and control – 2. ReactorSeparator-Recycle system. Comput. Chem. Eng. 18, 971-994. W. A. Parker, J. W. Prados (1964). Analog computer design of an ethylene glycol system. Chem. Eng. Prog., 60(6), 74-78. E. Ramirez, R. Gani (2007). Methodology for the design and analysis of reaction-separation systems with recycle. 1. The design perspective. Ind. Eng. Chem. Res., 46, 8066-8083. B. M. Russel, J. P. Henriksen, S. B. Jørgensen, R. Gani (2002). Integration of design and control through model analysis. Comput. Chem. Eng., 26, 213-225. P. Seferlis, J. Grievink (2001). Process design and control structure screening based on economic and static controllability criteria. Comput. Chem. Eng. 25, 177-188. P. Seferlis, M. C. Georgiadis (2004). The integration of process design and control. Amsterdam: Elsevier B. V.

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R. K. Sinnot (2005). Chemical Engineering Design, Volume 6, Elsevier, Butterworth-Heinemann, 4th. Ed.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Biodiesel by Reactive Absorption – Towards Green Technologies Anton A. Kiss AkzoNobel Research, Development & Innovation, Process & Product Technology, Arnhem, The Netherlands, [email protected]

Abstract This study takes previous work on separative reactors for biodiesel production to a new level by proposing a novel technology based on reactive absorption. This is a significant step forward as reactive absorption offers important advantages in addition to typical benefits of reactive distillation: reduced capital investment and operating costs due to the absence of the reboiler and condenser, and lower temperature profile in the column to avoid thermal degradation of the products. Computer aided process engineering tools such as AspenTech Aspen Plus are used for the process design and simulation of a plant producing 10 ktpy biodiesel from waste oil with high free fatty acids content. Keywords: reactive absorption, green catalysts, sustainable fuels

1. Introduction Biodiesel is an alternative fuel with similar propersties as petroleum diesel. Therefore, it can be used alone, or blended with conventional petrodiesel, in unmodified dieselengine vehicles. Tipically, biodiesel is produced from green sources such as vegetable oils, animal fat or even waste cooking-oil from the food industry.1,2 As a non-petroleum-based diesel fuel, biodiesel consists of short chain alkyl esters of fatty acids, currently produced by acid/base-catalyzed (trans-)esterification, followed by several neutralization and purification steps. Nevertheless, all the conventional methods suffer from problems associated with the use of homogeneous acid or base catalysts, leading to serious economical and environmental consequences, especially considering the recent growth of the overall biodiesel production scale. The increasing worldwide interest in biodiesel is illustrated by the exponential increase of the production, mostly in Western Europe, USA, and Asia (Figure 1). This study presents a novel biodiesel technology based on reactive absorption that offers significant advantages compared to conventional methods: simple and robust process, high conversion and selectivity, elimination of conventional catalyst-related operations, no thermal degradation of products, no waste streams, as well as reduced capital investment and operating costs. The process design proposed in this work is based on experimental results and rigorous simulations performed using AspenTech AspenONE Engineering Suite as computer aided process engineering tool.

A.A. Kiss

848 16000 14000 12000 10000 8000

Biodiesel consumption in EU, 2007 Biodiesel production per region (thousands tons / year)

Central & South America Central & Eastern Europe North America Asia Western Europe

Spain 5%

Others EU 13%

UK 5%

6000

Austria 6%

4000 2000

France 20%

0 2004

2005

2006

2007

2008

2009

Germany 51%

Figure 1. Biodiesel production per region (left), and biodiesel consumption in EU (right).

2. Problem statement There are three basic methods to produce fatty esters from oils/fats: 1) base catalyzed trans-esterification, 2) acid catalyzed esterification, and 3) enzymatic catalysis.1-3 The first method is the most frequently used. However, due to the escalating costs of fatty raw materials, the current trend is to use less expensive alternatives such as animal fat, waste cooking oil from catering premises, or waste vegetable oil (wvo). The problem with waste oils is the very high content of free fatty acids (FFA) that lead to soap formation in a conventional base catalyzed process. Therefore, in order to avoid production loss and soap associated problems, the FFA’s must be completely converted first to fatty esters by esterification. Moreover, the conventional biodiesel processes employ liquid catalysts, such as H2SO4, NaOH or methoxides.3 The problem is that homogeneous catalysts require neutralization, washing, separation, recovery, and waste disposal operations with severe economical and environmental penalties. To solve this problem we propose a novel fatty esterification process based on reactive absorption (RA) using solid acids as catalysts4,5 and therefore eliminating the additional separation steps and the salt waste streams, thus simplifying the downstream processing. Table 1 presents an overview of the available solid acid catalysts for biodiesel production.4-6 In this work we selected the metal oxides as acid catalysts, but the ionexchange resins are also suitable due to the moderate temperatures used in the process. Note that previous literature studies on separative reactors for biodiesel production are solely based on reactive distillation (RD).6-9 The novel RA technology proposed in this work offers additional advantages compared to RD, as for example lower temperature profile in the reactive separation column to avoid the thermal degradation of the fatty esters products. As a consequence the process becomes much simpler and more robust, meaning reduced capital investment and operating costs due to the absence of a reboiler (no product vapors return to the column) and condenser (no reflux of water by-product). Moreover, the integrated RA unit is able to shift the chemical equilibrium to completion by continuous removal of products instead of using an excess of reactant. This novel approach based on RA is particularly suitable for treating waste oil or animal fat, including tri-glycerides with up to 100% free fatty acids (FFA) – this is in fact the worst case scenario considered in the work described here.

Biodiesel by Reactive Absorption – Towards Green Technologies

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Table 1. Advantages and disadvantages of the acid catalysts tested for fatty acids esterification.

Catalyst type Ion-exchange resins (Nafion, Amberlyst) TPA (H3PW12O40) TPA-Cs (Cs2.5H0.5PW12O40) Zeolites (H-ZSM-5, Y and Beta) Sulfated metal oxides (zirconia, titania, tin oxide) Niobic oxide (Nb2O5)

Benefits Very high activity Easy regeneration Very high activity Super acid sites Controlable acidity and hydrophobicity High activity Thermally stable Water tolerant

Drawbacks Low thermal stability Possible leeching Soluble in water Low activity per weight Small pore size Low activity Deactivates in water, but not in organic phase Average activity

3. Simulation methods Based on the mixture of any particular starting oil/fat used in the biodiesel production process, there will be an associated blend of fatty acid esters in the final biodiesel product. Therefore, the simulation can be performed using one of the available simulation methods illustrated in Table 2: rigorous, shortcut or hybrid method. Note that each method has its key benefits but also specific drawbacks and the requirements can differ considerably. Although favored, the rigorous method is virtually not feasible in practice due to the amount of input data required. On the other hand, the shortcut method provides merely low-fidelity models with very limited practical applications. Therefore, for practical reasons, the hybrid approach gives the best results. Note that in the following simulations the experimentally determined kinetic parameters5,6 were used but the fatty components were lumped into one fatty acid/ester compound, according to the following chemical reaction: R-COOH + CH3OH ↔ R-COO-CH3 + H2O

Drawbacks

Benefits

Requirements

Table 2. Simulation methods for biodiesel production: requirements, benefits and drawbacks.

Rigorous method

Shortcut method

Hybrid method

Properties for all species. VLL data and BIP’s for all pairs of components. Kinetic parameters for all reactions possible.

Properties for single fatty acid/ester/tri-glyceride. VLL data for the system ester/glycerol/alcohol. Asumed conversion (no kinetic parameters). Simple model. Fast simulations. Easy-to-build mass and energy balance. No data needed for all species present. No comparison possible for various feedstocks. Low-fidelity model. Less ability to use RTO.

Single or reduced list of fatty acid/ester/TG. Short list of VLL data and BIP’s for components. Reduced list of kinetic parameters, few reactions. Optimization possible for reaction and separation. Certain ability to compare various feedstocks. Better model fidelity. Fast simulations for RTO. More effort to build component list and get kinetic parameters. More work to find VLL data and regress BIP’s.

Easy optimization of reaction and separation. High fidelity model. Usable for many plants. Easy comparison for various feedstocks. Slow simulations and convergence problems. Expensive measurements. Limited RTO and model based control usage.

A.A. Kiss

850

4. Results and discussion The physical properties of the components present in this process were determined experimentally,5-7 or estimated using state-of-the-art contribution methods such as UNIFAC – Dortmund modified. Vapor pressure is one of the most important properties with a critical effect in modeling reactive separations. At ambient pressure the boiling points of fatty esters are relatively high (over 300 °C). High purity products are possible in a RD setup, but the high temperature in the reboiler – caused by the high boiling points, is in conflict with the thermo-stability of the biodiesel product. This problem can be avoided by working at lower pressure or allowing methanol in the bottom product.5-7 By using reactive adsorption, the drawbacks of reactive distillation can be completely avoided and biodiesel can be produced at moderate temperatures and ambient pressure. Moreover, the water by-product is not refluxed in the RA column hence the detrimental effect of water on the equilibrium reaction and the catalyst is completely avoided. Figure 2 presents the flowsheet of a biodiesel production process based on a reactive absorption column (RAC) as the key unit. The process was rigorously simulated and optimized using AspenTech AspenONE. The production rate considered for the biodiesel plant designed in this work is 10 ktpy fatty esters. Note that the kinetic parameters used in the simulations were previosly reported in the open literature.5,6 The RAC is operated in the temperature range of 135–160 °C, at ambient pressure. Out of the 15 stages of the integrated unit, the reactive zone is located in the middle of the column (10 stages). The fatty acid is pre-heated then fed as hot liquid in the top of the column while a stoichiometric amount of alcohol is injected as vapor into the bottom of the column, thus creating a counter-current flow regime over the middle reactive zone. Water by-product is removed as top vapor, then condensed and separated in a decanter from which only the fatty acids are recycled back to the column while water can be reused. The fatty esters are delivered as high-purity bottom product of the RAC. The hot product is flashed first to remove the remaining methanol, then it is cooled down and stored. Further heat-integration is possible but this is beyond the scope of this study. HEX3

HEX1

TOP-LQ TOP F-ACID

ACID

DEC

REC-TOP RAC

COMP

WATER

REC-BTM FAME ALCO HEX2

F-ALCO

BTM

FLASH

COOLER

Figure 2. Flowsheet of biodiesel production by catalytic reactive absorption.

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Table 3. Mass balance of a 10 ktpa biodiesel production process based on reactive-absorption. F-ACID

F-ALCO

Temperature C 160 Pressure bar 1.05 Vapor Frac 0 Mass Flow kg/hr 1166.755 Volume Flow cum/hr 1.492 Enthalpy Gcal/hr -0.94 Mass Flow kg/hr METHANOL 0 ACID 1166.755 WATER 0 ESTER-M 0 Mass Frac METHANOL 0 ACID 1 WATER 0 ESTER-M 0

BTM REC-BTM REC-TOP

65.4 136.2 1.05 1.03 1 0 188.306 1261.295 157.565 1.417 -0.279 -0.904

TOP

WATER

FAME 30 0.203 0 1250 1.259 -0.957

246.2 1.216 1 11.295 8.949 -0.013

51.8 1 0 9.369 0.011 -0.009

162.1 1 1 114.43 213.042 -0.337

51.8 1 0 105.061 0.109 -0.395

0.127 1.573 0.017 0.112 104.917 0 0 1248.315

188.306 0 0 0

9.083 0.112 0 1252.1

7.51 0 0 3.785

0.002 9.13 0.237 0

0.129 9.147 105.154 0

1 0 0 0

0.007 0 0 0.993

0.665 0 0 0.335

0 0.974 0.025 0

0.001 0.08 0.919 0

0.001 0 0.999 0

0.001 0 0 0.999

The mass and energy balance is given in Table 3. High purity products are possible, the purity specifications exceeding 99.9%wt for the final biodiesel product (FAME stream). Water by-product is also recovered at high purity, hence this stream could be reused as industrial water on the same site. The energy usage is less than 135 kW/ton biodiesel. Note also that the total amount of the recycle streams (REC-TOP and REC-BTM) is not significant, representing only ~1.5% of the total biodiesel production rate. Figure 3 shows the molar composition profiles in both liquid and vapor phase. The concentration of fatty acid and water increases from the bottom to the top of the column, while the concentration of fatty ester and methanol increases from the top to bottom. Therefore, in the top of the reactive absorption column there are vapors of water and liquid fatty acids, while in the bottom there are vapors of the methanol feed and liquid fatty esters product (biodiesel). Figure 4 shows the temperature and reaction rate profiles in RAC, as well as the mass flowrates along the column. The temperature difference between the top section and the bottom part of the RA column is relatively low (~30 °C) compared to a RD column. However, the reaction rate profile is similar to the one in a RD column, exhibiting a maximum in the middle and thus keeping the best of both reactive-separation designs. 1

Molar fraction (vap)

Molar fraction (liq)

1 0.8 Methanol Acid Ester Water

0.6 0.4 0.2 0

0.8 Methanol Acid Ester Water

0.6 0.4 0.2 0

0

3

6

9

Stage

12

15

0

3

6

9

12

Stage

Figure 3. Profiles in RAC: liquid composition (left), vapor composition (right).

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852 170

160

2.5 2

150 1.5 1

140

0.5

130

0

0

3

6

9

Stage

12

15

Mass flowrate / kg/hr

3

Ester formation / kmol/hr

Temperature / °C

1400

3.5 Temperature Reaction rate

1200 1000 800 Liquid Vapor

600 400 200 0 0

3

6

9

12

15

Stage

Figure 4. Temperature and reaction rate profiles (left), mass flowrates profiles in RAC (right).

5. Conclusions This study uses computer aided engineering tools such as AspenTech Aspen Plus for the development of an innovative biodiesel process based on reactive absorption. This novel process radically improves the biodiesel production and dramatically reduces the number of downstream processing steps. The key benefits of this unique process are: 1. Simple and robust process with no catalyst-related waste salt streams, no soap formation, and sulfur-free biodiesel as solid catalysts do not leach into the product. 2. Elimination of conventional catalyst-related operations such as: handling of toxic chemicals and corrosive solutions, catalyst neutralization, separation and disposal of waste salts, waste water treatment, recovery and recycling of excess alcohol. 3. Reduced equipment costs, with up to ~60% savings on the total capital investment. 4. Low operating costs due to the integrated design with no reboiler or condenser. 5. Effective use of the reactor volume leading to significantly high unit productivity. 6. Efficient use of raw materials: no thermal degradation, down to stoichiometric reactants ratio, high conversion as equilibrium is shifted towards completion. 7. Multifunctional plant suitable for a large range of alcohols and fatty raw materials with very high FFA content, such as frying oils, animal tallow, waste vegetable oil.

References [1] [2] [3] [4] [5] [6] [7] [8] [9]

M. Balat, H. Balata, 2008, Energy Conversion and Management, 49, 2727. M.G. Kulkarni, A. K. Dalai, 2006, Industrial & Engineering Chemistry Research, 45, 2901. K. Narasimharao, A. Lee, K. Wilson, 2007, J. Biobased Materials & Bioenergy, 1, 19. T. Okuhara, 2002, Chemical Reviews, 102, 3641. A. A. Kiss, A. C. Dimian, G. Rothenberg, 2006, Advanced Synthesis & Catalysis, 348, 75. A. A. Kiss, G. Rothenberg, A. C. Dimian, F. Omota, 2006, Topics in Catalysis, 40, 141. A. A. Kiss, A. C. Dimian, G. Rothenberg, 2008, Energy & Fuels, 22, 598. S. Steinigeweg, J. Gmehling, 2003, Ind. Eng. Chem. Res., 42, 3612. A. C. Dimian, F. Omota, A. Bliek, 2004, Chem. Eng. & Proc., 43, 411.

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Distributed wastewater treatment network design with detailed models of processes Iryna Dzhygyrey,a Jacek Jezowski,b Olexander Kvitka,a Gennadiy Statyukhaa a

National Technical University of Ukraine, Department of Cybernetics of Chemical Technology Processes, Peremogy av. 37, 03056 Kyiv, Ukraine, [email protected] b Rzeszow University of Technology, Department of Chemical and Process Engineering, al. PowstaĔców Warszawy 6, 35-959 Rzeszów, Poland, [email protected]

Abstract This paper addresses design of wastewater treatment network by a sequential approach with mathematical models of treatment processes. This is a method applying insightbased techniques in first stage, namely water pinch analysis and wastewater degradation concept, followed by mathematical programming. The design approach can be used for synthesis and also for retrofit of wastewater treatment networks. Application of mathematical models of treatment processes allows taking into account relation between removal ratio of treatment process and treatment flow rate as well as concentration of certain contaminants. The approach was used for solving problems of designing and retrofitting wastewater treatment systems of various industrial plants. Keywords: wastewater treatment, network, design, optimization, model

1. Introduction An application of a distributed wastewater treatment networks (WWTNs) is a key way for reducing cost of treatment stations. The investment expenses and treatment plant's operating costs depend on a proper choice of system structure and parameters of wastewater streams treated in various processes. This paper presents design of WWTN by the approach that allows using detailed mathematical models of treatment processes. The basis of the method was developed in Statyukha et al. (2008a). This is sequential method applying insight-based techniques followed by mathematical programming. First, wastewater pinch analysis and wastewater degradation concept from Wang and Smith (1994), Kuo and Smith (1997) are employed to develop an initial structure. The solution from the first step is the good starting point for nonlinear optimization. Nonlinear programming (NLP) problem is formulated on the basis of WWTN superstructure. The design approach can be used for synthesis as well as for retrofit of wastewater treatment networks. It should be noted that in some cases obtaining removal ratios of treatment processes for treatment flow rate and contaminants concentration of streams is difficult from different reasons, for instance due to difficulties with measurements at operating industrial plant for retrofit case. Hence, the approximate models applied in many existing methods that use only removal ratio valid for current operating conditions can lead to incorrect results. To circumvent the problem more rigorous mathematical models of treatment processes have been applied in this work. The models account for influence of flow rate and contaminant concentration on removal ratio. Other key design parameters such as

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geometry of apparatus are included, too. The importance of applying detailed models of treatment processes is illustrated by several industrial case studies.

2. Overview of WWTN Design Method As we have mentioned above the use of approximate models of treatment processes can result in wrong solutions. The existing approaches to WWTN focus mainly on topology issues and use simple (or better to say simplistic) design models of processes reduced to fixed outlet concentration or, more often, to given removal ratio for contaminants. Hence, the change of WWTN parameters due to optimization does not influence the performance of the wastewater treatment. Additionally, important design parameters are not taken into account. However, it is also necessary to note that the models that are to be solved are nonlinear. Superstructure model is of NLP or MINLP type even for the simplistic model of processes. Hence, to make the overall problem solvable with available general purpose optimization solvers one has to apply relatively simple design equations for complex wastewater treatment processes. Such “compromise” models are applied in this approach. The overall solution approach consists of two stages: initial solution calculation and final design (see also Statyukha et al. (2008a) for more details). The first stage is based on insight-based techniques from Wang and Smith (1994), Kuo and Smith (1997) with exergy losses minimization as the objective. Hence, the parameters, such as flow rates or split fractions in splitters attached to treatment processes should be adjusted so as to minimize total cost of WWTN in the second stage. However, structural changes are possible, too. The overall procedure is designer driven. To account for structure optimization one can apply various types of superstructures: general superstructure or specific one based on the network from the first stage and conditions of the plant. Hence, the approach is easily adapted for retrofitting wastewater treatment facilities. Mathematical optimization is applied in the second stage, i.e. the solution of NLP problem. Overall goal function is the sum of capital and operating wastewater treatment cost and piping cost. It is important to note that the detailed models of treatment apparatus are used at this stage while fixed split ratios are employed in the first stage. Mathematical models of treatment processes are applied at the optimization stage to take into account a relation of the removal ratios of a process vs. treatment flow rate and concentration of certain contaminants. They have a general form shown below.

r k = f (Qink , Cink , ξ k )

(1)

k The parameters denote: r k – contaminant removal ratio in k-th treatment process; Qin – k inlet flow rate to k-th treatment process; Cin – inlet contaminant concentration to k-th

treatment process; ξ – set of design parameters for k-th treatment process. The specific form of the model depends on treatment process. It is also important that application of more rigorous model allows considering material losses and gains in a particular treatment process and, in result, changes of total flow rate in WWTN within design procedure. Because the total flow rate influences largely the cost the use of rigorous model allows achieving realistic results. If some design parameters are fixed, as it is the case for retrofit scenario, then, only removal ratios are new variables. Wastewater treatment facilities in plants built some years ago in east and central Europe (Ukraine and Poland to mention a few countries) have been designed according to wellestablished designing procedures (e.g. construction codes and regulations in SNiP, 1985). Equations, relationships, tabular and graphical data allow designing particular k

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treatment unit with engineering accuracy of calculation for given conditions of a total plant. In this work these procedures have been re-organized into simulation ones in order to obtain relations for determining removal ratios of contaminants in dependence of flow rate, contaminant concentrations and other process specific parameters such as those defined by eq. (1). The steady-state models allow considering not only removal ratio changes but also to reckon specific parameters of treatment process in, e.g. water loss in the network with sediment from settler, with froth from flotation, additional constraints for the inlets to the units etc. The application of mathematical models of treatment processes for WWTN design allows taking into consideration specific features of treatment methods. Changes in flow rate can result in shift of settling conditions or violation of boundary rate of filtration etc. Additionally, the application of models allows making recommendations on adjustment of process parameters that need no major constructional modifications of treatment unit, e.g. treatment cycle time. Due to space limitations we will not present detailed models. The reader is referred to the construction code (SNiP, 1985) and papers by Statyukha et al. (2006a), Statyukha et al. (2006b), Kvitka et al. (2007), Statyukha et al. (2007) and Statyukha et al. (2008b). The applications of the approach are described in the next section. The focus is on showing the changes of operating conditions in comparison with those calculated with the use of fixed removal ratio from the data.

3. Industrial case studies 3.1. Case Study 1 - The Cardboard and Paper Mill Plant There are three main wastewater streams: from stock preparation department, from cardboard, paper, printing and goffer departments and society's wastewater. It is necessary to design the distributed treatment system on a basis of already existing one retaining the arrangement of treatment units. Two treatment processes are in use: mechanical cleaning (TPI – settler) and biological treatment (TPII – aeration tank). The flow rates of streams and the concentrations of contaminants are given in Table 1 and the initial removal ratios – in Table 2. Wastewater pinch analysis in the 1st step shows that it is possible to reduce treatment flow rate only in TPII by 19 t/h. Then if superstructure optimization is used with the removal ratios from the data the following treatment flow rates can be obtained: 322.6 t/h for TPI and 388.3 t/h for TPII. Mathematical models of primary settler and bioaeration tank were used at the optimization stage. Table 1. Wastewater stream data for the cardboard and paper mill case study

Stream number 1 2 3

Flow rate (t/h)

Contaminant concentration (ppm) COD BOD Suspended solids 400 2000 600 250 1200 200 150 500 50

245 112 50

Minerals 350 200 50

Table 2. Treatment process data for the cardboard and paper mill case study

Treatment processes

Removal ratios (%) COD

BOD

Suspended solids

Minerals

TPI TPII

25 70

40 80

50 85

70 50

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We will show here the latter to some extent. Removal ratio (eq. 2) of the aerotank is complex function of following parameters: input treatment flow rate Qin , m3/h; inlet BOD concentration Cin , mg/l; aerotank capacity V A , m3; regenerators capacity V R , m3; dissolved oxygen concentration CO , mg/l; oxygen effect’ coefficient K O , O2l; organic contaminants properties’ coefficient K L , mgBOD/l; activated sludge recycle rate Ri ; maximum oxidation rate ρ max , mgBOD/(gÂh); sludge dose ai , g/l; ash value of sludge s; decay product inhibition’ coefficient ϕ , l/g.

r = f (Qin , Cin ,V A ,VR , CO , K O , K L , Ri , ρ max , ai , s, ϕ )

(2)

Additionally, aeration period, oxidation period and other process parameters can be obtained from full mathematical model (Statyukha et al., 2006a). Application of the models allowed obtaining new values of removal ratios of suspended solids in TPI and BOD in TPII. Removal ratio of suspended solids changes only slightly. Aerotank removal ratio of BOD has been increased up to 85% (from 80% in the data) due to changes of both treatment flow rate and BOD concentration.

Fig. 1. Final design for the cardboard and paper mill case study In the result TPI treatment flow rate is 322.4 t/h including flow rate losses with sediment equal to 1.4 t/h. TPII treatment flow rate is 386.8 t/h. These values were obtained due to the application of more rigorous treatment units’ models. The optimal network is shown in Figure 1. 3.2. Case Study 2 - Wastewater Treatment Scheme of the Electroplating Shop Wash acid-base wastewater, chrome wastewater (after electro coagulation), cyan wastewater (after catalytic oxidation) are fed into the ion exchange unit. Wastewater mix undergoes sedimentation in vertical or thin-layer settler for precipitation of difficult-to-dissolve compounds, which are generated through interaction of components when mixing of the streams. The ion exchange unit consists of wastewater balancing reservoir, settler, two mechanical filters, two sorption filters, H-cation filters, anion filters, preparation block of regenerating solution, reservoirs for collection of desalted water, eluates after ion exchangers regeneration and wash water, eluates’ processing block. Wastewaters are fed to collector after balancing and precipitation of coarsedisperse impurities and, after that, to mechanical sorption, H-cation and anion filters by pump. Desalted water is fed to collecting reservoir and returns to users. Mathematical models of settler, mechanical filter, sorption filtration unit and ion exchanger (Statyukha et al., 2008b) were used at the optimisation stage. The calculations showed that 15% of H-cation and anion filters inlet flow rate can be bypassed after

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sorption filters before the last collector as shown on Fig. 2. Due to the flow rate decrease the removal ratio of cations in H-cation filter changes from 84% to 97% and that of anions in anion filter increases from 77% to 90%. This also leads to outlet contaminants concentration reduction. The reader is referred to (Statyukha et al., 2008b) for details.

Fig. 2. Ion exchange unit retrofitting 3.3. Case Study 3 - Meatpacking Plant Wastewater of the meatpacking plant belongs to dangerous sewage because of a high content of organic contaminants. This case study addresses the problem of retrofitting the centralized treatment facility of this plant. Four treatment processes are in disposal: settling, pneumoflotation, electrocoagulation and biofiltration. The solution from the 1st stage allows the reduction of total treatment flow rate to 1315.8 t/h from 1560.4 t/h in the existing facility. Then mathematical models of primary settler, pneumatic flotation unit, electrocoagulator and biological aerated filter (Statyukha et al., 2006b) were used at the optimization stage. Due to decision of plant management the structure from the 1st stage was kept intact. The solution from the 2nd stage has the total treatment flow rate of 1300.1 t/h. The changes of removal ratio are noticeable. The removal ratio of suspended solids was calculated by the model of continuous-operated settler and amounts to 50% against initial 35% in the data. The application of biofilter model gives BOD5 removal ratio change from 90% in the data to final value of 92%.

4. Summary and conclusions The sequential approach for designing optimal WWTN has been applied to retrofit wastewater treatment systems of industrial plants. The investigations have shown that significant reduction of the wastewater treatment flow rate could be achieved for different treatment processes over existing wastewater treatment systems by effluent streams redistribution. The application of mathematical models of treatment processes allows taking into account changes of treatment process removal ratios and flow rates within design procedure. It enables to find contaminant losses and gains in particular treatment process and as the result to determine changes of WWTN total flow rate within design procedure.

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References W.-C.J. Kuo and R. Smith, 1997, Effluent treatment system design, Chemical Engineering Science, Vol. 52, Iss. 23, pp. 4273-4290. O. Kvitka, I. Dzhygyrey, J. JeĪowski, 2007, Optimal Design of Wastewater Treatment Network for Glass Container Plant, Chemical Engineering Transactions, Vol. 12, pp. 327-332. SNiP, 1985, Construction Codes and Regulations 2.04.03-85: Sewage. External systems and structures, 72 p. G. Statyukha, A. Kvitka, T. Boyko and I. Dzhigirey, 2006a, The use of mathematical models of wastewater purification processes in designing distributed treatment systems, Journal of Water Chemistry and Technology c/c of Khimiia i Tekhnologiia Vody, Vol. 28, part 6, pp. 6-10. G. Statyukha, O. Kvitka, J. Jezowski and I. Dzhygyrey, 2006b, An Application of Mathematical Models of Treatment Processes for the Design of Distributed Wastewater Treatment Networks, 33rd International Conference of Slovak Society of Chemical Engineering, Slovakia, May 22-26, Po-We-5, 012p.pdf. G. Statyukha, O. Kvitka, I. Dzhygyrey and J. JeĪowski, 2007, Optimal Design of Wastewater Treatment Network – Case Study of Synthetic Organic Dye Manufacturing Plant, Chemical and Process Engineering, Vol. 28, pp. 505-514. G. Statyukha, O. Kvitka, I. Dzhygyrey and J. Jezowski, 2008a, A simple sequential approach for designing industrial wastewater treatment networks, Journal of Cleaner Production, Vol. 16, Iss. 2, pp. 215-224. G. Statyukha, O. Kvitka and I. Dzhygyrey, 2008b, An Application of Ion Exchanger Model for the Electroplating Shop Wastewater Treatment Network Retrofitting, 35th International Conference of Slovak Society of Chemical Engineering, Slovakia, May 26-30, P-90.pdf. Y.-P. Wang and R. Smith, 1994, Design of distributed effluent treatment systems, Chemical Engineering Science, Vol. 49, Iss. 18, pp. 3127-3145.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Dynamic simulation of Chemical Engineering systems using OpenModelica and CAPE-OPEN Carl Sandrocka and Philip L. de Vaalb a b

University of Pretoria, Pretoria, 0171, South Africa, [email protected] University of Pretoria, Pretoria, 0171, South Africa, [email protected]

Abstract Modelica has emerged as a strong contender in the arena of dynamic simulation languages. It was developed to be a standard, with an open specification and a large and usable standard library. OpenModelica is an Open Source implementation of a Modelica compiler and environment which is being developed actively. Modelica’s object-oriented design makes it easy to develop chemical engineering unit operations and connect them to one another. Unfortunately, most proprietary databases of thermodynamic and physical properties and reaction data are not supplied in equation form, but rather as part of closed software. This means that such data must be exchanged with the programs that contain them if they are to be used in custom simulation codes. The CAPE-OPEN specification provides a standard architecture for these exchanges, in addition to support for incorporating new unit operations or algorithms into existing proprietary simulations. In this study, a Modelica library allowing interface between Modelica and CAPE-OPEN is developed. Its functionality is demonstrated using a model of a ten plate distillation column simulated in OpenModelica on a Linux machine, with thermodynamic and property data from Honeywell Unisim on a Windows machine. The data interfacing was done over a TCP/IP network using CORBA. It is found that real-time operation is possible, but that network overhead makes up a significant fraction of the running time, posing problems for faster-than-realtime off-line simulation and optimization. Keywords: Simulation, modelica 1. Introduction Flowsheeting has assumed a central position in modern process engineering practice. Diagrams describing the flow of material and energy through a plant are the main mode of communicating process design and several packages exist that solve the associated equations. Steady state flowsheeting is accepted in industry to such an extent that it is unlikely that a chemical plant of any size is designed without the use of at least one such tool. [3] Market penetration of dynamic simulation is lagging behind that of steady state simulations, partly due to the computational requirements associated with such simulation and partly due to the considerable additional effort involved in developing dynamic simulations. However, interest has increased in the development of dynamic plant simulations. In addition to dedicated process engineering tools like Aspen, ChemCAD, HYSYS/Unisim (Honeywell’s Unisim software is based on HYSYS), ProSim and SimSci,

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several modelling languages have emerged in the last 15 years that aim to provide an environment for modelling dynamic processes. Ascend and gPROMS are two examples of this approach. On another front, modelling systems have been developed for multi-discipline simulation. Modelica was specifically designed as a standard for such simulation, incorporating aspects from other languages[2, 4]. Modelica is a language, but is supported by graphical tools like Dymola, which allows a blend of graphical model-building and traditional programming. The OpenModelica project provides an Open Source implementation of a Modelica compiler and environment, allowing researchers in the field of simulation to access and tinker with the underlying simulation code instead of only working on models. This allows flexibility beyond that afforded by commercial simulation packages which are primarily focused on providing a stable environment for simulation of new processes rather than new simulation approaches for existing processes. The proprietary system gPROMS already has CAPE-OPEN support, and adding support for some CAPE-OPEN interfaces to OpenModelica may speed adoption of this open standard in the Process Engineering field. Simulation of a distillation column has been done before in Modelica [1]. However, the modelling strategy followed here is more modular, and abstracts the thermodynamics to the streams, allowing easy interfacing with an external thermodynamics package. 2. CAPE-OPEN interface CAPE-OPEN is a specification published and maintained by the CAPE-OPEN Laboratories Network (CO-LaN). CAPE-OPEN aims to provide application-neutral documentation of interfaces for CAPE tools and has been incorporated with varying levels of success in many commercial applications. There are two popular patterns for the use of CAPE-OPEN when developing custom simulation codes. The first is to make use of the Unit Operation support to embed a unit operation into an existing flowsheeting package, which then handles the simulation calculations. The second is to use a stand-alone modelling environment, but to interface with various packages for information like thermodynamic properties, equilibrium and/reaction kinetics. It was decided to abstract the property and equilibrium calculations into a class (SimulationStream) which is specified as a connector type for the column components. The SimulationStream objects that are instantiated when the components are simulated communicate with a host using the ICapeThermoPropertyPackage methods CalcProp and CalcEquilibrium. The interfacing is done using CORBA. Mico CORBA was used on the client (Linux) machine, accessed using the support for external C routines in OpenModelica. On the host (Windows) machine, the Unisim CORBA Server was used to interface with Unisim. Figure 1 shows the data flow conceptually. It should be noted that, although this implementation has used CORBA due to the lack of support of COM on the Linux platform, CO-LaN supplies a COM-to-CORBA bridge as part of the CAPE-OPEN effort, so using CORBA is not a significant problem.

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Linux/Mac Machine TCP/IP Network

Property package ICAPEThermoPropertyPackage

OpenModelica SimulationStream

ORB

ORB

Figure 1: Simulation data flow for multiple computers

3. Column model The distillation column modelled is a lab-scale glass distillation column fitted with a water-cooled total condenser and a steam thermosyphon boiler. It separates a mixture of ethanol and water. The Modelica components developed for modelling the distillation column are shown schematically in Figure 2

Vin

Win

Condenser

Lout

Vout

Wout

Plate

F

Vin

Vout

Lin

Q

Sin

Lout

Boiler

Sout

Lin

Figure 2: Distillation column components

A single generic plate model was developed that allows for a material and energy stream (both of which could be incoming or outgoing, labelled F and Q in the diagram) in addition to the normal vapour and liquid arrangement (two vapour streams and two liquid streams). This allows multiple feed columns to be modelled easily, even when the feeds are intermittend during the simulation. It also allows for energy losses or additions. The physical column that was modelled exhibits significant heat losses. The plate model assumes negligible vapour dynamics, with per-component hold-up on the liquid side. The pressure drop between the input and output vapour streams is estimated using the height of liquid on the plate. The Wilson thermodynamic model was used as it accurately describes the ethanol-water equilibrium. The material streams these components are specified as SimulationStreams, allowing the material properties and equilibrium to be calculated by the external thermo host.

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4. Results 4.1. Simulation accuracy To verify the accuracy of the model, it was run simultaneously with the column. Figure 3 shows the results of a sample run during which the feed flow rate was varied. The distillate drum level and the top plate (plate 1) temperature are shown to illustrate the behaviour of the column and the model.

Figure 3: Results of simulation compared to measurements. Solid lines are experimental results, dashed lines are model results.

It should be noted that the model does not accurately reflect the variation in the reflux drum, probably due to a mismatch between the controller parameters in the model and on the column. Further investigation into fitting model parameters should be done. However, the overall trends are similar, which is sufficient for this work. 4.2. Performance profiling Real-time operation of the column model proved difficult, and in order to speed up the simulation, profiling of the components making up the simulation was done. It was found that the simulation itself could achieve several times real time when simple equilibrium from tables and constant material properties were used instead of the external thermodynamic package. As an example, simulating the run shown in Figure 3 takes 30 minutes with simple thermodynamics and 4 hours using the external interface. Both the client and the host computers are Pentium 4 Machines with 1GiB of ram. The high sampling rate of the data (which is sampled at 1 second intervals) may force the integration engine to generate a time point each second, accounting for some of the

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computational effort. However, due to the large difference in running the simulation with and without the external interface, it was surmised that the integration routines of OpenModelica (which uses the DASSL routine from netlib) are not entirely to blame. In order to better understand the problem, the time spent in handling the network requests was logged. This is all the time spent blocked on the network request. The results are shown in Figure 4. Taking into account that a 30 minute simulation of about 20000 time

Figure 4: Networking overhead for intensive simulation

steps translates to 90 ms per time step and 4 hours 720 ms per time step, it can be seen that the network-blocked part takes about 40% of the simulation time in most cases, but can take the entire allocated time in some cases. The network overhead is therefore significant, even though not all of the performance issues can be attributed solely to the network layer. One other possibility that is being pursued is that the compilation of the model files when external routines are being used is not optimal. A possible explanation for this is that there are SimulationStream instances which all communicate with the server. This adds a large overhead due to multiple connections being maintained and property traffic being transmitted simultaneously. Currently, work is underway to develop a data broker that will structure the requests to the ORB in a more efficient way. The possibility of caching some of the data is also being investigated. Another explanation is that the external module does not supply derivative information when it is being evaluated, forcing the integration routines to resort to finite differences when estimating the derivatives of these units while solving the equations. Attempts are also being made to enable derivative information to be handled by the interface. 5. Conclusion A dynamic distillation column model has been developed using the Modelica language. The model utilises the object-oriented nature of Modelica by using generic models for the different distillation column parts. Together with the column model, a stream class has been developed that can use the external interface of OpenModelica to access thermodynamic information via CAPE-OPEN using CORBA. This enables thermodynamic properties to be calculated by any CAPE-OPEN compliant property package.

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Initial results look promising, but the network overhead poses a substantial barrier on running time. These effects are thought to be implementation problems and are being investigated on multiple fronts. References [1] N. Duro and F. Morilla. A modelling methodology for distillation columns using dymola and simulink. In M. H. Hamza, editor, Applied Simulation and Modelling, 2003. [2] Hilding Elmqvist and Dynasim Ab. An introduction to the physical modeling language modelica. In Proc. 9th European Simulation Sympossium ESS97, SCS Int, pages 110–114, 1997. [3] David A. Glasscock and John C. Hale. Process simulation. the art and science of modeling. Chemical Engineering, 101(11):82–89, November 1994. [4] Michael Tiller. Introduction to Physical Modeling with Modelica. Springer, Tiller, Michael.

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Integration of superstructure-based optimization and semantic models for the synthesis of reactor networks Claudia Labrador-Darder,a Franjo Cecelja,a Antonis C. Kokossis, a Patrick Linkeb a

Center for Process & Information Systems Engineering, University of Surrey, Guildford, Surrey, GU2 7XH, U.K. b Department of Chemical Engineering, Texas A&M University at Qatar, Education City, PO Box 23078, Doha, Qatar.Email [email protected]

Abstract The paper presents a novel framework for the optimisation and synthesis of complex reactor networks that combines superstructure-based optimisation, semantic models and analytical tools. The work addresses the representation and extraction of process synthesis knowledge during the optimisation process with the purpose to simplify and interpret design results. The simplification is achieved with a gradual evolution of the superstructure and corresponding adjustments of the optimisation search. The interpretation is accomplished with the use of analytical tools to translate data into descriptive terms understood by users. Means of analysis include dynamic ontologies populated by computer experiments and continuously upgraded in the course of optimisation. Keywords: Optimisation, ontology, superstructure, reactor networks

1. Introduction The paper presents a novel framework for the synthesis of chemical reactor networks that combines superstructure optimization [1-4], semantic models and analytical tools to address complex reactor design problems. The work is presented against stochastic optimisation techniques and addresses the representation and extraction of process synthesis knowledge during the optimisation process. The approach systematically extracts information with the purpose to simplify and interpret design results to enable monitoring the search. This paper outlines the components of the synthesis framework with emphasis on the knowledge representation and extraction aspects of the method. The approach is illustrated with an isothermal homogeneous reaction system example from the literature.

2. Synthesis Approach The approach is based on the gradual accumulation of design knowledge and its deployment in the course of synthesis experiments. The method attains knowledge to reduce the synthesis structure with the use of an ontology employed in parallel to the optimisation search. The latter takes the form of a gradual process, the initial stage of which is an exhaustive superstructure. The superstructure is optimised and updated at different stages. The transition from one stage to another represents different layers of abstraction. Each stage is assigned a knowledge model populated by features obtained

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from the optimisation solutions that captures the information of the superstructure. At the highest (initial) level, the method employs the largest superstructure and a general knowledge model where all feasible options are embedded. In the course of optimisation, the superstructure becomes leaner whereas the knowledge model becomes richer and is populated with solution features and relationships. The proposed synthesis strategy is illustrated in Figure 1 and is presented for the synthesis of reactor network but is not restricted to any particular type of application. Different stages correspond to different superstructure optimisation exercises. Each stage links with the ontology through the development of digital certificates. Digital certificates update the ontology, which is, in turn, used to update the synthesis model. 2.1. Superstructure representation and optimisation The reactor network superstructure representation employed in this work follows [4]. The superstructure is optimised using stochastic methods in the form of Tabu Search [5] following the implementation by [6]. 2.2. Knowledge representation The knowledge representation takes the form of a formal ontology for the domain of reactor networks that represents the design information captured by the superstructure representation employed in the optimisation. With such structured representation, the interpretation of the solution can be possible and thus monitoring the search is enabled. Ontologies [7] allow knowledge to be captured and made available to both machines and humans. By the use of an ontology, data related to reactor design solutions can be translated into descriptive terms understood by users. The design features define the concepts of the ontology. Concepts relate directly to the structural and operational components of the superstructure and include: number of reactive zones, mixing per reactive zone, feeding, connections in terms of recycles and bypasses (which are classified as intra- and interconnections), product source (structural components) and size and temperature profile along the network (operational components). They represent direct links with the optimisation stage and are populated by the solutions of a particular stage. Relationships between concepts are described in terms of taxonomic and associative relationships. Knowledge is extracted from input concepts. This is used to upgrade the synthesis model or support general. The ontology is encoded in OWL (Web Ontology Language) and edited using Protégé-OWL [8]. It is supported by the RACER [9] reasoner functioning as a logical classifier and ontology verification tool. Visualisation is enabled through GrOWL [10]. 2.3. Communication between superstructure and knowledge representation Knowledge availability has the potential to assist and guide the transition from one optimisation stage to the next. Design solutions represent specific cases of the superstructure and are associated with a specific ontology. The design solutions are in numerical format unlike the ontology, which is expressed in semantic terms. This demands a translation mechanism which we establish with the introduction of digital certificates.

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Ontology Well-Mixed

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OneZoneNetwork

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Figure 1. Synthesis strategy and components of the methodology 2.3.1. Digital certificates Digital certificates (DCs) gather specific information about design candidates in the form of a vector. They represent the information of the ontology in a numerical format to enable the analysis of solutions. DCs are issued for the solutions generated in the optimisation searches. DCs are auto-generated with the use of CLIPS [12] CLIPS enables connstruction of a rule-based system. The set of rules constitutes a knowledge base that draws on domain knowledge. In this case, rules represent “rules of thumb” which specify a set of actions to be performed for given conditions (i.e. relationships between the design variables of the superstructure). The rules relate to active reactive units and connections between them in the superstructure. The active reactive units are combined into reactive zones depending on the mixing pattern favoured and connections in the form of recycles and bypasses that relate to these reactive zones are extracted to be represented by the DCs. The rules are used as an input to the inference engine (CLIPS) which automatically matches facts (or data) against patterns (or conditions) and determines which rules are applicable. Valid rules are executed until no applicable rules remain. As a result of executing the rules, DCs are issued for each solution representing a simplified equivalent superstructure in terms of main features. For the purposes of the application, the digital certificates represent for each solution the number of reactive zones, the mixing pattern, the connections between reactive zones and the feeding and product policy (Fig. 2). The information that is captured by the certificates enables comparisons, analysis of trends and the population of the ontology.

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Figure 2. Synthesis representation and digital certificate for a solution

2.3.2. Clustering and analysis The approach makes a repeated use of clustering methods to group solutions in terms of the features they share. Best performing clusters are selected with the objective of: (i) setting up a new optimisation stage, and (ii) customizing features of the optimal search. Clusters are selected depending on their spread in performance, which is reduced as stages are performed. Through this approach, knowledge extracted from the analysis of the solutions, apart from updating the knowledge model, is systematically communicated through the course of the optimisation search (Figure 1). The acquisition of knowledge subsequently guides the search towards high performance regions branching off those superstructure features that are of limited importance. In such a way, the synthesis model is updated and adapted throughout the optimisation process as stages are performed, making the optimisation more effective and robust.

3. Numerical example The methodology is illustrated with the Van de Vusse reaction system. The maximisation of the outlet concentration of B is the objective. Feed conditions and the superstructure representation follows [2]. The superstructure includes up to four reactors units among CSTRs, PFRs and DSSRs. PFRs and DSSRs are approximated to a series of seven equal volume CSTRs [2]. Ten initial solutions are considered as starting point for the Tabu Search. Computer experiments are performed for a neighbourhood of seven. The Tabu List contains a single entry. The reduction of the superstructure is attained as DCs emerge with common features. Clustering identifies promising features, which are taken into account in next stages, whereas irrelevant features are gradually excluded. The best 50%, 10%, 5%, 2% and 1% of the clusters generated are selected in each stage respectively. Results are summarized in Table 1. Stage 1 eliminates the well-mixed pattern in the final reactive zone and removes connectivities of type recycle between reactive zones. In Stage 2 connectivities (recycles and bypasses) between reactive zones are eliminated. Stage 3 removes feed distribution. The mixing pattern for the first reactive zone is identified to be well-mixed which is, on the other hand, removed from the second zone. The penultimate stage breaks down the synthesis search into a pool of optimal and near-optimal designs where all clusters share the type of the first two reactive zones. In Stage 5, a CSTR followed by a PFR with a network size of 28.77 L is selected as the optimal solution.

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4. Conclusions The paper presents a systematic synthesis approach that combines superstructure-based optimization, knowledge models and analytical tools. The work addresses the representation and extraction of process synthesis knowledge during the optimisation process and is also applicable to other types of models, applications and optimization techniques. The method is illustrated with one example from the literature. The results show how important features and patterns are retrieved at very early stages of process design. In the initial stage, all possible solutions in terms of their features are included in the initial knowledge representation and an exhaustive superstructure where all feasible options are embedded is considered. As the optimisation goes on, relevant features emerge and others are eliminated delivering a reduced set of solutions (reduced synthesis model). This is represented in parallel in an enriched knowledge model that defines the set of optimal solutions with semantic terms understood by the user. The systematic interpretation of solutions yields to an understanding of the solution space and to a systematic reduction of the representation employed. The presented approach overcomes the inconclusiveness and difficulty of translation of the solutions usually found in classical stochastic optimisation approaches as well as reduces the experiments to be performed. The approach enables monitoring the search, which is carried out in terms of the extraction of design classes at each optimisation stage. Table 1. Evolution of the superstructure and results for Van de Vusse Stage

Superstructure

Digital certificates Max. obj.

0

1

...

...

4

-

-

21100000021 31110000021 12000000011 32410000011 ... 21200100011 12000100011 41214000011 21400000011 ...

3.4695 2.7397 3.5513 2.3991 ... 3.6395 3.5852 3.6298 3.5942 ...

41212000011

3.6445

21200000011

3.6527

31240000011

3.6413

21200000011

3.6527

0.12 – 0.60

5

References [1] [2] [3] [4] [5] [6] [7] [8]

L. K. E. Achenie and L. T. Biegler, Indust. Eng. Chem. Fund., 25(1986) 621-627. A. C. Kokossis and C. A. Floudas, Chem. Eng. Sci., 45(1990) 595-614. E. C. Marcoulaki and A. C. Kokossis, AIChE J.1, 45(1999) 1977-1991. V. L. Mehta and A. C. Kokossis, Comput. Chem. Eng., 21(1997) S325. F. Glover, Annu. Oper. Res., 41(3)(1993). P. Linke and A. C. Kokossis, Comput. Chem. Eng., 27(2003) 733-758. T. R. Gruber, Knowl. Acquis., 5(1993) 199-220. http://protege.stanford.edu/

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870 [9] [10] [11] [12]

http://www.racer-systems.com/ http://www.uvm.edu/~skrivov/growl/ http://www.co-ode.org/downloads/owlviz/OWLVizGuide.pdf http://clipsrules.sourceforge.net/

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Modeling using higraphs: an integrating approach Manuel Rodríguezª, Ricardo Sanzª ª Autonomous System Laboratory, Technical University of Madrid, Madrid 28006, Spain, [email protected]

Abstract The purpose of this paper is to introduce a new formalism to help in the aim of developing and integrating models for complex process systems. A new methodology to develop in a unique an integrated manner structural as well as functional models is presented. The methodology is based on a previous formalism named higraphs. In this paper the application of this approach will be mainly on risk analysis.

Keywords: Higraphs, functional modeling, autonomous systems 1. The modeling paradigm. Modeling is a very relevant task in all the engineering domains. Since the first half of the past century a general theory has been proposed to represent the knowledge of different domains following a common strategy and procedures. Initially formulated by Bertalanffy [1], general systems theory is seen as a general framework for universal, abstract systems modeling. Systems conception and systems modeling has evolved from the Cartesian paradigm (structure-function), the statistic-mechanics paradigm (evolution-function), the structuralist (evolution-structure-function) and cybernetic paradigms (homeostasis, goals) into the global systemic paradigm represented by the General Systems Theory that collects and merges somehow the last two paradigms. This unifying vision can be summarized as stated by Le Moigne in [2]: “ and object with a set of goals, in a well defined environment, exerts an activity (function) and at the same time experiences how its internal structure evolves through time keeping its identity”. This idea will be kept in the philosophy of what is presented next. In the following, the higraph formalism is presented and will be used to develop models that include functional (activity) and structural (ontologic) aspects of a process. The inclusion and need of the evolutionary (genetic) aspects is beyond the scope of this paper although it can be represented using this same formalism.

2. Higraphs formalism. An introduction. The higraph [3] is a general kind of diagramming object. It uses a visual formalism of topological nature. Higraphs are well suited for the behavioral specification of complex systems [4]. A diagram is composed of nodes, called blobs (rounded corner boxes), and edges (arrowed lines). Blobs can be arranged in an inclusion hierarchy and the edges can connect blobs at any depth. Edges crossing inclusion borders are called hyperedges [5]. Higraphs can be considered as a general extension of conventional graph representations by introducing means for representation of set enclosure, exclusion and intersection and the Cartesian product [6]. Higraphs are formed somewhat modifying Euler/Venn diagrams, by extending them to represent Cartesian products. In summary,

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higraphs extend the notion of graphs with the provision of depth (or hierarchy) and orthogonality; so they can be defined as: higraphs = graphs + depth + orthogonality [7]. Orthogonality is represented by a dashed line inside a blob, meaning an OR relation. One fundamental interpretation of higraphs, where blobs are interpreted as states and edges are interpreted as transitions between states, led to the language of statecharts.

3. Higraphs for process systems As presented before higraphs are a powerful visual formalism and it is well suited for topological complex systems as it can deal with complexity through hierarchical decomposition. Process systems are paradigmatical examples of topological and complex systems, hence falling into the category of systems suitable to be represented by higraphs. Following the ideas presented in [8] and introduced in the first section, it is interesting to have, in a single diagram, structural and functional components of a process. Some methodologies have developed functional models (such as Multilevel Flow Modeling –MFM- and Goal Tree Success Tree –GTST- [9,10]) and although both relate functional components with the physical devices, the relation is somehow not fully used (little attention is being usually given to it). Besides, the explicit appearance of these relations leads to more entangled, less clear diagrams. 3.1. Basic components Higraph models (representing process systems) are built using basically the following elements: Functional blobs. This box is identified by the function name. Its name describes the function realized (or achieved) by the components inside. Functional blobs can contain functional and/or structural blobs themselves in any depth. Structural blobs. This box is identified by the device/s name. Its name describes the device or set of devices that realize a function. Structural blobs can contain functional and/or other structural blobs. If a single structural blob performs a single function described by a functional blob, the box can be omitted and inside the functional blob appears only the name of the structural component. Edges. They connect two blobs, these can be blobs of different layers of the hierarchy. There are three types of connections (as in usual commercial simulators) depending on the type of information they transmit: material, energy (usually heat) and information. Material edges. Represent material connections between structural components. They perform a transport function and they always indicate transport of material (and the associated energy). A solid line represents them. Energy edges. Represent energy connections between structural components. Any type of energy can be transferred although the most common is heat transfer. They are represented using a dashed line. Information edges. Represent information connections between structural components. Mostly they represent the control structure. Represented by a dotted line.

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Fig 1. Shows the described elements.

Fig 1. Basic Process Higraph Components

3.2. Interpreting the diagram In order to analyze a process higraph, there are two things to take into account. The first one is the blob dependency through inclusion and the other one is the blob dependency through connections. When a functional blob fails it means that all the outer blobs that contain it do also fail. When a material or information connection into a blob fails it means that the function achieved by that blob fails. In the case of heat it is not necessarily the blob that the edge points to, but it can also be the blob source of that connection (as energy connections show the direction of the heat form hotter to colder). In most cases, causality assignment is not necessary. If not so, tags are added to the connections (causality explanation is beyond the scope of this paper and will be explained elsewhere). 3.3. A simple example A simple process illustrates the use of the higraph components. The process selected is presented in [11] along with a MFM functional model. It consists of an engine fed by gas and oxygen and its refrigeration circuit with two heat exchangers. Fig. 2 a) shows the process and 2 b) the MFM model where Ms are mass structures and Es are energy structures. Circles represent the system goals.

Fig 2. A simple process, engine refrigerated a) and the MFM of the process b)

Fig 3. shows the associated process higraph. It contains all the elements and goals of the MFM model in a very intuitive visual way along with the structural components that perform the functions (not indicated in the MFM diagram). The fault chain analysis is as follows, if, for example, the lubricate function fails, it means that the transport water function fails (it is an outer blob) and that the cool engine function fails, so does the keep engine temperature and finally the keep engine running. This type of diagram also allows a layered representation, displaying only the structural components (engine, coil

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plates, etc.) or the functional components or all the components but at one level of the hierarchy.

Fig 3. The Process Higraph of the refrigerated engine process

4. Application to an industrial process In this section, this modeling approach is applied to an industrial process. The process is the production of monomethylamine nitrate. This process (Fig 4) has been selected as its description as well as its MFM model can be found in [12]. Fig 5, shows that the main goal is to operate the plant safely (outest blob) to obtain the desired product with the desired quality. This goal is achieved through the subgoals (represented by inner functional blobs): keep quality, vaporize in operating conditions (OP), react in OP and store in good conditions. In the diagram other subgoals can be clearly observed.

Fig 4. The Monomethylamine nitrate process with the control structure

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The diagram is clear, the process (structural components) can be easily followed as well as the goals (functional components) and their dependencies. Different views can be displayed and different analysis can be performed based on this diagram or formal data representations of it (risk assessment, diagnosis, sensor validation, etc). For example, if the coil of the auxiliary water circuit breaks, it means that the function it realizes, heat tank, is not achieved, so, following the hierarchy of functional blobs, the temper function is not achieved and the store in good conditions fail as well, so finally the overall goal cannot be satisfied. Orthogonality is a property of higraphs that has not been used in this diagram but it can be added e.g. to represent explicitly not desired functionality that can happen in the process. Orthogonality in a blob means that one function or the other happens but not both. This will make easier the analysis of the consequences of a failure because the undesired behaviors are also connected and the sequence of undesired functions can be followed and foreseen in the diagram.

Fig 5. The Process Higraph of the Monomethylamine nitrate process.

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This methodology tries to merge in a single diagram structural views as presented usually in industry through P&I diagrams and functional views as those presented in MFM and GTST techniques.

5. Conclusions In this paper a new modeling methodology has been presented, this methodology applies and extends higraphs to process systems. The result is a simple, visual, hierarchical diagram that represents functionality as well as structure. It shows not only the process but also the information (control) structure. The diagram is easily understood without further explanation and can be used for multiple purposes from fault diagnosis or risk analysis, to process documentation. Different layers of the diagram can be displayed alone in order to have a more abstract or specific view or to have a functional or structural view. Further work includes using quantitative models along with the diagram for sensor validation, linking higraphs to ontologies, incorporate more sophisticated information structures (e.g. cognitive architectures) and integrate all of the above into a single framework.

6. References [1] Von Bertalanffy, L. General Systems Theory. New York, George Braziller, 1968 [2] Le Moigne, J.L. “La théorie du système général.”, 3 ed, Paris, PUF, 1990 [3] Harel, D. “On visual formalisms”, Comm. Assoc. Comput. Mach., vol 3, 514-530, 1988 [4] Harel, D. Statecharts: A visual formalism for complex systems. Sci. Comput. Program., 8(3):231–274,1987. [5] Harel, D. et al. “An algorithm for blob hierarchy layout”, Visual computer, March, 2002 [6] Evans, G.W. et al. “Visual modeling of DEVS-Based multiformslism systems based on higraphs, Proceedings Winter Simulation Conference, 1993 [7] Grossman, O and Harel, D. “On the algorithms of Higraphs”, [8] Rodriguez, M. “Merging functional and conceptual ontologies”, ESCAPE 17, Bucharest, Romania, 2007 [9] Lind, M. “Modeling goals and functions of complex industrial plant”, AAI , 8, 1994 [10] Modarres, M. “Function centered modeling of engineerig systems using the goal treesuccess tree technique and functional primitives.” Reliab. Eng. and Sys. Safety, 64, 1999 [11] Öhman, B. “Discrete Sensor Validation with Multilevel Flow Models”, IEEE Intelligent Systems, 55-61, May-June 2002 [12] Rodríguez M. and De la Mata, J. “Functional modeling for Risk Analysis”, ESCAPE 17, Bucharest, Romania, 2007.

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Interval Based MINLP Superstructure Synthesis of Multi-Period Mass Exchange Networks Adeniyi Isafiade, Duncan Fraser Department of Chemical Engineering, University of Cape Town, 7701, South Africa, [email protected]

Abstract A new method for the synthesis of mass exchanger networks for multi-period operations is presented in this paper. The new method which is called multi-period interval based MINLP superstructure (MIBMS) is adapted from the interval based MINLP superstructure for mass exchanger networks (MENs) presented by Isafiade and Fraser (2008). Parameters such as supply and target compositions and flowrates of streams can vary over a specified range. In this paper, the IBMS model for MENS is modified to handle variations in the aforementioned set of parameters by including the index ‘p’ in the IBMS model and using the maximum area approach in the objective function as presented by Verheyen and Zhang (2006) for multi-period heat exchanger networks synthesis (HENS). The index ‘p’ represents each period of operation which can be unequal. The maximum area approach ensures that each mass exchanger connecting the same pair of streams in more than one period is able to transfer mass in such streams for all the periods. This technique simplifies the model unlike the flexibility or stream bypass approach, as used in other studies, which is time consuming. The new technique is applied to one example adapted from the literature. Keywords: multi-period, mixed integer non linear program, mass exchanger network synthesis, superstructure.

1. Introduction Mass exchange network synthesis (MENS) has been used to accomplish pollution reduction in chemical based plants. It has also helped to minimise the use of scarce resources such as water. The approaches which have been used for the synthesis of MENs have included conceptual (pinch technology) and mathematical methods. However most of the techniques were developed for MENs problems involving fixed or single periods of operations which is not always the case in practical situations where there may be variations in operating conditions such as composition and/or flowrates. These variations could be as a result of changes in environmental conditions, it may even be due to economic reasons. MENS models which will be flexible and operable within the range of the variations need to be developed. The MENS multi-period problem can be stated as follows: Given a set R of rich process streams, a set S of lean process/external streams and a set P of periods of operations. Given also are the supply and target compositions of the rich and lean streams foe each period of operation. The task is to synthesize a network of mass exchangers which is capable of transferring certain species from the rich streams to the lean streams in a cost effective manner, the network must also be optimally operable for the finite set of P periods of operations.

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The synthesis of multi-period MENs has not received much attention unlike its heat exchanger network (HEN) counterpart which has been extensively studied. Chief among the approaches which have been applied to the synthesis of multi-period HENs include the multi-period version of the linear programming (LP) and mixed integer linear programming (MILP) of Papoulias and Grossmann (1983) and the NLP models of Floudas, et al. (1986). These multi-period models were developed by Floudas and Grossmann (1987a) for minimum utility and number of units networks. Floudas and Grossmann (1987b) developed the minimum investment cost network model. The aforementioned HENs multi-period models were improved by Floudas and Grossmann (1987b) by the inclusion of flexibility analysis techniques through the use of active set strategy. Papalexandri and Pistikopoulos (1994) set up a hyperstructure which is able to handle multiple periods of operations for heat and mass exchanger networks. Recently, Aatola (2003), Chen and Hung (2004), Verheyen and Zhang (2006) and Chen and Hung (2007) presented the multi-period version of the simplified MINLP stagewise superstructure (SWS) model of Yee and Grossmann (1990). A multi-period version of the IBMS for HENS has also been developed by Isafiade and Fraser. Verheyen and Zhang (2006) in their multi-period model of the SWS introduced the maximum area (Ai,j,m) approach in order to ensure that exchangers connecting pairs of streams which exchange heat in more than one period are large enough to handle such heat exchange for all the periods concerned. This approach was adopted by Isafiade and Fraser, however the objective function presented by these authors unlike those of Aaltola (2003) and Verheyen and Zhang (2006) involves a new utility weighting criteria which is more general. The weighting term will give an accurate annual operating cost (AOC) per period calculation. The maximum area approach together with the utility weighting technique of Isafiade and Fraser are adopted in this paper for multi-period MENS. Due to the non-linearities exhibited by multi-period MENS design equations, there cannot be a guarantee of obtaining optimum solutions using the previous techniques. In addition setting up initial points and bounds for the previous models can be challenging. Table 1. Stream and Capital Cost Data

Rich stream Ys Yt G (kg/s) Period 1 R1 0.13 0.1 0.25 0.06 0.02 0.1 R2 Period 2 0.14 0.1 0.306 R1 0.06 0.02 0.1 R2 Period 3 0.12 0.1 0.194 R1 0.06 0.02 0.1 R2 Lean stream Xs Xt Lc(kg/s) Cost ($/kg) S1 0.03 0.07 ’ 0.01 S2 0.001 0.02 ’ 0.012 Compositions in mass fractions. Equilibrium relations: R1-S1: Y1=0.734X1; R1-S2: Y1=0.111X2+0.008; R2-S1: Y2=0.734X1+0.001; R2-S2: Y2= 0.148X2+0.013. Capital cost: Sieve tray = 600 N0.74 ($/yr); Packed columns = 7500H0.81 ($/yr). Kw (1 m diameter column): S1 = 0.644 kg copper m-3 s-1; S2 = 0.139 kg copper m-3 s-1.

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2. MIBMS Model Formulation Objective function The objective function simultaneously minimises the operating and capital costs. The objective function equations are presented for continuous contact and stagewise mass exchangers respectively.

where indices r,l,k and p represent rich stream, lean stream, interval boundary location and period. DOPp and NOPp are the duration and number of period p respectively. ACl, CBr,l, Dr,l, ACHr,l and ACTr,l are per unit lean stream l annual operating cost, exchanger installation cost, area exponent cost, per height annual cost for continuous contact columns and per stage annual cost for satged columns. Ll,p, Hr,l,k, Nr,l,k and zr,l,k represent flowrate of lean stream l, height of exchanger r,l,k, number of stages of exchanger r,l,k and binary variable. The MIBMS objective functions can adequately account for unequal period durations based on the weighting term which has been included in the equations as used by Isafiade and Fraser.

3. Example The MIBMS is applied to an example adapted from El-Halwagi and Manousiouthakis (1990). The problem which consists of two rich and two lean streams involves non uniform exchanger specifications. S1 requires sieve tray columns while S2 requires packed columns. The stream and capital cost data are presented in Table 1. In this paper, fixed parameter points were selected to comprise three periods of operations for the supply composition and flow of R1, based on this, the solution cannot be compared with previous studies. The other set of stream parameters are fixed within these periods. In addition, the period durations are assumed equal. The MIBMS for this example involves four composition boundaries for each of the three periods. The solution network has a TAC of 256,842 $/yr with two units. The network is shown in Figure 1 with the mass exchange for the three periods shown in box. The composition illustrated in the figure are those of period 1, however the exchanger sizes are the maximum needed to exchange mass for the three periods.

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4. Conclusion A new synthesis method for multi-period MENs has been presented in this paper. The new method adapts and combines the IBMS for MENS of Isafiade and Fraser (2008) and the maximum area per period approach of Verheyen and Zhang (2006) for multiperiod HENS to the synthesis of multi-period MENs. The MIBMS was applied to an example adapted from the literature and it has been shown that it effectively synthesises multi-period MENS problems.

0.13

0.1

R1 0.13

1 stage

Flow 0.02 Kg/s

0.06

0.1 R2 0.06

0.3 m

0.25 0.1

0.03 S1 0.187

0.07 0.02

0.02

0.008 0.004 0.006

0.001 S2 0.210 0.004 0.004 0.004

TAC: 256,842

Figure 1: MIBMS network for the example problem

5. Acknowledgements This research was supported by the Claude Leon Foundation.

References A.J. Isafiade and D.M. Fraser (2008). Interval based MINLP superstructure synthesis of mass exchange networks. Chem Eng Res Des 86(8), 909-924. W. Verheyen and N. Zhang (2006). Design of flexible heat exchanger network for multi-period operation, Chem. Eng. Sci. 61, 7760-7753. S.A Papoulias and I.E. Grossmann (1983). A structural optimization approach to process synthesis-II. Heat recovery networks. Comp. & Chem. Eng. 7, 707-721. C.A. Floudas, A.R. Ciric and I.E. Grossmann (1986). Automatic synthesis of optimum heat exchanger network generation. AICHE J., 32(2), 276-290. C.A. Floudas and I.E. Grossmann (1987a). Automatic generation of multiperiod heat exchanger network configuration, Comp. & Chem. Engr., 11(2), 123-142. C.A. Floudas and I.E. Grossmann (1987b). Synthesis of flexible heat exchanger networks with uncertain flowrates and temperatures, Comp. & Chem. Engr., 11(4), 319-336. K.P. Papalexandri and E.N. Pistikopoulos (1994). A multiperiod MINLP for the synthesis of flexible heat and mass exchange networks, Comp. Chem. Eng., 18(11/12), 1125-1139. J. Aaltola (2003). Simultaneous synthesis of flexible heat exchanger networks. PhD thesis, Department of Mechanical Engineering Helsinki University of Technology.

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C.-L. Chen and P.-S. Hung (2004). Simultaneous synthesis of flexible heat exchange networks with uncertain source-stream temperatures and flow rates, Ind. Eng. Chem. Res. Des. 43, 5916-5928. C.-L. Chen and P.-S. Hung (2007). Synthesis of flexible heat-exchange networks and mass exchange networks, Comp. & Chem. Engr., 31, 1619-1632. T.F.Yee and I.E. Grossmann (1990). Simultaneous optimization models for heat integration-II. Heat exchanger network synthesis. Comp & Chem Eng, 14(10), 1165 - 1184. A.J. Isafiade and D.M. Fraser. Interval based MINLP superstructure synthesis of heat exchange networks for multi-period operations. Submitted to Chem. Eng. Res. Des. M.M. El-Halwagi and V. Manousiouthakis (1990). Automatic synthesis of mass exchange networks with single component targets. Chem. Eng. Sci., 45(9), 2813-2831.

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Towards an ontological infrastructure for chemical batch process management E. Muñoz, G. M. Kopanos, A. Espuña, L. Puigjaner Chemical Engineering Department –CEPIMA, Universitat Politecnica de Catalunya, Av. Diagonal 647, Pab. G-2 08028 Barcelona, Spain. E-mail: [email protected]

Abstract Chemical batch process management, regardless of the level where its analysis is focused (such as pre-formulation and new process development, supply chain management, scheduling, process control, fault analysis, etc.) implies the collection and exploitation of huge amounts of data, which should be viewed as sources of information. Consequently, the information infrastructure which supports different activities by streamlining information gathering, data integration, model development and decision making is a crucial component towards process improvement/optimization. In this work it a Batch Process Ontology (BaPrOn) is presented, wherein different concepts regarding batch processes are categorized, and the relationships between them are examined and structured. Properties and relationships are introduced in agreement with ISA-88 standard, which provides a solid and transparent framework for integrating batch-related information. Keywords: Ontology, Knowledge representation, Knowledge sharing, Batch process, Decision support systems.

1. Introduction Decision Support Systems (DSS) are defined as “Aid computer systems at Management Company level that combine data and sophisticated analytic models to support decisionmaking”. In fact, DSS must be maintained by the information obtained from a data base. In the last 40 years, many companies have been developing management information systems to help the end users to exploit data and models, with the final objective of discussing and decision making. Nowadays, global competition has made some of these decisions (related to certain manufacturing characteristics like economic efficiency, product quality, flexibility, reliability, etc.), essential for the viability of the enterprise [13]. The need for infrastructures that continuously and coherently support fast and reliable decision-making activities involving any aspect directly or indirectly related to the production process, has become of paramount importance. This need becomes more evident when a batch process system is considered, since in most cases the high-value products related to batch processes maintained chemical batch industries out of the competitiveness pressures until recent years. However recent shrinking profit trends makes it necessary to exploit large databases (many products with complex recipes, non-cyclically produced, etc.) by generic/blind methods. The performance of these methods can be drastically increased when combined with knowledge or expertise from the process itself.

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2. Background Information is data that is processed to be useful, and knowledge is the application of data and information, through the development of a system which models in a structured way the experience gained in some dominion. In the recent years there has been an effort for creating knowledge with a minimum of human interface, either in a straight and formal way (e.g. expert systems), or in a conceptual manner. But knowledge exists as soon as human interaction is or has been available at any step of the product/process development [2]. Ontologies constitute a means of specifying the structure of a domain of knowledge in a generic way that can be read by a computer (formal specification) and can be presented in a human-readable form (informal specification). Moreover, ontologies are emerging as a key solution for knowledge sharing in co-operative business environment [1] and, since they can express knowledge (and the relationships in the knowledge) with clear semantics, they are expected to play an important role in forthcoming informationmanagement solutions to improve the information search process [3–6]. Recently, several Ontologies in the field of chemical processes have been developed. Among them, it is worth mentioning OntoCAPE, which is an ontology development based on CLiP, a comprehensive data model for process engineering which is often applied in various process engineering tasks [7], and BioPortal (Physico-chemical process ontology) which is a Web-based application for accessing and sharing biomedical and chemical knowledge (http://bioportal.bioontology.org/). Those ontologies offer different alternatives for sharing knowledge but they are focused on existing product development processes, namely those approaches create an ontology that is suitable to already on-going processes. Instead, this work presents the development of a generic ontology following standards which allows creating a infrastructure that should be general enough to be applied to any batch system. Additionally, the proposed ontology may be used as a straightforward guideline for standardizing batch process management and control. Moreover, it offers a robust structure for sharing knowledge which may help making more appropriate decisions towards business performance improvement.

3. Proposed approach Batch Process Ontology (BaPrOn), is a procedural oriented ontology that regards different concepts (physical models, procedures, functions and processes) in accordance with ISA-88 batch process standard, categorizing them and examining the relationships between them. The language used in the ontology is essential for its future implementation and sharing. OWL (Web Ontology Language) was the language adopted because it, offers a good compelling for ontologies and also because it employs XML which seems to be the language of universal use (extensible markup language: http://www.w3.org/XML/) and RDF (Resource Description Framework: http://www.w3.org/RDF/) namespace protocols on the Web (http://www.w3.org). This unifying aspect, for instance, may make it easier to establish, through collaboration and consensus, the utilitarian vocabularies (e.g. ontologies) needed for far-flung cooperative and integrative applications using the Word Wide Web and internal servers.

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3.1. Methodology Various methodologies exist to guide the theoretical approach taken, and numerous ontology building tools are available. The problem is that these procedures have not coalesced into popular development styles or protocols, and the tools have not yet matured to the degree one expects in other software instances. The methodology used in this work is based in two ontology development methodologies. On the one hand, Methontology identifies 6 principal activities in the development of ontologies, being its most distinctive aspect the focus on maintenance [11]. In the other hand, On-toKnowledge methodology focuses on knowledge management, and is about acquiring, maintaining, and accessing the knowledge of an organization [12]. On the implementation side, Protègè (http://protege.stanford.edu/) was selected as tool for ontology editing and knowledge acquisition. It is aimed at making it easier for knowledge engineers and experts to perform knowledge management. From Protègè, it is possible to export ontologies to other knowledge-representation systems, such as RDF, OIL and DAML. All the abovementioned methodologies have been inserted in the PDCA Cycle (http://www.hci.com.au/hcisite3/toolkit/pdcacycl.htm), resulting in an ordering sequence of steps, easy for its understanding and tracking, shown in Fig.1.

Figure1. Methodology summary The proposed ontology is intended to promote a transversal process oriented management, allowing crossing over the different functionality silos in which businesses have been typically structured. In order to get (and manage) a comprehensive view of the overall process, new modeling structures are required able to recognize the existing trade-offs and impacts of the available alternatives at the different information aggregation levels, and also to discard non significant effects, through re-tuning the decision-making/optimization model according to the current process status. Thus, effective decisions can be made avoiding both a greedy/myopic hierarchical decision making structure, and a monolithic optimization model (impossible to solve in industrial-size scenarios). It should be emphasized that management process structures

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incorporated within this framework have been designed following ISA88 standard recommendations [8-9], but it is envisaged that this transversal ontology can be further extended to incorporate higher decision making hierarchies (supply chain) and to include the entire life cycle of the organization, from the design stages to the delivery of final products. 3.2. Experimental arrangement A first application of this ontology has been implemented to “close” the typical scheduling-fault analysis-rescheduling loop (control levels 1 to 4 of the Purdue Reference Model) [10]. The system is coordinated by an internal server acting as a information administrator consistent with the ontology structure. The working process of the ontology modeling approach is shown in Fig.2, where the relation between different actors is shown, besides it lets the user to create and add new design information into or reuse existing information from the modeling databases. The ontology is used to capture the common understanding in conceptual design and help to utilize the relations that are mined from the databases helping the user to get the data and information in proper, faster and in a standard way.

Figure 2. Graphic view of the ontology model process. 3.3. Case of study A Batch Pilot Plant (PROCEL), built in the Chemical Department of UPC brings an appropriate scenario to evaluate the ontology performance as well as study and develop new process strategies. This case study is dealing with the production of three chemical products everyone with different amount required. The production system has been integrated by 3 principal processing units, two reactors and one tank. One recipe for each product has been considered. Processing times, transfer times and cleaning times have been taken into account. BaPrOn consists of 76 classes, 115 axioms, and 86 sub-object properties. It is important to mention that the instances have been introduced to another ontology, thus considering one of the main ontology principles, which is to be universal (subjective) in a particular

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dominion. Activities like basic control, coordination control and scheduling have also formed part of this study. The main BaPrOn classes and subclasses are shown in Fig.3. Classes and subclasses hierarchical taxonomy has been done in accordance with the ISA88 standard. As a consequence, it is achieved a better understanding of this standard by potential users.

Figure 3. ISA88 basic

3.4. Results & discussions The ontology showed a good performance during the case of study, it was used to capture the common understanding in conceptual design and help to utilized the relations that are mined from the databases; helping to the user to get the data and information in a proper, fast and standard way by the use of an internal webpage portal. Furthermore, by testing the Ontological system with a real database, allowed to apply SWOT (Strength, Weakness, Opportunities and Threatens) analysis, identifying which modifications are necessary in order to further improve the current ontology. Finally, this work represents a step forward to support the integration (not just “communication”) of different software tools applicable to the management and exploitation of plant database information, resulting into and the enhancement of the entire process management structure. In this sense, the more significant advances consist of: • The creation of a consensual methodology considering On to Knowledge and Methontology; two of the most used methodologies already established, for easier development of ontologies. • The creation of a bridge between the Batch Process and the related information, enabling formal and informal models / knowledge / experience to exploit different optimization tools for helping in the Decision Making process.

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4. Future work Some research lines are still open in this “integration” line. Based on the experience of this work, it is worth to emphasize: • The improvement of the ontology to be able to reason with variation/transition of description values. • The integration with new ontologies in areas like nets super structures, applicable to Supply Chain Management.

5. Acknowledgements Financial support received from the Dirección General de Educación Superior Tecnológica (DGEST) from México and from the Spanish Ministry of Education scholarship number 072007004 E.A and Science (FPU grants) is fully appreciated. Besides, financial support from DPI2006-05673 project is gratefully acknowledged.

References [1] Venkatasubramanian, V., Zhao, C., Joglekar G., Jain, A.,Hailemariam L., Suresh, P., Akkisetty, P., Morris K., Reklaitis, G.V. Ontological informatics infrastructure for pharmaceutical product development and manufacturing, Comp. and Chem. Engng., 30 (2006) 1482–1496. [2] Missikoff, M., Taglino, F. Business and Enterprise Ontology Management with SymOntoX1 [3] Gruber, T.R.,. A translation approach to portable ontology specification, Knowledge Acquisition, An International Journal of Knowledge Acquisition for Knowledge-Based Systems 5 (2) (1993) 199–220. [4] Gruber, T.R., Toward principles for the design of ontologies used for knowledge sharing, International Journal of Human-Computer Studies 43 (5–6) (1995) 907–928. [5] Noy, N.F., McGuinness, D.L., Ontology development 101: A guide to creating your first ontology, Stanford Knowledge Systems Laboratory Technical Report KSL-01-05 and Stanford Medical Informatics Technical Report, March 2001. [6] Obrst, L., Ontologies for semantically interoperable systems, Proc. of Twelfth International Conference on Information and Knowledge Management, CIKM 2003, pp. 366–369. [7] Morbach J., Yang A., Marquardt W., OntoCAPE-A large-scale ontology for chemical process engineering, Engng. Applications of Artificial Intelligence 20(2): 147-161, 2007. [8] ISMC.ANSI-S88.01-1995, Batch control, Part I: Models and Terminology. 1995 [9] ISMC.ANSI-S88.01-1999, Data Structures and Guidelines for Languajes. Draft 14. 1999 [10] ANSI/ISA-95.00.01-2000 Enterprise-Control System Integration Part 1: Models and Terminology. [11] Fernández López, M.; Gómez-Pérez, A.; Pazos-Sierra, A.; Pazos-Sierra, J. Building a chemical ontology using Methontology and the Ontology Design Enmvironment. IEEE Intelligence Systems & their applications, pp. 37-46. January-February 1999. [12] Hans-Peter Schnurr, York Sure, Rudi Studer Hans Akkermans, On To Knowledge Methodology – Base Version, 2000. [13] Ontological informatics infrastructure for pharmaceutical product development and manufacturing, Venkatasubramanian et al, Computers and Chemical Engineering 30 (2006) 1482–1496.

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A co-operative model combining computer algebra and numerical calculation for simulation Karim Alloula,a Jean-Pierre Belaud,a Jean-Marc Le Lanna a

INPT-ENSIACET, Laboratoire de Génie Chimique (CNRS UMR 5503), 118, route de Narbonne, 31077 Toulouse Cedex 04, France

Abstract Following the principles of the Model Driven Approach we suggest that a process simulator should transform a platform-independent model, written in the MathML dialect, into mathematical expressions to be evaluated by either numerical or symbolic calculation systems. Simulation consists in a co-operation of those calculation systems: the computer algebra systems are in charge, during run-time, of symbolic model transformations providing the expressions required by the solving methods in the numerical calculation systems. Keywords: CAPE tools, computer algebra, Model Driven Approach, numerical methods, simulation

1. Introduction Previous work (Alloula, 2007) introduced a “hybrid” approach, mixing computer algebra and numerical methods, for solving CAPE models. The main objective was to handle mathematical expressions using computer algebra techniques, evaluating them to real numbers only when required by numerical methods. This paper considers that any simulation process should take advantage of alternating numerical evaluation steps and symbolic transformation steps for: • separating “problem specification” from “solution specification”, • and improving accuracy. In part 2, a calculation system model factorizes the common features of computer algebra and numerical calculation systems. A co-operative mechanism between two such calculation systems is introduced. Part 3 suggests starting any simulation process by symbolic transformations of a simulator independent problem specification. Part 4 enumerates some other symbolic transformations which could take place during a symbolic numerical simulation. Part 5 applies this original co-operative model to solve Rayleigh distillation.

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2. A co-operative calculation model Table 0. Calculation system model (UML 2 class diagram) FDOFXODWLRQV\VWHPV PDWKHPDWLFDOH[SUHVVLRQV

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Computer algebra systems deal with models involving both numbers and symbols whereas numerical calculation systems and automatic differentiation tools operate on numerical expressions only. So, in Table 0 the Expression class states for the computer algebra representation of mathematical expressions, considered as the most general one. A CalculationSystem provides the methods for creating new expressions, from scratch or from other expressions. Furthermore, each CalculationSystem keeps track of the Table 0. Cooperation mechanism (UML 2 communication diagram) VG ;HYDOXDWHV(ZLWK&

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Expression objects it creates. We suggest that any Expression can be evaluated by more than one CalculationSystem. As illustrated in Table 0, any Expression E created by a CalculationSystem C can be: • Evaluated according to C semantics; • Cloned in another CalculationSystem C’, and then evaluated according to C’ semantics. This alternative allows two calculation systems to cooperate for evaluating any expression. Obviously, such a mechanism can be extended to cooperation between more than two calculation systems.

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3. Model representation independent of modeling languages One of the first steps towards software reuse and quality is to clearly separate « problem specification » - models in simulation software - from « solution specification » numerical algorithms, hardware target, initial guess, etc. Even if those specifications are related, they are “different description types”, which should “be built explicitly and separately” (Houstis, 2000). The CAPE-OPEN standard applied such a principle when separating Equation Set Objects and Solvers. A step forward is to offer alternate model representations, independent of modeling languages. Recent works define XML dialects to support those independent representations. Using the XML representation for Modelica, ModelicaXML, “generation of documentation, translation to/from other modeling languages can be simplified” (Pop, 2005). “For exchanging mathematical models used in process engineering”, CapeML, “a modeling language-neutral intermediate format”, was designed. From the XML documents, transformation processes produce platform dependent representations, according to the software Model Driven Approach (OMG MDA). (Bischof, 2006) details an automatic differentiation strategy, implemented as an XSLT style sheet, and applied to a model written in the CapeML format. (Pop, 2005) reengineers Modelica models by using program composition and transformation techniques targeted to ModelicaXML documents. Our work deals with a key part of the model representation: mathematical expressions. From the initial problem specification, we generate various tool dependent specifications using computer algebra techniques. Here, the “Platform Independent Models” (PIM) are mathematical expressions coded in the standardized MathML dialect. A model is made of equations and functions, either explicit or implicit (Alloula, 2006). The drawbacks of writing the CAPE Platform Independent Models in MathML compared to CapeML have been detailed in (von Wedel, 2002). For example, models which are MathML coded as equation sets only, are not well suited for model composition and model decomposition. Model connections are based on variable name matching, and can lead to ambiguities. In order to suppress this limitation, we take advantage of the MathML csymbol tag to add the implicit function notion to the basic Content MathML semantics. Model composition is achieved by means of two operators: function composition when models are serially connected, function assembly ( Assembly( f , g ) : x  ( f ( x), g ( x)) ) when models are connected in parallel. Content MathML ci tags no longer represent named variables, but formal parameters or formal results of an implicit function. Because causality remains unknown until the flowsheet is defined, and may change during the simulation process, each implicit function may be dynamically defined from an equation set and an input variable set at any time. As illustrated by the causality change, the need for dynamic transformation capabilities on the process model is fundamental. Our answer to this requirement is to couple functional programming with our MDA-like approach: 1. each process model consists of a collection of Expression objects as introduced in Table 0, some of them being functions or function applications; 2. transformations are pattern matching rules, which may be coded as functions; 3. during the simulation, transformations are applied by the process simulator to each input expression, producing output expressions; 4. according to some strategy, each output Expression is evaluated by some CalculationSystem , maybe after the cloning step described in Table 2.

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This coupled approach conciliates the benefits of MDA, and those of functional programming. The model, the model transformations, and the transformed expressions are clearly separated entities. However, all of them being Expression objects, associated to evaluators, they can be composed and evaluated as functions. Furthermore, one representation independent of modeling languages is associated to each entity because the Expression class hierarchy is mapped to the MathML hierarchy.

4. Model symbolic transformations During the simulation process various symbolic transformations can be applied. The most obvious ones are related to derivative generation. Calculation of residual functions, substitution of inequalities by equations using slack variables, are some other symbolic transformations. They may take place before any numerical evaluation, or among numerical evaluation steps when the model equations involve implicit function evaluations. Table 3 lists the model symbolic transformations available today in eXMSL FORTRAN 90 Library, a simulation software applying the co-operative model combining computer algebra and numerical calculation for simulation. The generalized Newton formulation (Dedieu, 2006), based on the Moore-Penrose pseudo-inverse A+ , allows us to deal seamlessly with non linear equation systems, be they overdeterminated or underdeterminated. The implicit function theorem is used for evaluating numerically implicit function derivatives from the model partial derivatives obtained by using computer algebra techniques.

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Table 1. Model symbolic transformations available in eXMSL FORTRAN 90 Library Model classes

NLE DAE

Saturated, overdeterminated, underdeterminated NLE

Transformation

Input expression

Output expression

Computing residual function

­ x1 + x 2 + x3 = ln( x1 x 2 ) ® x1 x 2 x3 = 8 ¯

§ x + x 2 + x3 − ln( x1 x 2 ) · ¸ F ( x) = ¨¨ 1 ¸ x1 x 2 x 3 − 8 © ¹

Eliminating inequalities

­ x1 + x 2 + x3 = ln( x1 x 2 ) ® x1 x 2 x3 ≤ 8 ¯

­ x1 + x2 + x3 = ln( x1x2 ) ® 2 ¯ Δ + x1x2 x3 = 8

Newton generalized formulation

­° x1 + x 2 + x3 = ln( x1 x 2 ) ® x1 x 2 x3 = 8 °¯

Differential Newton generalized formulation

xk +1 − xk = − F ′( xk ) + ⋅ F ( xk )

x k + 1 − x k = − F ′( x k ) ⋅ ª« F ′( x k ) ⋅ F ′( x k )T º» ¬ ¼

−1

⋅ F (xk )

x′(t ) = − F ′( x(t ))+ ⋅ F ( x(t ))

DAE

Consistent initial conditions

DAE system , order 1, index 1

Initial values of the dependent variables and their derivatives

NLE DAE NLCMP

Implicit function definition

­° x1 + x 2 + x3 = ln( x1 x 2 ) ® x1 x 2 x3 = 8 °¯

­ x1 + x 2 + x 3 = ln( x1 x 2 ) f : x 2  ( x1 , x 3 ) with ® x1 x 2 x3 = 8 ¯

Jacobian matrix calculation

F (x)

F ' ( x)

Directional derivative calculation

F (x)

F ' ( x).d

Jacobian matrix calculation

f : x  y with F ( x, y ) = 0

f ′( x) with D1 F ( x, y ) + D2 F ( x, y ) ⋅ f ′( x) = 0

Directional derivative calculation

f : x  y with F ( x, y ) = 0

f ′( x) ⋅ d with D1 F ( x, y ).d + D2 F ( x, y ) ⋅ f ′( x).d = 0

Explicit function

Implicit function

5. Application to Rayleigh distillation A model of the Rayleigh distillation process, valid for the one phase and the two phase domains has been simulated. An equation V ⋅ y inert = 0 states that either the vapor flowrate is null, or the inert gas concentration. Following the (Pryce 2001) method, symbolic transformations have been applied to the original set of equations, providing automatically a semi-explicit differential algebraic system and a set of consistent initial

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conditions. A Runge-Kutta like solver is in charge of the numerical integration of the index-0 differential algebraic system built from symbolic transformations. Any additional expression required by the numerical solver are dynamically obtained by symbolic transformations. During the one phase simulation, there is no evaluation of some algebraic equation associated to the bubble point event. The solver detects any drop in the rank of the system Jacobian matrix. Such a drop indicates that the physical system trajectory has reached a singular variety, i.e. some kind of discontinuity. Even numerical, this rank analysis is robust and based on theoretical results. Moving on this singular variety to reach automatically an other point where the system Jacobian matrix recovers its rank, is under investigation. We plan to take full advantage of computer algebra techniques to achieve this task. For the time being, we compute new consistent initial conditions valid for the two phase domain from a poor initial guess.

6. Conclusion Because simulators deal with ever larger models and face ever tougher numerical challenges, various automatic model transformation techniques are considered for improving result accuracy and allowing model reuse. This work investigates new simulation processes where symbolic transformation steps alternate with numerical evaluation steps, thanks to an original framework allowing cooperation between calculation systems. Predefined co-operative strategies have been coded successfully. Future work will try to make any co-operative strategy evolve during each simulation, depending on the model semantics and the simulation context. References [1] Alloula, K., Belaud, J.-P., Leibovici, C., & Le Lann, J.-M. 2006, "Traitement symbolique et numérique de modèles thermodynamiques implicites", in SIMO 2006. [2] Alloula, K., Belaud, J.-P., & Le Lann, J.-M. 2007, "Mixing computer algebra and numerical methods when solving CAPE models", Computer-Aided Chemical Engineering, vol. 24, pp. 135-140. [3] Bischof, C., Büucker, H., Marquardt, W., Petera, M., & Wyes, J. 2006, "Transforming Equation-Based Models in Process Engineering," in Automatic Differentiation: Applications, Theory, and Implementations, vol. 50 Springer Berlin Heidelberg. [4] Dedieu, J.-P. 2006, Points fixes, zéros et la méthode de Newton Springer Berlin Heidelberg. [5] Houstis, E. N. & Rice, J. R. 2000, "Future problem solving environments for computational science", Mathematics and Computers in Simulation, vol. 54, no. 4-5, pp. 243-257. [6] Pop, A., Savga, I., Aßmann, U., & Fritzson, P. 2005, "Composition of XML Dialects: A ModelicaXML Case Study", Electronic Notes in Theoretical Computer Science, vol. 114, pp. 137-152. [7] Pryce, J.D. 2001, “A simple structural analysis method for DAES”, BIT, vol. 41, no. 2, pp. 364-394. [8] von Wedel, L. 2002, CapeML - A model exchange language for chemical process modeling., Lehrstuhl f¨ur Prozesstechnik, RWTH Aachen University.

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Adaptive moving pivot technique for growth dominated population balance equations Heiko Briesen Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstraße 1, D-39106 Magdeburg, Germany, [email protected] Present address: Chair for Process Systems Engineering, Technical University of Munich, 85350 Freising, Germany, [email protected]

Abstract An adaptive moving pivot technique for the solution of population balance equations is presented that extends previous pivot techniques (Kumar and Ramkrishna, Chem. Eng. Sci., 51(8):1311–1332, 1996; 51(8):1333–1342, 1996; 52(24):4659–4679, 1997) in two ways. Firstly, equations are derived to guarantee the preservation of two arbitrarily chosen integral properties. Secondly, a grid adaptation strategy is proposed. With these extensions the scope of pivot techniques is significantly broadened. The growth term is now also preserving two arbitrarily chosen integral properties. Keywords: Population balance, numerical solution, adaptive moving pivot

1. Introduction Population balance modeling has become a versatile tool to address many different applications (e.g. crystallization, polymerization, granulation). Consequently, there is still large interest in efficient and robust solution techniques for population balance equations. Although many different techniques have been proposed, most of them focus on specific aspects. Thus, no generally accepted all-purpose solution technique is available today. One widely adopted solution class are pivot techniques developed by Kumar and Ramkrishna [1, 2, 3]. Part I and II of their paper series mainly address aggregation and breakage problems with remarkably convincing results. Part III presents an extension of the technique to problems including growth and nucleation. For growth the method of characteristics is adopted to practically eliminate numerical diffusion and dispersion. Nucleation is handled in an ad-hoc manner by introducing new pivots at basically regular time intervals. While a consistent preservation for two integral properties is considered in the aggregation operator (or any general source and sink operator), the growth term violates this preservation. In this contribution an adaptive moving pivot technique is presented which extends previous pivot technique in two ways. Firstly, equations are derived to guarantee the preservation of two arbitrarily chosen integral properties. Secondly, a grid adaptation strategy is proposed.

2. Adaptive moving pivot technique 1.1. Discretization The population balance equation for arbitrary source and sink terms hr and a potentially size dependent growth rate G(ȟ) is given by

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∂n(ξ , t ) ∂G (ξ )n(ξ , t ) + = ¦ hr (ξ , t ). ∂t ∂ξ r

(1)

To obtain a discretization of this equation consider a property function p(ȟ), which is multiplied with the population balance equation. In the most intuitive case this can be monomials of ȟ which after integration over the whole domain would yield the wellknown moment representation. However, here the equation is only integrated sectionwise. Integration over (potentially time-varying) sections [ȟi , ȟi+1] and employing the generalized Leibniz formula, the equation can be recast to (see [3]):

d dt

∂p (ξ ) ³ξ p(ξ )n(ξ , t )dξ = ξ³ G(ξ ) ∂ξ n(ξ , t )dξ + i i

ξ i +1

ξ i +1

ξ i +1

³ p(ξ )¦ h (ξ , t )dξ . k

ξi

(2)

k

Implicitly, the method of characteristics is adopted here as the term on the l.h.s. represents a total derivative. I.e. the derivative describes the temporal change in a section noticed by an observer moving with growth velocity. The evolution equation of the section boundaries is therefore given by

dξ i dt

= G (ξ ) for

all but the leftmost

section boundary, which is kept to zero. For an actual discretization, discrete representations of the distribution function f need to be employed. Kumar and Ramkrishna [1, 2, 3] use a summation of Dirac impulses. The location of the Dirac impulses, which should contain a representative value of ȟ on the respective section, they called pivot. Introducing the Dirac representation in the time derivative only and performing the integration yields

dN ∂p(ξ ) dxi i+1 ∂p(ξ ) p( xi ) i + Ni = ³ G(ξ ) n(ξ , t )dξ + dt ∂ξ xi dt ξi ∂ξ ξ

ξi +1

³ p(ξ )¦ h (ξ , t )dξ . k

ξi

(3)

k

Note that the distribution terms on the r.h.s. have not yet been discretized. The standard pivot techniques by Kumar and Ramkrishna [1, 2, 3] uses Dirac impulses also for the r.h.s. terms. Any two property functions can be chosen. Obviously, it is reasonable to control the zeroth moment (total number of the population). Using p(ȟ) = 1, evolution equations for the total numbers in the respective sections are obtained in a straightforward manner. The time derivative of the numbers results from section-wise integration over all the nucleation sources. More interesting is the evolution of the pivots. It can be derived using e.g. a monomial of ȟ. Technically relevant is the control of the total mass (volume) of the population, which corresponds to p(ȟ) = ȟ3. Note, that the following equations are given for general p(ȟ). All results presented are computed using the third order monomial. From the knowledge of the total number and the section interval, the distribution can be approximated by a simple piecewise constant representation (see dashed representation in figure 1). This piecewise constant representation is used to integrate the growth term for each but the last section. As the last section’s right boundary is infinity, a Dirac representation is used there. Using the evolution equation of the total number for each section, the evolution equation for pivots can be recast to:

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­ Ni ξi+1 G(ξ ) ∂p(ξ ) ; i ≤ m −1 ξ dξ dp(ξ ) dxi i+1 °ξ −ξ ³ . (4) − ³ [ p(ξ ) − p(xi )]⋅ ¦hk (ξ , t )dξ = ® i+1 i ξi Ni ∂p(ξ ) dξ xi dt ξi G x t N i ( , ) ; 1 = k ° i i dξ xi ¯ In standard pivot techniques the growth term for every section would be the same as in the last section in the previous equation. The proposed extension seems quite simple. However, in the end this simple extension allows movement of the pivot within the particle size class different from the growth rate (for zero sources). By this different movement the desirable preservation of integral properties (like volume of particles) can be guaranteed also for growth processes. 1.2. Adaptation strategy The use of the piecewise constant representation also allows the derivation of an adaptation strategy based on a local error estimator. If the piecewise constant representation cannot properly reflect the integral property evaluated by the use of the Dirac impulse, the piecewise linear approximation is no longer valid: ξ i +1

N i p ( xi ) −

³ p (ξ )dξ

ξi

ξ i +1 − ξ i

(5)

m

< tol ⋅ ¦ N i p ( xi ) i =1

The above condition is checked at every time step. If it is violated, the section is split into two newly initialized sections. To identify the new boundary ȟnew a simple optimization problem can be formulated. First a linear approximation is constructed from the pivot information: Search for a piecewise linear function gi(ȟ) = ci,1ȟ + ci,2 on the interval [ȟi , ȟi+1] which preserves total number and a second integral property: ξ ξ i +1 ³ξ g (ξ ) dξ = N i and ³ξ i g (ξ ) p (ξ ) dξ = N i p ( xi ). The two equations can explicitly be solved for the coefficients of the linear approximation. The sections to be generated (boundaries and pivots) shall perfectly satisfy the error criterion: i +1

i

p (x 1 , new ) =

ξ new

³ p (ξ )d ξ / (ξ ξ

new

− ξ ),

p (x 2 , new ) =

i

ξ i +1

³ p (ξ )d ξ / (ξ

i +1

− ξ new ).

(6)

ξ new

Also the total number Ni and the integral property p(ȟ) in the original section shall be preserved in the newly formed sections: N i = N1, new + N 2, new , (7)

N i p ( xi ) = N1, new p (x1, new ) + N 2, new p (x2, new ).

(8)

From the above equations N1,new and N2,new can be eliminated as functions of p(x1,new) and p(x2,new). They are then used in the following optimization that yields the split point of the original section: 2

ξ new

2

ξ new ξ i +1 § · § · ¨ ¸ ¨ = arg min N1, new − ³ g (ξ )dξ + N 2, new − ³ g (ξ )dξ ¸ . ¨ ¸ ¨ ¸ ξi ξ new © ¹ © ¹

(9)

Note that the overall computational cost of the adaptation routine is negligible. A grid coarsening strategy, which is omitted here for brevity, can be derived by analoguous

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reasoning. However, grid coarsening is not important for the here investigated test cases. For time integration an explicit Euler scheme with adaptive step size control based on step doubling is used for simplicity.

3. Testcases In this contribution growth and nucleation will be considered. To focus on numerical behavior, only analytically solvable but numerically challenging test cases will be considered. As the method is particularly useful for problems with steep fronts by basically fully eliminating numerical diffusion and dispersion, the constant growth (G = 1) of a block function (initialized on the interval [0, 1]) is considered as test case 1. In other test cases, constant growth (G = 1) is coupled to different nucleation rates. In test case 2, a constant nucleation rate (h1 = 1) is considered. Test case 3 investigates a nucleation rate that changes by a saw-tooth function between 0 and 1 at intervals of 2. In each of the cases the analytical solution is trivial. However, the steep fronts and the step changes of the saw-tooth functions make the numerical solution difficult. Note that all test cases are interesting only from a numerical point of view. Therefore, units of measure are completely omitted here.

4. Results As figure 1 shows, the evolution of the pivots is very similar for the adaptive and the standard moving pivot technique. Note, that the adaptation does not play any role in this case as in both methods only one single pivot is needed to represent the solution. However, the differently discretized growth term in equation (4) allows for adjusting the pivot position to preserve the third order moment almost perfectly while the standard pivots technique produces relative errors up to 15%.

Figure 1: Comparison of adaptive and standard pivot technique for the solution of test case 1. Left: Position of the single pivot vs. time. Right: Relative error of the third order moment of the distribution.

Figure 2 show the equivalent plots for the test case 2. Here, the deviation between the adaptive and the standard pivot technique becomes obvious also in the pivot positions. Note, that the adaptive pivot technique only uses one single pivot to obtain the result. To properly handle nucleation processes in the standard pivot technique new pivot need to be inserted at regular time intervals [3]. Thus, the number of pivots increases with simulation time. The right of figure 2 therefore shows the relative error in the third order moment also for simulations where new pivots are inserted at regular intervals ǻnew = {1, 2}. While the adaptive pivot technique produces nearly optimal results with only one pivot, the standard pivot technique produces significant errors even if 10 pivots are used (ǻnew = 1).

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Figure 2: Comparison of adaptive and standard pivot technique for the solution of test case 2. Left: Position of the single pivot vs. time. Right: Relative error of the third order moment of the distribution.

The left of figure 3 shows the final state after a simulation time of 10 for test case 3. For the smallest tolerance the actual saw-tooth distribution is well recovered in the simulation. Note, that the step changes are detected by the adaptation procedure only. No a priori knowledge on the positions of the step changes is provided to the simulation. As the tolerance increases the representation of the density distribution gets worse. It should be stressed that the representation given in the left of figure 3 is not the actual result of the simulation. Recall that the simulation determines pivot (position and number). Thus, the actual result of the simulation is only a summation of Dirac impulses. The property to be controlled, i.e. the third order moment, is calculated only on the basis of these pivots. Figure 3 (right) shows the evolution of these third order moments for different simulations. It can be seen that even for the tolerance of 10−3 the agreement of the adaptive pivot and the analytical solution is remarkable. According to the adaptation criterion, errors for small particles are considered to be less important as they contribute less to the overall third order moment. Therefore, the erroneous representation given in the left of figure 3 for this tolerance does not significantly affect the third order moment. Again the standard pivot technique fails even if new pivot is introduced at perfectly chosen time intervals of ǻnew = 2.

Figure 3: Results for test case 3. Left: Final number density distribution calculated with the adaptive pivot technique for differently specified tolerances. Right: Evolution of third order moments for adaptive and standard pivot simulations as well as analytical results.

5. Conclusions With the above extensions the scope of pivot techniques is significantly broadened for the following reasons. The growth term is now also preserving two arbitrarily chosen integral properties. A grid adaptation strategy is introduced which reflects the dynamic

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behavior of the system (even including discontinuity detection). Nucleation (also at the left boundary) seamlessly integrates in the proposed framework.

References [1] S. Kumar and D. Ramkrishna. On the solution of population balance equations by discretization I. A fixed pivot technique. Chem.Eng. Sci., 51(8): 1311–1332, 1996. [2] S. Kumar and D. Ramkrishna. On the solution of population balance equations by discretization II. A moving pivot technique. Chem.Eng. Sci., 51(8): 1333–1342, 1996. [3] S. Kumar and D. Ramkrishna. On the solution of population balance equations by discretization III. Nucleation, growth and aggregation of particles. Chem.Eng. Sci., 52(24): 4659–4679, 1997.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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An Efficient Discretization Approach for Partial Differential Equations describing Chemical Reaction Systems Jan C. Schöneberger, Harvey Arellano-Garcia, Günter Wozny Chair of Process Dynamics and Operation, Berlin Institute of Technology, Sekr. KWT9, Str. des 17. Juni, D-10623 Berlin, Germany, E-mail: [email protected]

Abstract In this work, an efficient solution approach based on the orthogonal collocation on finite elements is proposed for PDE-Systems describing chemical reaction systems. For this purpose, three discretization methods are compared to each other in terms of convergence, accuracy, and computation time. First, the simplest and most applied discretization method is the method of lines (ML). Here, the differential terms in the equation system are replaced by linear difference approximations. The second one is the multiple shooting (MS), which makes use of the boundary conditions, and thus, the PDE is reformulated to a root finding problem on ODE. Finally, the orthogonal collocation (OC) is a Runge-Kutta type discretization method that leads to the highest possible error order by collocating the discrete points at their optimal positions. These three approaches are tested for different numbers of discrete points on a PDE of the type which results from modelling fixed bed reactors (FBR). A test system with an existing analytical solution was chosen for an impartial comparison. In addition, two further case studies are considered to point out the advantages of the proposed discretization approach.

Keywords: Partial Differential Equations, Discretization, Collocation, Multiple Shooting, Fixed Bed Reactor

Orthogonal

1. Introduction Catalytic fixed bed reactors have a wide range of industrial applications. The needs for the different heterogeneous catalyzed gas phase reactions led to different geometrical designs for these reactors e.g. tubular reactor, radial reactor, mono line reactor, etc. Due to the unknown precise geometry of the catalyst filling and the complex nature of the chemical reactions, it is generally not possible to apply CFD tools. However, the effects inside these reactors can be modeled very detailed by the consequent application of conservation equations, i.e. mass, energy and momentum balances, combined with transport equations. The resulting equation system contains partial differential equations (PDE), ordinary differential equations (ODE) and algebraic equations (AE) which are coupled in a complex manner. Even with today’s high CPU power it is still a challenging task to solve these kinds of problems. Moreover, the chosen discretization approach is decisive for success or failure. It affects considerably the robustness and the convergence velocity of the solving algorithm. The choice of the discretization method also affects the possibilities of physical modelling. The orthogonal collocation (OC) e.g. allows but does not require the application of a boundary condition for second derivatives. This second boundary condition often can not be declared physically, and in the case of ML, it additionally lowers the numerical accuracy.

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2. Problem Statement Reaction systems can be modeled using the conservation equations such as component balances (1), energy balance (2), and momentum balance [1]. The momentum balance is not considered here, because it is impossible to solve it without the knowledge of the exact geometry. Thus, based on the assumptions taken, the Ergun equation is used here for the pressure drop [2]. NR dci & = div (Di ∇ci ) − ∇(wci ) + ¦ Ȟi,j rj − n PI a PI dt j

NC

¦cc i

i

P ,i

dT = div (λ ∇ T ) − dt

NC

¦cc i

P ,i

(1)

& ∇ (w T ) +

i

NR

¦

− Δ h R , j r j − q PI a PI

(2)

j

From this type of PDE the generically test equation (3) can be derived for e.g. the Temperature T and one spatial dimension x.

dT ∂ 2T ∂T + k3 2 = k 0 + k1T + k 2 dt ∂x ∂x

(3)

Typical boundary conditions for these type of equations are a Dirichlet bound at the inlet (x = 0) and a Neumann bound at the outlet (x = L), given in Eq. (4).

T ( x = 0 ,t ) = T0

§ ∂T · =0 ¸ ¨ © ∂x ¹ x = L ,t

( Dirchlet )

(4)

( Neumann )

The parameters for the test equation are given in Tab. 1. The advantage of this equation is that it can be solved analytically for the steady state case. This makes comparable the numerical solutions with the different discretization approaches. Due to the large terms of the analytical solution it is not posed here. Table 1: Parameter Set for the test PDE

k0

k1

k2

k3

T0

L

1 J/s

0.001 J/(K s)

0.01 Jm/(K s)

0.01 Jm²/(K s)

1000 K

1m

3. Discretization Approaches 3.1. Method of Lines Due to its simplicity, the Method of Lines is the most common discretization approach [3]. The spatial differential terms are replaced by difference terms as shown in Eq. (5). This transforms the PDE into an ODE. But, the inclusion of the boundary conditions leads to additional AE, thus, resulting in a DAE system. This affects the numerical behavior and the computational effort as well. The error order of the ML is 2.

§ ∂ 2T · Tk +1 − Tk −1 ML ¨¨ 2 ¸¸ ⎯⎯→ x Δx 2 ∂ © ¹ x = xk

T −T § ∂T · ML ¨ ¸ ⎯⎯→ k +1 k −1 2Δx © ∂x ¹ x = xk

(5)

Moreover, the boundaries lead to an additional problem, namely, for the inclusion of the Neumann boundary, the central difference has to be replaced by the backward

An Efficient Discretization Approach for Partial Differential Equations

903

difference in the last element reducing the error order to 1. This effect can be seen in the resulting numerical solutions. 3.2. Multiple Shooting The approach of the multiple shooting is to apply common ODE solvers for the solution of the PDE. For this purpose the boundary conditions have to be transformed to initial conditions. In the single shooting method, it is done by introducing a new parameter s. This is determined by the solution of the root finding problem given in Eq. (6). For a set of equations this method is instable, but it can be stabilized by introducing intervals (i.e. discrete points) in which the single shooting is applied fulfilling new boundary conditions that guarantee a continuous solution. This approach is called multiple shooting [4]. The error order of the MS depends on the error order of the applied ODE solver.

§ ∂T · ¨ ¸ =s © ∂x ¹ x =0

· § § ∂T ( s ) · ¸ − 0 ¸¸ = 0 ¹ © © ∂x ¹ x= L

Φ ( s ) = ¨¨ ¨

(6)

3.3. Orthogonal Collocation The main idea of the proposed discretization approach based on the OC is that the numerical solution of the PDE is given as a polynomial, Eq. (7), [5]. The degree of the polynomial is determined by the number of discrete points NK, and dn represents the polynomial coefficients. NK

T ( t , x ) = ¦ d n ( t )x n −1

(7)

n =1

With this assumption, the differential terms in Eq. (3) can now be replaced as shown in Eq. (8) and (9). NK § ∂ 2T · OC ¨¨ 2 ¸¸ ⎯⎯→ d n ( n − 1 )( n − 2 )xk( n−3 ) ¦ ∂ x n =1 © ¹ x = xk

NK § ∂T · ⎯OC ⎯→ ¦ d n ( n − 1 )xk( n −2 ) ¨ ¸ © ∂x ¹ x = xk n =1

(8)

(9)

This is an approach that includes also the boundaries. If there is no need for the outlet boundary, the polynomial can be chosen in a different way excluding this point. Due to the extrapolation of the polynomial, a solution will be obtained anyway. The discrete point’s xk are neither equidistant nor free, but determined in the way that the error order is maximized. This leads to an error order of 2NK, which denotes the maximum order for Runge-Kutta type discretization methods. The inclusion of the Neumann boundary can be implemented properly without affecting the error order by making use of the features of a polynomial. Similar to the multiple shooting approach, the space can be divided into finite intervals, in which the polynomials can be determined. This is related to the Orthogonal Collocation on Finite Elements (OCFE), which is used here in order to solve the resulting ODE after the spatial discretization, because it allows step size

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control algorithms. Hence, it can be used as a common ODE solver. For this purpose, two and three OC points are used. The OCFE approach has the advantage over commercial ODE solver because derivative calculations can be included simply with the method of internal numerical differentiation. This also enables its use for the solution of optimization problems [6].

4. Comparison of the Approaches In Fig. 1 the analytical and the numerical solutions for 6 discrete points are shown. MS and OC give similar results but ML is far away from the solution. The error order, which reduces the influence of the Neumann boundary, affects also the accuracy of the solution at the inner points.

Figure 1: Trajectories of the Numerical Solutions with 6 Discrete Points.

The results for a varying number of discrete points are summarized in Tab. 2. To reach a comparable accuracy with the ML, 100 discrete points are necessary. In order to reach the same error with MS, only 4 points are used, and the computation time is reduced by the factor of 25. The OC with 4 points gives even better results and is 12 times faster than the MS. However, it should be noted that for few points the accuracy of the first derivative is higher with the MS. The results are mean values of 100 calculations. For the MS approach the Matlab® solver ode15s was employed, because it was found to be the most accurate solver for the examined system [7]. Table 2: Results for Different Numbers of Discrete Points

Method Discrete Points

ML 6

ML 100

MS 4

MS 6

OC 4

OC 6

Error in T [K]

5.85

0.06

0.06

0.03

5¨10-3

2¨10-6

Error in dT/dx [K/m]

23.89

0.28

0.02

0.08

Computational Effort [s]

0.08

3.18

0.12

7¨10-3 0.29

5¨10-5 0.02

0.01

Comparable results were obtained for the dynamic simulation of the problem. The additional dimension allows the combination of different approaches. These results are too extensive so as to be presented in detail here. However, the most efficient approach is the combination of the OC in spatial direction with the OCFE in time direction.

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5. Case Studies 5.1. Consecutive Chemical Reaction An isothermal consecutive reaction system with high differences in the reaction rates is analyzed. This case study is used to demonstrate the ability of the OC to solve extremely stiff equation systems. The results are compared to the solutions calculated with the commercial ODE solvers provided by Matlab®. 5.2. Two-Phase Model of a Catalytic Fixed Bed Reactor A catalytic fixed bed reactor is modeled using the conservation equations for the fluid phase and the solid phase. The two phases are coupled by complex heat- and mass transfer correlations. The time and space variant system involves a set of 15 state variables. This gives for 40 discrete points (that are a minimum for the ML) a set of 570 ODE and 150 AE. Here, the advantage of the few discrete points, which are necessary for the OC, is demonstrated.

6. Conclusions Although the ML is the most common and easiest to apply approach it is not giving satisfactory results for chemical reaction systems. Especially in multi phase systems the OC is of advantage because it manages a high accuracy with few discrete points which leads to much smaller algebraic equation systems. The MS also gives good results and is even more accurate than the OC when describing the gradients. Anyhow, to reach the same accuracy in the numerical solution more calculation effort is necessary. These positive effects are multiplied when the methods are applied to more dimensions, e.g. the time. Finally it can be concluded that the OC combined with the OCFE is the best approach for the considered PDE describing chemical reaction systems, especially catalytic fixed bed reactors.

Acknowledgements The authors gratefully acknowledge support from the Max-Buchner Forschungsstiftung.

References [1] H.D. Baehr, K. Stephan, Heat- and Mass Transfer, Springer, 1998 [2] J.C. Schöneberger, H. Arellano-Garcia, S. Körkel, H. Thielert, G. Wozny, Computer Aided Chemical Engineering, Vol. 25 (2008) [3] F. Shakeri, M. Dehghan, Computers & Mathematics with Applications Vol. 56, (2008), P. 2175 [4] R. England, R. Lamour, J. López-Estrada , Applied Numerical Mathematics, Vol. 42 (2002), P. 117 [5] B.A. Finlayson, Nonlinear Analysis in Chemical Engineering, McGraw-Hill, 1980 [6] L.T. Biegler,,Computers & Chemical Engineering, Vol. 8 (1984), P. 243 [7] L.F. Shampine, M.W. Reichelt, SIAM J. on Scientific Computing, Vol. 18 (1997), P. 1

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

907

A new numerical solution scheme for tracking sharp moving fronts Ala Eldin Bouaswaig a and Sebastian Engell a a

Process Dynamics and Operations Group , Technische Universität Dortmund, 44221 Dortmund, Germany, E-mail: [email protected]

Abstract The numerical solution of a hyperbolic or a convection dominated parabolic partial differential equation is challenging due to the large local gradients that are present in the solution. In this paper, a novel approach that is based on combining the high order weighted essentially non-oscillatory (WENO) scheme with a static moving grid method is presented. The proposed algorithm is tested on two case studies and enhancements in the performance are observed when compared with the conventional WENO scheme on a uniform grid making it a promising alternative when dealing with problems of this nature. Keywords: WENO scheme, Adaptive gridding, Burgers' equation, Population balance equation, Emulsion polymerization

1. Introduction The numerical solution of hyperbolic or convection-dominated parabolic partial differential equations (PDE) is challenging due to the large local gradients in the solution profile. If a uniform fixed grid is used for the discretization, it has to be sufficiently fine to be able to track the steep fronts that are associated with these large gradients. Such a distribution of the grid nodes over the discretization domain is, however, likely to be inefficient since in smooth regions less nodes are actually required and only in the vicinity of the steep front does the grid have to be dense. This stimulates the need to use a nonuniform grid and to adapt it continuously to track the evolving steep front in the solution. Grid adaptation techniques can be categorized into two groups, static and dynamic [1]. In the dynamic version, the grid is continuously moved with the solution and both subproblems, the grid adaptation and the solution of the original PDE, are tackled simultaneously. In contrast, when static grid adaptation is used, the grid is either refined (local grid refinement method) [2] or the grid cells are moved (moving mesh method) at discrete points of time [3]. Grid adaptation must be combined with an appropriate numerical method for discretizing the PDE. Recently high order discretization methods have gained increasing interest [1,2]. For example, the weighted essentially non-oscillatory (WENO) scheme has emerged as a promising alternative for handling hyperbolic PDEs on a uniform grid. Combining the WENO scheme with grid adaptation merges the benefits of having a high resolution scheme with those of adapting the grid. This has been applied to dynamic grid adaptation by Lim et al. [1] and static grid adaptation with local grid refinement by Smit et al. [2]. However, a combination of the WENO scheme with a moving mesh static grid adaptation technique has not yet been investigated. The aim of this contribution is to describe how the WENO scheme can be applied on a nonuniform grid that is composed of a fixed number of nodes and that moves at discrete

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points of time. To illustrate the benefits that are gained by such an implementation, the quality of the results obtained by using this novel approach is evaluated by testing it on the viscid Burger’s equation and on a challenging hyperbolic PDE, the population balance equation (PBE) that describes the growth of polymer particles in emulsion polymerization. The remainder of this paper is divided as follows: In Section 2, the mathematical formulation of the WENO scheme on a nonuniform grid is presented and the static grid adaptation algorithm is briefly addressed. In Section 3 the performance of the method is investigated on the two case studies mentioned above, and finally, Section 4 gives a summary and conclusions.

2. The numerical approach The WENO scheme on a non-uniform grid The WENO scheme on a nonuniform grid is presented here based on the paper of Shu [4], and the used notation is similar to that in [4]. Starting from the discrete form of a general one dimensional homogeneous hyperbolic conservation law of a quantity ( u ):

dui + dt

fˆ

i+

1 2

− fˆ

i−

1 2

= 0,

Δxi

cell averages of the function x

1 fi ≡ Δxi

i+

x

i = 1,2,..., N ,

(1)

f (x) are defined by Eq. (2):

1 2

³ f (ϕ )dϕ.

(2)

1 i− 2

For a WENO scheme of order k in smooth regions, k stencils are defined and on each th

of them a k order approximation of the flux is derived as follows: k −1

f ( r1) = ¦ cr( ,kj),i f i − r + j , i+

r = 0,...., k − 1,

(3)

j =0

2

k k § · ¨ k ¦ω =0,ω ≠m ∏ p =0, p ≠ m,ω ( xi + 1 − xi −r + p − 1 ) ¸ 2 2 ¸ =¨ ¦ Δxi −r + j . k ¨ m= j +1 ¸ ( x − x ) ∏ω =0,ω ≠m i−r +m− 1 i −r +ω − 1 ¸ ¨ 2 2 © ¹

cr( k, j),i

(4)

The desired numerical flux in Eq. (1) is now constructed by applying Eq. (5):

fˆ

i+

k −1

1 2

= ¦ ω ( q1) f ( q1) ,

where

q =0

i+

2

i+

2

ω ( q ) are nonlinear weights that depend on the smoothness of the solution.

(5)

A New Numerical Solution Scheme for Tracking Sharp Moving Fronts

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Grid adaptation The static grid adaptation technique is performed by firstly adapting the grid to suite the initial profile. The profile is then interpolated to obtain new initial conditions on the new nonuniform grid and the PDEs are discretized. Finally, the resulting set of ODEs is integrated for a certain time duration while keeping the grid fixed and the procedure is then repeated until t final is reached [3]. The location of the grid nodes is determined so as to equally distribute a monitor function m( x ) , which in this work is taken to be the arc-length of the solution defined by Eq. (6):

∂f ( x) m( x ) = 1 + ∂x

2

(6) 2

Thus, to perform the grid adaptation step, all points on the solution profile are connected with each other and the total length of the resulting polygon is divided into equal parts. The new position of the discretization nodes is consequently determined by projecting the points that result from this equidistribution on the x-axis.

3. Numerical experiments All simulation runs shown in this section are performed on a PC with an Intel® Core™2 Duo Desktop Processor and with 2.0 GB of RAM. gPROMS® is used as a DAE solver and for implementing grid adaptation, it is connected to a dynamic link library programmed in Compaq Visual FORTRAN. Additionally, the l2 error norm used for analyzing the results is defined as follows:

§ N · l 2 = ¨ ¦ (u i − uˆ i ) 2 ¸ , © i =1 ¹ where ui stands for the numerical solution and

(7)

uˆi is the corresponding analytical

solution. The Viscid Burgers’ equation (BE) The BE, given by Eq. (8), is frequently used to test grid adaptation [1,5]:

∂ 2u ∂ (0.5u 2 ) ∂u +μ 2 . =− ∂x ∂t ∂x

(8)

Fig. 2 compares the results of WENO35 with adaptive gridding (WENO35-AG) with the analytical solution of the BE taken from [5]. The corresponding grid is depicted in Fig. 4 at discrete points of time. The performance of the WENO35-AG is outstanding and the numerical solution can hardly be distinguished from the analytical one. This observation is also reflected in the results of the error norm shown in Fig. 1. It is obvious from the results that, using grid adaptation enhances the performance of the WENO scheme. For example, it follows from Fig. 1 that for the classical WENO35 to produce results as accurate as WENO35-AG on a grid made of 100 nodes, the uniform grid must consist of around 250 nodes.

A.E. Bouaswaig and S. Engell

910 0

10

1

Classical WENO35 WENO35-AG ] -[ -1 10 m r o N l2

0.8 0.6 x( u

0.4 0.2

-2

10

50

100

150 200 250 # Grid nodes [-]

0 0

300

0.2

0.4

0.6

0.8

1

x [-]

Figure 1. Influence of grid refinement on the l2 error norm for WENO35 and WENO35-AG scheme at t = 1.0 (-) when applied to the BE.

Figure 2. Comparison of the analytical solution of the BE with the solution of WENO35-AG. Number of grid nodes=100.

100 80

1

Classical WENO35 WENO35-AG

0.8 ] s[ e m ti U P C

60

] -[ t

40 20 0 50

0.6 0.4 0.2

100

150 200 # Grid nodes [-]

250

300

Figure 3. Comparison of the CPU time for the classical WENO35 scheme and WENO35-AG when applied to the BE.

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [-]

Figure 4. Location of grid nodes at discrete points of time during the simulation of the BE for theWENO35-AG scheme.

The required CPU time for the WENO35 on this uniform grid and for the WENO35-AG on a 100 nodes gird are approximately 58 [s] and 26 [s] respectively as illustrated in Fig. 3. Hence, even though the calls of the grid adaptation subroutines in the WENO35AG method entail an additional computational load, the total CPU time required to achieve a certain accuracy is considerably less than that for the classical WENO35 scheme due to the possibility of using a coarser grid with WENO35-AG. Growth of particles in emulsion polymerization Emulsion polymerization is a radical polymerization process that is used to manufacture several polymers of commercial importance. The modeling of the process is quite involved, and when it is desired to describe the particle size distribution (PSD), a PBE is usually used, and this significantly increases the complexity of the model. The reader is referred to [6] for detailed information about the process. The polymer particles are of different sizes ( r ) and are located at different positions in the reactor. Assuming a well-mixed reactor, the spatial variation can be neglected, furthermore, to simplify the task the particles are assumed to be colloidally stable (no coagulation) and only the growth of a seed of polymer particles is considered. The PBE for this case reads:

∂n(r , t ) ∂ (r(r , t )n(r , t )) , =− ∂t ∂r

(9)

A New Numerical Solution Scheme for Tracking Sharp Moving Fronts

1-

911

(a)

]

120

m

1-d

t=0.75 [-] t=1 [-]

100

l l o m [ n oi ct n uf y t si n e D

t=0.5 [-] t=0.25 [-]

80 60

t=0 [-]

40 20 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.3 0.4 0.5 0.6 0.7 Normalized particle radius [-]

0.8

0.9

1

(b) ] 1 -[ e m ti 0.75 h ct 0.5 a b d e 0.25 zil a m 0 r o 0 N

0.1

0.2

Figure 5. (a) Comparison of the MOC solution (continuous line) with the simulation results of the WENO35-AG scheme (− · − · −) for the PBE in emulsion polymerization on a 100 nodes grid. (b) Location of grid nodes during simulation for the WENO35-AG scheme.

where n(r , t ) is the population density function and r( r , t ) is the growth rate of polymer particles and is given by Eq.(10):

r(r , t ) =

k p MWM

[M ] p n (r , t ).

4πr ρ p N A 2

(10)

In Eq. (10), kp is the propagation rate coeffecient, MWM is the molecular weight of the monomer, NA is Avogadro’s number, ρp is the polymer density, [M]p is the monomer concentration in the particle phase and n is the average number of radicals per particle. Fig. 5 illustrates the evolution of the PSD and the grid over the normalized batch time. As can be observed, the grid moves to track the movement of the PSD and the nodes are concentrated in the regions of pronounced spatial variations. 120 1-

]

m

100

l l o m [ n oi ct n uf y t si n e D

80

1-d

60 40 20 0 0.35

0.4 0.45 Normalized particle radius [-]

0.5

Figure 6. Comparison of WENO35 on a grid made of 220 nodes (filled circles) with the WENO35-AG (dotted line) and MOC (continuous line) on a grid made of 100 nodes when applied to the PBE in emulsion polymerization.

A.E. Bouaswaig and S. Engell

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In addition, the solution profile is neither spoiled by spurious oscillations nor by numerical diffusion. This fact is more evident in Fig. 6 that depicts the PSD at the end of the batch. The results shown in this figure are for WENO35-AG on a grid consisting of 100 nodes, WENO35 on a uniform grid composed of 220 nodes and a semi-analytical solution obtained by applying the method of characteristics (MOC) [7]. The results are comparable, however, when WENO35 is used, the required computation time is 318 [s] while its counterpart for the WENO35-AG is 205 [s]. This supports the previous conclusion that, being able to use a coarser grid with WENO-AG reduces the total computation time despite the additional computational load that arises from the calls of the grid adaptation subroutine.

4. Conclusions To avoid the undesired excessive numerical diffusion when dealing with hyperbolic and convection dominated parabolic PDEs a combination of a high order numerical discretization method and grid adaptation can be applied. This will guarantee concentrating the grid nodes in the locations where they are needed the most and will enable the use of a relatively coarser grid without having to sacrifice the accuracy. It is shown here that coupling the WENO scheme with static grid adaptation provides a tool that has proven to be efficient when applied to two case studies of different nature: a non-linear parabolic PDE, the viscid Burgers’ equation, and a challenging nonlinear hyperbolic PDE, the PBE in the context of emulsion polymerization. Results in both cases reveal that the proposed algorithm provides better performance when compared with the classical WENO scheme making it a promising option for similar problems.

5. Acknowledgements The financial support of the General People’s Committee for Higher Education (Libya) and of The Graduate School of Production Engineering and Logistics (Technische Universität Dortmund) is gratefully acknowledged.

References [1] Y. I. Lim, J. M. Le Lann, and X. Joulia, Moving mesh generation for tracking a shock or steep moving front, Comp. Chem. Eng., 25(2001) 653. [2] J. Smit, M. van Sint Annaland and J. A. M. Kuipers, Grid adaptation with WENO schemes for non-uniform grids to solve convection-dominated partial differential equations, Chem. Eng. Sci., 60(2005) 2609. [3] J. M. Sanz-Serna and I. Christie, A simple adaptive technique for nonlinear wave problems, J. Comput. Phys., 67(1986) 348. [4] C.-W. Shu, Essentially non-oscilllatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, In: A. Quarteroni (Ed.), Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Math. vol. 1697, Springer-Verlag, Berlin, 1998. [5] A. Vande Wouwer, P. Saucez and W. E. Schiesser, Simulation of distributed parameter systems using a Matlab-based method of lines toolbox: Chemical engineering Applications, Ind. Eng. Chem. Res., 43(2004) 3469. [6] R.G. Gilbert, Emulsion polymerization: A mechanistic approach, Academic press, London, 1995. [7] S. Sarra, The method of characteristics & conservation laws, Journal of Online Mathematics and Applications, 3(2003).

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Criteria for Outliers Detection in Nonlinear Regression Problems Flavio Manenti and Guido Buzzi-Ferraris CMIC Dept. “Giulio Natta”, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milano, ITALY – Email: [email protected]

Abstract This research activity deals with robust methods for parameters estimation of nonlinear models and the outliers detection. It specifically discusses some advances in criteria to discriminate among gross errors, bad experimental design, and inadequate model selection. All the methods and the criteria proposed in this work are implemented in BzzMath library, a free scientific tool to solve numerical problems. Keywords: Outliers detection; Parameters estimation; Robust methods; Nonlinear regressions.

1. Introduction Numerous scientific and industrial fields have the need to identify and repair / reconcile / remove outliers that usually affect the raw data set of experiments, so to avoid large mistakes in the model parameters evaluation. There are different sources of outliers: • An outlier can directly affect an experimental value: it may be located on both dependent and independent variables and it may be generated either by an experimental problem or by a mistake in reading, writing, transcription, etc. (the so-called human factor). When it is due to the operator who acquired that value, the outlier is called gross error. • The current design of experiments may be inadequate to describe the phenomenon in study. In fact, masking problems can arise for the possibility to confuse a good experiment with an outlier and vice versa. Actually, a bad experimental design might lead to point out some good experimental points as outliers and, conversely, an outlier as a good point, with strong repercussions on the parameters estimation. • At last, the same mathematical model may be unable to fit satisfactorily the overall data set in the experimental domain. The work proposes some additional criteria to improve nonlinear regression method robustness, starting from one of the best methods in robust parameter estimation (Rousseeuw, 1984) and using some dedicated C++ classes belonging to BzzMath, a numerical library for scientific problems freely downloadable (Buzzi-Ferraris, 2008). A quantitative comparison between different methods is proposed in the last section of the paper.

F. Manenti and G. Buzzi-Ferraris

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2. Nonlinear Regression Analysis For a general description of a nonlinear regression problem, the following hypotheses shall be considered (Buzzi-Ferraris and Manenti, 2008, 2009): • there are n Y dependent variables y subject to experimental errors, with expected value h ; • there are n X independent variables potentially subject to experimental errors; • the model contains p adaptive parameters b , where b represent their estimates; • dependent variables are uniquely determined by n Y relations; • there are no gross errors contaminating model variables; • there are no correlations among experimental points; • experimental errors for y vector components are uncorrelated; • experimental errors for x vector components are uncorrelated. Relations among variables are:

­° y i = g ( xi , b ) + eyi ® °¯ z i = xi + exi

i = 1, n E 

(1)

where n E is the number of experimental points and eyi and exi stay for random variables with normal distribution, null expected value, and known diagonal variance matrices. n Y arbitrary complex functions, denoted by g , must univocally determine an estimation of y . Parameters b (estimates of ȕ ) and values x (estimates of ȟ ) are calculated minimizing the function: nE nX 2 2½ ­ nY S x1 ,..., x n E , b = ¦ ®¦ ª¬ωi,k ( yi,k − g k ( xi , b ) ) º¼ + ¦ ª¬ ωi,l ( zi,l − x i,l ) º¼ ¾  i =1 ¯ k =1 l =1 ¿

(

)

(2)

2 where: ωi,k = 1 / σi,k and σi,k is the variance of the k − th dependent variable in the 2 i − th experiment; ωi,l = 1 / σi,l and σi,l is the variance of the l-th independent variable

in the i-th experimental point. In many situations, this general formulation can be simplified. As an example, independent variables may be deterministic and not random, we may have just a single dependent variable etc.. A good program should be able to minimize the most adequate objective function and, at the same time, it has to suggest some additional experimental points in order to improve the parameters evaluation and to single out the best model as well. The program should also detect the possible outliers affecting the experimental data, since they could heavily modify the values of the parameters if they were not removed. A least squares analysis is generally inadequate and a more robust identification method must be adopted.

3. Algorithms for Outliers Detection Rousseeuw and Leroy (Rousseeuw and Leroy, 1987) clearly showed that the technique usually employed to detect outliers in the expected value estimation as well as the parameters estimation for linear models was inadequate. Actually, estimators like the arithmetic mean to evaluate the expected value of a population or the minimization of

Criteria for Outliers Detection in Nonlinear Regression Problems

915

the sum of least squares for evaluating parameters of a linear model try to reduce the outlier residual. As a consequence, the value of the estimator is inevitably biased when some outliers are present. Once the arithmetic mean or the parameters are estimated, the residuals are evaluated and normalized using the population variance estimation in the former case and the mean square error of the model in the latter one. Since both the variance estimation and the mean square error are based on the previous expected arithmetic mean or model parameters, they are even more biased and the analysis of the normalized residuals may be completely misleading. Specifically, as explained by Rousseeuw and Leroy (Rousseeuw and Leroy, 1987) through several examples, the following situations may occur: • Often, outliers are not detected; • Some experiments are usually indicated as outliers even though they are good points; • A model is discarded as inadequate, even though it is acceptable. The solution is straightforward for the expected value estimation: to normalize residuals, it is sufficient to replace the arithmetic mean and the variance estimate with the median and the MAD, respectively. For linear models with one dependent variable, Rousseeuw and Leroy proposed to evaluate parameters minimizing the function:

(

)

min median ( ei2 ) , b

i = 1, n E 

(3)

where ei is the residual, i.e. the difference between experimental and calculated values of the variable y in the i − th experiment. The minimization is very difficult, because of function discontinuities and multi-modality as well. However, it is not difficult to obtain a value that strongly reduces the function (3) that is sufficient for detecting the outliers. With nonlinear models, it is still necessary to minimize the function (3), but the minimum search is considerably harder. Classes belonging BzzMath library include some methods that do not stop the search as the first minimum is reached. Although the method cannot guarantee the finding of the global minimum, it is usually sufficient to significantly reduce the value of function (3) to detect outliers. When the outliers are identified, it is recommended to investigate about their origin before deleting them. Actually, they can indicate some model shortcomings in interpreting experimental data and, therefore, the necessity to revise the same model. It is worth remarking that Rousseeuw method is able to detect a number of outliers almost equal to the 50% of the number of experimental points. Nevertheless, it is correct to expect only a few of outliers and, when their number is significantly large, the model we are using could be probably inadequate to properly represent them.

4. Test Case for the Outliers Detection A comparison between the performances of least squares and robust methods is proposed here below. Data are generated through the following equation:

F. Manenti and G. Buzzi-Ferraris

916

ª §1 ·º yi = b1 ⋅ exp « −b 2 ⋅ ¨ − 0.003 ¸ » + ei x © i ¹ ¼» ¬« with:



(4)

b1 =1000. b 2 =2500. where ei are random errors of dependent variables with variance equal to 0.1. Parameters estimated without any outlier through the method of least squares are b1 =1.0034 ⋅103 and b 2 = 2.4979 ⋅103 . As a trial, an outlier is introduced by changing the last value of the independent variable x (from 373 to 383 ); hence, the model parameters b1 and b 2 are calculated using both the least squares and the robust methods. Table 1 shows data and normalized residuals obtained by applying these two methods. The outlier appears clearly visible (large residual) using the robust method, whereas the method of least squares fails in identifying it (the largest residual is in correspondence with x = 363 ). The method of least squares leads to a large inaccuracy in estimating parameters b . In such a case, resulting parameters are b1 = 999.61 and b 2 = 2198.8 , where the latter estimation is completely erroneous. Conversely, the robust method is not troubled by the presence of the outlier and, therefore, the parameter values are properly evaluated. Actually, the resulting estimations are b1 = 1003.6 and b 2 = 2496.8 . It is important to remark that the presence of outliers may also affect the discrimination among competing models. Sometimes, a valid model might be discarded or, conversely, an inadequate model might be accepted. On this subject, the BzzNonLinearRegression class gives the opportunity to simultaneously discriminate among competing models and to detect outliers though a robust method, but it is not discussed here for space reasons. Table 1. Residuals of least squares and robust methods (*outlier is in bold face).

x

y

273 283 293 303 313 323 333 343 353 363 383*

191.67 264.88 357.60 474.21 616.19 789.61 995.68 1239,71 1523.46 1850.92 2226.47

Normalized residuals with method of least squares -0.54 -0.59 -0.60 -0.56 -0.46 -0.26 0.04 0.48 1.06 1.82 -1.66

Weighted residuals with robust method -0.03 0.05 -0.29 0.09 -0.73 -0.13 -0.41 0.24 0.13 -0.13 -423.52

Criteria for Outliers Detection in Nonlinear Regression Problems

917

5. Conclusions This paper discussed the problem of outliers detection in nonlinear regression problems. When several outliers are identified, the model is probably inadequate to completely describe the overall experimental field. In this context, a robust method for parameters estimation of nonlinear models has to be associated to some specific class of criteria to get an accurate model discrimination and to cover the experimental design domain at the best.

6. References Buzzi-Ferraris, G. (2008). BzzMath: Numerical libraries in C++. Politecnico di Milano, http://chem.polimi.it/homes/gbuzzi. Buzzi-Ferraris, G., & Manenti, F. (2008). Kinetic Models Analysis. Chemical Engineering Science, doi: 10.1016/j.ces.2008.10.062. Buzzi-Ferraris, G., & Manenti, F. (2009). Interpolation and Regression Models. Library for Numerical Problems. WILEY-VCH, Weinheim, Germany, in press. Rousseeuw, P.J. (1984). Least median of squares regressions. J. Am. Stat. Assoc., 79, 871-880. Rousseeuw, P.J., & Leroy, A.M. (1987). Robust Regression and Outlier Detection. New York, John Wiley & Sons, US.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

919

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19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

925

Improving the Morris method for sensitivity analysis by scaling the elementary effects Gürkan Sin1 and Krist V. Gernaey2 1

CAPEC-DTU Chemical Engineering, Technical University of Denmark, Building 229, DK-2800 Kgs. Lyngby, Denmark ([email protected]) 2 Bioprocess Engineering-DTU Chemical Engineering, Technical University of Denmark, Building 229, DK-2800 Kgs. Lyngby, Denmark ( [email protected] )

Abstract The parameter importance ranking in the Morris method is based on elementary effects calculated at some randomly selected points in the input space. When applying this method to a complex dynamic fermentation model, the parameter significance ranking was observed to be dependent on the units of the factors used in the model hence leading to erroneous ranking results. To overcome this problem, this study argues to rank the factors’ importance on the scaled elementary effects. This solution was shown to correctly identify the important factors, thereby improving the resilience of the Morris method to type I error (the error committed when the statistical method identifies an input parameter as significant when in fact it is not). Overall we strongly suggest the use of a non-dimensional measure of elementary effects when using the Morris method to ensure a reliable screening of important factors in complex models.

Keywords: Morris screening, sensitivity, fermentation, S. coelicolor 1. Introduction Sensitivity and uncertainty analysis are important steps in developing and applying models to describe and better understand complex natural and engineered systems. A number of methods are available for sensitivity analysis ranging from sampling-based variance decomposition methods (global) to one-factor-at-a-time (OAT) local methods (Helton and Davis, 2003; Saltelli et al., 2006; Cariboni et al., 2007). These methods provide a sensitivity measure for each factor (e.g. parameters, input variables, etc) of the model whose magnitude indicates the importance of the corresponding factor on the model output. Such information is useful for example to discriminate between significant and less important input factors. The Morris method, named after its developer Morris (1991), is one of the global sensitivity methods considered to be valuable particularly for analyzing complex models that have many factors. The method relies on estimating the distribution of the elementary effects (EE) of each factor called Fi (for the ith factor). The EE of each factor is calculated following the OAT approach but at randomly sampled points in the input space. The Morris method also incorporates an efficient and randomized sampling algorithm suited for performing such OAT analysis. In this way the Morris method provides an unbiased estimate of Fi for each factor, which is then used to make inferences by using the estimated mean and standard deviation of the distribution. In this study, we propose a subtle but important refinement to improve the application of Morris screening in diverse model applications. This refinement consists of scaling the elementary effects to obtain a non-dimensional measure. This is needed for two

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particular reasons: (1) to prevent any misleading conclusions about the importance of the factors in complicated models and (2) to reliably compare the results of the analysis on different model outputs. This necessity arises especially when a model contains outputs and factors with large differences in their values/units, for example one or more orders of magnitude. This will be illustrated when ranking the factors in a complex fermentation model developed to describe the cultivation of S. coelicolor for antibiotic production (Sin et al., 2008). The Morris screening method and the fermentation model factors will be briefly described in the Methods section. The scaling of elementary effects will be presented in a separate section. In the results and discussion section, the original Morris screening results will be evaluated and compared with the proposed improvements.

2. Methods 2.1. Morris method: Elementary Effects (EE) The elementary effect attributable to each input factor is obtained from the following differentiation of the model output, y, with respect to the input factor, xi:

EEi

wy wxi

y  x 1 , x2 , xi  ',! xk  y  x '

(1)

Where xi is the ith factor of the model, ¨ is a predetermined perturbation factor of xi. y(x) is the model output evaluated at certain nominal values of model factors, x, while y(x1, x2, x3, xi+¨…,xk) is the model output corresponding to a ¨ change in xi. These elementary effects could be (i) negligible or zero (ii) a constant function of xi (iii) a nonconstant function of xi or (iv) a non-constant function of more than one factor. The Morris method is concerned with identifying those factors that have negligible effects (i), constant effect (ii) and other effects (iii and iv), which is achieved by analyzing the mean and standard deviation estimates of Fi (see below). The finite distribution of the elementary effects, Fi, for each factor is obtained by performing r calculations of the elementary effects at randomly sampled points in the input space. This is done by an economical OAT design proposed by Morris (1991), which is an independent random sampling and provides r observations of Fi for k factors at a cost of r * (k+1) model evaluations. 2.2. The case study: A dynamic fermentation model The fermentation model used in this study is based on first-principles and describes the interaction between biological, chemical and gas-liquid exchange processes occurring in a batch cultivation reactor of S. coelicolor for antibiotic production (Sin et al., 2008). The model provides dynamic predictions of the concentrations of macromolecular compounds in the batch reactor including glucose, biomass, oxygen, base addition for pH control and off-gas CO2 among others. The model state variables, kinetics and stoichiometry are reported elsewhere (Sin et al., 2008). The model contains 56 parameters denoted by T. (for definitions the reader is referred to Sin et al., 2008). The fermentation model was implemented and simulated in Matlab (R14, Mathworks). The Morris sampling algorithm was implemented in Matlab.

Improving the Morris Method for Sensitivity Analysis by Scaling the Elementary Effects

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3. Refined Morris Method: Standardized Elementary Effects (SEE) To obtain a non-dimensional measure, the elementary effects are scaled using the standard deviation of model outputs, Vyj, and factors, Vxi, as follows:

SEE ij

wy j V xi wxi V yj

(2) In eq.2, SEEij is the standardized elementary effect of the factor xi on the model output yj. In the original method of Morris, there was no need for such standardization since the method was developed for one scalar model output and the factors considered were already scaled for uniform range between [0 1]. Further, Morris used an aggregate of several other model outputs (Morris, 1991). However, even if one is compelled to aggregate different model outputs, a proper scaling would still be required to ground the aggregated term on a non-dimensional basis. For proper interpretation of the results in diverse model applications, one may also be faced with different units and magnitudes of the factors, which is the case here. Hence the above proposed SEEij measure sets out to take these two issues into account. Note that for clarity the distribution of SEEij obtained in this way is denoted as SFij to distinguish it from the Fi obtained by the original Morris method.

4. Results and Discussion 4.1. Morris sampling results The fermentation model has 56 input factors; hence k is equal to 56. Each of these input factors are assigned a uniform distribution with a lower and upper bound. The Morris sampling was then performed using the following degrees of freedoms: p equal to 4 levels, the perturbation coefficient, ' equal to 2/3 (p/2(p-1)) and the number of repetitions, r, equal to 35. The resulting dimension of the sampling matrix, M, was 35*(56+1). These subsets were simulated using the dynamic fermentation model (see below). 4.2. Morris screening results The simulation of the Morris subset sample (r=35) provided 35 calculations of elementary effects per factor per model output, which are randomly drawn observations of the effect distribution, Fi. Similarly, the scaled elementary effects, SEEij, were readily obtained from the elementary effects via Eq. 2, which are random observations of SFij.

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G. Sin and K.V. Gernaey

Figure 1 Screening the effects of the most significant factor on glucose (model output) based on Elementary Effects (EE) and Scaled Elementary Effects (SEE)

The mean and standard deviation estimates of these distributions are plotted in Figure 1 for glucose as the model output. The very first difference between the two methods is the scale of the effects, which were found to be extremely large numbers for the EEi. To properly plot the results of the EEi, the log basis had to be used for the mean and standard deviation estimates (Figure 1-top). However the most important difference is found when it comes to ranking the importance of the factors, which is done according to the absolute mean values: the higher the better. The first top 10 ranking factors are shown in Figure 1, which indicates that except for one factor, T4, all the other factors were different. In general, Fi based ranking identified the physical factors to be most significant, whereas the SFij based ranking identified the factors related to metabolism of the culture more important on the model prediction of glucose. This discrepancy becomes clear by analyzing the results in detail as shown in Table 1. The highest ranking parameters found according to Fi have one certain property in common: their nominal values were in the order of 10-5, i.e. very low values. Since differentiation of model outputs involves division with the absolute change in the factors, the calculated elementary effects become in that case quite sensitive to this numerical division step (see Equation 1). This in turn leads to inflated mean and standard deviation estimates of Fi, which causes a type I error, meaning false identification of important factors (see below).

Improving the Morris Method for Sensitivity Analysis by Scaling the Elementary Effects

929

Table 1 Comparison of parameter ranking: Fi versus SFij Fi: Glucose SFij:Glucose Rank          

Factor T T T T T T T T T T

P 1.16e7 -2.23e5 -1.66e5 98378 88972 54201 39863 -18683 -14647 7883.4

V 4.81e7 1.72e6 1.51e6 8.64e5 7.34e5 3.27e5 22754 99727 97908 43626

Factor T T T T T T T T T T

P 0.75 -0.30 0.30 0.29 -0.21 -0.13 -0.12 0.082 0.068 0.054

V 0.43 0.31 0.17 0.21 0.16 0.11 0.28 0.12 0.14 0.09

From a process knowledge point of view, it is known that the glucose consumption in a fermentation model is mostly influenced by the stoichiometric and kinetic parameters of the culture (see e.g., Roels, 1984; Holmberg, 1982; among others). These metabolic factors were successfully detected by ranking based on the SFij, which includes physiological factors such as the phosphorus and the nitrogen content of the biomass and kinetic parameters such as maintenance and maximum growth rate of the culture among others. The false identification of important factors when ranked based on the Fi was also observed on the other model outputs (not shown) Another advantage of using scaling is that the effects on different model outputs can be compared to one another, since the SEEij are non-dimensional. For example, one can observe that the mean effect of T on the oxygen output is around 0.06, (i.e. one unit changein the factorcauses 0.06 unit change in the output) where as it is as high as 0.75 on the glucose output. Such comparisons are valuable for model builders to probe more information concerning which factors are most influential on a certain output. Overall these results confirm the necessity to use SEEij hence SFij for ranking the important factors. This conclusion should not be regarded specific to the fermentation models, but should be understood as strong caution in general for any model that contains input factors with large order of magnitude difference in the nominal values.

5. Conclusions This study shows the necessity of scaling the elementary effects when using the Morris method to correctly identify the important factors on model outputs. Further, un-scaled (or dimensional) elementary effects lead to false identification of important factors hence committing a type I error. The extent of false identification depends primarily on the scale (or units) of different factors of the model. Moreover the scaling also allows the comparison of the effects of factors on different outputs, a valuable extension to the original method. Overall, as the calculation of the scaled elementary effects comes at no cost of additional model evaluation, we strongly suggest the use of a non-dimensional measure when using Morris screening to any model application, which is expected to improve the resilience of the method to type I errors, hence helps modelers make reliable decisions.

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6. Acknowledgements The research work of Dr. Gürkan Sin is financed by a H.C. Ørsted postdoctoral fellowship of the Technical University of Denmark and by the Danish Research Council for Technology and Production Sciences (FTP project # 274-07-0339).

7. References [1] Helton JC, Davis FJ. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Engng Syst Saf 2003;81:23–69 [2] Saltelli A, Ratto M, Tarantola S, Campolongo F. Sensitivity analysis practices: Strategies for model-based inference Reliab Engng Syst Saf 2006;91(10-11):1109-1125 [3] Cariboni J, Gatelli D, Liska R, Saltelli A. The role of sensitivity analysis in ecological modelling. Ecol Modell 2007;203 (1-2):167-182. [4] Morris MD. Factorial sampling plans for preliminary computational experiments. Technometrics 1991;33(2):161–74. [5] Sin G, Ödman P, Petersen N, Eliasson A, Gernaey KV. (2008) Matrix notation for efficient development of first-principles models within a PAT framework: Integrated modeling of antibiotic production with S. coelicolor Biotech. Bioeng., 101, 153-171. [6] Roels J.A. (1980) Application of macroscopic principles to microbial metabolism Biotech. and Bioeng., 22:2457-2514. [7] Holmberg A. (1982) On the practical identifiability of microbial growth models incorporating Michealis-Menten type nonlinearities. Math. Biosci., 62:23-43.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

931

Spectral reduction on empirically derived orthogonal basis of the dynamical model of a Circulating Fluidized Bed Combustor Katarzyna Bizon a, Gaetano Continillo b a

Istituto di Ricerche sulla Combustione CNR, Via Diocleziano 328, Naples 80124, Italy, [email protected] b Department of Engineering, Università del Sannio, Piazza Roma 21, Benevento 82100, Italy, [email protected]

Abstract Spectral reduction of the 1-D distributed dynamic model of a circulating fluidized bed combustor (CFBC) in isothermal operation is presented. The continuum model is first approximated by a finite–difference method to provide a “reference” solution. Then, Proper Orthogonal Decomposition (POD) with Galerkin projection is introduced to derive a reduced order model (ROM). The POD modes are then tested in the low-order approximation of the system evolution. POD–based models prove to be effective, being able to reproduce steady–state with as little as four basis functions and computing speed-up in the order of 104. Keywords: Fluidized Bed Combustors Modeling, Model Reduction, Proper Orthogonal Decomposition

1. Introduction Spectral methods have long been used in the numerical analysis of dynamical systems described by partial differential equations. These methods considerably reduce the number of ODEs necessary for accurate description of the dynamics of the original PDE models. This is very useful in the dynamical analysis of reactive systems since they require accurate analysis in the parameter space and thus large amount of numerical computations. Choice of the proper classes of functions for expansion of the dependent variables as well as the techniques for determining their coefficients are crucial in the determination of stable, accurate and low order numerical models. One of the possible choices is use of empirically derived orthogonal basis functions that can be determined by conducting Proper Orthogonal Decomposition (POD) of the spatio-temporal profiles of the system, and hence describe its behavior in the optimal sense. In this work, a combination of the Galerkin spectral method with empirical orthogonal set of basis functions obtained by means of POD is applied to build a reduced order model (ROM) of the circulating fluidized bed combustor (CFBC) for solid fuel combustion.

K. Bizon and G. Continillo

932

2. CFBC model The circulating fluidized bed system is idealized as a 1-D distributed, unsteady tubular reactor with recycle [1]. In order to emphasize the dynamical aspects of the system, model details are kept to a minimum. Namely, quasi-steady approximation is made for interphase momentum exchange. Combustion is modeled as a single one-step heterogeneous reaction (C+O2ĺ CO2). Moreover, both volatile matter and ash content of the fuel have been neglected and the balance equation for the solids have been limited to fixed carbon lumped into two phases of different particle diameter, namely coarse and fine char. In this work, isothermal operation is addressed, which eliminates the need of an energy balance equation. Mass balances for the coarse phase, which is depleted both by combustion and attrition, and for the fine phase, enriched by attrition and depleted by combustion, are given respectively, in dimensionless form, by:

∂α c

+

∂τ ∂α f

∂ ( vc α c ) ∂ (vf α f

+

∂τ

= −σ aα c − σ cα c

∂ζ

(1)

)

= σ aα f − σ f α f

∂ζ

with the boundary conditions at the bottom of the riser:

vc ( 0,τ ) α c ( 0,τ ) = β Fc + η c vc (1,τ ) α c (1,τ ) (2)

v f ( 0,τ ) α f ( 0,τ ) = η f v f (1,τ ) α f (1,τ )

The mass balances for gas phase for O2 and CO2 , the corresponding boundary conditions at the bottom of the bed, and the continuity conditions at the secondary air injection level are:

(

∂ εα O

(

2

∂τ

∂ εα CO ∂τ

) + ∂ ( v εα ) = −k g

O2

∂ζ

2

1

CO 2

∂ζ

α O ( 0,τ ) = 0.21α g ,0 ; 2

1

+σ fαf

)

(σ α c

c

+σ fα f

)

2

+

H ex

sec

ª¬α CO ( ζ ,τ ) Qtot ( ζ ,τ ) º¼ ζ = H 2

c

α CO ( 0,τ ) = 0

ª¬α O ( ζ ,τ ) Qtot ( ζ ,τ ) º¼ ζ = H 2

c

(3)

) + ∂ ( v εα ) = k g

(σ α

+ sec

H ex

= ª¬α O ( ζ ,τ ) Qtot ( ζ ,τ ) º¼ 2

= ª¬α CO ( ζ ,τ ) Qtot ( ζ ,τ ) º¼ 2

−

ζ = H sec H ex

+ 0.21Qsecα sec

(4)

−

ζ = H sec H ex

3. Proper Orthogonal Decomposition Proper Orthogonal Decomposition is the procedure that delivers an optimal set of empirical basis functions, in the L2 sense, from an ensemble of observations u(x,t) obtained either experimentally or from numerical simulation [2], which usually are given in the form of a vector-valued function:

Spectral Reduction on Empirically Derived Orthogonal Basis of the Dynamical Model of a Circulating Fluidized Bed Combustor

ª u ( x1 , t1 ) u ( x1 , t2 ) « u( x , t ) u( x , t ) 2 1 2 2 U =«   « «u ( x , t ) u ( x , t ) ¬ M 1 2 M

 

933

u ( x1 , t N ) º

u ( x2 , t N ) »

» » »  u ( xN , t N ) ¼ 



(5)

where M is the number of positions in the spatial domain, and N is the number of samples taken in time. The POD basis is obtained by solving the eigenvalue problem:

Cϕ = λϕ

where

C = U ,U

T

(6)

When M > N it is more convenient to use the so-called method of snapshots proposed by Sirovich [3]. Then, the approximated solution can be written as the combination of the POD functions and their coefficients: K

u ( x , t ) = ¦ an ( t ) ϕ n ( x )

(7)

n =1

Because of the empirical character of this technique, the reliability of the determined basis strongly depends on the strategy of sampling which is not clearly defined, however different approaches can be found in the literature [4-6]. The ROM based on the POD derived orthogonal functions is usually obtained by Galerkin projection of the governing PDEs system onto the modes [7]. In case of strong sensitivity of the problem onto boundary conditions or inflow time-dependent boundary conditions, the use of modified versions of the Galerkin method such as Tau, penalty or discontinuous Galerkin method might be necessary [7].

4. Results A finite difference method with staggered grid, employing 501 spatial nodes – resulting in 2000 ODEs – with Adams implicit method for time integration, was used to solve the full model, given by Eqs. (1-4), in order to build the reference solution and collect the snapshots. A number N=250 of equally spaced snapshots in time is used for each state variable (separate POD basis are determined). N was determined basing of the convergence criterion proposed in [6]. A set of snapshots collected for fine char is shown in Fig. 1a. In Fig. 1b the three leading POD orthogonal functions are reported. It can be seen that the shape of the first function (solid line) corresponds very closely to the concentration profile of the fine char particles at steady-state. The performance of the ROM is then investigated. Fig. 2 reports comparison of the solution in early transient (a) and steady state (b) obtained by means of the full order model and two ROM, i.e. POD 1 and POD 11. In the POD 1 model, each mass balance equation for gas phase and solid phase is projected onto 1 (leading) function, resulting in a total of 4 evolutionary equations. In the second reduced model, POD 11, 1 function is used for approximation of each gas phase mass balance and 11 for each solid phase mass balance; hence, a ROM composed of 24 ODEs is obtained.

K. Bizon and G. Continillo

934 0.04 0.03

α

0.02

f

0.01

a) 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ζ 0.4

φ f,1 φ f,2

0.2

φ

φ f,3

n, f

0

b) -0.2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ζ Figure 1. Set of snapshots for fine char (a); three leading POD modes for fine char (b). -4

8

x 10

full POD 1 POD 11

6 4

α

f

2 0 -2

a) 0

0.2

0.4

0.6

0.8

1

ζ 0.03 full POD 1 POD 11

0.02

α

f 0.01

b) 0 0

0.2

0.4

0.6

0.8

1

ζ

Figure 2. Comparison of solution at early transient (a); steady state (b).

As it could be predicted from the shape of the first POD basis function, POD 1 model is not able to predict the concentration at the early transient. Adding more modes is then required to capture the solution more accurately. On the other hand, in steady-state, both models predict correctly solids’ profile from the qualitative point of view, however again, in order to increase accuracy, it is necessary to use more modes.

Spectral Reduction on Empirically Derived Orthogonal Basis of the Dynamical Model of a Circulating Fluidized Bed Combustor

935

Constructed ROMs give also quite significant computational savings. Simulation of the full order model with 2000 equations takes approximately 3500 s, while for ROM this time is reduced to 2.5 and 0.35 s for models with 24 and 4 ODEs, respectively.

5. Conclusions Application of the spectral Galerkin method coupled with empirically determined POD orthogonal functions to the reduction of a distributed dynamical model of circulating fluidized bed combustor has been reported. It has been shown that, by means of this technique, a substantial reduction of the order of the original model can be obtained, resulting in significant computational savings. The introduction of energy balance, leading to a non–isothermal system, is expected to reproduce more complex regimes, for which a larger number of modes are expected to be necessary to accurately reproduce the system dynamics [5].

6. Acknowledgements The authors gratefully acknowledge Professor Piero Salatino for the time spent in several helpful discussions about CFBC model formulation.

References [1] [2] [3] [4] [5] [6] [7]

D. Barletta, A. Marzocchella, P. Salatino, S.G. Kang, P.T. Stromberg, 17th FBC Conference 2003. P. Holmes, J.L. Lumley, G. Berkooz, Turbulence, coherent structures, dynamical systems and symmetry, Cambridge University Press, Cambridge, 1998. L. Sirovich, Quart. of App. Math. 45 (1987) 561. M.D. Graham, I.G. Kevrekidis, Comp. & Chem. Eng. 20 (1996) 495. K. Bizon, G. Continillo, L. Russo, J. Smuła, Comp. & Chem. Eng. 32 (2008) 1305. K. Kunisch, S. Volkvein, SIAM J. of Numerical Analysis 40 (2002) 492. J.S. Hesthaven, S. Gottlieb, D. Gottlieb, Spectral methods for time dependent problems, Cambridge University Press, Cambridge, 2007.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

Tight, Efficient Bounds for Chemical Kinetics Models Joseph K. Scott,a Paul I. Barton,b a Dept. of ChE, MIT, 77 Massachusetts Ave. 66-363, Cambridge MA 02139, USA, [email protected] b Dept. of ChE, MIT, 77 Massachusetts Ave. 66-464, Cambridge MA 02139, USA, [email protected]

Abstract An efficient method for bounding the solutions of chemical kinetics models over given ranges for the reaction rate parameters and initial conditions is presented, based on the use of affine reaction invariants. Most chemical kinetics models must be solved approximately via numerical integration, so the dependence of the solution on parameters and initial conditions is rarely known in closed form. Thus, time-varying solution bounds can provide information about the parametric dependence of a model that is generally difficult to obtain otherwise, such as the propagation of uncertainty in rate constants and/or initial conditions through the model. The construction of such bounds is also a crucial part of global dynamic optimization techniques, which are used for parameter estimation in chemical kinetics models and for the global solution of optimal control problems. Finally, such bounds can be used to verify safe operating conditions for reacting systems subject to a particular range of disturbances.

Keywords: Dynamic optimization, optimal control, parameter estimation 1. Introduction and Background This work considers a procedure for bounding the solutions of kinetic models given an interval in which the model parameters are known to lie. Kinetic models are assumed to be in the form of explicit ordinary differential equations (ODEs) with parametric dependence. Methods are available which can generate bounds on the solutions of general parametric ODEs, but these are either computationally expensive or they result in bounds which are too weak to be of use for most kinetic models. However, for kinetic models, much additional information is known, such as physical bounds on species concentrations and affine reaction invariants, but it is not immediately clear how to incorporate this information into existing bounding procedures. This work presents a modification of an existing technique which allows such information to be effectively utilized without additional computational cost. Bounds on the solutions of differential equations, referred to as state bounds, have many important uses in mathematics and engineering. An early application was to provide rigorous bounds on the error introduced through numerical integration [1]. Subsequently, state bounds have found much use in global dynamic optimization (GDO) algorithms [2,3], for which problems involving kinetic models have been a primary application. Among these are kinetic parameter estimation problems, where finding the global solution is crucial in order to draw conclusions about the model based

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J.K. Scott and P.I. Barton

938

on the statistical significance of the data fit obtained. GDO can also be used to solve optimal control problems globally, which often involve reacting systems. Finally, state bounds are useful for formal safety verification, where they may be used to determine rigorously if a hazardous region of state space is accessible for a reactive system subjected to a set of possible disturbances. Procedures for generating state bounds can be roughly categorized into two types, the first using Taylor models [1] and the second stemming from the study of differential inequalities [4,5,6]. Both methods make heavy use of interval arithmetic. Taylor model approaches are capable of generating extremely tight state bounds, but are quite involved and potentially very expensive. In contrast, methods based on differential inequalities are very inexpensive, but generate bounds that are typically quite weak. To mitigate this problem for kinetic models in particular, Singer and Barton noted that these systems obey natural bounds derived from independent physical arguments and incorporated this information into the differential inequalities bounding approach. It was concluded in [4] that incorporating this physical information dramatically improved the computed bounds in many cases. In addition to natural bounds, it is well known that reacting systems with mass-action kinetics also obey certain affine invariants, which restrict the possible solutions of the kinetic model to lie in an affine subspace of the full state space of species concentrations. However, no method has been proposed for enforcing these affine constraints when using bounding techniques involving interval arithmetic. In the method proposed, this complication is circumvented by using the invariants to define a bijective mapping from the full state space to the affine subspace of admissible species concentrations, and to define an equivalent system of ODEs there. In this reduced space, established bounding techniques [4] are applied directly. Bounds on the kinetic model solutions can then be calculated through the inverse mapping. This method typically produces much tighter bounds than those computed without using reaction invariants, while the additional computational cost is negligible.

2. Construction of a Reduced System of ODEs In what follows, vector quantities are denoted by bold type. Consider the system of n parametric ordinary differential equations

x (t , p) f (t , p, x(t , p));

x(t0 , p) x0 (p),

(1)

where the parameters p are known to lie in some interval P . The bounding procedure presented in [4] is based on a fundamental result from the study of differential inequalities [6]. For each state variable, interval arithmetic is used to construct two coupled auxiliary differential equations that describe upper and lower bounding trajectories in t . Ultimately, these bounds describe a hyper-rectangle at each t  [t0 , t f ] which contains the image of x(t ,·) on the set P . Here, we consider the case where the solution vector x is known by an independent physical argument to satisfy a set of affine relationships for any (t , p)  I u P . When this is true, as is the case for ODEs describing mass-action kinetics, it is possible to apply the approach in [4] to some reduced set of variables and, having bounded these, to construct valid bounds for the

Tight, Efficient Bounds for Chemical Kinetics Models

939

original variables through the definitions of these reduced variables. However, doing so requires that a system of ODEs can be constructed in the reduced variables which is equivalent to the original set of ODEs in the sense that a bijective mapping exists between their solutions. That development follows. Consider the differential equations described in (1) and define the affine lumping

y (t , p) Q(x(t , p)  x0 (p))

(2)

where Q is an n-by-m matrix and y (t , p) is a m-dimensional vector. Suppose further that Q is full rank, so that (2) defines a mapping onto \ m such that every point in \ m corresponds to at least one point in \ n . Let R be any {1}-inverse of Q so that, by definition [7], QRQ Q , which, because Q is full rank, implies that QR I . It follows from these two properties that RQR R , so RQ is a projection onto the range space of R along the nullspace of Q (both of which are subspaces of \ n ). Assume that it is known from an independent physical argument that x(t , p) satisfies the invariant

(x(t , p)  x 0 (p)) RQ(x(t , p)  x 0 (p)),

(3)

for all (t , p)  I u P . Then it is clear that x(t , p)  x 0 (p) lies in a subspace of \ n ; namely, in the nullspace of (I  RQ) . The construction is such that, under these assumptions, Q provides an invertible mapping from this subspace to \ m , and R provides the inverse mapping. Define the reduced ODE

y (t , p) Qf (t , p, Ry (t , p)  x 0 (p));

y (t0 , p) 0.

(4)

Let x(t , p) denote the solution of the ODEs defined in (1). If x(t , p) satisfies the affine invariants (3), and y (t , p) is defined as in (2), then it is follows from the discussion above that y satisfies the reduced ODE (4). Conversely, if y satisfies (4), then

x(t , p) Ry (t , p)  x 0 (p) satisfies (1). From these facts, it follows that the bounding procedure described in [4] can be applied to the differential system (4) to generate bounds for y , and by propagating these bounds through the relation x(t , p) Ry (t , p)  x 0 (p) using standard interval arithmetic, valid bounds for x can be constructed. The following example demonstrates the advantage of bounding with the reduced system (4).

3. Application to a Simple Enzymatic Network Consider the enzymatic network

J.K. Scott and P.I. Barton

940

F  A q F : A' o F  A' R  A ' q R : A ' o R  A.

(5)

with reaction rate constants k1 through k6 . These reactions are assumed to obey massaction kinetics. The ODEs describing these reactions in a batch reactor at constant volume can be found in [8]. Denote the initial conditions xF 0 , x A0 , xR 0 , xF : A0 , x A '0 , and xR: A '0 . This system has six species but only three linearly independent reactions, so there are three independent affine invariants. They are

x A (t , k )  x A ' (t , k )  xF : A (t , k )  xR: A ' (t , k )

(6)

x A0 (t , k )  x A '0 (t , k )  xF : A0 (t , k )  xR: A '0 (t , k ) xF (t , k )  xF : A (t , k ) xF 0 (t , k )  xF : A0 (t , k ) xR (t , k )  xR: A ' (t , k ) xR 0 (t , k )  xR: A '0 (t , k )

(7) (8)

for all (t , k )  [t0 , t f ] u K , where K is a 6-dimensional interval containing the possible values of k1 through k6 . It is easily verified that the following matrices satisfy the criteria outlined above:

Q

ª1 0 0 0 0 0 º «0 1 0 0 0 0 » , « » «¬0 0 0 0 1 0 »¼

T

R

ª1 0 1 1 0 0 º « 0 1 0 1 0 0 » . « » «¬ 0 0 0 1 1 1»¼

(9)

The bounding differential equations were solved using differential inequalities and interval arithmetic in the full 6-dimensional space, as described in [4], and in the 3dimensional reduced space as described above. The solutions of this model were bounded for initial conditions and a large range of rate constants given in [8]. The bounds obtained for both methods as well as several sample trajectories are shown in Figure 1 for the complexed species R : A ' . Clearly, the bounds obtained by bounding the reduced system are much tighter.

4. Conclusions The previous example demonstrates that the bounding procedure described here is a substantial improvement over previous efforts. Moreover, since the same bounding procedure is used in the full and reduced spaces, the additional computational cost is negligible. Finally, it should be noted that the improvement achieved by bounding the reduced system (4) is not simply due to the fact that there are fewer variables, but also because the reduced variables are significantly decoupled.

Tight, Efficient Bounds for Chemical Kinetics Models

941

Figure 1: State bounds for species R : A ' , computed in the full and reduced space, along with several sample trajectories corresponding to elements of the parameter set K.

References [1] M. Neher, K.R. Jackson, and N.S. Nedialkov. On Taylor Model Based Integration of ODEs. SIAM Journal on Numerical Analysis, 45(1):236-262, 2007. [2] Youdong Lin and Mark Stadtherr. Deterministic global optimization of nonlinear dynamic systems. AIChE Journal, 53(4):866-875, 2007. [3] A.B. Singer and P.I. Barton. Global optimization with nonlinear ordinary differential equations. Journal of Global Optimization. 34:159-190, 2006. [4] A.B. Singer and P.I. Barton. Bounding the solutions of parameter dependent nonlinear ordinary differential equations. SIAM Journal on Scientific Computing, 27:2167-2182, 2006. [5] G.W. Harrison. Dynamic models with uncertain parameters. Volume 1 of Proceedings of the First International Conference on Mathematical Modeling, pages 295-304, 1977. [6] W. Walter. Differential and Integral Inequalities. Springer-Verlag, New York, 1970. [7] A. Ben-Israel and T.N.E. Greville. Generalized Inverses: Theory and Application. Springer-Verlag, New York, 2 edition, 2003. [8] Bambang S. Adiwijaya, Paul I. Barton, and Bruce Tidor. Biological network design strategies: discovery through dynamic optimization. Mol. BioSyst., 2:650-659, 2006.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

943

3D Reversible Cellular Automata for Simulation of the Drug Release from Aerogel-Drug Formulations Pavel A. Gurikova, Andrey V. Kolnoochenkoa, Natalia V. Menshutinaa a

Mendeleev University of Chemical Technology of Russia, Miusskay sq., 9 , Moscow, 125047, Russia, [email protected]

Abstract According to the recent investigations great attention is paid to using high porosity bodies like aerogels as drug delivery systems. Being nontoxic and environmental friendly they have high potential to be applied in pharmaceutics. Modeling of drug release process from aerogel-drug formulations by means of cellular automata with Margolus neighborhood is presented in this paper. Margolus cellular automata have an important property of microscopic reversibility as well as real diffusion process. To apply this method high computational power is required. Special computer with parallel calculations based on CUDA technology was designed for this purpose. Keywords: drug release, aerogel, modeling, cellular automata, diffusion

1. Title of first Chapter, e.g. Introduction Aerogels seemed to be the lightest solid bodies. The density of some aerogel samples (they are often called “frozen smoke”) is only three times more that the density of air. Aerogels consist of spherical particles of nanometer sizes, which formed united threedimensional structure. The space between particles forms pores with average size about 10-20 nm. Due to the variety of multi-sized pores specific surface area of aerogels reaches 1500 m2/g. The first aerogel based on SiO2 was prepared by Kistler [Kistler, 1931]. Today aerogels can be produced from several organic and inorganic substances. Modern conventional method of SiO2 based aerogel production consists of two stages. The first stage is the hydrolysis of tetraalkylorthosilicates Si(OR)4 with sol formation. Further sol becomes more and more viscous and reaction mixture turns to a gel filled with solvent. At the end the space particles joined in 3D structure. On the second stage supercritical drying of gel makes solvent evaporate and leave pores without 3D structure destruction. Owing to many unique properties (extremely low density, low thermo conductivity, transparency) aerogels have many applications. According to the recent investigations attention is paid to using them as drug delivery systems. Aerogels based on SiO2 are nontoxic, environmental friendly. No harmful substances are used in its production. Close physical and chemical similarity has Aerosil® (Evonik). This product successfully passed all clinical tests [Degussa, 2001]. There are different ways to fill pores by drugs: in the sol solvent before drying stage or by adsorption from the solvent in supercritical CO2. Depending on the aerogel surface (hydrophilous or hydrophobic) and drug chemical nature, aerogel-drug formulations show fast or slow drug release. In [Smirnova, 2002] shown ketoprofen release from aerogel matrix is much faster than from crystalline state (50 min vs. 250 min), but the release of miconazole is vice versa (120 min vs. 60 min.). It is clear that the simulation of drug release from aerogel-drug formulations is actual task. Modeling of diffusion process with Fick law in porous media is rather arduous task with complicated boundary

944

P.A. Gurikov et al.

conditions. Moreover hygrophilous aerogels collapse in water solutions. That means that boundary conditions should also depend on time. The aim of this research is the application of cellular automata with Margolus neighborhood to describe and model drug release process from aerogel-drug formulations. To describe aerogel structure two different approaches were taking into account.

2. Methodology First of all, to simulate diffusion process of drugs modeling of internal aerogel structure is required. This model should correlate with experimental data about pore size distribution, specific surface area and porosity. Overlapped spheres method and stochastic cellular automata are presented in this paper. 2.1. Overlapped spheres method, OSM Generation process consists of two stages: 1. Creation of the set of equal-size spheres (size for SiO2 particles d = 4 nm), overlapping each other not more than specific value (in our case 40% of particle diameter). Every new sphere with random center coordinates is added to the previously created. If new particle overlaps the neighbor one more than 40% of its diameter, this particle moves along the line between centers of the particles to reduce the overlapping. Process terminates when required porosity is reached (should be less than 50%), or in case of no possibility to add new sphere. Thus rather dense structure is generated (fig. 1).

Fig. 1. Close-pack configuration in OSM 2. Random spheres are removed from the structure. Spheres can be removed only if percolation cluster is kept. This condition was controlled by cluster labelling technique introduced by Hoshen and Kopelman. [Hoshen, Kopelman, 1976]. Process is finished when real aerogel porosity is reached (5–15% for different types of aerogels and depends on production method). 2.2. Generation by means of stochastic cellular automata, SCA To describe this approach lets imagine a heterogeneous system with solid phase formation and allocate a cube of volume V. This volume is divided into NxNxN cells of the equal volumes. Each cell can have two states: solid or liquid. Concentration of component c in the solution can vary from 0 to the density of this component in the solid phase ȡ.

3D Reversible Cellular Automata for Simulation of the Drug Release from Aerogel-Drug Formulations

945

Mass transfer between liquid cells describes by the Fick law. It means that in each cell diffusion equation is being solved. Crystallization probability p of the liquid cell depends on the concentration in it. Dissolution probability q of the solid cell depends on average concentration in the nearest cells:

c (i, j , k ) =

1 ¦ c(i′, j′, k ′) 6

(1)

The most simple expression for p = p(c) and q = q(c) subjections are:

­0, c(i, j , k ) < C0 ° p = ® c(i, j, k ) − C0 , c(i, j , k ) ≥ C0 ° ρ −C 0 ¯

(2)

­1, c (i, j , k ) < C 0 ° q = ® c (i, j , k ) − ρ ° C − ρ , C 0 ≤ c (i, j , k ) ≤ ρ 0 ¯

(3)

C0 – equilibrium concentration in the solution. The crystallization of any cell implies that the component concentration is less than the crystal density that is why lacking substance should come from neighboring cells. The dissolution of any cell leads to the mass transfer into the ambient solution by diffusion. The cell state changes to “solution”. Moreover diffusion, dissolution and crystallization any single solid cells can move with equal probability along one of the axes to reach the position of one of the nearest liquid neighbor. The equilibrium state between liquid and solid characterized by equality of crystallization and dissolution rates. Number of particles in the equilibrium state should fluctuate in the order of the mean value. 2.3. Diffusion simulation by means of cellular automata with Margolus neighborhood, CAMN Reversible cellular automata with Margolus neighborhood proposed by Norman Margolus [Toffoli, Margolus, 1990] were used to model the drug release from the aerogel-drug formulation. Our CAMN uses the partitioning scheme where the 3D lattice is divided by two ways (even and odd) in isolated blocks of size 2x2x2. Each block rotates at ʌ/2 clockwise or counter-clockwise on one of three axes, which has drawn at random. All cells were marked out ‘1’ or ‘0’. ‘1’ corresponds to silicon oxide, ‘0’ corresponds to pore. If one or more cells have ‘1’ mark there is no rotation. For simulation with CAMN special algorithm was implemented.

3. Algorithm All computations need high computer power and special parallel algorithm for effective data processing. Therefore, the computer based on Compute Unified Device Architecture (CUDA) has been used. CUDA technology allows using the C programming language to code algorithms for execution on the graphics processing unit (GPU). CUDA has been developed by NVIDIA and to use this architecture it requires

946

P.A. Gurikov et al.

an NVIDIA GPU. The main advantage of this technology is a great performance superiority of GPU over central processing unit. Our computer has four graphic cards NVIDIA GeForce GTX 280 (with 1 Gb memory and 240 stream processors on the each card). It allows us to operate with systems up to 1000 x 1000 x 1000 cells. Each cell was coded by byte (char type). It means that about 250 Mb of memory per GPU was used. Every step produces set of threads, each thread was processed by one block 2x2x2. Thereby it was possible to use main advantage of SIMT Technology (Single Instruction, Multiple Thread), allowing to create, manage, schedule and execute threads in groups of 32 parallel threads. Having finished operation with even blocks boundary areas were synchronized, than the same was done with the odd ones.

4. Discussion Aerogel structures were generated by the methods described in the Methodology section. For the SCA modeling following parameters were selected: Cinitial=0.30 mol/l, C0=0.10 mol/l, density of SiO2 2.2 g/cc and D=0.20 in (ǻx)2/ǻt units. For OSM diameter of silicon dioxide particle was chosen to 4 nm and volume to 50x50x50 nm3. Iterations in both methods were performed until 90% free space has been achieved. Fig. 2 shows the structure obtained by the OSM and the SCA.

Fig. 2. SCA model (left). There is no percolating cluster. Final OSM configuration (right) consists of one percolation cluster (take into account the periodic boundary conditions). It should be noted that some of the cells in the SCA structure are not connected to the main cluster. Further simulations showed that SCA and OSM structures give a very close result in the drug release simulation. Moreover with an increase of the modeling volume, SCA method requires a lot of computations. Therefore, in further simulation has been used only OSM structure.

3D Reversible Cellular Automata for Simulation of the Drug Release from Aerogel-Drug Formulations

947

Fig. 3. Typical time dependence of drug release from aerogel.

Diffusion simulation by CAMN was used technique described above. The drug distributed in the pores randomly with mass fraction 15%. During the simulation numbers of cells with drug, which went away from aerogel are calculated (fig. 3). The release rate in our model depends on concentration in the solution media as well as real diffusion process. The time dependence of drug release is in qualitative agreement with paper [Smirnova, 2002].

5. Future work In our opinion the difference in release rate [Smirnova, 2002] is the cause the interaction of drugs molecules with –OH or –OR groups in the aerogel pores. Accounting polarity of drugs and the surface can be easily implemented in the framework of our model and will be subject to the future investigations.

References S. Kistler, 1931, Coherent Expanded Aerogels and Jellies, Nature, 127, 741. Degussa, 2001, Technical Bulletin Aerosil & Silanes, Company publication, Dusseldorf. I. Smirnova, 2002, PhD Thesis, Technical University of Berlin. J. Hoshen, R. Kopelman, 1976, Percolation and Cluster Distribution. I. Cluster Multiple Labelling Technique and Critical Concentration Algorithm, Phys. Rev. B, 14, 3438–3445. T. Toffoli, N. Margolus, 1990, Invertible cellular automata: A review, Physica D, 45, 229–253.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

949

A new experimental relation for effective thermal conductivity of nanofluids J. Thulliea, L. Kurowskia, K. Chmiel-Kurowskaa a

Silesian University of Technology, Department of Chemical and Process Engineering, Gliwice, POLAND, e-mail: [email protected]

Abstract The work presents a new experimental formula to describe effective thermal conductivity of nanofluids. It depends on volume fraction of nanoparticles and bulk temperature. The formula could be used when simulating nanofluids behavior by CFD.

Keywords: nanofluid, thermal conductivity 1. Introduction Many theoretical and experimental works concerning effective thermal conductivities of nanofluids were published in last years. They were summarized in [1,2] with the conclusion of the lack of agreement between experimental results from different groups of researchers. However when performing numerical heat transfer simulation one should decide which formula to use for the prediction of effective thermal conductivities of nanofluids. Usually the authors base their calculations on effective medium theory or on basic relationships with parameters estimated by performing a least-square curve fitting of some experimental data available [3,4]. The curve fitting approach is cumbersome because the nanofluids already described in the literature did not have enough data points to show clearly the relationship between thermal conductivity and the parameters such as volume concentrations of nanoparticles, temperature, size and shape of nanoparticles and many other [3,5]. The situation is changing because of publishing of new results. Most recently some interesting results were published by Li and Peterson [6,7] for Al2O3 and CuO nanoparticles in water, which may lead to more general expressions than originally proposed by the authors. These results were correlated [6] by the empirical expression which offer rounding off to four decimal points gives

Oeff  O f Of

= 0.7645α + 0.0187t –0.4621

(1)

for Al2O3/water suspensions, and

Oeff  O f Of

= 3.7611α + 0.0180t – 0.3073

(2)

for CuO/water suspensions. The equations (1) and (2) give the dependence of effective thermal conductivity of nanofluid λeff on volume fraction of nanoparticles α and nanofluid bulk temperature t (0C).The thermal conductivity of the base fluid is denoted by λf.

J. Thullie et al.

950

However these formulas are valid for the range for Al2O3 α = 2-10 %, t = 26-36oC for CuO. α = 2-6%, t = 26-36oC

and

This is important, because for small concentration of nanoparticles λ eff should in the limit be equal to λf (for α = 0) and both equations (1) and (2) give some intercept.

2. Classical Theory The theoretical Hamilton-Crosser [8] formula

Oeff Of

O p  (n  1)O f  (n  1)D (O f  O p ) O p  (n  1)O f  D (O f  O p )

(3)

where λeff - effective heat conductivity of nanofluid, λf - heat conductivity of base fluid, λp - heat conductivity of a nanoparticle, n - shape factor, is more general and gives of course no intercept, because for α = 0 λ eff =λf. This equation is accepted by some authors [9] to describe the behavior of Al2O3 based nanofluids at room temperature. The Hamilton–Crosser equation can lead to expression

Oeff  O f Of

=

 (n  1)D (O f  O p )  D (O f  O p )

O p  (n  1)O f  D (O f  O p )

=

D

O p  (n  1)O f D  n (O p  O f ) n

,

So

Oeff  O f Of

=

D a  bD

.

(4)

When experimental data are available this results can give way to determine shape factor, by estimating two constants a and b in equation (4)

a

O p  (n  1)O f n(O p  O f )

;b = -1/n

(5)

Formally one can estimate only shape factor n and calculate constant a according to the relation (5), but the results would be poor, because a lot of influences are hidden in estimated constants. Moreover Yu and Choi [10] suggested that liquid molecules close to a solid surface form layered solid-like structure which can be accounted for by introducing a new corrected value of the thermal conductivity of a nanoparticle

O*p

into classical

A New Experimental Relation for Effective Thermal Conductivity of Nanofluids

951

relationship. This new value could be determined as well, so both constants a and b should be determined by regression.

3. Functional Dependence and Parameter Estimation A separate problem is a temperature dependence of constants a and b which is solved by introducing following relationship:

Oeff  O f Of

=

D A  BD  C / t  DD / t

(6)

The constants A, B, C and D are listed in Table 1. They were estimated with the use of data published by Li and Peterson [6,7]. For the sake of comparison the data points are plotted together with curves given by equation (4) in figures 1 and 2. Fig. 1 gives much better description than Fig. 2. This is caused by the scatter of the data in Fig. 2. A comparison with the data points obtained by Das et al.[11] is shown in Fig. 3. The agreement is even better than in Figs 1 and 2. An inspection of the Table 1 gives an influence of nanoparticles size. It is difficult to give any formula based on the results presented but some trends are evident. Nethertheless further research is needed. The same form of function was applied to predict effective thermal conductivity for a suspension of CuO nanoparticles in water and the results were presented in Table 2. The fit is not so good as for Al2O3 nanoparticles. The results are also presented in Fig 4. It is visible that the mechanism of thermal conductivity enhancement is more complicated for CuO than for Al2O3 nanoparticles, and a simple form of eq. (6) may be not enough. The function given by eq. (6) for a particular temperature reduces to eq.(4). Such results for t=22qC are listed in Table 3. A striking thing is that values of constants a for similar nanoparticles diameter are quite the same even for different research groups, however b values differ greatly. All a values are less than 1. A theoretical value of b from the mean- field theory of Maxwell for well-dispersed spherical particles is 1/3 and should not depend on temperature. The values in Table 3 are much higher. The value of a should depend on temperature and for 22qC is:

a

O p  2O f 3(O p  O f )

where

0.3487

(7)

Op=39.1498 W/(m.K)Of=0.5920 W/(m.K)

The values obtained are near to this value. Anyway the presented results are different than obtained from the Maxwell equation.

J. Thullie et al.

952

4. Conclusions The work presents a formula given by eq. (6) which could be helpful for estimating effective heat conductivity of nanofluids. The equation is simple and have correct asymphtotic behaviour. The formula gives the dependence of effective thermal conductivity on volume fraction of nanoparticles and temperature. It can be recommended for Al2O3 suspensions. In the case of CuO suspensions the equation can be used but with some care. The parameters should be estimated by comparing with experiments, and first shot can be done using the values listed in Tables 1 and 2. Table 1 Constants of eq (6) for Al2O3 nanoparticles Al2O3 A B C D 36 nm [7] -0.243 -7.786 10.52 378.428 47 nm [7] -0.581 4.113 27.781 -143.600 38 nm [11] -0.066 0.708 6.685 87.847

R 0.992 0.939 0.996

Table 2 Constants of eq (6) for CuO nanoparticles CuO A B C D R 29 nm [6] -0.023 0.101 1.444 52.297 0.876 28.6 nm [12] -0.019 0.431 1.392 112.92 0.981 Table 3 Constants of eq (4) for t = 22 °C Al2O3 a b 36 nm [7] 0.23468 9.41537 38 nm [11] 0.23806 4.70149 41 nm [13] 0.14587 1.1301 47 nm [7] 0.6818 -2.4143 47*nm [7] 0.4018 6.9678 The asterisk denotes calculations based only on results for volume fractions 0.005; 0.02; 0.04 Table 4 Constants of eq (4) for t = 28 °C Al2O3 a b 36 nm [7] 0.1322 5.7294 47 nm [7] 0.4111 -1.0156 47* nm [7] 0.3175 2.1291 The asterisk denotes calculations based only on results for volume fractions 0.005; 0.02; 0.04

A New Experimental Relation for Effective Thermal Conductivity of Nanofluids

953

0.6

α=0.005 α=0.02 α=0.04 α=0.06 exp. α=0,005 exp. α=0,02 exp. α=0,04 exp. α=0,06

0.5

0.4 Oeff  O f Of 0.3 0.2 0.1 0 25

27

29

31 T [°C]

33

35

37

39

Fig 1. The thermal conductivity enhancement for Al2O3 nanoparticle (36 nm) suspensions vs temperature, see [7] 0.4 α=0.005 α=0.02 α=0.04 α=0.06 exp. α=0,005 exp. α=0,02 exp. α=0,04

0.3 Oeff  O f Of 0.2

0.1

0 25

27

29

31

T [°C]

33

35

37

39

Fig 2. The thermal conductivity enhancement for Al2O3 nanoparticle (47 nm) suspensions vs temperature, see [7] 0.3

D  0.25

D 

0.2

exp. α=0,01 exp. α=0,04

0.15

Oeff  O f Of

0.1

0.05 0 25

30

35

T [°C]

40

45

50

Fig 3. The thermal conductivity enhancement for Al2O3 nanoparticle (38 nm) suspensions vs temperature, see [11]

J. Thullie et al.

954 0,6 0,55 0,5

0,45

Oeff  O f O f 0,4

D  D  D  exp. α=0,02 exp. α=0,04 exp. α=0,06

0,35

0,3 0,25 0,2

28

29

30

31

T [°C]

32

33

34

35

36

Fig 4. The thermal conductivity enhancement for CuO nanoparticle suspensions vs temperature, see [6]

5. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

X-Q. Wang, A.S. Mujumdar, Int J. Therm. Sci. 46, 1 (2007) V. Trisaksri, S. Wongwises, Renev. and Sustain. Energ. Rev. 11, 512 (2007) S.E.B. Maiga, S.J. Palm, C.T. Nguyen, G. Roy, N. Galanis, Int. J. Heat Fluid Flow 26, 530 (2005) S.J. Palm, G. Roy, C.T. Nguyen, Appl. Term. Eng. 26, 2209 (2006) T-K. Hong, H-S. Yang, J Appl. Phys. 97, 064311 (2005) C.H. Li, G.P. Peterson, J. Appl. Phys. 99, 084314 (2006) C.H. Li, G.P. Peterson, J. Appl. Phys. 101, 044312 (2007) R.I. Hamilton, O.K. Crosser, IEC Fundam, 1, 182 (1962) S. Lee, S.U.S. Choi, S. Li, J.A. Eastman, J. Heat Transfer 121, 280 (1999) W.Yu, S.U.S. Choi, Journal of Nanoparticle Research 5. 167 (2003) S.K. Das, N. Putra, W. Roetzel, Int. J. Heat Mass Trans. 46, 851 (2003) S.K. Das, N. Putra, P. Thiesen, W. Roetzel, J. Heat Transfer 125, 567 (2003) D. Wen, Y. Ding, Int. J. Heat Mass Trans. 47, 5181 (2004) L.S. Sundar, S. Ramanathan, K.V. Sharma, Int. J. Material Sci., 2, 229 (2007)

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

955





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19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Diffusion in semi-crystalline polymers Richard Pokorny, Libor Seda, Zdenek Grof, Hana Hajova, Juraj Kosek Department of Chemical Engineering, Institute of Chemical Technology in Prague, Technicka 5, 166 28, Prague 6, Czech Republic, [email protected]

Abstract This contribution demonstrates the developed modeling tools capable of mapping between the semi-crystalline polymer morphology and transport of penetrants. Thus an understanding is brought to the area dominated by empirical knowledge that fails to describe even simple sets of experimentally measured transport characteristics. In this contribution we reconstruct spatially 3D structures of spherulites consisting of lamellae and calculate effective diffusivity of the reconstructed semi-crystalline structures.

Keywords: spherulite, semi-crystalline polymers, reconstruction, AFM, diffusion in hetero-phase media 1. Introduction Many commercially important polymers have semi-crystalline structure, that is, they consist of amorphous and crystalline phase. Examples of semi-crystalline polymers are HDPE, LLDPE and PP. Crystalline phase in these polymers is organized in lamellae of characteristic thickness of 10 nm. Lateral growth of lamellae from nucleation center, their branching, twisting and stacking creates spherulites of characteristic size 100 nm to 10 microns. Diffusion of penetrants in semi-crystalline polymers is important in manufacturing, in packaging applications and in membranes, where the ratio of crystal phase to amorphous phase is crucial for the membrane selectivity and permeability. The information about the morphology of spherulites can be obtained from SAXS and WAXS measurements. Another information about the morphology can be obtained from statistical characterization of the Atomic Force Microscopy (AFM) images of etched polymer samples. AFM images of PE samples are visualized in Fig. 1. Spherulite boundaries are shown in Fig. 1a and the lamellar structure of etched PE sample is presented in Fig. 1b.

R. Pokorny et al.

300 nm

100 nm

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(a)

(b)

Figure 1. AFM images of etched PE sample. (a) spherulite boundaries (b) detailed view of the etched compact PE.

2. Digital reconstruction of spherulites Our algorithm of digital reconstruction of spherulite structure arises from the concept of Mattozzi et al. (2006,2007). However, our approach is enhanced about many improvements in the generation algorithm leading to high, i.e., real crystallinities around 60%. The simulation of the lamellar growth starts from the single crystal element, which is defined by the position of its center of gravity P, thickness L, width W, height H and by its direction given by vectors v and g, cf. Fig. 2.

Figure 2. Basic lamellar element. The growth process is initiated from two opposite sides of the single crystal lamella in directions of vectors g and −g. Crystal growth proceeds in subsequent steps by adding further basic crystal elements with the same width, thickness and length as the lamella nucleus. During the growth of the initial lamella the new lamellae are randomly disbranched and start their own growth, cf. Fig. 3a. All crystal lamellae also undergo random twisting about their growth direction g, cf. Fig. 3b. Probability of both the disbranching and the twisting is controlled by the random number generator. The growth of the crystal lamella proceeds until it collides with other crystal or until the maximum spherulite radius is achieved. Hence, the lengths of lamellae are varied. When the growth of all lamellae is finished, a secondary growth is started to obtain a spherulite structure with roughly spatially uniform distribution of crystalline lamellas that is observed in polyethylene. The algorithm checks the local crystallinity (i.e., volume fraction of crystalline phase) in the resulting spherulite particle and in the regions with insuĜcient crystallinity starts the growth of new secondary lamellae, which grow from the already existing primary lamellae. This algorithm ensures that the local crystallinity is within acceptable limits, which means approximately ±10% of the average volume crystallinity.

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g´ a g

Y

v v´

β

(b) (a) Figure 3. Lamellar growth: (a) branching; (b) twisting With the previously described algorithm we are able to reconstruct spherulites with crystallinities up to 35% (νc = 0.35). When we want to achieve higher values of crystallinity, we have to apply the stacking of lamellae during primary growth and widening of lamellae after the primary growth. With these improvements we can achieve crystallinites about 60%, which corresponds well to experimental data provided by DSC and WAXS measurements. The obtained list of lamellae elements is at the end of the generation discretized to ones (amorphous phase) and zeros (crystalline phase) to the cubic grid and this resulting bitmap (spherulite particle) is visualized in Fig. 4.

(a)

(b)

Figure 4. Digitally reconstructed spherulite particle. (a) whole particle, (b) cut through spherulite

3. Diffusion in spherulite particles, effective diffusivity and tortuosity The effective diffusivity is a very important quantity for prediction of penetrant transport in porous or crystalline polymer particles. In the case of isotropic material we introduce the geometrical 3×3 tensor σ into the Fick’s law

J = − Dı ∇c

(1)

where D is the bulk diffusivity, J is the space-averaged molar flux intensity and ∇c is the space-averaged concentration gradient. In order to obtain σ, the concentration field in the hetero-phase media, for example, in polymer spherulite, is obtained as the solution of the equation

in crystalline phase ½ ­0 ∇ ⋅ (– D∇c ) = 0, where D = ® ¾. –10 2 ¯1 × 10 m /s in amorphous phase¿

(2)

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The boundary condition of zero flux at the interface between crystalline phase and amorphous phase is imposed. The arbitrary non-zero concentration difference is applied between two opposite walls in the x-direction while zero-flux boundary conditions are applied to remaining four walls. The average molar flux density vector J is then evaluated from the computed concentration field c(x, y, z). This allows us to obtain the x-column of the diffusivity geometrical tensor σ and the y- and z- columns are consequently calculated in an analogous way. The diffusivity tensor σ is symmetrical for isotropic porous medium and the factor

ȥ = D eff /D = tr ı /3 ,

ȥ = D eff /D is calculated as (3)

where “tr” is the trace operator. The steady state concentration profile in the cubic section of the spherulite particle from which the effective diffusivity is calculated is shown in Fig. 5.

Figure 5. Steady state concentration profile in reconstructed spherulite particle subjected to dimensionless concentration cleft = 1 and cright= 2. The effective diffusion coefficient can be related to the spherulite structure using the tortuosity factor

τ=

νa D eff /D

,

(4)

where νa is the volume fraction of amorphous phase (νa = 1 – νc). The dependencies of effective diffusivity and tortuosity on crystallinity and lamellae width to thickness (W / L) ratios are shown in Figs. 6 and 7, respectively. It is evident that the increase in crystallinity causes higher diffusion resistance to transport and the Deff/D ratio decreases. On the other hand tortuosity τ increases.

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0,30

W / Lavg = 10 W / Lavg = 20

0,25

W / Lavg = 30

0,15

D

eff

/D

0,20

0,10 0,05 0,00 0,30

0,35

0,40

0,45

0,50

0,55

0,60

νc

Figure 6. Dependency of effective diffusivity on crystallinity νc and width-to-thickness ratio W/L of lamellae. 12

W / Lavg = 10 W / Lavg = 20

10

W / Lavg = 30

τ

8 6 4 2 0 0,30

0,35

0,40

0,45

0,50

0,55

0,60

νc

Figure 7. Dependency of tortuosity of amorphous phase on crystallinity.

4. Conclusions The algorithm capable to generate spherulite structures comparable to those observed in polyethylene was developed. The lamellar growth starting from the crystal nucleus was achieved by adding of basic crystal elements to the growing lamellae. This was accompanied with branching, twisting, stacking and widening of lamellae. The spherulite structures generated by our algorithm have volume crystallinity up to 60% and attainable width-to-thickness ratio increased up to W/Lavg = 30. The equations for the prediction of eěective diěusivity and for the modeling of nonstationary diěusion have been derived and processed by the Finite Volume Method. The systematic parametric studies have shown, how the transport properties (especially the

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diěusivity and tortuosity) of semicrystalline polymers depend on the variation in the degree of crystallinity and width-to-thickness ratio of lamellae.

5. Acknowledgement The support from GACR 104/07/1127 and from KAN 208240651 is acknowledged.

References M. Bobak, T. Gregor, B. Bachman, J. Kosek, 2008, Macromolecular Reaction Engineering 2, 176-189. J. Kosek, F. Stepanek, M. Marek, 2005, Modeling of transport and transformation processes in porous and multiphase bodies, in Advances in Chemical Engineering, Vol. 30 „Multiscale Analysis“, edited by Marin G.B., Elsevier, pp. 137-203. A. Novak, M. Bobak, J. Kosek, B.J. Banaszak, D. Lo, T. Widya, W.H. Ray, J.J. de Pablo, 2006, Ethylene and 1-hexene sorption in LLDPE under typical gas-phase reactor conditions: experiments, J. Appl. Polym. Sci. 100, 1124-1136. L. Seda, A. Zubov, M. Bobak, J. Kosek, A. Kantzas, 2008, Transport and reaction characteristics of reconstructed polyolefin particles, Macromolecular Reaction Engineering 2, 495-512. A. Mattozzi, P. Serralunga, M.S. Hedenqvist, U.W. Gedde, 2006, Mesoscale modelling of penetrant diěusion in computer generated polyethylene spherulite-like structures. Polymer 47, 5588-5595. A. Mattozzi, M. Minelli, M.S. Hedenqvist, U.W. Gedde, 2007, Computer-built polyethylene spherulites for mesoscopic Monte Carlo simulation of penetrant diěusion: Influence of crystal widening and thickening. Polymer 48, 2453-2459.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

967

Numerical simulation of heat transfer in nanofluids Lukasz Kurowski,a Klaudia Chmiel-Kurowska,a Jan Thulliea a

Silesian University of Technology, Department of Chemical and Process Engineering, Gliwice 44-100, Poland, [email protected]

Abstract Numerical simulation of convective heat transfer in nanofluid based on Cu nanoparticles and ethylene glycol in a horizontal minichannel has been studied. Several models have been used and compared. Two phase mixture model has been selected to investigate hydrodynamic and thermal behavior of nanofluid. Keywords: CFD, nanofluid, laminar flow, heat transfer, microchannels 1. Introduction Nanofluid is a mixture of liquid and dispersed ultra-fine particles [1]. The behavior of nanofluid connected with the heat transfer enhancement can be described in several different ways. The work compares the most common models from practical point of view. The problem is important because applications of nanofluids are still in development [2]. There are few studies on convective heat transfer performance of nanofluids. Li and Xuan [3] and Xuan and Li [4] investigated experimentally convective heat transfer coefficient of Cu-water nanofluid for laminar and turbulent flow in a tube with constant heat flux, and found that nanofluid showed enhanced heat transfer. For a given Reynolds number, heat transfer coefficient was shown to be approximately 60% higher for nanofluid with 2 vol.% of Cu nanoparticles than for pure water. Wen and Ding [5] studied heat transfer in laminar flow at constant wall heat flux for Al2O3-water nanofluid. They observed the increase of heat transfer coefficient with Reynolds number and nanoparticles concentration particularly at the entrance region and found that thermal developing length was greater for nanofluid than for pure water. Oposite results were presented in other papers Yang et al. [6], Pak and Cho [7]. Convective heat transfer with nanofluids can be modeled using two-phase or single phase approach. The first provides the possibility of understanding functions of both fluid phase and solid particles in the heat transfer process. The second one assumes that fluid phase and particles are in thermal equilibrium and move with the same velocity. The effective parameters for this model are determined by an experiment. This model is simpler than the two-phase model and requires less computational time. Therefore it has been extensively used for heat transfer simulation of nanofluids. In general the numerical predictions of this approach are not in good agreement with experimental results. The main reason for this is that the effective properties of nanofluids are not known precisely. Due to several factors such as gravity, Brownian diffusion, sedimentation and dispersion, the slip velocity in nanofluid between the fluid and particle may not be zero, therefore the two phase model seems to be better for application. The main object of this study is numerical simulation of nanoparticles influence on laminar convection in a horizontal uniformly heated minitube. Comparison between thesingle phase model, discrete phase and multiphase model has been made. Based on

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the multiphase model for a given mean diameter of nanoparticle the effect of particle volume fraction on the heat transfer coefficient has been presented.

2. Mathematical formulation Assuming, negligible slip motion between particles and fluid and the thermal equilibrium conditions, nanofluid may be considered as conventional single-phase fluid. Its effective physical properties are function of properties of both nanoparticles and base fluids. One may expect that the classic theory developed for conventional single-phase fluids can be applied to nanofluids as well. Thus, all the equations of conservation (mass, momentum and energy) as well known for single-phase fluids can be directly extended and employed for nanofluids [8]. Based on literature data [9] we can found that nanofluid behavior is generally attributed to thermal dispersion and intensified turbulence, caused by nanoparticle motion. Therefore during the next step the discrete phase model was applied to describe process investigated. The discrete model realised by Fluent code follows the Euler-Lagrange approach. The fluid phase is treated as continuum by solving Navier–Stokes equations, while the dispersed phase is solved by tracking a large number of particles. The continuity, momentum and energy equations written in vector form are: Nanofluid continuity:

∇⋅v = 0

(1)

Nanoparticle continuity:

∇T º ∂φ ª + v ⋅ ∇φ = ∇ ⋅ « DB ∇φ + DT ∂t T »¼ ¬

(2)

Nanofluid momentum:

[

ª ∂v º t ρ« + v ⋅ ∇v » = −∇P + ∇ ⋅ μ ∇v + (∇v ) ¬ ∂t ¼

]

(3)

Nanofluid energy:

∇T ⋅ ∇T º ª ∂T º ª + v ⋅ ∇T » = ∇ ⋅ k∇T + ρ p c p « DB ∇φ ⋅ ∇T + DT »¼ T ¬ ∂t ¼ ¬

ρc «

(4)

Such behavior was simulated in 2D and 3D with commercial CFD code. The Lagrange approach does not effectively model particles suspended indefinitely long in continuum. However the unsteady state discrete phase model is capable of modeling the behavior of continuous suspension of particles. On the other hand the general multiphase mixture model has also been used. In the mixture model the phases are treated as interpenetrating continua. This model consists of the following equations:

Numerical Simulation of Heat Transfer in Nanofluids

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Continuity equation:

∂ (ρ m ) + ∇ ⋅ ρ m v m = 0 ∂t

(

)

(5)

Nanofluid momentum equation can be obtained by summing up the individual momentum equation for each phases:

[ (

)]

n ∂ (ρm vm ) + ∇ ⋅ (ρ m vm vm ) = −∇p + ∇ ⋅ μm ∇vm + ∇vm T + ρ m g + F + ∇ ⋅ §¨ ¦ φk ρ k vdr ,k vdr ,k ·¸ ∂t © k =1 ¹

(6)

Energy equation: n · ∂§ n ¨ ¦ φ k ρ k hk ¸ + ∇ ⋅ ¦ (φ k v k (ρ k hk + p )) = ∇ ⋅ (k eff ∇T ) ∂t © k =1 k =1 ¹

(7)

This set of conservation equations with appropriate boundary conditions was solved in 2D and 3D with commercial CFD code using the finite volume approach. In order to ensure that the solution does not depend on the number of grid points several different types of grids were tested. After preliminary calculations a non-uniform grid with 100k of cells was chosen. The solution was assumed to have convergence when residuals reached 10-6.

3. Results and discussion Calculations were performed by FLUENT code version 6.3 for the single phase, multi phase and a discrete phase model. The last model demands huge CPU and up till now (to authors knowledge) was not applied to nanofluids. 2.25

1.75

2

1.5

1.75 1.25

V/V0

V/V0

1.5 1 0.75

Models: Base fluid Pseudo homogenous Discrete phase Mixture

0.5 0.25

1.25 1 0.75

Models: Base fluid Pseudo homogenous Discrete phase Mixture

0.5 0.25

0

0 -1

-0.75 -0.5 -0.25

0 r/R

0.25

0.5

0.75

1

-1

-0.75 -0.5 -0.25

0 r/R

0.25

0.5

0.75

1

Fig.1. Fully developed axial velocity profile at vertical plane for nanofluid (0.15% Cu glycol), Re=100, Termophysical properties: in f(T) – left, const.-right

L. Kurowski et al.

970 1 Models: Base fluid Pseudo homogenous Discrete phase Mixture

0.8

T-T0 Tw-T0

0.6

0.4

0.2

0 -1

-0.75 -0.5 -0.25

0 r/R

0.25

0.5

0.75

1

Fig.2. Dimensionless temperature profile for fully develop region (0.15% Cu glycol), Re=100, Termophysical properties: the functional dependence on T given in [8]

Fully developed axial velocity profiles at vertical plane for nanofluid are showed in Fig.1. Comparison between all three models indicates that regardless of the model applied more or less the same values of velocity have been obtained. The assumption of constant physical properties of nanoparticles caused the velocity profile more steep. Moreover, for the same example dimensionless profiles of temperature for the fully developed region are presented in Fig. 2. We can infer that there is not clear difference in temperature profiles for investigated models. 3200

have (W/m2K)

2800

2400

φ of nanoparticles 0.15 % 0.25 %

2000

0.50 %

0.75 % 1600 0

50

100

150

200

250

Re

Fig.3. Average heat transfer coefficient versus Re for different content of nanoparticles

Single phase models require experimental determination of effective transport parameters (as thermal conductivity, viscosity etc). Multiphase models only require determination of base fluid parameters and nanoparticles, both easy accessible in

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1.76

1.76

1.74

1.74

1.72

1.72 max(V)/V0

max(V)/V0

literature. This is the reason that for preliminary calculations of heat transfer in nanofluids the two phase mixture model was selected. Numerical simulations have been done for different Re numbers and particle volume fractions. Fig. 3. gives a dependence of the heat transfer coefficient on Re number for four different content of nanoparticles. It is evident that a volume fraction of nanoparticles significantly affected the average heat transfer coefficient of nanofluids. Another interesting feature is the influence of nanoparticles on the velocity profile.

1.7

1.68

φ of nanoparticles 0.15 % 0.25 % 0.50 % 0.75 %

1.7

1.68

φ of nanoparticles 0.15 % 0.25 % 0.50 % 0.75 %

1.66

1.64 0

50

100

150 Re

200

250

1.66

1.64 20

30

40 Q [W]

50

60

Fig.4. Effect of volume fraction of nanoparticles on the velocity profile for fully developed region versus Re (left) and Q[W] (right) (thermo physical properties in function of temperature)

The maximum value of v/v0 in the central axis of a tube is plotted as a function of Re number (Fig.4 left). The velocity profile depends on nanoparticles concentration. Calculations have been carried out for temperature-dependent thermophysical properties given in [8]. Additionally in Fig. 4 (right) max. value of v/v0 versus transferred heat has been presented. With increasing heat exchange or Re number a presence of nanoparticles results in elongating of velocity profile.

4. Conclusions Three different models give similar results. As a rule the simplest model should be chosen. However, when modeling with limited access to experimental measurements of effective parameters the most suitable is two phase mixture model.

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5. Nomenclature c – specific heat, kJ/kgK DB – Brownian diff. coef., m2/s DT – thermal diffus. coef. , m2/s h – aver. heat transfer coefficient, W/m2K k – thermal conductivity, W/mK r –radial coordinate, m Q – heat , W Subscripts k – no. of phase ave – average w – wall

R – radius, m T – temperature, K V – velocity, m/s ĭ – volume fraction, ȡ – density, kg/m3 μ – viscosity, Pa s

0 – inlet m – mixture dr – drift

6. References [1] [2] [3] [4] [5] [6]

S.U.S.Choi, Seoul National University, Seoul, Korea, February, 17, 2002. V.Trsaksri, S. Wongwises, Renewable and Sustainable Energy Reviews, 11, 512, 2007. Y. Xuan , Q. Li, Heat Int. J. Heat Fluid Flow, 21, 58, 2000. Y.Xuan, Q.Li, J. of Heat Transfer, 125, 151, 2003. D.Wen, Y.Ding, Int. J. Heat and Fluid Flow, 26, (6), 855, 2005. Y.Yang, Z.G. Zhang, E.A. Grulke, W.B. Anderson, G. Wu, Int. J. Heat and Mass Transfer, 48,(6), 1107, 2005. [7] B.Pak, Y.Cho, Experimental Heat Transfer, 11(2), 151, 1998. [8] Ł. Kurowski, K. Chmiel-Kurowska, J. Thullie, G. Dzido, 18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 [9] J. Buongiorno, J. Heat and Mass Transfer, 128, 3, 240, 2006

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

973

A Continuous-Time Approach to Supply Chain Planning: Managing Product Portfolios subject to Market Uncertainty under Different Partnership Structures Ana Cristina Santos Amaroa, Ana Paula Ferreira Dias Barbosa-Póvoab a b

ISCAC, Quinta Agrícola, 3040 Coimbra, Portugal, [email protected] CEG-IST, IST, ,UTL, , Av. Rovisco Pais, 1049-001 Lisboa,Portugal, [email protected]

Abstract In this paper a continuous time approach is developed for the supply chain planning problem. The formulation allows for the explicit representation of the supply chain topology, operability and market demand uncertainty while accounting for different partnership relations as well as for product recovery. A decision criteria involving the evaluation of the supply chain planning profit is defined as the problem goal. The proposed contribution considers a central management strategy defined over a multiperiod planning problem, where decisions on the actual period should meet demand uncertainties induced by price changes (i.e. different probabilistic price forecasts) while accounting for some pre-defined contract driven demands. The economical concept of demand to price elasticity is used to model demand uncertainty and a set of planning scenarios with a probability of occurrence corresponding to the price forecasts is considered. The supply chain dependency on third-part logistic companies, that ensure the materials transportation, is studied. The applicability of the developed formulation is illustrated through the solution of a real industrial chain. Keywords: Supply chain, optimal planning, continuous-time model, uncertainty, partnership, demand to price elasticity.

1. Introduction Supply chain (SC) planning problems are commonly subject to uncertainty since worldwide business environments are progressively more volatile and demanding (Varma et al., 2007). This has been motivating practitioners and academics into the study of optimal supply chains structures where flexible operational procedures need to be implemented (Grossmann, 2005). Market uncertainty is a critical issue in such structures for efficient capacity utilization and robust infrastructures decisions. Furthermore, so far supply chains studies mainly focused on traditional SC structures ignoring transportation and reverse logistic issues. This paper tries to integrate, operational issues as materials transportation and the recovery operations within a collaborative SC structure where market uncertainties may occur. A centralized managing strategy defined over a multi-period planning problem under an uncertain environment is modelled. Production decisions on the actual period should meet not only the uncertain demand in the future period but also some pre-defined contract driven demands. Furthermore, this paper studies how different partnership structures influences the supply chain global planning.

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A.C.S. Amaro and A.P.F.D. Barbosa-Póvoa

A Mixed Integer Linear Programming formulation (MILP) is obtained. The final results consider details on the supply chain partners production, transportation and inventory, at each planning period. General resource capacities, resource sharing policies and economical distribution benefits for both contracted and uncertain product demands are accounted for. The applicability of the developed formulation is illustrated through the solution of a practical example involving a real industrial chain.

2. Problem Characterization The present contribution considers a supply chain structure with a set of partners such as suppliers, industrial facilities, transportation providers, distribution, customers, and disposal sites, geographically distributed. A collaborative relation between partners is assumed. A wide range of products is manufactured at industrial facilities essentially through multipurpose batch processes. These are distributed to customers (i.e. marketplaces or aggregated market regions) through distribution sites that represent centralized storage positions. Disposal sites can be seen as incineration entities where non-conforming products are processed. Finally, transportation providers guarantee the material flows among SC partners and into/from customers’ positions.

3. Modeling Approach, Problem Definition and Formulation A continuous-time approach is developed coupled with the aggregation procedure proposed by Amaro and Barbosa-Póvoa (2008). A set of macro entities involving materials (e.g. macro states, product families), operations (e.g. macro tasks and flows) and resources (e.g. macro-units) is considered. The time horizon is divided into several intervals (slots), with events taking place only at the interval boundaries. The planning objective is the maximization of the SC global profit, GPP. The solution optimizes the slot dimension and the planning objective while accounting for the SC topology, operability, product recovery, partnership relations and market demand uncertainty. Modeling Details and Concepts Continuous-time concepts The dimension of time slots is defined by the duration of the limiting event. This can result from different occurrences, namely: (1) allocation of a processing macro task or transportation flow; (2) replication of the same batch macro tasks; (3) linear combination of different macro task events allocated to the same resource instance and (4) a linear combination of transportation events allocated to suitable transportation structures. The occurrence of transportation events can represent the allocation of transportation flows performed by the same product family or the allocation of different transport families to a given suitable transportation structure. A sharing mode of operation is permitted for each transportation family in a given transport structure. Overlapped and the non-overlapped operation modes are considered. The former represents a sharing mode of operation were the limiting time describes the allocation of a specific transportation structure by a master event representing the simultaneous occurrence of a given set of transportation flows belonging to the same family. While in the later, the limiting time accounts for the linear combination of the transport times characterizing the allocated set of compatible or incompatible transportation flows.

A Continuous-Time Approach to Supply Chain Planning

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Economical/ market and Partnership concepts Elasticity: The demand to price elasticity coefficient, α , is a general economical concept defined as the modulus or absolute value of the logarithmic derivative of demand to price, as follows: ln( D)' ( dD dpm ) ⋅1 D dD pm (1) α =

ln( pm)'

=

=

1 pm

dpm

⋅

D

where dD dpm represents the absolute variation of demand to price (i.e. the first derivative of demand function, D = D( pm) , in order to price). A constant elasticity α coefficient is raised when demand is a polynomial function of price, D = β ( pm ) . In this case a relative change in price, ( dpm pm ) , results into a constant relative demand variation, ( dD D ) , whose value is α. Accordingly to the concept of demand to price elasticity, demand is elastic when its relative change is greater than or equal to the corresponding relative price variation, α ≥ 1 and it is inelastic when its relative variation is less than the relative price change, α < 1 . (2) § Δ Dˆ stˆ ˆ · § Δ pm § ˆ stˆ ˆ · * ˆ stˆ ˆ · Δ pm D ¨ ¸ = α sˆ ˆ st*ˆ ˆ ¹ © pm

¨¨ ˆ * ¸¸ © D stˆ ˆ ¹

⇔

ˆ *ˆ Δ Dˆ stˆ ˆ = Dˆ stm ˆ ˆ − D st ˆ ˆ stˆ ˆ = pm ˆ stmˆ ˆ − pm ˆ st*ˆ ˆ Δ pm

Dˆ = ¨ 1 + α sˆ ¸ Dˆ ˆ ˆ st*ˆ ˆ ¹ stˆ pm ©

∀ sˆ ∈ Sˆ ⊆ Sˆ

Products with an elasticity coefficient −1 < α sˆ < 1 are demand inelastic and, as a consequence, less sensitive to price variations, while those having α sˆ ≤ −1 ∨ α sˆ ≥ 1 are high sensitive to price changes. Partners’ weight: Moreover, the influence of partnership structures in terms of any supply chain entity under an uncertain environment is analysed. Particularly the supply chain dependency on third-part logistic companies, that ensure the materials transportation among partners and to marketplaces, is studied. Uncertainty: The demand uncertainty caused by price changes is modelled through a set of planning scenarios with a probability of occurrence corresponding to the price forecasts. In each scenario the demand uncertainty is considered through the demand to price elasticity coefficient. Different market characteristics that influence supply chain performance are captured based on the elasticity to price coefficient observed for each product family, at each market place. Supply Chain Planning Formulation A continuous multi-period, multi-location and multi-product problem is studied under market demand uncertainty, while accounting for partners operational and economical requirements and for any feasible products recovery. The supply chain planning formulation can be summarized as follows: Objective function, Max GPP : GPP = ¦ ϒSc

¦ξ

Sc

ip

ip

NSl § ¨ FEip + ¦ PCfθˆt t =1 ©

ip

· ¸ ¹ Sc

1. Global Cash-flows, GCfip Sc Nts § = ¨ FEip + ¦ PCf θˆ t t =1 ©

GCf ip

Sc

PCf θˆ

ip Sc

t

(

ip

· ¸ ¹

= Incomesθˆ − Costsθˆ t

2. Partnership Structure, ip

(ξ

ip

, GCf ip Sc

)

t

with

)

∧

θˆt

t =0

= θˆ0 = 0

∧ θˆt

t = NSl

= θˆNSl = Hp

FE ip ≡ Fixed costs of partner ip

∀ip , ∀ Sc

ip Sc

3. Uncertainty, Sc

(ϒ

Sc

ˆ stˆ ˆ % ) , pm

Sc =1,..., NSc

with

¦

Sc

ϒ Sc = 1

Constraints: Slot Boundaries, Processing and Recovery; Transportation; Supply; Deliver; Store to all or some SC partners. Variables: Integer - assignment of tasks and flows to resources; Continuous – time slots, capacities, demands, supplies, etc.

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The planning goal is the SC global planning profit (GPP). This considers fixed, FEip, and variable, PCfθˆ ipSc economical flows at each SC partner, ip, during the planning horizon, Hp. The global cash-flows of each partner, GCfip Sc , are balanced for each scenario, Sc, accordingly to the probability of the correspondent price forecasts, ϒ Sc . In this work, due to the dimension of planning horizon (i.e. 3 months) and to the available market indicators, only three scenarios where considered as adequate. These where chosen in accordance to the historical data available for the considered final products. In each one of these scenarios the demand uncertainty caused by each price probabilistic change is considered through the demand to price elasticity coefficient (eq. (2) above). A set of operational constraints involving the assignment of processing and storage operations (i.e. macro task events), the allocation of transportation structures (i.e. macro flow events) as well as the variable bounds representing the material states’ receipt, inventory and delivery conditions are also considered (Amaro & Barbosa-Póvoa, 2008). The continuous-time approach considers a fixed set of time points within the planning horizon. These are generated to represent weekly operational break (week ends) and partners working schedules with a detailed time description. Residence time is used to represent the time allocated to each event and no integrality conditions are a priori defined for events duration.

4. Case-Study The case study is an industrial pharmaceutical SC, involving three industrial plants (I1 and I2, located in Portugal and I3 in Spain) with a distribution channel with five warehouses (WH1, WH2 and WH3 in Portugal and WSH1 and WSH2 in Spain) and seven distribution points (i.e. warehouses, airport AP and seaport SP). Three product families: injection, soft-tablet and oral suspension medicines are supplied to local customers and to the European and African markets. The distribution is ensured by three transportation structures, having different capacities and number of transportation resources. The planning problem was solved for a three months planning horizon with twelve weekly periods. Two aspects were studied in the supply chain: i. the effect of uncertainty; and ii. the influence of partnership structure, particularly for transportation logistic partners, in the global planning profit. To illustrate each one of these aspects a set of operational scenarios was considered. Firstly, a centralized managing strategy with no a priori partnership relations was adopted (i.e. Ref. case). The global planning profit obtained for the Ref. case was then compared with the profit values obtained under price uncertainties (u1 and u2 cases). The cases generically denoted by *u1 represent 80% probability of a 5% increase on the actual medicines’ price, 20% probability of a 5% decrease on actual price and a null probability of a constant price; while cases *u2 define 20% probability of a 5% increase on products’ price, 80% probability of a 5% price decrease and a null probability of unchanged price values. Table 1 presents a summary of the achieved results. These consider both probabilistic behaviours occurring at a 6th week, till the end of the planning horizon. As it can be observed, the demand reduction caused by the most probabilistic price increase, at cases *u1, is not enough to cause a global SC profit reduction. Smaller amounts are delivered to customers but at a higher unitary profit that equilibrates the observed demand reduction. On the contrary in cases *u2 the demand increase caused by the price reduction is not sufficient to balance the associated unitary profit reduction.

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Table 1. Economical results for different uncertainty sources. Reference Case, Ref. - Without Uncertainty, F.O.=9606904 m.u ; 4.5% SP (SPu1; SPu2) R.Gap IP (IPu1; IPu2) R.Gap SE (SEu1; SEu2) R.Gap F.O. SPu1 = 9862115 ; 4.6% F.O. SPu2 = 9387312 ; 4.2%

F.O. IPu1 = 10238482 ; 3.0% F.O. IPu2 = 9314600 ; 3.4%

F.O. SEu1 = 9895236 ; 3.6% F.O. SEu2 = 9471934 ; 3.3%

Same Product within different markets– Soft tablets, S, at the Portuguese, SP, and at European market, SE, except for Portugal Δ (SEu1-SPu1) = 33121 m.u Δ (SEu2-SPu2)= 84622 m.u Same Market for different products– Portuguese market, P, for soft tablets, SP, and for injection solutions, IP. Δ (SPu1-IPu1) = -376367 m.u Δ (SPu2-IPu2)= 72712 m.u On the other hand, the influence of the market place can be analyzed by comparing cases SP and SE, for both demand uncertainty scenarios. Soft tablet medicines have an higher elasticity coefficient at the Portuguese market (α=-1,5) than at the European positions (α=-0.8) and accordingly a more sensitive behaviour was expected for the uncertainty scenarios reported to the Portuguese market. Although, the demand levels for the European market are higher than the ones observed for the Portuguese. The high sensitive behaviour of the Portuguese market was reduced by its smaller dimension while at the European market the uncertainty effect was enlarged due to dimension. To analyze how a defined market behaves for a common uncertainty scenario occurring for different product medicines, we compare the results achieved for soft tablet and injection solution medicines at the Portuguese market, SP and IP, respectively. Softtablet medicine are high sensitive to price changes than injection solution (α=-0,5), although the later are at the top of the demanded medicines at the Portuguese market. A similar effect to the one observed when different marketplaces were analyzed was observed. The enlarged economical effect observed for the injection medicines is then essentially explained by the observed demand levels. Moreover, concerning the partnership relations a study focus on the transportation partners was developed. Three transportation partners were considered, TS1 to TS3, and its influence on the defined partnership structure was analyzed by the consideration of a 10% cost increase implemented, figure 1. Only the results achieved for the ' ůŽ ďĂ ů^ ƵƉƉLJ ŚĂ ŝŶW ƌŽĨŝƚ͕' W W centralized partnership structure are 9606904 m.u reported. SC performance is high 9517371 m.u sensitive to the transport operations done by partner TS2, followed by TS3 9286403 m.u 9213108 m.u and by TS1. It was expected that a larger number of transport operations would be defined for partner TS2 and TS3. In fact it is not the case (TS1-49 flows, TS2-29 Cases: Ref. Δ CostTS1 Δ CostTS2 ΔCostTS3 flows and TS3-22 flows). Partners TS2 Figure 1 – Global Supply Chain with diverse and TS3 are the ones responsible for almost all transportations done to transportation partners costs. distribution centers connected with local (country) and EC markets while TS3 is essentially responsible for the intermediate and final medicines transfers between production partners. A large economical impact is associated with TS2 and TS3.

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The model was implemented using GAMS/CPLEX 22.8 involves 57754 continuous variables, 15450 integer/binary variables and 102769 equations. The problems were solved on average after 7000 CPU seconds for a relative gap less than 5%.

5. Conclusions, Remarks and Future work This paper presents a continuous-time formulation for the optimal planning of a generic supply chain. The proposed contribution accounts for detailed aspects involving not only supply chain production but also storage, transportation and products’ recovery are considered. The global planning profit is considered as well as demand and price uncertainties related to each product, by the elasticity to price coefficient. Different partnerships structures were considered and the influence of the demand/price uncertainty on the global supply chains economical and operational performance was studied. The formulation applicability was tested to a real industrial case involving a pharmaceutical supply chain. The results achieved are promising but improvements should be further explored.

References [1] Amaro, A.C.S., Barbosa-Póvoa, A. P. F. D. (2008), FOCAPO, 481-484,. [2] Grossmann, I. E. (2005), , AIChe Journal, 51, 1846-1857. [3] Papageorgiou, L.G. (2008), FOCAPO, 33-38 [4] Varma, V.A., Reklaitis, G.V., Blau, G.E. and Pekny, J.F. (2007), Comp. Chem. Eng., 31, 692-711.

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Agent based model for performance analysis of a global chemical supply chain during normal and abnormal situations Behzad Behdania, Zofia Lukszoa, Arief Adhityab, Rajagopalan Srinivasanb,c a

Delft University of Technology, Technology, Policy and Management, the Netherlands Institute of Chemical and Engineering Sciences, Singapore c National University of Singapore, Dept of Chemical and Biomolecular Eng, Singapore 1 Corresponding author: [email protected]

b

Abstract A global chemical supply chain is a complex network of different world-wide companies producing, handling, and distributing specific chemical products. For improving the overall performance of such systems, it is necessary to view them on one hand as a whole, and on the other as an aggregation of lower-level constituents – the production sites, plants etc, linked through various business processes. Agent-based modeling is a proven approach for modeling complex network of intelligent and distributed actors. In this paper we will demonstrate how an agent-based model can be developed to evaluate the dynamic behavior of supply networks, considering both the system-level performance as well as the components’ behavior particularly during abnormal situations. As an illustrative case, an agent-based model of a global supply chain is introduced. The behavior of supply network during an abnormal situation is also studied along with strategies to mitigate the effects of disruption. Keywords: Agent based models, global chemical supply chain, abnormal situation management, multi-plant enterprise

1. Introduction A global supply chain consists of a set of interrelated companies in different geographical locations that create and deliver products and services to end customers. Such a network of companies can be seen as a socio-technical system in which the physical network and the social network of actors involved in its operation collectively form an interconnected complex system where the actors determine the development and operation of the physical network, and the physical network affects the behavior of the actors. Usually, each actor in this complex network has some local goals that are sometimes in conflict with others. Achieving the optimum overall system performance does not necessarily mean the optimum for all local actors. In many cases the relation between the local goals and the overall performance is not clear and therefore appropriate modeling and simulation tools supporting understanding of a supply network components’ behavior and their effects on system performance are called for. During last two decades many analytical models of chemical supply chains - mostly using mathematical programming approaches - are presented. Shah described a comprehensive literature on different mathematical models for chemical supply chain [1]. Most of them do not easily take into account social aspects of the intra- and interorganizational complexity of the global problem. An alternative can be offered by agent-based models which have actor-centric perspective instead of the activity-centric

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one [2]. Compared with many efforts on optimization-based methods, the work on agent-based models for supply chain support is very limited. Garcia-Flores & Wang presented a multi-agent system for chemical supply chain simulation and management support [3]. Their architecture gives a basis for implementing distributed and cooperative supply networks over the internet. Srinivasan et al. developed a platform for modeling and simulating chemical supply chains using a task-based agent-based approach [4]. This paper contributes to the area of the performance analysis of a supply chain in normal and abnormal situations. Section 2 describes a generic agent-based modeling approach. In section 3, the global supply chain problem is discussed, followed by a numerical example of a lube oil supply chain in Section 4. Finally, Section 5 gives some concluding remarks.

2. Agent-based Modeling Agent-based modeling is a promising approach for modeling systems comprised of interacting autonomous agents [5], [6]. In this approach a system is described by defining its actors (agents) and technology they own or operate as well as possible interactions between them. The system behavior then emerges from the behavior of the model components and their interactions. In fact, instead of taking a top-down view in modeling, it is possible to model the system from a bottom-up perspective. Because of this, agent-based modeling can be a natural approach to model distributed and decentralized problems.

3. Problem Statement: Global Chemical Supply Chain Generally speaking, a global supply chain comprises of three main parts: customers, a multi-plant chemical enterprise and suppliers. Often, the enterprise comprises some production plants at different locations. The performance of each plant is a result of its departments' behavior and their interactions. The main actors in a chemical supply chain and their interactions are shown in Fig.1.

4. Case Study: Agent- based Model for a Chemical Supply Chain Based on problem definition, an agent-based model for a supply chain is implemented in Repast simulation platform [7] and Java programming environment. Each actor is modeled as an autonomous agent with specific roles and goals and communication behavior.

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Customers Customer1 •

Customer2

Customer3

Customer …

Sending orders on the basis of Market Demand.

Global Sales Department (GSD) • Receiving the orders from Customers. • Sending the orders for Production Plants and receiving the first possible fulfillment time from each plant. • Assigning the order to one Plant according to its Assignment Policy. • Negotiation with Customers, if none of the plants are able to produce and deliver the product on time. Production Plant 1 (the same structure for Production Plant 2, Production Plant 3 …) Scheduling Department • Receiving the new orders from GSD, doing scheduling and reporting the required information to the GSD. • Determining the current job (order) for Operation Department according to the current schedule. Operation Department • Processing raw materials into final products (Sending the required raw material information to the Storage Department and receiving the desired material accordingly) • Sending the products to the Packaging Department. • Informing the Scheduling Department about the processing information. Storage Department • Providing raw materials for the Operation Department. • Managing the raw material inventory level (Reporting to Procurement Department to place an order for the desired raw material according to raw material procurement policy, if it is necessary) Packaging Department • Packing the finished product according to Customer requested packaging type. • Informing GSD about finishing an order to arrange the finished product delivery, according to order pick-up type. • Sending the required information to GSD for each new to decide on plant assignment. Procurement Department • Communicating with the Suppliers and placing orders for raw materials. • After receiving an order, informing the Logistics and Storage Departments for order delivering. Logistics Department • Arranging the raw material transportation and product distribution • Reporting the required delivering information for deciding about new orders for GSD.

Suppliers Supplier1 •

Supplier2

Supplier3

Supplier …

Providing raw materials according to the order sent by the Procurement Department. Information Flow

Material Flow

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Figure 1. Main actors and their behavior/interactions in a global supply chain

Figure 2. Inventory level for Raw Materials for Production Plant1 Table 1. The effect of procurement policy (reorder point) on overall system performance number of Orders assigned to Production Plant1 number of Orders assigned to Production Plant2 number of Orders assigned to Production Plant3 Number of Orders assigned to All Production Plants number of Finished Orders by Production Plant1 number of Finished Orders by Production Plant2 number of Finished Orders by Production Plant3 Number of Finished Orders by All Production Plants number of Late Orders by Production Plant1 number of Late Orders by Production Plant2 number of Late Orders by Production Plant3 Number of Late Orders by All Production Plants Total tardiness for Production Plant1 (Days) Total tardiness for Production Plant2 (Days) Total tardiness for Production Plant3 (Days) Total tardiness for all Production Plants (Days) Average Inventory Level for production Plant1 (units) Average Inventory Level for production Plant2 (units) Average Inventory Level for production Plant3 (units) Average Inventory Level for all Plants (units)

15% 163 149 138 450 162 148 136 446 3 1 2 6 14 1 3 18 10790 11281 10669 10913

20% 163 145 142 450 163 145 142 450 3 0 1 4 8 0 1 9 12304 11281 11320 11635

25% 163 147 140 450 162 147 140 449 0 0 0 0 0 0 0 0 12312 11933 11422 11890

30% 163 147 140 450 162 147 140 449 0 0 0 0 0 0 0 0 12666 12335 11881 12294

The main model assumptions are: • There are three different MTO plants at three locations. • Each plant process one order at a particular time. • There are three product types with five different grades. • There are 50 customers around the world and six of them are more important than others. • The plant assignment policy is the first Completion Date. • The scheduling policy is Processing Earliest Due Date. • Reorder point policy for raw materials is on 10% safety level. • The maximum capacity for base oils is 5000 units and for other raw materials are 1000 units. The model makes it possible to perform many experiments and to study important factors that influence the behavior of each actor separately as well as the performance of

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the enterprise as a whole. For example, considering reorder point policy set to 25%, Fig. 2 shows the inventory level for raw materials for production plant1. Similar figures can be presented for the other two plants. As presented in Table 1, there is one non-finished order during 360 days time horizon. Apparently, any change in these policies can influence the system performance as a whole. In Table 1, the effect of changing the reorder point (procurement policy) on system performance is shown. As the reorder value increases, the overall performance of enterprise improves (total tardiness and number of late orders decrease); of course, this improvement is limited and after 25% the performance indicators don’t change. In other words, after this point the raw material availability will be no longer a bottleneck for production plant. Next to studying the normal behavior, many experiments can be formulated to study and steer the supply chain performance during an “abnormal situation”. Table 2 shows the simulation results for a scenario with a shut down in plant1 at the 240th day of the time horizon. Therefore, the related agent is not active after this time (its economic activities are stopped during disruption) and consequently, all orders should be fulfilled by production plants 2 and 3. As expected, the overall performance is worse, resulting in a 4 non-finished and 9 late customer orders. To handle this disruption, some policies can be defined and their effects can be easily studied. The following three policies are defined to mitigate the effects of disruption: Policy1- changing the procurement policy: changing reorder point to 30%. Policy2order rejection after disruption: to reduce the effects of disruption, GSD rejects 20 percent of orders, if they are not from important customers. Policy3- increasing the due date range after shut down: in this scenario, GSD negotiates with customers to increase their due dates by 10%. Table 2 shows the results for these policies. Increasing the reorder point doesn’t have any significant effect on supply chain performance but increasing the inventory holding cost. This implies that raw material availability is not a bottleneck for production plants. Other two policies improve the overall system performance. Policy2 shows better results by reducing total tardiness to 12 days; but it should be considered that here the total revenue will decrease due to fewer orders from customers. Table 2. The effect of plant disruption on overall system performance number of Orders assigned to Production Plant1 number of Orders assigned to Production Plant2 number of Orders assigned to Production Plant3 Number of Orders assigned to All Production Plants number of Finished Orders by Production Plant1 number of Finished Orders by Production Plant2 number of Finished Orders by Production Plant3 Number of Finished Orders by All Production Plants number of Late Orders by Production Plant1 number of Late Orders by Production Plant2 number of Late Orders by Production Plant3 Number of Late Orders by all Production Plants Total tardiness for Production Plant1 (Days) Total tardiness for Production Plant2 (Days) Total tardiness for Production Plant3 (Days) Total tardiness for all Production Plants (Days) Average Inventory Level for production Plant1 (units) Average Inventory Level for production Plant2 (units) Average Inventory Level for production Plant3 (units) Average Inventory Level for all Plants (units)

Plant Disruption 113 182 155 450 113 179 154 446 0 4 5 9 0 37 35 72 12732 11927 11401 12021

Policy1 113 182 155 450 113 179 154 446 0 4 5 9 0 37 35 72 12732 12083 11515 12110

Policy2 113 153 148 414 113 148 144 405 0 4 0 4 0 12 0 12 12732 12013 11232 11993

Policy3 113 176 161 450 113 174 159 446 0 4 3 7 0 31 28 59 12732 12120 11202 12018

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Similar to a plant disruption, other abnormal situations can be defined and the effect of mitigation policies can be studied. In another case study, supplier disruption is modeled in which the supplier for one month (from day 240 to 270) can not provide raw material as regularly and the delivering duration for this period is twice its usual duration. This disruption affects the overall system performance and there are 4 late orders with 17 days total tardiness. To handle this disruption, two policies are simulated; firstly, increasing the due date range after shut down and secondly, considering another supplier during disruption. In the second case, 50 percent of raw material orders are fulfilled by a second supplier with 20 percent higher delivering time than normal delivery time for main supplier. The simulation results show that the first policy can be an appropriate policy by reducing the total tardiness to zero and having only one nonfinished order. The second policy also improves the overall system performance by reducing the late orders to 3 orders and the total tardiness to 8 days.

5. Conclusion Application of agent-based modeling as a decision support tool in a global chemical supply chain is discussed. The model allows evaluating different policies for different components and their effect on overall system performance. The analysis is extended to abnormal situations and the mitigation the effects of disruption by different policies. The next step in the future work concerns applying the model to real cases.

References [1] N. Shah, Process Industry Supply Chain: Adv. and Chall., Comp. Chem. Eng., 29, 2005. [2] K.H. van Dam, et al., Benchmarking numerical and agent-based models of an oil refinery supply chain, ESCAPE 18, 2008 [3] R. Garcia-Flores and X. Z. Wang, A Multi-agent System for Chemical Supply Chain Simulation and Management Support, OR Spec., 24, 2004. [4] R. Srinivasan, et al., A multi-agent approach to supply chain management in the chemical industry, In: Multiagent-Based Supply Chain Management, Ed: B. Chaib-draa and J. P. Müller, Studies in Computational Intelligence, vol. 28. Berlin: Springer, 2006. [5] C. M. Macal, M. J. North, Tutorial on agent-based modeling and simulation, Winter Simulation Conference, Orlando, FL, 2005. [6] M. Wooldridge, N. Jennings, Intelligent agents: theory and practice, Know. Eng. Rev, 10, 1995. [7] M.J North, et al., Experiences Creating Three Implementations of the Repast Agent Modeling Toolkit, ACM Trans. Model. Comp. Sim., 16, 2006.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

Agent Based Modelling and Simulation of Intelligent Distributed Scheduling Systems Milagros Rolóna, Mercedes Canavesiob, Ernesto Martíneza a

INGAR (CONICET/UTN), Avellaneda 3657, S3002GJC Santa Fe, Argentina E-mail: [email protected] b UTN, Lavaise 610, S3004EWB Santa Fe, Argentina

Abstract For responsiveness and agility disruptive events must be managed locally to avoid propagating the effects along the value chain. In this work, emergent distributed scheduling is proposed to overcome the traditional separation between task scheduling and manufacturing execution systems. An interaction mechanism designed around the concept of order and resource agents acting as autonomic managers is described. Results obtained for different scenarios using a simulation model of the mechanism implemented in Netlogo are presented. Keywords: emergent distributed scheduling, mechanisms, autonomic systems, simulation.

agent-based

models,

interaction

1. Introduction For responsiveness and agility there exists an increasing trend towards decentralizing task (re)scheduling and execution control (Leitao, et al., 2005). The above situation has prompted the design of manufacturing execution systems (MES) that account for a given schedule but retain their robustness and flexibility (Ueda, et al., 2004). The most common MES in industrial practice today is to heavily resort to a given schedule so as to focus only on handling details and contingencies in task execution. To highlight decentralized control the concept of holonic MES has been proposed (Valckenaers and Van Brussel, 2005). More recently, the issue of autonomy in MES has been addressed (Valckenaers, et al., 2007). However, it is argue here that for agility and responsiveness decentralized schedule generation and execution control must be tightly integrated using autonomic agents that managed two types of objects: orders and resources. To this aim, an interaction mechanism must be designed based on generative modeling (North and Macal, 2007) to guarantee the desired dynamic behavior.

2. Emergent Distributed Scheduling Emergent distributed scheduling is the result of ongoing interactions among decentralized decision-making agents conceived as autonomic manager units (IBM Corp., 2006). There are two different roles that can be assigned to an agent. It can be either an order agent or a resource agent as shown in Fig. 1. Each agent playing its role implements the monitor-analyze-plan-execute (MAPE) loop which comprise both scheduling and control for a given order or resource. For the agent to be self-managing regarding its managed object, it must have an automated method to collect the details it needs from the manufacturing system (monitor function); to analyze those details to determine if something needs to be changed (analyze function); to create a plan, or

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sequence of actions that specifies the required course of action (plan function); and to perform those actions (execute function).

Fig. 1. Order agent and resource agent as autonomic managers

Fig. 2. Goal hierarchy of the distributed scheduling system

In the proposed scheduling mechanism order agents interact with resource agents whilst carrying out the following activities to achieve the goal hierarchy in Fig. 2: • Schedule monitoring, where are agent sensors constantly look up the Gantt chart to detect disruptive events and schedule updates; order agents supervise tasks from the viewpoint of order attributes whereas resource agents take care of their resource plan usage. • Order acceptance, where the order agent checks through the Gantt if the new order is feasible and so would be added to the current schedule or otherwise, should be rejected; • Process route selection and resource earmarking, where the resource agents returns the data to constitute the list of solutions from which the top solution will be chosen by the concerned order agent ;

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• Resource booking and task registration, where an order agent asks for time slot reservations to concerned resource agents seeking for the best solution, and the resource agents update their resource usage plans in the common Gantt chart; • Availability checking, where a resource agent checks its plan to assess the actual resource availability; • Task execution and task control, where the selected solution by the order agent is executed by the involved resource agents, and if a problem appears, the order agent tries to solve it locally by rescheduling.

Fig. 3. Class diagram of the distributed scheduling system

In the proposed mechanism design, there is one resource agent for each equipment item whereas each order agent only deals with a specific order type. A class diagram fo the distributed mechanism is given in Fig. 3. The communication is achieved through direct contact among concerned agents and indirect interactions through the Gantt chart which is used as a blackboard as it is shown in Fig. 4. When a new order arrives, the corresponding order agent looks up the Gantt in order to discover if the new order is feasible. If so, the order is accepted, and if not, it is rejected with a feasible due date. If it is accepted, the order agent asks candidate resource agents, stage by stage, different options for the probable arriving time at their queue and makes them a request about the probable finalization time at their resource. These options given by resource agents allows making a list of solutions. Given the different solutions provided by resource agents, the order agent selects the top one, with the aim of booking the time slot corresponding to the different tasks in the order. In the current intention selection, feasible orders can be placed according to different resource agent decision rules such as SPT: shortest processing time, EDD: earliest due date and FIFO: first in first out. As a response to the demand for reservation of the order agent, the resource agent registers the task and updates the Gantt chart. The mentioned procedure is repeated until all processing stages have the required resources secured. When the last task in the order plan is finished, the order agent stores the information previously collected in the system to give room for some collective memory about resources quality and reliability.

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Fig. 4. Direct and indirect interactions between agents in the scheduling mechanism

3. Case study To exemplify the proposed approach let’s consider applying the distributed scheduling mechanism to a multiproduct batch plant comprising of 4 stages and 10 units to obtain 5 different products (Fig. 5). Each order has different attributes such product type and due date whereas arrival times, processing times and machine failure rates are stochastic. A batch (order) can follow many different routes through the batch plant while using different pieces of equipment. So there is a great deal of flexibility in order scheduling and it is not obvious how smoothly each order will flow through the system due to a number of disruptive events.

Fig. 5. Multi-product plant network structure

This case study seeks to assess how the plant will operate under the proposed mechanism for distributed scheduling and to foresee its capacity to reschedule tasks while controlling their execution to account for unplanned events such as an increase in processing time at a given stage for an order type or a sudden increasing of machine breakdown rates. Also, it is assumed here that order agents have the objective of decreasing late deliveries, so they have some relevant criteria to choose from the list of solutions the earliest global finalization time alternative. In relation to the objectives of the resource agents, it is considered that all of them have the FIFO dispatching rule. A computational model was implemented in Netlogo® (Wilensky, 1999), a friendly software environment specifically designed for generative modeling of artificial agent societies. Netlogo is in continuous development at the Center for Connected Learning and Computer-Based Modeling, and is particularly well suited for modeling complex adaptive systems, or “worlds,” where many agents interact and take decisions whilst learning. This generative modeling approach allows exploring the connection between

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the micro-level behavior of individual agents and the macro-level patterns that emerge from the interaction of agents in an open artificial society. Fig. 6 exhibits the dynamics of the plant for the normal operating scenario. As can be seen the total processing times of both order types shown tend to stabilize roughly after a time equal to 1000 mins. This is a very important outcome which highlights that the emergent scheduling mechanism is robust and stable despite the total autonomy given to order and resource agents and the lack of a master schedule. Fig. 7 shows the impact of total processing time for the order types 2 and 3 when orders of type 3 experiments and instantaneous increment in the processing time at stage II.

Fig. 6. Total processing time for order types 2 and 3 for the normal scenario

Fig. 7. Total processing time for order types 2 and 3 for the scenario when order type 3 become more demanding of processing time at stage II since time 2000

Fig. 8 describes the dynamic response of the scheduling mechanism when the resource 1 experiments a sudden increase in its breakdown rate. Order type 3 is somewhat affected whereas type 2 orders are severely disrupted in their processing times even when this order type is not processed at resource 1. In Fig. 9, the total averaged queuing times for all order types and for different scenarios are shown. As can be seen orders of type 2 experiment the longest waiting times for resources in each stage of the multiproduct plant in all scenarios.

4. Final comments This paper proposes a novel mechanism for emergent scheduling based on a welldefined interactions between autonomic agent which manage two different type of objects: orders and resources. A generative simulation model was used to assess the performance of integrating schedule generation with local control.

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Figure 8. Total procèssing time for order types 2 and 3 for the scenario where an increase of resource 1“breakdown rates between minutes 1000 and 2000 is simulated

30 25 Without disturbances 20 More demanding orders type 1 at stage II

Minutes 15

Increasing of resource 0 breakdowns

10 5 0

1

2

3

4

5

Product Type

Figure 9. Average queueing times for the 5 order types and for the different scenarios

5. Acknowledgements The authors thanks to the ANPCyT of Argentina which partially supports the work presented here through project PICT 1099/06.

References IBM Corporation, 2006, An architectural blueprint for autonomic computing. Available at www03.ibm.com/autonomic/pdfs, Last access 29/10/2008. P. Leitao, A. Colombo, F. Restivo, 2005, ADACOR: A collaborative production automation and control architecture, IEEE Intelligent Systems, 20, 58–66. M. North, M. Macal, 2007, Managing Business Complexity. Discovering Strategic Solution with Agent-Based Modeling and Simulation, Oxford University Press. K. Ueda, A., Lengyel, I. Hatono, 2004, Emergent synthesis approaches to control and planning in make to order manufacturing environments, Annals of the CIRP, 53, 385–388. P. Valckenaers, H. Van Brussel, 2005, Holonic Manufacturing Execution Systems, CIRP AnnalsManufacturing Technology, 54, 427-432. P. Valckenaers, H. van Brussel, P. Verstraete, B. Saint Germain, Hadeli, 2007, Schedule execution in autonomic manufacturing execution systems, J. of Manufact. Systems 26, 75–84. U. Wilensky, 1999, Netlogo Modelling Environment, available at http://ccl.northwestern.edu/netlogo, Last access 29/10/2008.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Optimal Design of Large-Scale Supply Chain with Multi-Echelon Inventory and Risk Pooling under Demand Uncertainty Fengqi You, Ignacio E. Grossmann Department of Chemical Engineeirng, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Abstract We address the optimal design of a multi-echelon supply chain and the associated inventory systems in the presence of uncertain customer demands. By using the guaranteed service approach to model the multi-echelon stochastic inventory system, we develop an optimization model for simultaneously optimizing the transportation, inventory and network structure of a multi-echelon supply chain. We formulate this problem as an MINLP with a nonconvex objective function including bilinear, trilinear and square root terms. By exploiting the properties of the basic model, we reformulate the problem as a separable concave minimization program. A spatial decomposition algorithm based on Lagrangean relaxation and piecewise linear approximation is proposed to obtain near global optimal solutions with reasonable computational expense. Examples for industrial gas supply chains with up to 5 plants, 50 potential distribution centers and 100 markets are presented. Keywords: Supply Chain, Safety Stock, Risk-pooling, Uncertainty, MINLP

1. Introduction Due to the increasing pressure for remaining competitive in the global market place, optimizing inventories across the supply chain has become a major challenge for the process industries to reduce costs and to improve the customer service (Grossmann, 2005). This challenge requires integrating inventory management with supply chain network design, so that decisions on the locations to stock the inventory and the associated amount of inventory in each stocking location can be determined simultaneously for lower costs and higher customer service level. However, the integration is usually nontrivial for multi-echelon supply chains and their associated inventory systems in the presence of uncertain customer demands (Zipkin, 2000). The objective of this work is to develop optimization models and solution algorithms to address the problem of joint multi-echelon supply chain network design and inventory management. By using the guaranteed service approach to model the multi-echelon inventory system (Graves & Willems, 2005) we capture the stochastic nature of the problem, and develop an equivalent deterministic optimization model. The model determines the supply chain design decisions such as the locations of distribution centers (DCs), assignments of markets to DCs, assignments of DCs to plants, shipment levels from plants to the DCs and from DCs to customers, and inventory decisions such as pipeline inventory and safety stock in each node of the supply chain network. The model also captures risk-pooling effects (Eppen, 1979) by consolidating the safety stock inventory of downstream nodes to the upstream nodes in the multi-echelon supply

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chain. The model is first formulated as a mixed-integer nonlinear program (MINLP) with a nonconvex objective function, and then reformulated as a separable concave minimization program. To solve the problem efficiently, a decomposition algorithm based on Lagrangean relaxation and piece-wise linear approximation is developed to obtain near global optimal solutions within 1% optimality gap with modest CPU times. Examples are presented to illustrate the application of the model and its performance.

2. Problem Statement We are given a potential supply chain consisting of a set of plants (or suppliers) i ∈ I , a number of candidate sites for distribution centers j ∈ J , and a set of customer k ∈ K demand zones whose inventory costs should be taken into account. The market can represent a local distributor, a regional warehouse, a dealer, a retailer, or a wholesaler. Alternatively, one might view the customer demand as the aggregation of a group of customers operated with vendor managed inventory, which is a common business model in the industrial gases industry and some chemical companies. In the given potential supply chain, the locations of the plants, potential distribution centers and markets are known and the distances between them are given. The investment costs for installing DCs are expressed by a cost function with fixed charges. Each market k has an uncorrelated normally distributed demand with mean μk and variance σ k2 in each unit of time. Single sourcing restriction, which is common in the specialty chemical supply chain, is employed for the distribution from plants to DCs and from DCs to markets. That is, each DC is only served by one plant, and each market is only assigned to one DC to satisfy the demand. Linear transportation costs are incurred for shipments from plant i to distribution center j with unit cost c1ij , and from distribution center j to market k with unit cost c2 jk . The corresponding deterministic order processing times of DCs and market that includes the material handling time, transportation time and inventory review period, are given by t1ij and t 2 jk . The service time of each plant, and the maximum service time of each markets are known. We are also given the safety stock factor for DCs and markets, λ1 j and λ 2k , which correspond to the standard normal deviate of the maximum amount of demand that the node will satisfy from its safety stock. A common review period is used for the control of inventory in each node. Inventory costs are incurred at DCs and markets, and consist of pipeline inventory and safety stock, of which the unit costs are given. The objective is to determine how many distribution centers (DCs) to install, where to locate them, which plants to serve each DC and which DCs to serve each market, how long should each DC quote its service time, and what level of safety stock to maintain at each DC and market so as to minimize the total installation, transportation, and inventory costs.

3. Model Formulation The joint multi-echelon supply chain design and inventory management model is a mixed-integer nonlinear program (MINLP) that deals with the supply chain network design for a given product, and considers its multi-echelon inventory management. 3.1. Objective Function The objective function of this model (the total supply chain design cost) is given by,

Optimal Design of Large-Scale Supply Chain with Multi-Echelon Inventory and Risk Pooling under Demand Uncertainty

min :

§

¦ f Y + ¦ ¨© g ¦ χ Z j

j∈J

j

j

j∈J

k∈K

·

jk

§

993

·

μk ¸ + ¦¦ ¨ c1ij X ij ¦ χ Z jk μk ¸ + ¦¦ c 2 jk χ Z jk μ k ¹

i∈I j∈J

©

¹

k∈K

j∈J k∈K

§ · + ¦¦ ¨ θ 1 j t1ij X ij ¦ Z jk μk ¸ + ¦¦ θ 2k t 2 jk Z jk μk + ¦ λ1 j h1 j N j ⋅ i∈I j∈J © k∈K j∈J ¹ j∈J k∈K

¦ σ k2 Z jk + ¦ λ 2k h2k ⋅ σ k Lk

k∈K

(1)

k∈K

which includes the following items: DC Installation Cost: The cost of installing a DC in candidate location j is expressed by a fixed-charge cost model that captures the economies of scale in the investment. The annual expected demand of DC j is ( ¦ k∈K χ Z jk μ k ), which equals to the annual mean demand of all the markets served by DC j. Hence, the cost of installing DC j consists of fixed cost f j and variable cost ( g j ¦ k∈K χ Z jk μ k ), which is the product of variable cost coefficient and the expected demand of this DC in one year. Thus, the total installation cost of all the DCs is given by ¦ j∈J f jY j + ¦ j∈J ( g j ¦ k∈K χ Z jk μk ) . Transportation costs from plants to DCs and from DCs to markets: The product of the annual mean demand of DC j and the unit transportation cost ( ¦ i∈I c1ij X ij ) between DC j and the plant that serves it yields the annual plant to DC transportation cost, ¦ i∈I ¦ j∈J ( c1ij X ij ¦ k∈K χ Z jk μk ) . Similarly, the product of yearly expected mean demand of market k ( χμk ) and the unit transportation cost ( ¦ j∈J c 2 jk Z jk ) between market k and the DC that serves it, yields the coresponding transportation cost,

¦ ¦ j∈J

k∈K

c 2 jk χ Z jk μk

.

Pipeline inventory costs in DCs and markets: Based on Little’s law, the pipeline inventory PI j of DC j equals to the product of its daily mean demand ( ¦ k∈K Z jk μ k ) and its order processing time ( ¦ i∈I t1ij X ij ), which is in terms of days. Thus, the annual total pipeline inventory cost of all the DCs is given by, ¦ i∈I ¦ j∈J (θ 1 j t1ij X ij ¦ k∈K Z jk μk ) , where θ 1 j is the annual unit pipeline inventory cost of DC j. Similarly, the total annual

pipeline inventory cost of all the markets is given by,

¦ ¦ j∈J

k∈K

θ 2k t 2 jk Z jk μ k , where θ 2k

is the annual unit pipeline inventory cost of market k. Safety stock costs in DCs and markets: The demand at market k follows a given normal distribution with mean μk and variance σ k2 . Due to the risk-pooling effect (Eppen, 1979), the demand over the net lead time ( N j ) at DC j is also normally distributed with a mean of N j ¦ k∈J μk and a variance of N j ¦ k∈J σ k2 , where k

k

J k is the set of markets k

assigned to DC j. Thus, the safety stock required in the DC at candidate location j with a safety stock factor λ1 j is λ1 j N j ⋅ ¦ k∈K σ k2 Z jk . Considering the annual inventory holding cost at DC j is h1 j , we have the annual total safety stock cost at all the DCs equals to,

¦

j∈J

λ1 j h1 j N j ⋅

¦

k∈K

σ k2 Z jk . Similarly, the demand over the net lead time of markets k

( Lk ) is normally distributed with a mean of

Lk μk

and a variance of

annual safety stock cost at all the markets is given by,

Lkσ k2 .

¦ k∈K λ 2k h2k ⋅ σ k Lk .

Thus, the

F. You and I.E. Grossmann

994

3.2. Constraints Three constraints are used to define the network structure. The first one is that if DC j is installed, it should be served by only one plant. If it is not installed, it is not assigned to any plant. This can be modelled by, (2) ¦ X ij = Y j , ∀j i∈I

The second constraint states that each market k is served by only one DC, ¦ Z jk = 1 , ∀k

(3)

j∈J

The third constraint states that if a market k is served by the DC in candidate location j , the DC must exist, Z jk ≤ Y j , ∀j , k (4) Two constraints are used to define the net lead time of DCs and markets. The replenishment lead time of DC j should be equal to the guaranteed service time ( SI i ) of plant i, which serves DC j, plus the order processing time ( tij ). Since each DC is served by only one plant, the replenishment lead time of DC j is given by

¦

i∈I

( SI i + tij ) ⋅ X ij

.

Thus, the net lead time of DC j should be greater than its replenishment lead time minus its guaranteed service time to its successor markets, given by the linear inequality, N j ≥ ¦ ( SI i + t1ij ) ⋅ X ij − S j , ∀j (5) i∈I

Similarly, the net lead time of a market k is greater than its replenishment lead time minus its maximum guaranteed service time, Rk , is given by the nonlinear inequalities, Lk ≥ ¦ ( S j + t 2 jk ) ⋅ Z jk − Rk , ∀k (6) j∈J

Finally, all the decision variables for network structure are binary variables, and the variables for guaranteed service time and net lead time are non-negative variables. X ij , Y j , Z jk ∈ {0,1} , ∀i, j , k (7) S j ≥ 0 , N j ≥ 0 , ∀j

(8)

Lk ≥ 0 , ∀k

(9)

3.3. Reformulation The original model is a nonconvex MINLP. To reduce the computational efforts, we use linearization techniques to reformulate the model as a separable concave minimization problem. The reformulation model (AP) has a new objective function given as follows. (10) min ¦ f jY j + ¦¦ ¦ Aijk XZ ijk + ¦ ¦ B jk Z jk + ¦ q1 j NZV j + ¦ q 2k Lk j∈J

i∈I j∈J k∈K

j∈J k∈K

j∈J

k∈K

In addition to linear constraints (2), (3), (4), (7), (8), (9), the reformulated model includes the following linear constraints for linearization the product of a binary variable and a continuous variable (Glover, 1975): N j ≥ ¦ Sij ⋅ X ij − S j , ∀j (11) i∈I

XZ ijk ≤ X ij , ∀i, j , k

(12)

XZijk ≤ Z jk

(13)

, ∀i, j, k

XZ ijk ≥ X ij + Z jk − 1 , ∀i, j , k

(14)

SZ jk + SZ1 jk = S j , ∀j , k

(15)

SZ jk ≤ Z jk ⋅ S

(16)

U j

, ∀j, k

SZ1 jk ≤ (1 − Z jk ) ⋅ S

U j

, ∀j, k

(17)

Optimal Design of Large-Scale Supply Chain with Multi-Echelon Inventory and Risk Pooling under Demand Uncertainty

995

NZ jk + NZ1 jk = N j , ∀j , k

(18)

NZ jk ≤ Z jk ⋅ N

(19)

U j

, ∀j, k

NZ1 jk ≤ (1 − Z jk ) ⋅ N

U j

, ∀j, k

(20)

NZV j = ¦ σ ⋅ NZ jk , ∀j

(21)

Lk ≥ ¦ SZ jk + ¦ t 2 jk ⋅ Z jk − Rk , ∀k

(22)

XZ ijk ≥ 0 , SZ jk ≥ 0 , SZ1 jk ≥ 0

(23)

2 k

k∈K

j∈J

j∈J

, NZ jk ≥ 0 , NZ1 jk ≥ 0 , NZV j ≥ 0 , ∀i, j, k

4. Solution Algorithm

Figure 1. Lagrangean Relaxation Algorithm To effectively solve the proposed MINLP model, a global optimization algorithm based on Lagrangean relaxation is developed. The algorithm flowchart is given in Figure 1. The basic idea of this algorithm is to consider the alternative formulation (AP) of the model. Next, we dualize the assignment constraint (10) to allow decomposing the entire problem based on DC j. To solve each subproblem, we used piece-wise linear approximation to underestimate the square root terms. We should note that the entire solution algorithm requires at least an MILP solver; the NLP solver is not required. Due to the duality gap, this algorithm stops after a finite number of iterations. As will be shown in the computational results, the dual gaps are quite small.

5. Results To illustrate the application of the proposed model, we consider an industrial gas supply chain (liquid oxygen-LOX) with two plants, three potential DCs and six customers. The associated superstructure, as well as the optimal network structures with and without considering inventory cost, is given in Figure 2. The results show that although inventory cost only make up less than 20% of the total cost, it is necessary to take into account in the supply chain design. Comparison of the performance of the proposed

F. You and I.E. Grossmann

996

algorithms and commercial MINLP and global optimizers for medium and large scale instances (5 plants, 50 DCs, 150 markets) are given in Table 1. The advantage of using the Lagrangean relaxation algorithm for solving the proposed model can be clearly seen. 257 L/day

Op timal n etwor k w/o inven tor y cost

257 L/day

Op tima l netwo rk w/ inven tor y cost

86 L/day

86 L/day 462 L/day

387 L/day 194 L/day

194 L/day

343 L/day 75 L/day

75 L/day

292 L/day

269 L/day

537 L/day 292 L/day 95 L/day

95 L/day Plants

Distribution centers

Customers

Plants

Distribution centers

Customers

Plants

Distribution centers

Customers

Figure 2. Optimal network structure for the LOX supply chain Table 1. Comparison of the performance of the algorithms for medium and large scale instances Solve (P0) directly with BARON i

j

k Solution

LB

Gap

2

20

20

1,889,577

1,159,841

5

30

50

---*

---*

---*

10 50 100

---*

---*

20 50 100

---*

3

---*

50 150

Time (s)

62.92% 36,000

Solve (P2) with CPLEX for at most 1 hour, then solve (P1) with DICOPT or SBB DICOPT SBB Solution Time(s) Solution Time(s)

Lagrangean Relaxation Algorithm Solution

Global LB

Global Gap

Time (s)

Iter. 11

1,820,174

140.3

1,813,541

163.6

1,776,969

1,775,957

0.06%

175.0

36,000

---**

36,000

---**

36,000

4,417,353

4,403,582

0.31%

3,279

24

---*

36,000

---**

36,000

---**

36,000

7,512,609

7,477,584

0.47% 27,719

42

---*

---*

36,000

---**

36,000

---**

36,000

5,620,045

5,576,126

0.79% 27,748

53

---*

---*

36,000

---**

36,000

---**

36,000

12,291,296 12,276,483 0.12% 16,112

32

* No solution or bounds were returned due to solver failure.; ** No solution was returned after 10 hours

6. Conclusion In this paper, we present an MINLP model that determines the optimal network structure, transportation and inventory levels of a multi-echelon supply chain with the presence of customer demand uncertainty. The well-known guaranteed service approach is used to model the multi-echelon inventory system. The risk pooling effect is also taken into account in the model by consolidating the demands in the downstream nodes to their upstream nodes. To solve the resulting MINLP problem effectively for large scale instances, a decomposition algorithm, based on Lagrangean relaxation and piecewise linear approximation was proposed. Computational experiments on large scale problems show that the proposed algorithm can obtain global or near-global optimal solutions (typically within 1% of the global optimum) in modest computational expense without the need of a global optimizer.

References G. Eppen, 1979, Effects of centralization on expected costs in a multi-echelon newsboy problem. Management Science, 25, (5), 498. M. L. Fisher, 1985, An application oriented guide to Lagrangian relaxation. Interfaces 1985, 15, (2), 2. F. Glover, 1975, Improved Linear Integer Programming Formulations of Nonlinear Integer Problems. Management Science, 22, (4), 455. S. C. Graves, S. P. Willems, 2005, Optimizing the supply chain configuration for new products. Management Science, 51, (8), 1165. I. E. Grossmann, I. E., 2005, Enterprise-wide Optimization: A New Frontier in Process Systems Engineering. AIChE Journal, 51, 1846. P. H. Zipkin, 2000, Foundations of Inventory Management. McGraw-Hill: Boston, MA, 2000.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

997

Optimal Planning of Supply Chains for Bioethanol and Sugar Production with Economic and Environmental Concerns Fernando D. Melea, Gonzalo Guillén-Gosálbezb, Laureano Jiménezb a

Universidad Nacional de Tucumán, Av. Independencia 1800, S. M. de Tucumán T4002BLR, Argentina, [email protected] b Universitat Rovira i Virgili, Av. Països Catalans 26, Tarragona 43007, Spain, [email protected], [email protected]

Abstract This work addresses the design of supply chains (SC) for sugar/ethanol production with economic and environmental concerns. The design task is formulated as a bi-criterion mixed-integer linear program (MILP) that simultaneously minimizes the total cost of the network and its environmental performance over the entire life cycle of the product (i.e., sugar and ethanol). The capabilities of our approach are highlighted through a case study based on a real scenario, for which a set of Pareto optimal alternatives is calculated. Keywords: bio-ethanol supply chain, Life-Cycle Assessment.

1. Introduction The interest on renewable fuels has greatly increased in the last years. Particularly, the fast expansion of the ethanol market has affected the sugar cane industry, whose production is tightly linked with the former one. Following this trend, Argentina approved the National Act 26 093 that aims to promote the production of bio-ethanol for fuel blending. This new policy constitutes a big challenge for the sugar cane industry, which turns out to be one of the main manufacturing activities in the NW of Argentina. To achieve the transition from the current energy system towards a new one based on biofuels, it is still necessary to increase the efficiency and flexibility of the sugar cane industry. This could be done by adopting adequate energetic and environmental policies at different decision-making levels (Borrero et al., 2003; von Blottnitz and Curran, 2007). Unfortunately, despite the effort made so far, there are still some important industrial aspects regarding product quality, process safety, and logistics that have not been properly addressed and hence merit further attention. In particular, one of the key points that still remains open is how to determine the optimal configuration of the productiondistribution network capable of fulfilling the sugar and ethanol demand in the growing markets. This is not a trivial task, since it requires the understanding of the complex temporal and spatial interdependencies arising between the supply chain (SC) entities. The problem is further complicated by the need to account for different conflictive criteria at the design stage. This work addresses this last technical issue, and proposes a novel bi-criterion mixed-integer linear program (MILP) that aims at facilitating the decision-making in this area.

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2. Motivating case study The sugarcane industry of the NW of Argentina has been taken as reference to develop our optimization approach. The model assumes that sugar and alcohol are both produced from sugarcane. The formulation considers two different types of sugar: white and raw sugar, which differ in the purity. The ethanol produced is assumed to be anhydrous (for fuel blending) and azeotropic. The SC of interest includes (1) a number of plants that produce sucrose and bio-ethanol, (2) a set of warehouses where these products are stored before being delivered to the markets and (3) a set of transportation links that connect the SC entities. The aforementioned SC nodes can be established in a set of potential locations or grids that must be provided as input data to the model. The goal of the study is to find the set of Pareto optimal SC configurations, including the associated production plans, capable of satisfying the demand in the markets. Decisions to be made include the number, type and capacity of the storage and production facilities, the sugar and ethanol production rates and inventory levels at each facility, and the transportation flows. The standard production scheme of sugar and ethanol in the NW of Argentina is showed in Figure 1. For sugar production, the following activities are considered: milling, clarification, evaporation (vacuumed continuum quadruple effect tanks), crystallization (three cooked masses), centrifugation and drying. For ethanol production, the process includes: substratum preparation, fermentation, centrifugation, distillation, rectification and dehydration. The model also assumes that ethanol can be produced from different process streams: sugarcane syrup, molasses A, B or C. This consideration provides more flexibility to the sugar/alcohol production.

3. Mathematical formulation Our approach relies on postulating a superstructure that embeds all possible logistic alternatives to the SC design problem. This mathematical representation is then converted into a bi-criterion MILP problem that is solved via standard branch and bound techniques. To construct such a superstructure, the overall region of interest (i.e., NW of Argentina) is first divided into a set of grids, each of which is featured by a specific sugar/ethanol demand. The production plants and storage facilities can be established in any of these grids, and may be expanded in capacity over time in order to follow a specific demand pattern. The model includes three main sets of equations: mass balances, capacity constraints and objective function calculations. A brief outline of each of these blocks of equations is next given. Mass balances equations The mass balance must be satisfied in every grid (i.e., region) and time period. Thus, for every product i and time period t, the initial inventory kept in region g in storage facility s (Sgist-1), plus the amount purchased (Pgit), the input flow rate from other grids (Qg’git) and the production rate (Wgijt), must equal the final inventory (Sgist) plus the demand (Dgit), the amount sent to other grids and the amount consumed: ¦ S gist −1 + Pgit + ¦ Qg ' git +

s∈S (i )

¦S

s∈ S ( i )

g '≠ g

gist

+ Dgit +

¦Q

gg 'it

g '≠ g

+

¦

j∈OUT (i )

¦W

Wgijt =

gijt

j∈IN ( i )

∀g , i, t

(1)

Optimal Planning of Supply Chains for Bioethanol and Sugar Production with Economic and Environmental Concerns

999

Capacity constraints The actual capacities and capacity expansions of the production and storage facilities are represented by a set of continuous variables (CPLgjt, CWHgst, CEPLgjt and CEWHgst, respectively), whereas the number of capacity expansions executed in a grid are given by integer variables (NPLgjt and NWHgst). PL PL PL C git = C git −1 + CE git

∀g , i, t

(2)

PL PL PL N git C giPL ≤ CEgit ≤ N git C giPL ∀g , i, t

(3)

WH WH C gst = C WH gst −1 + CE gst

(4)

∀g , s, t

WH WH WH WH N WH gst C gs ≤ CE gst ≤ N gst C gs

∀g , s, t

(5)

On the other hand, the existence of a transportation link between any two grids is represented by a binary variable (Xgg’it) that takes a value of one if the corresponding link is established and zero otherwise.

Qgg 'it X gg 'it ≤ Qgg 'it ≤ Qgg 'it X gg 'it

∀g , g ' , i, t

(6)

Objective function calculations The model must attain two targets: minimum cost and environmental impact. The total cost of the sugarcane industry is calculated on a daily basis, and includes the capital and operating cost associated with the SC entities (FCC and FOC, respectively). The operational cost in a specific time period t is given by the manufacturing and inventory costs (FOCt) as well as the transportation expenses (TOCt). TC =

FCC + TCC + ¦ (FOCt + TOCt ) αCCF t

(7)

Here, Į represents the operating days per year, CCF is the useful life of the investment in years and TCC is the transportation capital cost. Environmental performance In this work, the environmental impact of the network is measured according to the principles of Life-Cycle Assessment (LCA). The scope of the study includes the entire SC (see Figure 1). The functional unit is the amount of sugarcane and ethanol consumed during the time horizon. The biochemical oxygen demand (BOD20) has been chosen as the environmental metric to be minimized, mainly because of its importance as an indicator of the pollution of the watercourses, as indicated in the Argentinean environmental legislation. The calculation of such a metric is performed by including in the model a set of equations that express the life-cycle emissions of the SC as a function of the tasks carried out in the network. These emissions are further translated into the corresponding impact.

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F.D. Mele et al.

Figure 1. System boundaries for the LCA-based environmental impact assessment

4. Results Our approach was applied to a case study based on a real scenario that addresses the strategic planning of an existing SC located in the NW of Argentina. The input data of the model was taken from existing facilities and complemented with different sources of information found in the literature (Hugot, 1982). The optimization model, which features 1.2·103 discrete variables, 5·104 continuous variables and 3·105 equations, was solved via the epsilon constraint method on a Pentium M 730 machine, 1.6 GHz using CPLEX 9.0 accessed through GAMS. It took around 200 CPU seconds on average to solve each single iteration of the epsilon constraint method.

Optimal Planning of Supply Chains for Bioethanol and Sugar Production with Economic and Environmental Concerns

1001

Figure 2 shows the Pareto set of the problem. As can be observed, the slope of the Pareto curve is rather smooth on its left side and then becomes sharper as ones moves to the right. These results indicate that it is possible to achieve significant environmental improvements at a marginal increase in cost in the Pareto points that are close to the minimum cost solution, whereas the same is not true for those near the minimum environmental impact one. Moreover, Figure 3 shows the configurations corresponding to the two extreme SC designs. As can be observed, the minimum cost solution entails a more decentralized network configuration. This is because the reduction in the total SC capital cost that is attained by opening a lower number of nodes (economies of scale) compensates the increase in the transportation cost. On the other hand, in the minimum environmental impact solution, the transportation tasks are minimized in order to reduce the emissions released to the environment.

Figure 2. Pareto points between two objectives

Figure 3. Pareto extreme solutions (minimum total cost on the left, and minimum environmental impact on the right).

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F.D. Mele et al.

5. Conclusions This work has addressed the design of SCs for sugar/ethanol production with economic and environmental concerns. The design task has been formulated as a bi-criterion MILP that minimizes the total cost and environmental impact of the SC. The latter criterion has been measured according to the principles of LCA. Our method has been applied to the optimization of an existing SC in the NW of Argentina. The method presented has identified Pareto alternatives that may lead to significant environmental savings at a marginal increase in cost. Furthermore, the mathematical model has provided valuable insight into the design problem, suggesting the convenience of adopting more decentralized SC configurations in which the transportation tasks are reduced.

6. Acknowledgments Financial support received from the Spanish “Ministerio de Educación y Ciencia” (projects DPI2008-04099, PHB2008-0090-PC and BFU2008-00196) and the Spanish “Ministerio de Asuntos Exteriores” (projects A/8502/07, HS2007-0006 and A/020104/08) is fully appreciated.

References M. Borrero, J. T. V. Pereira, E. E. Miranda, 2003, An environmental management method for sugar cane alcohol production in Brazil, Biomass & Bioenergy, 25, 287-299. H. von Blottnitz, M. A. Curran, 2007, A review of assessments conducted on bio-ethanol as a transportation fuel from a net energy, greenhouse gas, and environmental life cycle perspective, J. Cleaner Prod., 15, 607-619. E. Hugot, 1982, Manual para ingenieros azucareros. C. E. Continental: Mexico.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Optimisation of Regional Energy Supply Chains Utilising Renewables: P-Graph Approach Hon Loong Lam, Petar Varbanov, JiĜí Klemeš EC MC Chair (EXC) INEMAGLOW,Research Institute of Chemical Technology and Process Engineering, FIT, University of Pannonia, Egytem u. 10, H-8200 Veszprém, [email protected]

Abstract A method for regional energy targeting and supply chains synthesis is presented. A demand-driven approach is applied to assess the feasible ways for transferring energy from renewable sources to customers in a given region. The studied region is partitioned into a number of clusters by using the Regional Energy Clustering (REC) algorithm. The REC targets aim at minimising the system carbon footprint (CFP). Energy supply chain synthesis is performed next within each cluster by using the P-graph framework. The synthesis algorithm generates a maximal structure of all feasible options and optimal structure is obtained by minimising the energy cost and carbon footprint. Keywords: Regional Energy Supply Chains, Renewable Energy, P-Graph Optimisation, Clustering Algorithm, Carbon Footprint

1. Introduction With unstable fuel prices and the ongoing climate change the long-term secure and sustainable energy supply becomes an important issue for regional management and national policies. Previous studies have reviewed the important potential of renewable energy sources (RES) [1, 2]. However, exploiting RES is limited by various barriers as unstable and limited availability, high production cost, conversion technology limitations and complex supply chains [3]. Compared to other RES, biomass resources are locally available requiring extensive infrastructure networks for harvesting, transportation and storage. The low energy density of biomass increases the cost and complexity of supply chains. To evaluate the scope of the energy supply chains in a region, an energy targeting method and a biomass supply chain synthesis, integrating multiple sources and points are proposed.

2. Regional Energy Clustering (REC) Algorithm An energy cluster is formed by combining smaller zones to secure sufficient energy balance within the cluster [4]. A zone can be a province/county, an industrial park or an agricultural compound from the studied region. REC is used to manage the energy balancing among the zones. The energy surpluses and deficits from various zones can be matched and combined to form energy supply chain clusters. Forming the clusters aims at reducing energy waste and minimising the CFP during the biomass transportation and conversion.

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A suggested procedure for REC Algorithm is: i) Tabulate the energy source and demand data. The table has to contain the quantity of the potential energy sources, the bioenergy demand and the locations of the collection and distribution centroid is specified by 2-D Cartesian coordinate system and the centroid point for zone 1 is marked as reference point. This is illustrated in Tab 1. Tab 1. Biomass potential in studied region

Zi 1 2 3 4 5 ii)

Location (km,km) (0, 0) (4.1, 0.2) (4.4, 2.5) (5.3, 2.4) (7.9, 5.1)

Area (km2) 6.12 11.60 7.58 6.35 8.38

Supply Demand Zi (PJ/y) (PJ/y) 0.05 2.90 6 2.35 0.12 7 0.78 0.41 8 0.69 0.23 9 1.07 0.21 10

Area (km2) 5.57 10.63 7.83 4.12 3.15

Location Supply Demand (km,km) (PJ/y) (PJ/y) (6.4, 5.5) 0.22 2.1 (2.4, 6.8) 2.02 0.05 (9.4, 5.5) 0.82 0.15 (3.2, 6.6) 1.31 0.26 (2.3, 7.3) 0.78 3.06

Obtain an optimised targeting result for the biomass supply chain using LP. The objective is to minimise the total CFP [5] within the boundary of the given region. For biomass transfer from Zone i (source) to Zone j (sink) varying i = 1..Nzones; j= 1..Nzones , i  j, the following objective function is defined:

¦ CFP

MinCFP=

(1)

i, j

ij

CFPi , j = FCi , j × Dist i , j ×

Bi , j C

× CEF

(2)

where, CFPi,j is the Carbon Foot Print, FC i,j - Fuel Consumption, Disti,j Distance, B i,j - Biomass load, C - the lorries capacity, and CEF is the Carbon Emission Factor for diesel lorries. The following constrains are necessary: a) The total amount of biomass transported out from Zonei to other zones can not exceed the available surplus ABi:.

¦B

≤ ABi

i, j

∀i. , Bi , j

j

i= j

=0

(3)

b) The total bioenergy delivered to Zonej cannot exceed the deficit in that zone and the biomass load in the system must be non-negative:

¦ HV × B i

i, j

≤ D j ∀j.

(4)

i

HVi is the heating value for the particular biomass from Zonei and Dj is the total demand in Zonej. iii) Clusters are formed based on the priority that the residual bioenergy imbalance within the newly formed cluster is minimised (preferably zero).

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iv) The zones are arranged in a sequence starting with the largest surplus in the cluster and followed by the descending order. iv) The clustering result is then illustrated with a pair of monotonic cumulative curves. Plot the clustering curves: cumulative area in order of clustered zones sequence as x- axis and the accumulated energy balance on the y- axis. The result of the REC based on the data in Table 1 is illustrated in Fig 1. The solid line is the cumulative surplus curve, and the dashed line represents the cumulative deficit. Fig 1 indicates the size of each cluster and the total energy involved in the supply chain within the cluster.

Cumulative Energy (PJ/y)

12 10 8

Cluster 3

6 4

Cluster 2 2

Cluster 1 Cumulative Area (km2)

0 0

20

40

60

80

Fig 1. Cumulative Surplus-Deficit Curves

3. Energy supply chain synthesis by P-Graph Optimisation The energy supply chain synthesis within clusters is based on the P-Graph optimisation. P-graph is a directed bipartite graph with vertices representing the operating units and materials in the process flow [6]. The optimisation procedure uses a combinatorial technique based on axioms of the combinatorially feasible process structures, algorithms for maximal structure generation (MSG), solution structure generation (SSG) and accelerate branch and bound (ABB) [6, 7] Let us consider the cluster from Tab. 2. The biomass can be burned directly or converted to liquid biofuels. The residue from the conversion can be used as a fuel too. The solid biomass is transported to conversion plants such as CHP and biomass boilers to fulfil the cluster’s energy demand. Any extra biomass from the cluster is supplied to the energy export market and it fixed for only liquid biofuels as higher market price, more application and low transportation cost. Fig. 2 shows the problem maximal structure, with Tab. 3 listing the legend.

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40 20 30

Residue

25.1 285 25.4 350 20.6 220

Biofuel

5.06 4.10 5.30

Heating Value (GJ/t) Solid

3.55 4.67 1.64

56,512 135,082 45,511

Price ((€/t) Residue

Transportation Distance (km)

Biofuel

A B C

Production Energy (MJ/t)

Solid

Biomass Sources (t/y)

13.49 26.9 17.40 37.3 15.37 26.9

17.31 17.45 18.41

Tab 3. List of materials and operating units in the regional energy supply chain

Materials/ Operating units

Symbols

Biomass sources, residue and liquid fuel for A, B, C

A, B, C, RA, RB, RC, LA, LB, LC LPA, LPB, LPC

Liquid biomass conversion plant Transportation for biomass products Total solid biomass, total liquid biofuels

TA, TB, TC, TRA, TRB, TRC, TLA, TLB, TLC TSB, TLB

Cluster energy demand, Energy export market Fuel for transportation and Energy for liquid biofuels

CED, EEM F, E

Biomass A A

Biomass B E

LPA F

RA TRA

TA

TSB

Biomass C









LA TLA TLB RSM

BCP " CED

" EEM

Fig. 2: Maximal structure for energy supply chain in cluster 1

The network for minimum production cost is in Fig. 3. This is the optimal solution for the combination of transportation cost and liquid biofuel production cost. CFP analysis has been done and the result is shown in Fig. 4. The CFP has been reduced from 686,774 kg CO2/y to 683,001 kg CO2/y compared to the minimum cost solution. Transportation distance for biomass B is the longest, and converting product into liquid form could reduce the transportation load and hence - the CFP. A sensitivity analysis for the market price shows that, if the price for LB was increased to 370 €/t , biomass B is the first priority to produce the liquid biofuel as shown in Fig. 4.

Optimisation of Regional Energy Supply Chains Utilising Renewables: P-Graph Approach B

A 19498.15 t/y

37013.85 t/y

1007

C

135082 t/y

RA

LA TLA

TA

TRA

TB

TC

TSB

TLB BCP

RSM

" 3.16 PJ/y CED

" 155595 €/y EEM

Fig. 3: Optimal solution for minimum production cost

A 56512 t/y

C

B 135082 t/y

28733.10 t/y

16777.90 t/y LC

RC TA

TC

TB TSB BCP

TRC

TLC

46.98 t/y

220327.1 t/y

RSM " 3.16 PJ/y

10335.6 €/y

CED Fig. 4: Optimal solution for minimum CFP A C 56512 t/y

45511 t/y

122712.54 t/y

TB

TC

12369.46 t/y

TRB

LB TLB TLB

TSB BCP " 3.16 PJ/y CED

" EEM

B

RB TA

TLB

RSM 164761 €/y

" EEM

Fig. 5: Optimal solution for high liquid biofuel B, LB price

4. Conclusion A new approach to optimisation of renewable energy supply chain has been developed. The REC algorithm combines energy surplus and deficit from various zones, which can be matched and combined to form energy supply chain clusters. Forming the clusters

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aims to overcome the energy waste and to minimise the CFP during biomass transportation. The supply chain synthesis is carried out by P-graph optimisation. The solutions depend on the objective of the optimisation such as minimum production cost or minimum CFP.

5. Acknowledgements The financial support from the EC MC Chair (EXC): INEMAGLOW, MEXC-CT-2006-042618 is gratefully acknowledged.

References [1] [2] [3] [4] [5] [6]

WEA 2000, World Energy Assessment UNDP, New York. IEA 2007,.International Energy Agency Report, IEA/OECD,Paris,France. T. Nakata, Progress in Energy and Combustion Science 30 (2004) 417. H.L.Lam, P. Varbanov, J. Klemeš, UoP University Press 2008/50, 209 S. Perry, J.Klemeš, I.Bulatov (2008) , Energy 33 (10) October 2008, 1489-1497 . F. Friedler, K. Tarjan, Y. W. Huang, L. T. Fan. Comp. and Chem. Eng.. 1992, 16, 313.

I. Heckl, Z. Kovacs, F. Friedler, L

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1009

The supply-chain pick-up and delivery problem with transshipments Rodolfo Dondoa, Carlos A. Méndeza, Jaime Cerdáa* a

INTEC (UNL-CONICET), Güemes 3450, 2500- Santa Fe, Argentina, Email: [email protected]

*

Abstract In this work, a strict MILP formulation for the supply-chain pick-up and delivery problem with transshipments is presented (SC-PDP-T). This problem adds the option for transferring goods from one vehicle to another. This additional flexibility is very attractive for the optimal management of supply chains. Based on the novel features of the SC-PDP-T, this work addresses the major modeling and solution issues related to this problem by presenting a new MILP-based strategy to find the set of decisions to optimally manage complex multi-site distribution systems of moderate-size. Keywords: Supply-chain, pick-up and delivery, transshipments.

1. Introduction The cost-effective management of multisite production system is a complex task that needs to be aided by efficient computational tools. In this direction, the pickup and delivery problem (PDP) has been one of the most studied network logistic problems in the transportation-research literature [1, 2]. In the emerging area of enterprise-wide optimization, a great deal of effort is focussed on the optimization of complex supply chains. So, in the last years, the inherent features of real-world supply chains have motivated the development of numerous and more realistic variations of the classical PDP. Following this trend, the so-called supply-chain PDP (SC-PDP) have been defined by [3] aiming at generalizing the typical PDP by considering alternative supply sites, inventory constraints, multiple visits to the same site and multiple commodities. Sometimes, forcing each load to be directly transported from its source to its final destination by using a single vehicle is a hard assumption. This limitation explains why the PDP, a widely studied problem in the transportation research area, has not been widely used in supply chains applications. The possibility for goods to be transferred from one vehicle to another adds a higher flexibility to the operation that could improve the overall productivity by exploiting the interaction between vehicles at specific transfer points. Obviously, if the added flexibility reduces the total load-transported and travel times, one could try to find favorable conditions for implementing a support system that allows transfers instead of rigid PDP formulations. So, the PDP is here extended to consider transfer points, i.e. distribution centers, where some vehicles can drop its load to allow others to pick up it later, as defined by [4]. The modeling of this new feature generates a new logistic problem called the SC-PDP with transshipment (SC-PDP-T).

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2. Problem statement Consider a routes-network represented by a graph G[{p ‰ I ‰ T }; A], where p is the vehicles base; I = {I+ ‰ I-} is the set of customers, being I+ = {i1, ..., in: li > 0 for all ii }the set of pick-up customers; I- = {j1, ..., jn’: li > 0 for all ji } the set of delivery clients; and T is a transshipment base, i.e a distribution center, defined as T = {T+ ‰ T-}, where T+ represents the set of reception nodes and Tthe set of delivery nodes. Both sets are linked by a set of transfer operations R. Therefore, if the load delivered to node i T- must be transferred to the node j T+, then operation r  R is defined by the couple r = {i, j}. Finally, A = {aij / i, j  I+ ‰ I- ‰ T+ ‰ T- ‰p} defines the net of minimum cost arcs among customers i I; the warehouse p and the transshipment base T. A distancebased traveling-cost matrix C = {cij} and a travel-time matrix * = {tij} are associated to the net A. The service-times to pickup/deliver the load li from (to) nodes i  (I ‰ T) are denoted by sti and they must be fulfilled by some truck of vehicles fleet V = {v1, v2, ..., vm}. The solution must provide a finite sequence of arcs, called route, for some of the vehicles of V such that: (i) each vehicle starts and ends the trip at p; (ii) each site i  I is assigned to exactly one route; (iii) a delivery transfer-node i  T- may be used or not. If used, its paired pick-up transfer node(s) must also be visited by some vehicle; (iv) the actual load carried by a vehicle must never exceed its transport capacity qv; (v) the service for any node i  I must start within the time-window [ai, bi]; (vi) the duration of the vehicle-v trip must be shorter than a maximum routing time tvvmax. The problem goal is to minimize the total cost for providing pickup/ delivery service to every node i  I. 3. The MILP model Objective function. The objective aims at minimizing the total routing cost. Min

(1)

¦ CVv

vV

Assignment constraints. According to eq. (2.a), each customer i  I must be visited by a single vehicle, while eq. (2.b) states that a transshipment node i  Tmay be used (Yiv = 1) or not (Yiv = 0). Finally, if the delivery node i  T- is used, eq. (2.c) forces that its paired node j  T+: r = (i,j) R to be also visited.

¦ Yiv

1

i  I

(2.a)

vV

¦ Yiv ¦ Y jv

vV

¦Yiv d 1

vV

vV

i  T  , j  T  , r

{ i, j }  R

i  T 

(2.b) (2.c)

Cost-based constraints. Eq. (3.a) computes the least travelling cost (Ci) from the vehicle base to any location i  I ‰ T. Eqs. (3.b)-(3.c) sequence customers and transfer nodes in the cost dimension. Thus, if nodes i and j are allocated to

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the vehicle-v tour (Yiv = Yjv = 1), the ordering of both nodes is determined by the value of the sequencing variable Sij. So, if location i is visited before j (Sij = 1), according constraints (3.b), the travel cost up to location j (Cj) must be larger than Ci by at least cij. In case node j is visited earlier (Sij = 0), the reverse statement hold and constraint (3.c) becomes active. If one or both nodes are not allocated to the vehicle-v tour, eqs. (3.b)-(3.c) become redundant. Finally, eq. (3.d) states that the overall cost of using any vehicle v  V (CVv) must be larger than the travelling cost up to any site i (Ci), by at least the cost of the arc i-p (cip). Mc is an upper bound for variables Ci and CVv. i  I ‰ T

Ci t c pi







­°C j t Ci  cij  M C 1  Sij  M C 2  Yiv  Y jv ® °¯ Ci t C j  cij  M C Sij  M C 2  Yiv  Y jv CVv t Ci  cip  M C 1  Yiv





½°

¾ v V ,i , j  I ‰ T : i  j °¿

v  V ,i  I ‰ T

(3.a) (3.b) (3.c) (3.d)

Time-based constraints. Eq. (4) forces the service time on any customer i  I to start at a time Ti bounded by the interval [ai, bi]. Also, due to eq. (5), the total routing time TVv for vehicle v  V must be lower than the bound tvmax. Eqs (6.a) to (6.d) state visiting-time constraints that are similar to eqs (3.a)-(3.d) but apply to the time dimension. MT is an upper bound for variables Ti and TVv.

ai d Ti d bi

(4)

i  I

TVv d t v max

Ti t t pi







­°T j t Ti  sti  tij  M T 1  Sij  M T 2  Yiv  Y jv ® °¯ Ti t T j  st j  t ji  M T Sij  M T 2  Yiv  Y jv





½° ¾ °¿

TVv t Ti  sti  tip  M T 1  Yiv

v V

(5)

i  I ‰ T

(6.a)

v  V ,i , j  I ‰ T : i  j

(6.b) (6.c)

v  V ,i  I ‰ T

(6.d)

Cargo constraints. Eq. (7.a) states that the cargo Įi to be picked-up from any customer i I+ must be equal to li, while the cargo ȕi to be delivered to this client must be zero. Conversely, the cargo ȕi to be delivered to any customer i  I- must be li while the cargo Įi to be picked-up from this customer must be zero (eq. 7.b). Eq. (8.a) states that the quantity of goods picked from a transfer node i  T+ is equal to the quantity previously delivered to the paired delivery-node j  T-: (i,j) R and constraint (8.b) states that the quantity of goods Ȗiv delivered to a transfer node i  T- by the vehicle v must be at least the collected quantity Ȗiv. ­D i ® ¯ Ei

li ½  ¾ i  I 0¿

(7.a)

­D i ® ¯E i

0½ ¾ li ¿

i  I 

(7.b)

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8.(a)

­D i E j ½ i , j  T : { i , j }  R ® ¾ ¯ Ei 0 ¿

Di 0 ­ ½  ® ¾ v V ,i  T ¯E i t J iv  M L 1  Yiv ¿

(8.b)

Vehicle constrains on the transshipment base. Eq. (9.a) states that the quantity Ȗiv to be delivered to transfer node i  T- must be zero if the vehicle v does not visit such a node. Otherwise, it must be smaller that the total quantity collected on pick-up sites. Conversely, according to eq. (9.b), the quantity įiv picked-up by the vehicle v from the transfer node i  T+ must be zero if v does not visit such a node. Otherwise, it must be equal to the quantity of goods to load from this transfer point. ­ J iv d M LYiv ½ ° ° v  V , i  T  ®J iv d ¦ l j Y jv ¾ °¯ °¿ jI 

(9.a)

G iv d M L Yiv ­ ½ ° ° v  V , i  T  ®G iv d D i  M L 1  Yiv ¾ °G t D  M 1  Y ° i L iv ¿ ¯ iv

(9.b)

Vehicle-cargo constraints. Variables Li and Ui compute respectively the total cargo loaded and unloaded by a visiting vehicle up to the node i  I ‰ T. So, eq. (10.a) states that the current load transported on the visiting vehicle up to the node i  I ‰ T, computed as the difference (Li - Ui) must be larger than zero and smaller than the vehicle capacity qv. Constraints (10.b)-(10.e) determines the accumulated loaded and unloaded cargo in a similar way to eqs. (3.a)-(3.d). Eq. (11.a) states that the load available on vehicle v after visiting node i (Li) must be larger than the quantity Įi to be picked-up from the node and smaller than the total quantity of goods collected by the visiting vehicle in case vehicle v visits the site i (Yiv = 1). Constraint (11.b) is similar to (11.a) but for the cargo unloaded after servicing node i (Ui). ML is an upper bound for Li and Ui. 0 d Li  U i d

i  I ‰ T

¦ Yiv qv

vV

 



 

½ °°

­ L j t Li  D j  M L 1  Sij  M L 2  Yiv  Y jv °U t U  E  M 1  S  M 2  Y  Y ° j i j L ij L iv jv ® t      L L D M S M 2 Y Y i j i L ij L iv jv ° ° Ui t U j  Ei  M L Sij  M L 2  Yiv  Y jv ¯ ­D i d Li d ¦ Y jv l j  ¦ G jv  M L 1  Yiv ½

 

° ° jI  jT  ® ¾  E U Y l J M 1 Y d d    ¦ jv j ¦ jv L iv ° i ° i jI jT ¯ ¿



¾ ° ° ¿

(10.a) (10.b) (10.c)

v V ,i , j  I ‰ T : i  j

v V ,i  I ‰ T

(10.d) (10.e) (11.a) (11.b)

Time and inventory constraints on transshipment bases. As the number of pick-up/delivery tasks within the nodes of a transfer base is known beforehand and can be pre-ordered, eq. (12) fixes the vehicles visiting times to the transfer base and eqs. (13.a)-(13.b) track of the cargo inventoried in the base by sequencing variables Ii (unloaded cargo) and Di (delivered cargo). The actual

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inventory of goods, computed by the difference (Ii - Di), is bounded by the interval [0, Qmax] enforced in Eq. (14). i  T  , j  T  : { i , j }  R

Ti t T j  st i ­ I j t Li  E j ½ ® ¾ ¯D j d U i  D j ¿ 0 d I i  Di d Q max v

(i, j )  T : i  j

i  T

(12) (13.a) (13.b) (14)

4. An Illustrative example The proposed MILP model was developed in ILOG OPL Studio 3.7 and solved in a 2 Ghz 2 MB RAM Pentium IV PC. The logistics problem addressed comprises twenty geographically dispersed customers with known demands of a single commodity produced in two different production plants. Demands can be directly satisfied from the plants or from two distribution centers located in urban areas by using two vehicles (VL1, VL2). In addition, each distribution center hosts a small vehicle that can subsequently deliver a given quantity of a commodity to neighboring clients. Delivery tasks must be fulfilled within given time windows and the problem solution must provide the optimal sequence of clients to be visited by each vehicle while minimizing the total travelling cost. Cartesian coordinates that specify locations for the vehicle-base, the plants, the distribution-centers and the clients as well as their respective time-windows are presented in Table 1. Vehicles characteristics are also presented in this Table. Inter-nodal Euclidean distances are computed from the reported coordinates and the arc cost/travelling-times are numerically equal to those distances as defined by Solomon (1987). The optimal solution, found in 536 s CPU time, implies a total travelled distance of 399.9 units and is explicitly illustrated in Figure 1. Table 1: Problem data Nodes X coord Y coord Readytime Duedate Demand Vehicles

Vbase; Plant1; Plant2; Ssite1;Ssite2;1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20 40;55;30;20;5; 25;22;22;20;18;15;15;10;10;8;8;5;2;0;0;55;25;20;30;50 50;60;25;85;45; 85;75;85;80;75;75;80;35;40;40;45;35;40;40;45;20;30;50;60;35 -;-;-;-;-; 145;0;109;141;95;79;0;0;119;0;0;0;0;0;0;83;52;91;140;130 -;-;-;-;-;255;300;139;171;125;109;300;300;149;300;300;300;300;300;300;113;82;121;300;160 -;-;-;-;-;20;30;10;40;20;20;10;20;30;40;20;10;20;20;20;19;3;5;16;19 Large (VL1, VL2): qVL = 300; tVLmax = 300/ Small (VS1, VS2): qVS = 150; tVSmax = 300

DETAILED SOLUTION - VL1: Vbase; Plant2; 19; 18; 23; 9; 11; T2; 17; 22; Base. (TV VL1 = 293.7; CV VL1= 185.0) - VL2: Vbase; Plant1; T1; 20; 10; Base (TV VL2 = 181.7; CV VL2= 141.7) - VS1: T1; 7; 6; 2; 8; 4; 3; 1; T1 (TV VS1 = 206.0; CV VS1 = 45.0) - VS2: T2; 12; 13; 15; 16; T2 (TVVS2 = 399.3; CV VS2 = 28.2)

Figure 1. Optimal solution for the SC-PDP-T problem

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5. Conclusions This work has introduced a novel MILP formulation for the SC-PDP-T. Its applicability has been successfully illustrated by solving a typical supply chain problem. This problem fully exploits the possibility of cargo-transfers between vehicles in order to find flexible supply programs. This feature is of utmost importance for saving transportation cost while keeping a high level of supply efficiency. Future work should include the possibility of considering alternative supply sites, inventory constraints; multiple visits to the same customer and multiple commodities. References [1] Desrosiers J. Y. Dumas, M. Solomon and F. Soumis. M. Ball et al. (eds). Handbook in OR & MS. Vol 8. Elsevier science. 35-139 (1995). [2] Savelsbergh M. and M. Sol. Transp. Sci. 29, 1, 17-29 (1995). [3] Méndez C., R Dondo and J.Cerdá. Proceedings FOCAPO 2008 (2008). [4] Cortes C. Matamala M. and C. Contardo. Submitted to E. Jor. Op. Res. (2008).

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1015

How to Estimate True Effect of Changing Operating Condition on Product Quality: ICA-Based Approach Manabu Kano, Yosuke Mukai, Shinji Hasebe Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan, [email protected]

Abstract To improve product quality and yield effectively, it is important to quantify the effect of each operating condition variable on the product quality. In practice, input variables associated with larger regression coefficients in a linear model are considered to have greater effects on the quality. However, the estimated coefficients are biased due to correlation among input variables. In the present work, a unique sensitivity calculation method with consideration for correlation among input variables is proposed. The problem is formulated as a quadratic programming problem; the square norm of independent component scores is minimized under the constraint of a unit change of the focused variable. The proposed method can accurately quantify the effect of each input variable on output variables by using independent component analysis (ICA). In addition, the usefulness of the proposed method is demonstrated through a case study.

Keywords: Statistical Modeling, Sensitivity Analysis, Multivariate Analysis, Independent Component Analysis, Principal Component Regression 1. Introduction As the product life cycle becomes shorter, the issue of how to improve product quality in a brief period of time becomes more critical in every industry. To solve this problem, it is important to quantify the effect of each operating condition variable on the product quality [1]. In practice, input variables associated with larger regression coefficients in a linear regression model are considered to have greater effects on the product quality; but this is not true. The estimated coefficients are biased due to correlation among input variables. In reality, many engineers have taken a risk of making a misjudgment without knowing it. In the present work, a method for estimating the true effect of process variables on product quality with consideration for the correlation among process variables is proposed. The key is to understand that changing one manipulated variable affects other process variables through the inherent characteristics of the process and the function of the control systems; it is impossible to change only one manipulated variable while keeping all the other variables unchanged. Therefore, it is necessary to estimate the influence of the focused variable on the other process variables and to estimate the total effect of the change on the product quality. To achieve this goal, both the relationship among process variables and the relationship between product quality and process variables have to be estimated. The proposed method can accurately quantify these two types of relationships by using independent component analysis (ICA) and principal component regression (PCR). The problem is formulated as a quadratic programming problem. The objective is to minimize the square norm of independent component scores under the constraint of a unit change of

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the focused variable. Independent components have no relationship among them; they are statistically independent by definition. Ideally, independent components correspond to manipulated variables and disturbances changing independently. To minimize the square norm of independent component scores means to change all the variables including disturbances as less as possible. The constraint means that only the focused variable can change. The influence of the focused variable on the other process variables can be estimated from the derived independent component scores. In addition, the total effect of the change on the product quality can be estimated from the regression model. In this paper, after explaining the proposed method, its usefulness is demonstrated through a case study of the Tennessee Eastman process.

2. Estimating True Effect The present work proposes a method to estimate true effect of input variables on output variables even when there are a large number of strongly correlated input variables. In the proposed method, ICA is used to derive a few independent variables and capture the correlation among variables. Independent Component Analysis ICA is a signal processing technique for transforming measured multivariate data into statistically independent components, which are expressed as linear combinations of measured variables [2]. It is assumed that P measured variables x1, x2, ···, xP are given as linear combinations of R unknown independent components s1, s2, ···, sR. The independent components and the measured variables are mean-centered. The relationship between them is given by

x = As , x = [ x1

x2  xP ] , s = [ s1 T

s2  s R ]

T

(1)

where A is a full-rank matrix, called the mixing matrix. The basic problem of ICA is to estimate s or A from x without any knowledge of s or A. Regression Model First, a linear regression model is built to predict output variables such as product quality. In this work, PCR is used for coping with colinearity. Conventional multiple regression analysis (MRA) is not the best choice for building accurate linear regression models. Partial least squares (PLS) is very popular and good from the viewpoint of estimation performance. However, PLS should not be used for estimating true effect because its loading matrix of input variables is affected by output variables; this characteristic is not desirable. In fact, true effect cannot be always derived by using PLS. Therefore, PCR is chosen in the proposed method. The singular value decomposition of an input data matrix X is written as

X = USV T = U R S RVRT

(2)

where U and V are orthogonal matrices and S is a diagonal matrix having singular values in its diagonal elements in decreasing order. R denotes the number of principal components to be retained in a PCA model. The rth principal component is given as the rth column vr of the loading matrix VR, and the score matrix is given by

TR = XVR = U R S R .

(3)

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In PCR, the scores are used as input variables of multiple regression analysis. The colinearity problem does not occur anymore, because the scores are uncorrelated with each other. The PCR model can be written as

Y = TR K + E

(4)

where K is a regression coefficient matrix and E is an error matrix. By least squares, K is determined as follows:

K = (TRT TR )−1TRT Y .

(5)

The prediction of output variables can be given by

Yˆ = TR K = XVR K = XK PCR

(6)

The coefficient matrix KPCR shows the influence of input variables on output variables. Basically, the input variable with the larger coefficient has greater influence on the output variable. However, the estimated coefficients are biased due to correlation among input variables; they are not true effect. Estimating True Effect: ICA-Based Approach Input variables cannot be determined independently when they have correlation. Since such correlation is modeled through PCA, any set of input variables should be located on the subspace spanned by principal components. As a result, to estimate true effect of a focused input variable on the output variables, it is necessary to estimate: 1) changes of the other input variables on the subspace spanned by principal components when the focused input variable changes by a unit, and 2) changes of the output variables by the total effect of changes of all input variables. In this procedure, it is also necessary to minimize the influence of manipulated variables and disturbances other than the focused input variable on the output variables. The present work proposes an ICA-based method for solving this problem and estimating the true effect of the focused input variable on the output variables. Let s be the independent components derived by ICA.

s = Wx

(7)

The mixing matrix is estimated by T Aˆ = [ aˆ1 aˆ2  aˆ P ] = W +

(8)

where W+ denotes the pseudo-inverse matrix of W. When the focused input variable changes by a unit, the changes of the other input variables can be estimated by solving the following optimization problem:

s<* p > = arg min s*T s* , s.t. x p = aˆ Tp s* = 1 *

(9)

s

This quadratic programming aims to minimize independent components under the condition that the focused input variable xp changes by a unit. If an operator changes a manipulated variable independently of the other variables, then the manipulated variable is automatically selected as an independent component. If an independent disturbance is fed to the process, then the disturbance is automatically selected as an independent component regardless of measured or unmeasured.

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Therefore, minimizing independent components is equivalent to minimizing the influence of manipulated variables and disturbances other than the focused input variable on the output variables. This is the reason why the ICA-based approach is significantly useful for estimating the true effect. The changes of all input variables is given by

ˆ * Δx< p > = As < p>

(10)

and the true effect of variable xp on y is given by T Δy< p > = K PCR Δx< p > .

(11)

3. Case Study: Application to the TE process In this case study, the proposed method is applied to the Tennessee Eastman process [3] with the control system [4]. The process consists of five major unit operations: a reactor, a product condenser, a vapor-liquid separator, a recycle compressor, and a product stripper. Two products are produced by two simultaneous gas-liquid exothermic reactions, and a byproduct is generated by two additional exothermic reactions. The process has 12 manipulated variables, 22 continuous process measurements, and 19 composition measurements sampled less frequently. The objective is to build a PCR model for estimating product concentration in the product stream and to identify a key variable having strong influence with product concentration. For the analysis, operation data were generated by changing setpoints and manipulated variables by 10% and feed condition by 2% around their base steadystate values. Three manipulated variables, five controlled variables (setpoints), and the other 13 process variables are used as input variables of the PCR model. All the variables are normalized (autoscaled). 500 samples are used for modeling and other 500 samples are used for validation. The number of principal components retained in the PCR model is 10. The correlation coefficient between measurements and estimates of the product concentration is 0.95 for validation data; PCR functions successfully. The regression coefficients of the PCR model are shown in Table 1. Due to the space limitation, the coefficients for only eight variables, which are setpoints and manipulated variables, are shown. Since all the regression coefficients are very small, it might be concluded that any variable does not have significant effect on the product concentration. In other words, there is no way to improve the product concentration. However, this is not true. In fact, it is confirmed through additional simulations that the reactor pressure affects the product concentration significantly and it is the key variable. The proposed ICAbased method can identify the reactor pressure as the key variable successfully as shown in Table 1. The estimated effect of the reactor pressure on the product concentration is 0.72, which is significantly larger than the others. Furthermore, the estimated effect is correct even quantitatively. This case study clearly shows the usefulness of the proposed ICA-based method for estimating true effect.

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Table 1. Regression coefficients vs. estimated effects.

Base value Compressor recycle valve Stripper steam valve Agitator speed Separator level Stripper level Reactor level Reactor temperature Reactor pressure

22.210 % 47.446 % 200 rpm 50 % 50 % 75 % 120.4 C 2705 kPa

Regression coefficients of PCR model −0.04 0.004 0.01 −0.03 0.02 0.06 0.03 −0.02

Estimated effect by ICA-based method −0.05 −0.12 −0.03 −0.10 0.10 0.06 −0.05 −0.72

4. Conclusions Linear regression models have been widely used everywhere for finding key variables to improve product quality and yield. In practice, input variables associated with larger regression coefficients in a linear regression model are considered to have greater effects on the product quality; but this is not true. The estimated coefficients are biased due to correlation among input variables. In the present work, a method for estimating the true effect of input variables on output variables with consideration for the correlation among input variables is proposed. The key is to understand that changing one input variable affects other input variables as well as output variables through the inherent characteristics of the process and the function of the control systems. The proposed ICA-based method can accurately quantify the effect of each input variable on output variables. In addition, the usefulness of the proposed method is demonstrated through the case study. Currently, the proposed ICA-based method is applied to industrial processes and its practicability is validated.

References [1] [2] [3] [4]

M. Kano and Y. Nakagawa, Comput. chem. Engng., 32 (2008) 12 C. Jutten and J. Herault, Signal Processing, 24 (1991) 1 J. J. Downs and E. F. Vogel, Comput. chem. Engng., 17 (1993) 245 N. L. Ricker, J. Proc. Cont., 6 (1996) 205

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Information system in the field of carbon nanomaterials Que H. Tran,a Eleonora M. Koltsova,b Philipp V. Batseleva,b a

Mendeleyev University of Chemical Technology of RUSSIA (MUCTR), Cybernetics of Chemical Technological Processes, Miusskay Square, 9, 125047 Moscow, Russian Federation, [email protected] b Mendeleyev University of Chemical Technology of RUSSIA (MUCTR), Information of Computer Technology, Miusskay Square, 9, 125047 Moscow, Russian Federation, [email protected]

Abstract The specialized information system in the field of carbon nanotubes (CNTs) applications is developed in this work. One of the main advantages of the system is lack of similar specialized systems, synthesizing and systematizing information on CNTs and their derivatives (nanotube-based composites). The systems of general orientation certainly exist but they do not consider of several subtleties inherent in this subject area. The specialized orientation of the developed information system allows increasing the accessibility of information. Keywords: database, carbon nanotubes, nanomaterials, information system, composites

1. Introduction The discovery of carbon nanotubes in 1991 caused new ways of researching in many fields of science, especially in material science. The physical, electrical and other properties of enhanced carbon nanostructure based materials are improved significantly. Owing to their unique physical properties, such as high strength and stiffness, together with excellent thermal and electric conductivities, as well as low mass, CNTs have become a key candidate, among others, for future electronic materials and advanced nanocomposites. They are considered to be ideal materials in various applications such as nanofillers for the fabrication of composite materials, conductors in micro- and nanoelectronics, as well as platforms for truly molecular electronics and potential nanotransporters in nano-fluidic applications. Lots of investigations in study of CNTs properties, methods of their obtaining and improving the properties of existing materials were carried out. Lots of researches are held everyday therefore we receive a lot of new information, so many publications appear, which need to be arranged. All this makes the development of specialized information system in this field relevant. The calculation modules included in the information system enable to carry out various computing experiments. Computing experiment assumes a shift from study to study the substantial object of its mathematical model. And even if the inclusion of an ability to introduce such experiment in the information system is preceded with the period of research and development of related program module, the useful effect overlaps these expenses. The continuous work of such system must be at the highest level. Such continuity is easy to implement using the Internet. As a platform the Win32 was chosen which in

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difference from the web-platform does not impose the restrictions on the ability of the user interface.

2. Information system “I.S. Nanotube” The information system is a client-server application. The client part of the information system, so-called "thick" client, was developed for Win32 platform. The programming language is Turbo Delphi, the development environment is Borland Delphi 10 Turbo Edition. The server part is a database (DB) controlled by DBMS (database management system) Oracle. The client application is optimized for work with this DBMS. In the further, the translation of the system into three-tier architecture is supposed. The third layer which will be located between the existing two layers would constitute an application server (Fig. 1). Client Client

Application server

Oracle DB Server

Client Fig. 1. The client-server application The information about carbon nanocomposites is presented in the form of hierarchy “Article - Composites - Properties of the composite”. For the field “Article” the following points are considered: title, the authors, the year of publication, country, name of the journal in which the article was published, volume and pages. The field “Composites” is considered is the term of its title, the composite type (polymer, ceramic, textile, etc.) and all combinations of “question -answer”. The information stored in the DB and used in the information system is thematically divided into information related to individual carbon nanostructures; information of the application of individual carbon nanostructures and their mixtures to obtain composite materials, to improve the properties of initial polymeric material; and information about manufacturers concerned to the materials and substances. Individual carbon nanostructures are analyzed primarily by the physical, chemical and other useful properties of nanostructures, the methods and conditions of their synthesis, the researchers and the manufacturers; while the composites are analyzed by the improved properties, the obtaining methods and the possible areas of their application. At the same time the composite materials are classified by type. The information system in the field of nanomaterials consists of (Fig. 2): 1. Database for systematization of current information into a single whole specialized archival storage and operational storage for new data; 2. Tools to increase the accessibility of information in searching data, generating reports of various difficulties, including the use of specific data aggregation; 3. Calculation modules for the study and modelling of different processes, as well as designing of production.

Information System in the Field of Carbon Nanomaterials

User

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Expert

Interface

Increasing accessibility units

Main units Unit “Composites”

Searching engine Unit “Nanostructures” Report engine Unit “Producers”

Unit “Computation application” Database Computation of kinetics of processes

Composites Nanostructures

Pyrolysis of hydrocarbon raw

Reference data

Computation of continuously working reactor

Fig. 2. The structure of information system “I.S. Nanotube” 1.1. Database. Composites and Nanostructures The structure of the database has a special scheme of data storage built on a principle “question-answer” (Fig. 3). Such structure allows to make changes to any lists, whether a list of composite types or a new considered property without a single change in the client part that is often connected with big problems both for the developer, and for the user. Thus the continuity and simultaneously the flexibility of the system are provided. Thus, the database contains the list of “questions” and variants of their “answers”. The answer can have any type – numerical, text, and boolean. The combination “question answer - value of the answer” gives a description of one of the composite properties. Reference of questions

Table of relations “question-answer”

Reference of answers

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Fig. 3. The principle of database construction 1.2. Database. Reference data of chemical and physical properties of the substances The data required for work of calculation modules, reflecting one of the physical and chemical properties of the substance or other technical information is included in this part of the DB: - formula of substance, - molecular mass, - density of crystals, - latent heat of crystallization, - atomic volume of mole of substance, - solubility – temperature dependence, - heat capacity – temperature dependence. 1.3. Tools to increase the accessibility of information “Searching engine” At present there are many information systems, including in scientific orientation. The storage of information in these systems is carried out without using any DBMS or use means of DBMS in the minimum. The basic methods of the search used in the systems are text-full search and search by keywords. The first in conditions of huge amount of data is slow and little selective, the second – inefficient because of the possibility of discrepancy of opinion on the composition of keywords of author of article and the person who is carrying out search. In the information system the specialized search engine combining in efficiency and speed of work is developed. Through the application of the scheme of data storage “question – answer” it is possible to apply a specialized system of search. In addition to conventional filters by field, fragment of field and sorting (implemented on the server that allows increasing speed in times), there is a possibility of the advanced search on one of the properties of composite. The list of such properties stored in the DB also can be enlarged without changing of the client part. 1.4. Tools to increase the accessibility of information “Reporting engine” One of the important tasks is to develop a convenient mechanism of management of data accessibility – search, reports, etc. This can not be achieved by using one of the general approaches to construction the data storage structure and the general method of search. Only development of specialized system is capable to solve this problem. The information system is able to provide various reports and export them to different formats of data. Type of report presentation is selected by user.

3. Computing applications The expandable modular system that enables to connect to any calculated modules, including third-party developers, should be mentioned. Current modules are designed to carry out calculations and to put the computing experiments. At the moment a number of such modules had already developed, basically on modelling pyrolytic methods of obtaining CNTs, and their development is proceeding. The mathematical models of calculation modules have the adequacy for computer simulation and researching of working properties, planning and constructing industrial units, and controlling the functioning of the scientific and engineering solutions. All modules apply the user’s computer capacity to calculate, however there is a possibility of transposition of a part or even all loading entirely to the central server. Almost all the calculation modules use the unique mathematical models. Modelling is an objective practical criterion for verifying the validity of knowledge if the adequacy

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of model is considered reasonable. The models are adequate enough to use the results of calculations instead of statement of real experiment. Such computing experiment significantly reduces the funds. This method of research recently is widely applied, and the information system uses it effectively. Thus, using the information system it is possible to investigate the process or the phenomenon.

4. Conclusions The flexibility, scalability, easy expansibility, as well as availability, safety and data integrity of developed system is provided by the best up to date DBMS - Oracle. The maintenance of availability, safety and integrity of data are the three actions determining the quality of DBMS. The system can easily react to the changes The system provides all the necessary information (including calculations) without using the additional software packages and databases because of its universality. Earlier the reception of necessary data and knowledge was preceded with long search of corresponding scientific articles, their attentive studying and the further calculation (or computing experiment), now all can easy and effectively make these stages in one information system. Developed IS can be applied for the following purposes: -systematization of an available information in a single whole of the specialized archival storage and operative storage of new data; -searching system, report generator, including the use specific data aggregation, for the management of accessibility of the information. -information-commercial as data base displaying CNTs market situation at the moment; -computer simulation, for the research of working properties, planning and designing of industrial aggregates of correct functioning of the design and scientific decisions; -searching system, enables not only to find out the necessary information but also to establish a relational connection between fields; -design-theoretical, that enables to carry out mathematical modeling stages for the process of nanotubes obtaining by the method of hydrocarbon material pyrolysis for the purpose of operational characteristics investigation, for design conveniences, for testing of design and scientific decisions.

5. Acknowledgements This work was supported by grants RFBR ʋ 08-08-00496a.

References [1] [2] [3] [4] [5] [6]

X. Cullem, Y E.G. Rakov, Russian Chemical Reviews 70, 10 (2001), pp. 827-863 Chenyu Wei, Applied Physics Letters 88, 093108 (2006) B.W. Smith, M. Monthioux, D.E. Luzzi, Chem. Phys. Lett., 315, 31 (1999) M. Grujicic, G. Cao, B. Gersten, Applied Surfase Science 191 (2002) 223-239 Bernadette A. Higgins, William J. Brittain, European Polymer J. 41 (2005), pp. 889-893 Igal Szleifera, Rachel Yerushalmi-Rozen, Polymer 46 (2005), pp. 7803-7818

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Managing financial risk in the coordination of supply chain and product development decisions José Miguel Laínez,a Gintaras V. Reklaitis,b Luis Puigjanera a

Department of Chemical Engineering, Universitat Politècnica de Catalunya, Barcelona, Spain, [email protected] b School of Chemical Engineering, Purdue University, West Lafayette, USA.

Abstract In today's highly competitive marketplace, supply chain (SC) and product development activities should be coordinated and synchronized so that market demand, product release and capacity requirements are matched in a financially sustainable fashion. In this work, an integrated model is developed which incorporates simultaneous treatment of SC design-planning and R&D decisions in the pharmaceutical industry. Moreover, the aforementioned cross-functional model embeds a capital budgeting formulation enabling the quantitative assessment of the firms’ value. The model also considers the endogenous uncertainty associated with product test outcomes during the development process. To tackle this problem, a scenario based multi-stage stochastic mixed integer linear programming (MILP) formulation is proposed. This model includes risk constraints which allow finding optimal solutions within accepted risk levels. A decomposition technique is applied in order to reduce the computational effort required for the solution of the monolithic model, thus facilitating the solution of realistic industrial problems of moderate scale. Keywords: Supply Chain Management, Product Development, Corporate Value

1. Introduction Enterprise-Wide Modeling and Optimization (EWMO) has emerged recently as an attractive research challenge consisting in the integration of information and decision making among the various functions that comprise the SC of the company. It has been widely recognized that closer coordination between logistics and other functional units can improve overall business performance. In this regard, enterprises must carefully assess the capital budgeting tradeoffs among the launch of new products and the SC capacity expansion and resource allocation in order to assure financial sustainability. As stated by Varma et al.[1], there is a need to incorporate financial planning decisions, R&D resource allocation as well as capacity expansion decisions within an integrated framework. We should expect that such integrated framework may lead to enhanced business value generation. Certainly, R&D decisions necessarily impact the design and the regular activities of the entire SC. Thus, such operational impact should be considered and assessed at the time R&D and SC decisions are taken. In this work an integrated model is developed which incorporates simultaneous treatment of the SC design-planning and R&D issues in the pharmaceutical industry. Moreover, the aforementioned cross-functional model embeds a risk management and capital budgeting formulation enabling the quantitative assessment of the firm’s value.

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2. Problem statement One of the industries for which R&D pipeline management is particularly significant is pharmaceuticals. No pharmaceutical product can be placed on the market without receiving prior authorization from the relevant public health agencies. For this type of businesses in which 50% of new product development resources are spent on failed or cancelled products, solutions from holistic approaches are a necessity so as to support strategic decision making allowing financial sustainability to be achieved. New products in the development phase are required to go through strict tests. Generally, tests can be classified into pre-clinical tests; clinical trials (this stage is comprised of three phases), and regulatory approval. This study is focused on the clinical trials stage. Failure to pass any clinical trial implies termination of the R&D project. Each new product trial has a probability of success, an associated duration and cost. On the SC side it is assumed that various items of technological equipment are available to be installed in existing and potential facility sites. Regarding the financial area, the formulation endeavors to model cash management and value creation. Finally, a minimum desired level of risk is assumed to be given. The proposed model offers robust decision support to business managers; it determines the most appropriate subset of potential products to be launched, the clinical trials timing, capacity expansion of production processes, and production profiles so as to maximize Corporate Value (CV).

3. Mathematical formulation The problem is formulated as a multi-stage stochastic mixed integer linear programming (MILP). The variables and constraints of the model can be classified into five groups which are briefly explained next. Product Development Pipeline Management The endogenous uncertainty associated with the outcome of clinical trials is modeled following the work of Colvin and Maravelias [2]. For a pair of scenarios (ς,ς’) that become distinguishable in period tς,ς´, the decisions D in previous periods (t
{t < t } Ÿ {D ς ,ς '

tς

= Dtς ' }

The number of pairs of scenarios for which this non-anticipativity condition must be applied can be reduced to those that differ in the outcome of merely one product clinical trial (ϑ). Eq. (1) defines the variable Ωictς which indicates the periods following the clinical trial c completion of potential new product i. Binary variable Aictς indicates the period when the clinical trial c of product i starts. Here, εi and IN are the trial duration and the set of new products, respectively.

Ωictς = Ωict −1ς + Αict −ε iς

∀i ∈ I N , c, t , ς

(1)

The non-anticipativity logic condition is expressed as an integer constraint in Eq. (2). Additional constraints are added to model R&D resources, but they are omitted in the manuscript.

Managing Financial Risk in the Coordination of Supply Chain and Product Development Decisions

−Ωi ' c 'tς ≤ Αictς − Αictς ' ≤ Ωi ' c 'tς ∀i, c, t , (ς , ς ') ∈ ϑ , (i ', c ') ∈ Iϑ

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(2)

Design-planning formulation The design-planning approach is based on the work developed by Laínez et al [3]. The formulation has been extended to account for the different scenarios (clinical trial outcomes). In this formulation, a four echelon SC is considered as shown in Figure 1.

Figure 1. Supply chain model structure

Integration of Product Development Management and SC Operations The integration between formulations is carried out through the non-anticipativity constraints associated with capacity allocation variables (see Eq. (3)). Vjstς is a binary variable that takes a value of 1 if the facility being represented (equipment j at processing site s) is expanded in capacity in period t, being 0 otherwise. Similar equations are incorporated for distribution centers and for those continuous variables which denote the capacity expansion magnitude of the different network facilities during period t.

−Ωictς ≤ V jstς − V jstς ' ≤ Ωictς ∀(ς , ς ') ∈ ϑ , (i, c) ∈ Iϑ , j , s, t

(3)

Eq. (4) states that production prior to third trial completion must be equal to zero for ς ). every successful new product in scenario ς ( i ∈ I suc ς Pijstς ≤ M Ωictς ∀ς , i ∈ I suc , c ∈ III , j , s, t

(4)

ς In addition, no production of products that fail any trial c in scenario ς ( i ∉ I suc ) is

allowed as expressed in Eq. (5). ς Pijstς = 0 ∀ς , i ∉ I suc , j , s, t

(5)

Financial formulation The financial component of the problem is tackled through the inclusion of a set of constraints that characterize economic issues, such as R&D costs, payments to providers, loans, pledging decisions, etc. Furthermore, the expected Corporate Value

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(E[CV] ), is the objective function used in this work. The CV of a company is a function of four factors: (i) investment, (ii) cash flows, (iii) economic life, and (iv) capital cost. Specifically, our work applies the discounted-free-cash-flow (DFCF) method to compute the CV. Such method rates an entire company by determining the present value of its future free cash flows and discounting them, taking into account the appropriate capital cost during the evaluating time horizon [4]. Capital cost is calculated using the weighted average method (WACC) which considers the firm’s overall equity and debt. Free cash flow at every period t (FCFtς) is defined by a function that depends on net operating profit after taxes, change in net working capital (¨NWCtς), net change in investments (NetInvesttς) and R&D costs ( RDCosttς ). This can be seen in Eq. (6).

FCFtς = Profitts (1 − trate ) − ( ΔNWCtς + NetInvesttς − RDCosttς ) ∀t , ς

(6)

Eqs. (7) and (8) are to compute the CV for each scenario and the total expected CV, respectively. For financial formulation details the reader is referred to Laínez et al.3 T

FCFtς

t =0

(1 + WACCt )

CVς = ¦

t

∀ς

− NetDebt0

E[CV ] = ¦ probς CVς

(7)

(8)

ς

Financial risk management The risk management formulation is presented next. Financial risk associated with a planning project can be defined as the probability of not meeting a certain target performance level referred to as ρ [5]. Let us notice that for our case, the performance is measured by the CV. Eqs. (9) to (11) have been added to constraint the risk of obtaining CVs less than target ρ. According to Eq. (9), Rζ is a binary variable which takes a value of 1 if CV of scenario ζ is less than ρ, being 0 otherwise. Riskmax indicates the maximum risk that decision makers are willing to accept for target level ρ.

ρ − Rς M ≤ CVς ≤ ρ + (1 − Rς ) M Risk ( ρ ) = ¦ pς Rς

∀ς

(9) (10)

ς

ρ Risk ( ρ ) ≤ Riskmax

∀ς

(11)

4. Illustrative example The advantages of the proposed approach are demonstrated by solving a retrofittingplanning problem of a SC; which contains three processing sites (S1-S3, S1 and S3 are already operational), three distribution centers (W1-W3) and three market locations. Six products (P1-P6) can be manufactured on three different equipments types (TA to TC). A time horizon of 15 years is considered. This is composed of 15 periods with a length of one year each. In this example, products P4-P6 are regarded as new products. For

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comparison purposes, the problem has been also solved using the traditional sequential approach (SA). Under the sequential scheme, financial and other functional decisions are made following a hierarchical decision-making process. First the SC and R&D decisions are made and then the financial ones are determined. The operational decisions are typically obtained by optimizing NPV, while the financial decisions are computed by maximizing the CV using the model presented in section 3.4. Numerical results show that the solution calculated by the integrated approach (IA) offers improved performance over the SA. Certainly, the optimal expected CV from the IA is considerably higher than the one computed by utilizing SA results. The IA renders an expected CV of 12.8x109 m.u.; while a CV of 2.79x109 m.u. is obtained by applying the SA. The two approaches also yield different project selection decisions. The SA launches the product development process for P4 in first period, P6 in second period and P5 in fifth period, while the IA launching policy is P6 in first period and then waits until the fourth period to launch P5. Furthermore, the SC capacity allocation decisions are different. The SA proposes to install TA and TB in site S2, while the IA proposed to install merely TA in the same site. As shown in Figure 2, a significant risk reduction is achieved by using the IA, the probability of obtaining negative CVs is reduced from 59% to 1.5%. Moreover, risk management constraints have been applied to the IA assuming that no negative CVs are desired (ρ=0). For this case, no equipment capacity expansion is proposed. It is worth noticing that the expected CV has decreased to 12.8x109m.u. by using the risk constraints. Nevertheless, there is a reduction in the risk associated to those CVs which are lower than 10.0x109m.u. as depicted in Fig.2.

Figure 2. Risk curves of different solutions for the illustrative example

Optimal condition decomposition The Optimal Condition Decomposition (OCD), which is a particular case of the Lagrangean relaxation procedure, is applied to overcome the computational cost of solving monolithic problems. One of its advantages is that it provides information to update multiplier estimates in each sub-problem iteration[6]. Non-anticipativity equations are treated as complicating constraints in the integrated problem since they

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prevent the solution by blocks. Each block includes the equations related to each scenario ζ. Monolithic (M) and decomposition sub-problems (D-S) complexity for different cases are presented in Table 1. Considerable problem simplification is gained, however the decomposed problem requires to be solved iteratively until solution convergence. In spite of this, significant total CPU time reductions are achieved by using the OCD as shown in Table 1. Table 1. Complexity comparison between monolithic and decomposed problems Scen.

Equations M

16 64 256

Cont. Var.

D-S

M

3064

210

7.03

7.06

165

95

279377 6422 13584

240

8.21

8.15

24370

1026

1354398 98848 1138667 7402 60167

270

-

9.22 >50000

15345

7282

290662 22735

M

D-S

68897 5562

D-S

Total CPU sec

M

62102

D-S

E[CV] (109)

Dis. Var.

M

D-S

*Experiments were executed on an Intel 2 Core Duo- 2.0 GHz – 2 GB RAM – 3% integrality gap

5. Remarks A model integrating R&D pipeline management, SC design/retrofitting and capital budgeting decisions is presented which incorporates the endogenous nature of trial uncertainties. Performance comparison with the traditional sequential decision approach is also made, demonstrating the significant economic benefits of holistic approaches. Moreover, the model is able to account for financial risk restrictions that may be imposed by stockholders. It is shown that probabilities of low SC performance are considerable reduced by incorporating the risk management formulation. Finally, Lagrange decomposition has been utilized to successfully reduce the significant computational burden associated with solving this kind of problems. Further work is focused on applying the decomposed problem in a parallel computing scheme so that large industrial size cases can be tackled using the proposed model.

6. Acknowledgements Financial support received from the "Generalitat de Catalunya" (FI grants; Comissionat per a Universitats i Recerca del Departament d’Innovació, Universitats i Empresa), and from the e-Enterprise Center, Purdue University is gratefully acknowledged. Besides, financial support from Xartap (I0898) and ToleranT (DPI2006-05673) projects is fully appreciated.

References [1] Varma V., Reklaitis G. V., Blau G., Pekny J., 2007. Comput. Chem. Eng., 31, 692. [2] Colvin M., Maravelias C.T., 2008. Comput. Chem. Eng., 32, 2626. [3] Laínez J.M., Guillén-González G., Badell, M., Espuña, A., Puigjaner, L., 2007. Ind. Eng. Chem Res., 46 (23), 7739. [4] Grant, J. L., 2003. Foundations of Economic Value Added; John Wiley and Sons. [5] Barbaro A., Bagajewicz M. J., 2004. AIChE Journal, 50, 963. [6] Conejo A. J., Nogales F. J., Prieto F.J., 2002. Math. Program., Ser. A , 93, 495.

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Normalization for cDNA microarray data of gene expression profiles from the human prostate cancer cell lines (PC3) by Pre-Processing Two-Color Data Dorina Bratfalean*a, Ramona Suharoschib, Crina Muresanb, S. P. Agachia, M.V. Cristeaa, Ana-Maria Cormosa, Àlex Gómez Garridoc, Miguel Hernández Sánchezc a

Babes Bolay University, Faculty of chemistry and Chemical Engineering, Cluj-Napoca, Romania, E-mail:GRULQHW#\DKRRFRP b University of Agricultural Sciences and Veterinary Medicine of Cluj-Napoca, Romania, E-mai: ODVORUD#\DKRRFRP c Computational Biochemistry and Biophysics lab, Research Group on Biomedical Informatics (GRIB) - IMIM/UPF Parc de Recerca Biomèdica de Barcelona

Abstract The objective of the present work is normalization of cDNA microarray data of gene expression profiles from the human prostate cancer cell lines (PC3) treated with Genistein compared with untreated prostate cancer cells through pre-processing TwoColor Data. In this study, we utilized the high throughput gene chip, which contains 4486 known genes, to determine the alternation of gene expression profiles of PC3 prostate cancer cells exposed to Genistein at therapeutically and physiologically doses as well. The Limma was used to implement a range of normalization methods for spotted microarrays. Normalization was performed, for the experimental DNA microarray data, for three experimental groups, and the results show a very good accuracy Keywords: cDNA Microarray, Normalization, Prostate cancer, Genistein, Gene expression

1. Introduction The prostate cancer is a leading cause of death among men in the United States and Western Europe. In last years, a number of biological technologies data are available in orders of magnitude. In the new setting for biological research DNA array technologies allow for thousands of gene expression levels in a single experiment and they have acquired a special role. This technology has opened a new ways of looking at organisms in a genome-wide manner [Joaquin, 2005]. cDNA microarray high-throughput technology can measure the differentially gene expression level for thousands of genes in a single experiment or serial experiments in different conditions. In the two-color cDNA platform, mRNA from two samples is reverse-transcribed to cDNA, labeled with fluorescent dye Cy3 and Cy5 (Amersham), and simultaneously hybridized to microarray containing clones probes of DNA sequences. Ratios of fluorescence intensities provide a relative measure of expression to each spot of the array. [Davis, 1999]. In this paper we applied normalization which means to adjust microarray data for effects which arise from variation in the technology rather than from biological differences between the RNA samples or between the arrays.

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2. Problem statement The first problem in any microarry assay is the selection of an appropriate set of gene data. The solution for this problem could be solved by using numerical methods. Researches on micoarray data processing and analysis have been previously reported: Normalization methods are based on robust local regression and account for intensity and spatial dependence in dye biases for different types of cDNA microarry experiments [Yee Haw Yang et al., 2002]; Print-tip loess normalization provides a well tested general purpose normalization method which has given good results on a wide range of arrays[Gordon, 2003]; Normalization for cDNA microarry data are illustrated using gene expression data from a study of lipid metabolism in mice [Yee Haw Yang et al., 2002, Ramona Laslo et al., 2004, Li et al., 1999]; Diagnostic and normalization of MicroArray Data was presented in 2004 as a tool integrated within the Gene Expression Pattern Analysis Suite (GEPAS)[David Montarnerm, 2006]; GEPAS webbased interface offers diverse analysis options from the early step of preprocessing such as: normalization of Affymetrix and two-colour microarray experiment and other preprocessing options [Juan M., 2004]. Nanoparametric methods for identifying differential expressed in micoarray data were studied by Russ B. Altman in 2002 [Olga G. Troyaskay, 2002]. Gene expression profiles of Genistein treated PC3 prostate cancer cells were presented by Sarkar.(1999, 2002) The objective of the present work is normalization of cDNA microarray data of gene expression profiles from the human prostate cancer cell lines (PC3) treated with Genistein compared with untreated prostate cancer cells through pre-processing TwoColor Data.

3. Material and methods 3.1. Methodology Microarray data analysis is divided into three main sections: experimental design, data normalization and data analysis. The workflow is illustrated in fig 1.

Normalization for cDNA Microarray Data of Gene Expression Profiles from the Human Prostate Cancer Cell Lines (PC3) by Pre-Processing Two-Color Data

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Biological Samples

Biological sample 1 (eg. PC3+T)

Biological sample 2 (eg. PC3)

Image processing

Visualization

Image Quality

Data AnalysisNormalisation

Group 1 -normalised Group 2 -normalised Group 3 -normalised Results-Table delimitated

follow up analysis in R or export to other tools (Matlab statistical tools)

Figure. 1 Experimental arrangement in microarray data analysis

3.2. Experimental arrangement Experimental design was described by molecular model of a two-colour cDNA microarray hybridization. Common Reference Design and Swap Dye Design – SDD were combined and competitively hybridized to the microarray samples. The experiments were grouped according to applied treatments (T1 and T2) and replicated. The detailed description of the two different protocols can be found in literature [David, J.N, 1999, R. Laslo et al., 2004]. Experimental design is presented correlated with the types of treatment and sample labeling such as: two groups for the first treatment and one group for the second treatment (table 1). Table 1. Experimental Design for cDNA microarrays study – prostate cancer cells PC3 incubated for 48h with Genistein at therapeutically and physiologically doses Groups 1 2 3

Experiments E_002+E_004+E_005+E_007+ E_009 E_003+E_011 E_006+ E_008+ E_010

PC3 1 0 1

PC3 + T 0 1 0

T T2 T1 T1

PC3: prostate cancer cells; PC3+T: prostate cancer cells with treatment; T: treatment with Genistein

Results obtained after experimental design were presented as images in txt format. For normalization of cDNA arrays, the relevant packages are Limma using free statistical programming environment R. The Limma packages contain liner models for microarray data and was used to implement a range of normalization methods for spotted microarrays. Two-colour cDNA array was processed following several steps: data acquisition and reading image as background intensities correlation (within and between arrays of normalized data) and the finally generating a list of select genes saving in data files. Two normalization methods were used: the first method normalizes the M-values for each array separately (within-array normalization) and the second method which normalizes compared intensities different arrays (between-array normalization) [4].

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These methods adaptively adjust the foreground for setting the background spot intensities. They result in strictly positive adjusted intensities, i.e. negative or zero corrected intensities are avoided. Main results of interest produced by the image analysis methods (segmentation and background correlation) are the (R, G) fluorescence intensity pairs s for each gene on each array (where R=red and G=green for Cy3) and AM-plot which is subsequently used to represent the (R, G) data. The M and A values are computed b: M = log 2

R G

A = log 2 R * G

(1)

(2)

It was found MA-plots to be helpful in terms of identifying spot and detecting intensity dependent patterns of normalisation M. Global methods assume that the red and the green intensities are related by constant factos , i.e. R=kG. the center of the distribution of loss ratios is shifted to zero.

log 2 R / G → log 2 + c = log 2 R /( kG )

(3)

A common choice for the location paramenter c=log2k is the mean of the intensity log ratios M for a particular gene set. Within-print tip group normalization is simply a (print tip +A) dependent normalisation i.e.

log2 R / G → log2 R / G + c( A) = log2 R /[ki ( A)G]

(4)

where c(A) is the lowess fit to the AM-plot for the ith grid only . Software to carry out the normalization methods described in this paper is freely available from the bioconductor project site http://www.bioconductor.org. 3.3. Results and discussions The performance of the normalization methods are demonstrated in a simulation study. The dimension of the file contains: 12 Metarows, 4Metacols with 15 Rows and 16 Cols on 11520 spots. Density distributions are presented by MA-plot and RG-plot for all groups illustrated in figure 2, 3 and 4.

Figure 2 MA - array T2- normalizeBetweenArrays, RG - arrayT2- normalizeWithinArrays(RG) (group 1)

Normalization for cDNA Microarray Data of Gene Expression Profiles from the Human Prostate Cancer Cell Lines (PC3) by Pre-Processing Two-Color Data

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Figure 3. MA - array T1 - normalizeBetweenArrays, 29 RG – arrayT1- normalizeWithinArrays (RG) group 2

Figure 4. MA - array - grup 3 normalizeBetweenArrays, RG – array – normalizeWithinArrays (RG) (group 3)

To better understand the precise molecular mechanisms by which Genistein exerts its apoptotic inhibitory effect on PC3 prostate cancer cells (androgen insensitive –AR) we utilized cDNA microarrays to interrogate 4486 active genes to determine the expression profile altered by the Genistein treatments at therapeutically and physiologically doses as well. We found a total of 602 genes that show a greater expression than two fold change after Genistein treatment from five independent experiments with a high degree of concordance. Among these genes, 506 genes were up-regulated and 96 genes were down-regulated with T2 Genistein treatment. In the T1 Genistein treatment cDNA microarrays experiment we found a total of 908 genes differentially expressed than two fold, a number of 380 genes up-regulated and a number of 528 genes down-regulated with T1 Genistein treatment.

4. Conclusions In this paper, we have the used normalization method for cDNA microarray data based on R style library. Normalization was performed, for the experimental DNA microarray data, for three experimental groups, and the results show a very good accuracy. The results from cDNA microarray provided a genome-wide analysis of the cellular response to Genistein treatment. Cellular responses to any antiproliferative agents involve modulations of complex pathways that ultimately determine whether a cell survives or dies. Cellular and molecular responses of PC3 cells to Genistein are intricate and are likely to be mediated by a variety of regulatory pathways that underlain the several hundred of genes differentially expressed between PC3 untreated and treated cells. The normalization data could be used for empirical Bayes methods to borrow information between genes. The overall perferomace of the normalization method was comparable to the composite normalization method and in the same range of other

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tested methods cited in the literature. However these conclusions are based on limited number of data sets and therefore further validation will be required.

5. Acknowledgements The authors acknowledge for the support offered by the CEEX 180/2006 MOLPATPCa project. We thank Associate professor and CBBL group leader Jordi Villà i Freixa (Computational Biochemistry and Biophysics lab, Research Group on Biomedical Informatics (GRIB) - IMIM/UPF Parc de Recerca Biomèdica de Barcelona) for helpful discussion and possibility to know about the bioconductor project.

6. References Joaquin Dopazo, Microarray data processing and analysis, (2005), Kluver Academin.Publ. 43-63 Davis, J. N., Kucuk, O. & Sarkar, F. H. Nutr. (1999), Cancer 35 167–174. Yee Hwa Yang, Sandrine D., …., P Speed, Normalization dor cDNA Microarray Data, (2002), Oxford University Press Vol. 30 No.4el5 Gordon K. Smyth and Terry Speed, Normalization of cDNA Microarry Data, (2003), 31 265-273 Yeee Hwa Yang Oxford University Press, Normalization for cDNA microarray data: a robust composite methods addressing single and multiple slide systematic variation (2002) Nucleic Acids Research Vol. 30 No.4el5 David Montanerm, Joaquin Dopazo and col, (2006), Nucleic Acids Research Vol. 34 Web server issue Juan M. Vaquerizas, , Joaquin Dopazoand, Ramon Diaz Uriate, (2004), DNMAD: web-based diagnosis and normalization for microarray data, Bioinformatics, 18, 3656-35358 Olga G. Troyaskay, MitchellE., Russ B. Altman, (2002), Bioinformatics vol 1 8 no 111454-1461 Ramona Laslo, I. Rowland, H. Klocker, RL Hancock, RS Pardini, Al I Baba, 2004, USAMV Proceedings, vol. 60:346-353 Li, Y. & Sarkar, F. H. Clin., Gene Expression Profiles of Geistein-Treated PC3 ProstateCancer Cells, (2002), Cancer Res. 8 2369–2377 Li, Y., Bhuiyan, M. & Sarkar, F. H. Int. J. (1999), Oncol. 15 525–533 Alhasan, S. A., Aranha, O. & Sarkar, F. H. Clin. (2001), Cancer Res. 7 4174–4181 Li, Y., Upadhyay, S., Bhuiyan, M. & Sarkar, F. H. (1999),Oncogene 18 3166–3172

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Reconstruction of flame kinematics and analysis of cycle variation in a Spark Ignition Engine by means of Proper Orthogonal Decomposition Katarzyna Bizon a, Gaetano Continillo b, Simona S. Merola c, Bianca M. Vaglieco c a

Istituto di Ricerche sulla Combustione CNR, Via Diocleziano 328, Naples 80124, Italy, [email protected] b Department of Engineering, Università del Sannio, Piazza Roma 21, Benevento 82100, Italy, [email protected] c Istituto Motori CNR, Via Marconi 8,Naples 80125, Italy, [email protected]

Abstract This paper reports on the analysis of cycle variation in Spark Ignition Engine. 2D measurements of combustion-related luminosity were taken in optically accessible engine and Proper Orthogonal Decomposition (POD) is applied to the acquired images. The coefficients of the decomposition are then used for the analysis of cycle variability. The advantage is that statistical analysis can be run on a small number of scalar coefficients rather than on the full data set of pixel–valued luminosity. POD modes are discriminated by means of normality tests, to separate the mean from the coherent and the incoherent parts of the fluctuation of the luminosity field, in a non–truncated representation of the data. Keywords: Spark Ignition Engine, Optical Engine, Imaging, Proper Orthogonal Decomposition

1. Introduction Various optical systems allow nowadays two– or even three–dimensional measurements of in-cylinder variables. The fast development of these systems allows the investigation of the entire spectral range of flame light emission, with high spatial and temporal resolution. The amount of data collected can be impressive and computational methods for data reduction and analysis, such as Proper Orthogonal Decomposition (POD) are being developed and used. Most literature focuses on the application of POD to velocity measurements; however it appears that measurements of light emission during the combustion process also carry information on cycle–to–cycle variation phenomena, which can occur in all forms in engines. This work reports 2D measurements of flame light emission taken during experiments conducted in optically accessible Spark Ignition (SI) engine. Proper Orthogonal Decomposition (POD) is applied to the recorded data. It is shown how POD permits the analysis of cycle variability, by extracting mean, coherent and incoherent parts of the luminosity field and by visualizing their morphology, in a non-truncated representation of the collected data. One of the main advantages of POD is that the analysis can be reduced to a small number of scalar coefficients rather than conducted on full data set of pixel–valued luminosity.

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2. Experimental engine An optically accessible single cylinder port fuel injection (PFI) spark ignition (SI) engine was used for the experiments; more detail regarding experimental setup can be found in [1]. During the combustion process, the light passed through a UV–fused silica window located in the piston and it was reflected towards the optical detection assembly by a 45° inclined UV–visible mirror located in the bottom of the engine. Then the light was focused by a 78 mm focal length, f/3.8 UV Nikon objective on an intensified cooled CCD camera (ICCD). The ICCD had an array size of 512x512 pixels and 16-bit dynamic range digitization at 100 kHz. The ICCD spectral range spread from UV (180 nm) until visible (700 nm).

3. Proper Orthogonal Decomposition Proper Orthogonal Decomposition is the procedure that delivers an optimal set of empirical basis functions, in the L2 sense, from an ensemble of observations u(x,t) obtained either experimentally or from numerical simulation [2], which usually are given in the form of a vector-valued function:

ª u ( x1 , t1 ) u ( x1 , t2 ) « u( x , t ) u( x , t ) 2 1 2 2 U=«  «  «u ( x , t ) u ( x , t ) ¬ M 1 M 2

 

u ( x1 , t N ) º

u ( x2 , t N ) »

» » »  u ( xN , t N ) ¼ 



(5)

where M is the number of positions in the spatial domain, and N is the number of samples taken in time. The POD basis is obtained by solving the eigenvalue problem:

Cϕ = λϕ

where

C = U ,U

T

(6)

When M > N it is more convenient to use the so-called method of snapshots proposed by Sirovich [3]. Then, the approximated solution can be written as the combination of the POD functions and their coefficients: K

u ( x , t ) = ¦ an ( t ) ϕ n ( x )

(7)

n =1

Application of POD allows for a decomposition and analysis of the considered scalar field, by computing some statistical properties of the coefficients. Namely, calculation of mean, standard deviation, skewness and kurtosis of modal coefficients allows to decompose first the luminosity field into mean and fluctuating part, and afterward fluctuating part into coherent and incoherent fluctuations; more details and appropriate formulae can be found in [4].

Reconstruction of Flame Kinematics and Analysis of Cycle Variation in a Spark Ignition Engine by Means of Proper Orthogonal Decomposition

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4. Results Digital images of the flame luminosity have been collected at selected crank angles over 50 cycles. For cyclic variability analysis each crank angle is treated separately i.e. separate POD basis are determined.

Figure 2. Typical frames at 6 CAD for five combustion cycles.

Some typical digital images, collected at 6 crank angle degrees, are reported in Figure 1. It can be seen that the flame front arrives to the walls of the combustion chamber, and the luminosity of the flames, due to the burning of the fuel film deposition, results intense. Fig. 2 shows six POD modes, the leading three and some higher order modes, computed at this position for an ensemble of 50 images. It is commonly thought that the first few modes correspond to the average structure of the data, whereas higher order modes contain information about fluctuations.

Figure 2. POD modes.

Using the approach formulated in a previous work [4] where cyclic variability of the flame luminosity in Diesel engine has been investigated, determined POD modes and their modal coefficients are subsequently employed for extraction of coherent and incoherent fluctuations.

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POD modes are first reordered (in their natural order their corresponding eigenvalues are always in decreasing order, Fig. 3, top) according to quantity ȡ:

ρi =

( β ) + (γ ) *

2i

2

2

1i

(8)

which is a distance from the origin in a excess kurtosis–skewness space of coefficients. Reordered eigenspectrum is shown in Fig. 3 (bottom plot). In order to discriminate incoherent (random, Gaussian) components from coherent (non-Gaussian), the value ȡ=0.35 is chosen. The rationale for choosing this threshold value is based on the theory of normality tests on samples of random variables [4]. This value roughly corresponds to choosing to rate a sample of 50 instances “normal”, when its skewness and flatness values fall in the middle 50% of the estimated cumulative distribution about their expected values.

Figure 3. Decomposed luminosity field.

The morphology of the fluctuation is then analyzed. Fig. 4 reports the first captured experimental frame (u1) in the sequence of combustion cycles, the mean field nj1 for 6 CAD, and its fluctuation u1’; then the z1 (coherent part) and w1 (incoherent part) of u1’. First we note that the combustion of the locally rich mixture at the valve borders is present in the mean field, as “crescent moon”–shaped spots, being a repeatable phenomenon. However, the fluctuations of these spots are well visible in u1’, indicating the random shape of these flames’ borders. As anticipated in Fig. 3, most of the fluctuation is coherent (there are only three Gaussian modes and the corresponding eigenvalues are relatively small). In fact, w1 is almost invisible.

Reconstruction of Flame Kinematics and Analysis of Cycle Variation in a Spark Ignition Engine by Means of Proper Orthogonal Decomposition

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Figure 4. Decomposed luminosity field.

5. Conclusions Cycle–to–cycle variations were observed by analyzing sets of 50 images taken at different values of the crank angle for a transparent Spark Ignition engine. Proper Orthogonal Decomposition (POD) was applied to the collected images and the statistical analysis was run on POD coefficients only. A spatial structure of the coherent part of fluctuation can always be recognized. A Gaussian part of the fluctuation can be clearly identified at those values of the crank angle corresponding to high variability of the luminosity field over the cycles.

References [1] S.S. Merola, B.M. Vaglieco, SAE Paper 2007-24-0003. [2] P. Holmes, J.L. Lumley, G. Berkooz, Turbulence, coherent structures, dynamical systems and symmetry, Cambridge University Press, Cambridge, 1998. [3] L. Sirovich, Quart. of App. Math. 45 (1987) 561. [4] K. Bizon, G. Continillo, K.C. Leistner, E. Mancaruso, B.M. Vaglieco, Proc. Comb. Inst. (2009) doi:10.1016/j.proci.2008.08.010.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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A global optimization strategy to identify quantitative design principles for gene expression in yeast adaptation to heat shock Gonzalo Guillén-Gosálbeza, Carlos Pozoa, Laureano Jiméneza, Albert Sorribasb a b

Department of Chemical Engineerin, University Rovira i Virgili, Tarragona, Spain Departament de Ciències Mèdiques Bàsiques, Universitat de Lleida, Lleida, Spain

Abstract In this paper, we present a new method that is able of identifying the optimal enzyme activity changes that allow a system to meet a set of physiological constraints. The problem is formulated as a nonlinear programming (NLP) model, and it is solved by a novel bi-level global optimization algorithm that exploits its mathematical structure. Keywords: Optimization, Power-law, Evolution 1. Introduction The emergence of design in biological systems was a mystery until natural selection was established as the driving force for their evolution. At the molecular level, the identification of design principles in these systems has led to a better understanding of their adaptation. This knowledge may be used in building new gene and metabolic networks that attain specific targets. Quantitative evolutionary constraints play also an important role in the evolution of biological systems. Once the basic design is in place, the adaptive response of the cellular mechanism to different situations would be attained by tuning gene expression and enzyme activity. Understanding the evolution of adaptive strategies in different conditions is a major goal in Systems Biology. The evolution of adaptive stress responses can be seen as a multi objective optimization problem. In that sense, the observed response represents an optimal (in some sense) combination of changes that ensure appropriate survival in the considered conditions. Evolution results in adaptations that are admissible solutions fulfilling important physiological restrictions. Those restrictions are the selective pressures over which natural selection works. Within this general context, we develop a new approach that focuses on identifying optimal enzyme activity changes that satisfy a set of physiological constraints. The method presented allows to identify the possible evolutionary solutions that are expected to contain the actual adaptive response. This general framework focuses on the properties of a particular class of non-linear mathematical representation, the GMA (Generalized Mass Action) models that are based on the power-law formalism. The proposed algorithm is very efficient for realistic problems. The solutions found would represent the landscape in which evolutive solutions are expected. Comparison of our results and actual data allows discussing the practical usefulness of the proposed method.

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2. Modeling approach: GMA representation Our method considers a general metabolic network with p fluxes, each of which can contribute to the change in the concentration of the pool of any of the n internal metabolites. The mathematical representation of such a network is: p dX i = ¦ μir vr dt r =1

i = 1,...n

Here, μ ir is a stoichiometric factor that indicates how many molecules of Xi are produced or used by the process vr; it is a positive integer if the flux r produces Xi and it is a negative integer if the flux r depletes the pool of Xi. Each velocity can be represented by different functional forms, which would include various parameters. From all the available formalisms, the so-called power-law formalism is one of the most convenient. In this formalism, each velocity is represented as: n+ m

vr = γ r ∏ X j rj f

j =1

In this representation, Xj accounts for the concentration of metabolite j, r is an apparent rate constant for flux r, and frj is the kinetic order of variable Xj in re- action r. Each kinetic order quantifies the effect of the metabolite Xj on flux r and corresponds to the local sensitivity of the rate vr to Xj evaluated at the corresponding operating point. Using this representation, a Generalized Mass Action (GMA) model is defined as [1]: p § n+m dX i f · = ¦ ¨¨ γ r ∏ X j rj ¸¸ dt r =1 © j =1 ¹

i = 1,...n

In this expression, m indicates independent (external) metabolites. 3. Mathematical formulation The method presented relies on formulating a non-linear programming (NLP) model that is solved via global optimization techniques. NLP models based on the power-law formalism were first proposed by Voit [2]. In this context, the use of an S-system representation allows performing a transformation to logarithmic coordinates, so the original model can be converted into a linear formulation. Unfortunately, this technique cannot be generally applied with GMA models.

A Global Optimization Strategy to Identify Quantitative Design Principles for Gene Expression in Yeast Adaptation to Heat Shock

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Figure 1. Proposed algorithm.

The task of the NLP problem is to seek those values of vr, Ȗr and Xj that maximize a given criterion and satisfy simultaneously the equations of the GMA representation. Such a model can be expressed as follows:

ONLP = min U (vr , γ r , X j ) p

s.t.

¦μ

v =0

i = 1,...n

ir r

r =1

n+ m

vr = γ r ∏ X j rj f

r = 1,..., p

j =1

vr , γ r , X j ∈ ℜ + The complexity in solving ONLP is given by the non-convexities of the model, which usually give rise to multiple local optima, some of which may be far away from the global optimum. When performing a biological study, this limitation may result in

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wrong conclusions as well as low quality predictions. Hence, to circumvent this issue, it is necessary to employ global optimization techniques that ensure the optimality of the solutions found within the desired optimality tolerance. The specific method used in this paper is inspired on the works of Bergamini and co-workers [3] and Polisetty et al. [4], and relies on hierarchically decomposing the problem into two levels, an upper level master problem CMILP an a lower level slave problem RNLP, between which the algorithm iterates until a termination criterion is satisfied (see Figure 1). Glcout

HXTa

Glcin

GLKbb Ribulose -5P

G6P G6PDH

PYK

d

PFKc

TDHc TPS ATPase GLK

TPSb 2 Glycerol

F16P

TDH

ATP

GLY

GOL

2PEP +

PYK c

PFK 2PYR

Figure 2. Scheme of the modeled pathways and ranges used for generation of the in silico gen expression profiles (GEPs)

The master level of the algorithm entails the solution of a mixed integer linear (MILP) problem, which is a relaxation of model ONLP (i.e., it rigorously overestimates the feasible region of ONLP), and therefore predicts a valid lower bound on its global optimum. In the lower level, the original problem is locally optimized in a reduced search space, thus yielding an upper bound on its global solution. The upper and lower level problems are solved iteratively until the bounds converge. Due to space limitations, technical details of the main features of the proposed algorithm are omitted. 4. Adaptive response of yeast to heat shock The method presented in this work was applied to study the optimal adaptive response of yeast to heat shock. The model developed includes the core of the glycolytic pathway and the first step of the pentose phosphate pathway. It also accounts for the synthesis of glycogen, trehalose and glycerol, as shown in Figure 2. The notation used in this figure is as follows. Glcout: Extracellular Glucose; Glcin: Intracellular Glucose; G6P: Glucose-6-phosphate; F16P: Fructose-1,6-biphosphate; PEP: Phosphoenolpyruvate; PYR: Pyruvate; HXT: Hexose transporters (HXT1–4, HXT6–8, HXT12); GLK: Glucokinase/Hexokinase (GLK1, HXK1, HXK2); PFK: Phosphofructokinase (PFK1, PFK2); TDH: Glyceraldehyde-3-phosphate dehydrogenase (TDH1, TDH2, TDH3); PYK: Pyruvate kynase (PYK1, PYK2); GLY: Production glycogen; TPS: Trehalose 6phosphate syntase complex (TPS1, TPS2, TPS3); G6PDH: Glucose 6-phosphate dehydrogenase (ZWF1). Table 1. Results obtained in the optimization of trehalose, NADPH and ATP.

Maximization objective

TRE

NADPH

ATP

A Global Optimization Strategy to Identify Quantitative Design Principles for Gene Expression in Yeast Adaptation to Heat Shock

Fluxes (rate of synthesis (mMmin-1) Gene expression fold-change with respect to pre-stress situation

1049

2.08

46.21

1755.9

HXT

20.00

20.00

20.00

GLK

0.50

0.50

0.50

PFK

0.25

0.25

20.00

TDH

0.50

20.00

0.25

PYK

20.00

20.00

20.00

GLK-TPS+GOL

20.00

0.25

0.25

G6PDH

0.25

20.00

0.25

Glycerol production

0.25

0.25

0.25

ATPase 0.25 0.25 20.00 Considering the set of constraints identified by Vilaprinyo et al. [5], we ran an optimization procedure for maximizing different objective functions. First, we computed the optimal profile of enzyme activities so that the rate of trehalose synthesis was optimized. Second, we maximized the NADPH production. Finally, we optimized the synthesis of ATP. The mathematical model, which features 15 continuous variables and 43 constraints, was implemented in GAMS and solved with CPLEX 9.0 (master problem) in conjunction with CONOPT (slave problem) on an Intel 1.2 GHz machine (see Table 1). It took less than one CPU second to close a 1% optimality gap in all the cases. The solutions obtained agree with those presented in the literature as they are included in the optimal set identified in [5]. Note that the expected adaptive solution found by natural solution is expected to be close to these solutions, but it does not necessarily have to correspond to the global optimum. 5. Conclusions A systematic method for identifying the optimal enzyme activity changes that allow a system to meet a set of physiological constraints has been introduced. The approach presented relies on formulating a nonlinear programming (NLP) problem that is solved by a novel bi-level global optimization algorithm. The capabilities of our modeling framework and solution strategy have been illustrated in the study of the optimal adaptive response of yeast to heat shock. Our method has been proved to provide valuable insight into the evolution of adaptive responses to environmental changes. Furthermore, our strategy can be used in other applications such as the evaluation of parameter changes that are compatible with healthy and disease states. 6. Acknowledgments Financial support received from the Spanish “Ministerio de Educación y Ciencia” (projects DPI2008-04099, PHB2008-0090-PC and BFU2008-00196), the Spanish “Ministerio de Asuntos Exteriores” (projects A/8502/07, HS2007-0006 and A/020104/08) and “Generalitat de Catalunya” (FI programs) is fully appreciated.

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References [1] Voit EO: Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and Molecular Biologists. Cambridge, U.K.: Cambridge University Press 2000. [2] Voit EO: Optimization in integrated biochemical systems. Biotechnol Bioeng 1992, 40(5):572-582. [3] Bergamini ML, Aguirre P, Grossmann IE: Logic-based outer approximation for globally optimal synthesis of process networks. Computers and Chemical Engineering 2005, 29:1914-1933. [4] Polisetty PK, Gatzke EP, Voit EO: Yield optimization of regulated metabolic systems using deterministic branch-and-reduce methods. Biotechnol Bioeng 2008, 99(5):11541169. [5] Vilaprinyo E, Alves R, Sorribas A: Use of physiological constraints to identify quantitative design principles for gene expression in yeast adaptation to heat shock. BMC Bioinformatics 2006, 7:184.

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A Graph Theory Augmented Math Programming Approach to Identify Genetic Targets for Strain Improvement Sudhakar Jonnalagaddaa, Balaji Balagurunathana, Lee Dong-Yupb, c and Rajagopalan Srinivasana,b* a

Institute of Chemical and Engineering Sciences, Agency for Science, Technology and Research, 1, Pesek Road, Jurong Island, Singapore, 627833. b Dept of Chemical and Biomolecular Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 119260. c Bioprocessing Technology Institute, 20 Biopolis Way, Singapore, 138668. * Corresponding Author: ƌĂũƐƌŝŶŝǀĂƐĂŶΛŶƵƐ͘ĞĚƵ͘ƐŐ

Abstract Improvement of biological strains through targeted modification of metabolism is essential for successful development of bioprocesses. The computational complexity of optimization procedures routinely used for identifying genetic targets limits their application to genome-scale metabolic networks. In this study, we combined graph theoretic approaches with mixed-integer liner programming (MILP) to reduce the search space and thus reducing computational time. Specifically, we used cut-sets (minimal set of reactions that cuts metabolic networks) as additional constraints to reduce the search space. The efficacy of proposed approach is illustrated by identifying minimal reaction set for Saccharomyces Cerevisiae. Keywords: Strain improvement, MILP, Cut-sets,

Introduction Bioprocesses using microorganisms are becoming common for production of chemicals, fuels and food ingredients due to the depletion of fossil resources. Industrially used microorganisms generally do not produce significant quantities of all desired products since microorganisms are typically evolved for maximizing their other cellular objectives (e.g. growth). Hence, it is essential to develop engineered and improved microbial strains with enhanced yield of desired product in order to make bioprocesses economically viable [1]. Strain improvement has been traditionally achieved through random mutagenesis followed by screening process. However, rational design strategies based on genetic engineering techniques have been employed in recent years. The first step in this approach is to identify target genes for genetic engineering leading to desired phenotype. Initial approaches for gene target selection largely relied on known literature of organisms. The large number of inter-connected cellular compounds and redundancies in metabolic networks make the gene target selection a difficult problem. Often the effects of genetic modifications are beyond our intuition; hence the success rate is low. The availability of genome sequence of organisms enabled development of genomescale models of metabolism.

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Constraint-based analysis of Genome-scale metabolic models enables identification metabolic bottlenecks and subsequently the redesign of metabolism to achieve an optimal phenotype that improves yield of desired products [2]. One such optimization framework using mixed-integer linear programming (MILP) has been proposed by Burgard et al. (2003) [3] to identify genes which when knocked-out from organism yields more desired product. However, identifying gene knock-out strategy is combinatorial, consequently the computational time increases exponentially with the size of the problem (number of reactions in model). Burgard et al. considered only the reactions in central metabolism to achieve results in reasonable time. A more practical approach using Genetic Algorithms has been proposed by Patil et al. (2005) [4] for the same purpose. Genetic Algorithms is a stochastic optimization approach and hence provides no guarantee for the global optimal solution. Besides identification of gene knock-out strategies, researchers are also focusing on identifying genes for targeted insertion leading to desired microbial properties. Pharkya et al. (2004) [5] proposed a MILP approach for identifying minimal set of gene insertions that achieve a maximal yield of chemical. Here, we propose a method to reduce the computational complexity of the MILP formulation. The proposed method combines graph-theoretic approaches with the optimization framework. Specifically, constraints inspired by graph-theory are imposed on optimization to reduce the search space, thus improving the optimization performance. We demonstrate the efficacy of the proposed method by redesigning genome-scale metabolic network of Saccharomyces cerevisiae.

1. Method Modeling Metabolism The metabolic profile of organism is directly related to organism’s phenotype. Hence modeling and analysis of metabolic networks plays an important role in bioprocess development. The metabolic network of a given organism with N metabolites and M reactions is represented as

dX i = dt

M

¦S

ij

v j , i = 1, 2,..., N

(1.1)

j =1

where Xi is the concentration of metabolite i, Sij is the stoichiometric coefficient of ith metabolite in jth reaction, vj is the flux (rate) of reaction j. The mass balance constraints on metabolic network arising from steady-state assumption is represented as M

¦S

ij

v j = 0 i = 1, 2,..., N

(1.2)

j =1

The stoichiometric modeling approach characterizes all feasible metabolic phenotypes (flux distributions) in the organism. Since the number of reactions is generally higher than the number of metabolites, multiple flux distributions can satisfy the system of equations in Eq 1.2. Flux Balance Analysis (FBA) is the approach generally used to determine the metabolic phenotype. FBA uses linear programming to identify flux distribution while optimizing the flux (objective function) through a reaction (or linear combination of reactions). The growth rate is generally selected as objective function in FBA. Mathematically, this can be represented as

A Graph Theory Augmented Math Programming Approach to Identify Genetic Targets for Strain Improvement

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max imize z = Vbiomass

(1.3)

M

s.t

¦S v ij

j

= 0 i = 1, 2,..., N

j =1

v min ≤ v j ≤ v max j = 1, 2, ..., M j j vj ∈ℜ vjmin and vjmax are the minimum and maximum bounds on vj. The reactions j also includes transport reactions for uptake and secretion of metabolites by cell. MILP Approach for target selection Solving Eq. 1.3 results in a particular metabolic flux distribution that leads to maximum biomass. However, the objective of strain improvement is to improve the yield of desired chemical. This is achieved by diverting most of the flux towards the chemical production with sufficient biomass through modifying the metabolic reactions. Two different approaches currently in practice are to knock-out some of reactions or insert heterogeneous reactions into the cells. Identification of such genetic targets for knockout or insertion is generally formulated as a MILP problem. In this approach, genes/reactions are represented as binary variables where 1 indicates presence of reactions and 0 indicates absence of reactions.

­° 1 if reaction flux of v j is active yi = ® °¯ 0 if reaction flux of v j is inactive

(1.4)

where yj is a binary variable corresponding to vj. In order to identify gene knock-out targets, the optimizer searches the feasible space and finds a flux distribution solution that maximizes chemical production along with biomass by elimination a few reactions from network [4]. To identify gene insertion candidates, the heterogeneous reactions are represented by binary variables and the optimizer minimizes number of gene insertions while achieving the desired production of chemical [5]. Similar approach is used for identification of minimal reaction sets sufficient to make predefined quantity of biomass [6]. The mathematical representation of minimal reactions set is given as: M

minimize z = ¦ y j

(1.5)

j =1

M

s.t

¦S v ij

j

= 0 i = 1, 2,..., N

j =1

v min ⋅ y j ≤ v j ≤ v max ⋅ yj j j y j ∈ {0,1} j = 1, 2,..., M

j = 1, 2, ..., M

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vbiomass = vmax vj ∈ℜ where vmax is the maximum biomass possible for given environment (glucose and other nutrients). Though the MILP approach is successful in some cases, the solution time for MILP approach increases tremendously with increasing number of reactions. It is essential to improve the efficiency of optimizer in order to employ this approach for genome-scale models. In this paper, we propose the use of graph theory to reduce the search space and thus reduce the computational time. Improvement of MILP using Cut-sets Cut-sets are the minimal set of reactions which when removed together from the system break the connectivity between biomass (or products) and substrates [7]. Since cells have to produce sufficient quantity of biomass compounds for their survival, eliminating all cut-set reactions together is not advisable for any situations. In the present study, we exploit this concept to reduce the number of binary variables and shrink the search space by further constraining the metabolic network. First, cut-sets of varying sizes are extracted from the metabolic network while keeping the maximum predefined size. Cut-sets of size one contain the set of essential genes. Knocking-out of essential genes makes the organism non-viable, hence they should not be knocked-out, i.e., no binary variables are necessary for these. Cut-sets of size greater than 1 include genes that are co-essential. These cut-sets provide additional constraints for optimization. For example, if reactions 1 and 2 form a cut-set, additional constraints can be placed such that both these reactions should not be removed together from the system. For each cut-set c additionally a constraint is added to Eq. 1.5

1≤

¦

yj ≤ c

y j ∈c

where |c| is the size of cut-set c. Such constraints reduce the search space and improve the optimization performance.

2. Case Study In this section, we illustrate the proposed method to identify a minimal reaction set for Saccharomyces cerevisiae. The creation of minimal cell that can survive with minimal reactions is a fascinating goal in biology [8]. Such minimal cells are suitable for efficient production of chemicals. The proposed approach is employed with genome-scale model of Saccharomyces cerevisiae containing 1061 metabolites and 1266 reactions [9]. All reactions except the biomass reaction are considered as binary variables. Nine additional constraints are imposed from cut-sets of size two. The proposed approach identified 270 reactions as minimal reaction set in order to make biomass. CPLEX required 4,715,260 iterations to identify this solution. This number of iterations is about 41 % of the iterations needed for the same algorithm without additional constraints arising from cut-set analysis. This clearly shows the benefits of the proposed hybrid approach. The 270 reactions identified

A Graph Theory Augmented Math Programming Approach to Identify Genetic Targets for Strain Improvement

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by the proposed approach include several reactions in central metabolism including conversion of glucose to other major metabolites f6p, 3pg, dhap etc., Five transport reactions (excluding glucose transport) allowing exchange of O2, H2O, H, Phosphate, and CO2. Activity of these transport reactions is necessary for efficient conversion of glucose to biomass through TCA cycle. In this study, we do not consider cut-sets of size one to make a fair comparison on the effect of the additional constraints. Currently, we have an ongoing study to comprehensively identify the general affects of cut-sets and other graph theory-based analysis on solution time and quality.

References [1] Stephanopoulos, G (2002) Metabolic engineering: Perspective of a chemical engineer, AIChE Journal, 48, 920-926. [2] Price ND, Reed JL, and Palsson BO (2004) Genome-scale models of microbial cells: evaluating the consequences of constraints. Nature Reviews, 2, 886:897. [3] Burgard AP, Pharkya P, and Maranas, CD (2003) OptKnock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnology and Bioengineering, 84, 647-657. [4] Patil KR, Rocha I, Förster J, and Nielsen J (2005) Evolutionary programming as a platform for in silico metabolic Engineering. BMC Bioinformatics, 6:308 [5] Pharkya P, Burgard AP, and Maranas, CD (2004) OptStrain: A computational framework for redesign of microbial production systems. Genome Research. 14: 23672376. [6] Burgard AP, Vaidyaraman S, and Maranas CD (2001) Minimal Reaction Sets for Escherichia coli Metabolism under Different Growth Requirements and Uptake Environments. Biotechnology. Progress 17, 791-797 [7] Klamt S and Gilles ED (2004) Minimal cut sets in biochemical reaction networks. Bioinformatics. 20, 226-234. [8] Forster AC, and Church GM (2006). Towards synthesis of a minimal cell. Molecular Systems Biology. 2:45. [9] Förster J, Famili I, Fu P, Palsson BO, and Nielsen J (2003) Genome-scale reconstruction of the saccharomyces cerevisiae metabolic network. Genome Research. 13,244-253

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.



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Combinatorial Optimisation Algorithms for Strategic Biopharmaceutical Portfolio & Capacity Management Edmund D. George, Suzanne S. Farid The Advanced Centre for Biochemical Engineering, Department of Biochemical Engineering, University College London, Torrington Place, London WC1E 7JE, UK, [email protected]

Abstract The development of a stochastic combinatorial multi-objective optimisation framework is presented which addresses the challenge of exploring large decision spaces while also capturing the multitude of decisions, trade-offs and uncertainties involved in R&D portfolio management. Detailed process economic models were linked to models of the drug development pathway to predict the technical, financial and risk implications of alternative strategies for portfolios of biopharmaceutical drugs proceeding through development. Machine learning and evolutionary computation techniques were harnessed to evolve strategies to multi-objective optimality. An industrially-relevant case study is presented that focuses on the following decisions for a portfolio of therapeutic antibodies: the portfolio composition, the scheduling of critical development and manufacturing activities, and the involvement of third parties for these activities. The impact of budgetary constraints on the optimal set of solutions is also illustrated. Keywords: portfolio management, capacity planning, biopharmaceutical drug development, stochastic combinatorial optimisation, multi-objective

1. Introduction Important strategic considerations for survival and success of biopharmaceutical drug developers include how best to structure portfolios, to schedule development and manufacturing activities and to acquire access to manufacturing capacity. These portfolio and capacity management decisions are further complicated by constraints on resources such as available budget and capacity as well as uncertainties that include the risk of clinical failure. Hence, the impact of making sub-optimal decisions in this environment can be severe. Frameworks that incorporate both the problems of portfolio management and manufacturing capacity planning simultaneously exist [e.g. 1, 2] and have typically used mathematical programming methods. Due to the size and complexity of this problem, a stochastic and multi-objective combinatorial optimisation approach utilising evolutionary algorithms is explored in this paper. Such approaches facilitate the capture of the interdependent activities involved in the development of drug portfolios, along with their technical, financial and risk characteristics and hence also have the capacity to give richer insight to the decision maker on the problem itself. The overall framework is a combination of a simulation-based evaluative framework based on George et al. [3] and a bespoke estimation of distribution algorithm (EDA) [4] to iteratively evolve a population of candidate strategies.

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2. Model Formulation The stochastic optimization process makes use of an evaluative framework (Fig. 1) coupled with evolutionary computation. The latter makes use of an estimation of distribution algorithm (EDA) (Fig. 2) that operates the optimization procedure through the machine learning of instances of decision variables that are associated with superior strategy performance using Bayesian networks. The model was designed using C++, which offers significant savings in computational time, with MS Excel as the main graphical user interface and Visual Basic for Applications (VBA) for modules controlling the flow of data in the simulation and optimization procedures. The reward and risk metrics used to to identify top performing strategies were the profitability indicators mean positive net present value (NPV) and p(NPV>0).

Evaluation Contractual Dependency Analysis

Generation G(t)

Selection of Superior Strategies

Revenue Dependency Analysis

Analysis of NPV & p(NPV>0)

Individual gi

Capital Dependency Analysis

Identify Top Performing Individuals

Stochastic Variables

Data Manufacturing Collation Facility Model, Drug i

Cluster individuals into i groups.

Timeline

Nondominated Sorting Algorithm

Data Collation P&L for Drug i

Clustering Algorithm

Crowding Distance Algorithm

Probabilistic Model Building and Sampling Parent Matrix & Conditional Probabilities

Learning Bayesian Network Algorithm

Fig. 1. Schematic of the entire simulation and optimization framework.

Population Regeneration

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Estimation of Distribution Algorithm Initial population: Let the population of candidate solutions be G(t). t=1 Randomly generate the initial population of candidate solutions, G(1). Let tmax be the maximum number of populations to be evolved. For t = 1 to tmax: Evaluation: Simulate each g in G(t) and record stochastic properties. Selection: Use the fast nondominated sorting and crowding distance algorithms to select the top 50% of solutions, S(t), from G(t). Clustering of the objective space: Using the k-means clustering algorithm, separate S(t) into z clusters. For each cluster, Kz: Probabilistic model building: Construct the Bayesian network, Bz, using a hill climbing procedure to optimize the Bayesian Dirichlet metric over Bz. Sampling of the probabilistic model: Generate a new set of strategies Oz(t) by randomly sampling the joint probability distribution encoded by Bz. The number of strategies to be generated will be twice the original cluster size. Population regeneration: Generate the new population G(t+1) by randomly by replacing all strategies in G(t) with all strategies in each Oz(t). Fig. 2. Pseudocode for the EDA

3. Case Study Description A hypothetical case was formulated to illustrate and examine the ability of the framework to discover optimal strategies for performance against multiple objectives in an uncertain environment. The case study concerns a biopharmaceutical company that has 10 monoclonal antibody drug candidates available for development but can only construct a drug development portfolio of limited size. It needs to know which drug candidates should be chosen, their order of their development, the timing schedule of development activities, and which corporate bodies should be assigned to each development activity. Additionally, the company is interested in knowing how solutions which are nondominated in the objective space change with the magnitude of constraint on cash flow. The optimization model is considerate of the commercial characteristics of drug candidates, technical probabilities of success for each drug group, durations and costs

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associated with various stages of the drug development and dependencies for revenue, capital expense and royalty payments. The stochastic variables included in this work are exclusively characterized by way of triangular probability distributions because of their convenience when limited sample data are available. The cash flow constraints applied to this portfolio of -$200MM, -$100MM, and -$75MM. represent the possible cash limitations of a company when funding portfolio development. If this negative cash flow is breached then clearly the company is stretched beyond the limit of finance it had intended to use. The following settings were used for the mechanics of the optimization procedure: maximum number of iterations to be evolved (tmax) = 17, number of candidates in each generation at each iteration (|G(t)|) = 1000, number of Monte Carlo trials per candidate strategy (U) = 250, and number of superior candidate strategies in G(t) at each iteration (|S(t)|) = 500.

4. Results and Discussion Fig. 3 shows the final results for a five drug portfolio subject to the various constraints considered. The Pareto frontiers indicate that a negative relationship between mean positive NPV and p(NPV>0) exists for all constraints. It can also be seen in each case that for a given p(NPV>0) value the more restrictive the cash flow constraint the lower the mean positive NPV. Similarly, for a given target in mean positive NPV these constraints reduce the probability of achieving this profit.

Mean Positive NPV ($MM)

$1,600 $1,400 $1,200 $1,000 $800 $600 $400 $200 $0 0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

p(NPV>0)

Fig. 3. Pareto frontiers of reward (mean positive NPV) versus risk (p(NPV>0)) for a five drug portfolio for the following cash flow constraints: unconstrained (-), -$200MM (c), -$100MM(), -$75MM (ƒ).

The impact of such constraints on third party, timing and drug selection strategies was analysed. An example of the most probable constituents of third party strategies for the unconstrained example alongside the -$200MM and the -$100MM constraints is given below as an example.

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Third Party Strategies When analyzing the third party strategies in the final generation for each constraint (Table 1) it is clear that the general trend in third party strategy is to develop and manufacture all drugs in-house under the presence of no constraints and then move towards the increased involvement of partners as constraints become more severe. This is understandable from the viewpoint that increasing the severity of cash flow constraints makes it imperative that more cost-effective strategies be formulated and in the problem formulation used here partners offer the most cost-effective route for drug development. For the -$200MM constraint it can be seen that in the most probable strategies partners are chosen for the clinical manufacturing stages for the first two drugs and contract manufacturers for successive drugs, indicating that this level of constraint makes inhouse commercial manufacturing to be economically unattractive. The use of partners appears to be the most extensive for the -$100MM constraint. The above examples clearly show that third parties are an important resource in managing the risk and impact of failure. Table 1. Most probable third party strategies for a five drug portfolio with different cash flow constraints for the middle cluster of strategies. No cash flow - $200MM cash flow - $100MM cash flow constraint constraint constraint Drug PI PII PIII M PI PII PIII M PI PII PIII M 1 ‘I’ ‘I’ ‘I’ ‘I’ 'P' 'P' 'P' 'P' 'P' 'P' 'P' 'P' 2 ‘I’ ‘I’ ‘I’ ‘I’ 'I' 'P' 'P' 'P' 'I' 'I' 'C' 'I' 3 ‘I’ ‘I’ ‘I’ ‘I’ 'I' 'C' 'C' 'P' 'P' 'P' 'P' 'P' 4 ‘I’ ‘I’ ‘I’ ‘I’ 'C' 'C' 'C' 'C' 'P' 'P' 'P' 'P' 5 ‘I’ ‘I’ ‘I’ ‘I’ 'I' 'C' 'C' 'C' 'P' 'P' 'P' 'P' Note: ‘I’ – in-house activity, ‘C’ – outsourced activity, ‘P’ – partnered activity, PI-PIII manufacturing for clinical phases I-III, M – manufacturing for the market phase.

5. Conclusions A stochastic multi-objective combinatorial optimisation framework has been used to identify optimal strategies that address three key decisions simultaneously relating to portfolio and capacity management. Due to the complexity of this problem, a principle contribution of this work is in demonstrating a formulation based on techniques from evolutionary computation and machine learning employed for an efficient search of the decision space and for effective discovery of a dense and widespread Pareto frontier. It has been seen in the cases investigated here that mean positive NPV and p(NPV>0) are conflicting measures however both are desirable to the decision maker. The introduction of cash flow constraints can lead to a reduction in the expected rewards or probability of success of strategy and it directly influences the choice between in-house and external manufacturing.

Acknowledgements The Advanced Centre for Biochemical Engineering (ACBE) and support for the Innovative Manufacturing Research Centre for Bioprocessing (IMRC) housed in the ACBE by the EPSRC are gratefully acknowledged. Financial support in the form of an

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EPSRC Engineering Doctorate (EngD) studentship for E. George is also gratefully acknowledged.

References [1] C.T. Maravelias and I.E. Grossman, Ind. Eng. Chem. Res., 40 (2001) 6147. [2] A.A. Levis. and L.G. Papageorgiou, Comput. Chem. Eng., 28 (2004) 707. [3] E.D. George, N.J. Titchener-Hooker, and S.S. Farid, Comput. Chem. Eng., 31 (2007) 889. [4] M. Pelikan, D. Goldberg, and E. Cantú-Paz, Evol. Comput., 8 (2000) 311.

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Dynamic Simulation Framework for Design of Lean Biopharmaceutical Manufacturing Operations Adam Stoniera, Martin Smithb, Nick Hutchinsonb, Suzanne S. Farida a

University College London, Department of Biochemical Engineering, Torrington Place, London, WC1E 7JE. UK.([email protected], [email protected]) b Lonza Biologics plc, Manufacturing Science and Technology, 228 Bath Road, Slough, SL1 4DX, UK. ([email protected], [email protected])

Abstract Upstream advances in mammalian cell culture processes have increased pressures for downstream processes intensification efforts to alleviate downstream bottlenecks and improve process economics. This paper describes a decision support tool to facilitate such efforts and design robust optimal purification strategies to match the high productivity cell cultures. The tool integrates process economics, discrete-event simulation and uncertainty analysis whilst harnessing the benefits of a database-driven approach. The tool has also been configured to easily handle both single and multiproduct facilities as well as facility constraints relative to multiple suites. A case study is presented to illustrate how the tool can be used to select the optimal chromatography column sizes for both current and future fermentation titres. A novel approach is presented to demonstrate the robustness of the optimal configurations to both titre fluctuations and change in scale over the lifecycle of a drug. Keywords: biopharmaceutical manufacturing processes, stochastic decision-support tools, discrete-event simulation, MySQL database, process economics.

1. Introduction Conventional chromatography-based purification sequences employed in mammalian cell culture processes pose key capacity challenges as cell culture titres continue to increase. This has shifted the focus of biopharmaceutical process development efforts to re-evaluate the feasibility of conventional purification steps. [1,2] Downstream capacity bottlenecks potentially arise with increased titres since they result in greater mass loads on chromatography steps and can, for example, prompt a decision between opting for additional cycles or investment in larger columns which may breach either time or budgetary constraints respectively. Process intensification efforts require the ability to rapidly identify facility limits as well as the sequence of optimal equipment sizes that minimise process cost whilst satisfying time constraints. This paper presents a decisionsupport tool to address these issues and hence facilitate in the design of robust and costeffective manufacturing strategies, which meet regulatory compliance requirements. This research builds on previous work at UCL [3-6] and investigates the possibility of linking both simulation and optimisation in a dynamic environment, combined with process economics, uncertainty analysis and a capacity to handle multiple processes and suites. Furthermore, previous work [5, 6] relied on the use of spreadsheets for key inputs and outputs. The limitation of working with spreadsheet applications becomes apparent when working with large amounts of data; to overcome these issues data can be contained and managed more effectively in a relational database. Hence in this paper emphasis is placed on how best to integrate powerful

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databases with simulation engine when designing biopharmaceutical manufacturing facilities.

2. Model Definition and Implementation A database-driven approach using MySQL (MySQL AB, Uppsala, Sweden) and a discrete event simulation engine. (Extend v6, Imagine That! Inc, San Jose, USA) has been developed to capture the process, business and risk features of biopharmaceutical manufacture, as illustrated in Figure 1. INPUTS

OUTPUTS

Facility data: eg. Description of suites eg. Resource availability

Key metrics:

Database (MySQL)

eg. Operating hours

Scheduling parameters:

eg. Process sequence

eg. Buffer recipes Economic data:

eg. Mass throughput eg. Cost of goods (DSP)

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eg. Operating parameters

eg. Batch throughput

eg. Batch times

Simulation Engine (Extend)

eg. Time in hold eg. Idle time Scale optimisation:

eg. Raw material costs

eg. Optimal equipment sizes

eg. Consumables costs

eg. Process robustness

Figure 1: Summary of model structure showing a number of key inputs and outputs.

MySQL provides the framework with a powerful data storage engine capable of handling the large datasets required for multiple processes, uncertainty analysis and optimisation. It has been designed to allow rapid and flexible access to the data by both the core simulation engine and the front end. It was identified early in the development of the framework that the separation of data and model is key to providing increased flexibility. This was driven partly by the limited data management features available in the version of Extend used but mainly through the need to develop a stand-alone data structure that can also be of use independent from the simulation. The use of SQL provided the opportunity for multiple instances of the simulation engine to work from the same dataset and allowed for the simulation runs to be distributed over a network of computers. Additional advantages of a server-based database include making the database available to multiple users helping to focus process development efforts across a team as well as maintaining an archive of data from which to improve consistency of design across multiple projects. The discrete-event simulation engine developed in Extend works with the data stored in the database. Extend runs in the background requiring no end-user interaction. Traditionally when building a process model the order and function of the unit operations is fixed within the largely linear structure of the model. In order to create an adaptive model this approach was replaced with a structure based around a router; the router controls the order in which the procedures in the simulation are called. The order is derived from the sequence of unit operations and subtasks specified by the user in the database. In addition to adapting to any process specified, logic coded in the database is able to automatically scale a process based on established rules of scale up. This allows the user to rapidly assess the performance of a given process across multiple scales without having to recode the model or make process changes. Where the scale up rules

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result in multiple process configurations the simulation is able to assess each option and select the optimum in terms of both the schedule and cost. Upon completion the simulation engine exports an extensive set of raw data. This data contains information on every event and changing parameters throughout the run time of the simulation as well as logs which contain more specific information about the timings of key elements. This data can be a valuable source of information when investigating and assessing process performance. A graphical user interface (GUI) allows the specification of process and facility configurations and guides the user through the construction of simulation jobs. Based on a tree structure, the user is provided with the functions and information necessary to navigate through the data set and extract the information required. The user is also able to quickly access preset result sets generated using Crystal Reports™ (Business Objects SA, Paris, France).

3. Case Study 1 – Process Economics and Throughput Set-up The aim of this study was to use the framework to investigate the performance of a monoclonal antibody (MAb) purification process in a multi-suite bioprocessing facility. The goals were to test the simulation engine and provide insight into where bottlenecks may form within the process as fermentation titres increase over the coming years. The selected process represents a typical manufacturing process for the purification of MAbs. The process and facility configuration investigated along with additional information are outlined in Figure 2. The key parameters investigated were cost of goods, mass throughput and batch throughput.

Figure 2: Process sequence, facility configuration and additional information used in the case studies. (CC= Cell culture, DSP = Downstream processing, VI = Virus inactivation, UFDF = Ultrafiltration/diafiltration, ProA = Protein A chromatography, AEX = Anion exchange chromatography, CEX = Cation exchange chromatography, VRF = Virus retention filtration.)

Results Figure 3a illustrates that the facility simulated encounters bottlenecks above titres of 6g/l. Further investigation of the simulation results identified that the increasing titres

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caused the processing time to increase beyond a critical point which reduced the overall batch throughput. The tool was used to identify contributory factors to this bottleneck and the increasing batch times were linked to the chromatography operations (Figure 3b) which had insufficient capacity to handle larger product masses with the desired batch slot. This suggests that improvements or alternatives to chromatography could result in more robust platform processes. This drop in batch throughput has a knock-on effect on cost of goods which up to 6g/l is seen to fall rapidly whilst beyond 6g/l the value remains largely constant; this signifies that the economic advantages of operating at higher titres are not seen in this process above 6g/l.

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Titre (g/l)

Figure 3: (a) Annual mass produced (−) and batch throughput (Β) vs. titre. (b) Average batch time (−) and number of chromatography cycles (,) vs. titre. The dotted line indicates the ideal batch time.

4. Case Study 2 – Process Optimisation and Robustness Set-up A case study is presented to illustrate the tool’s ability to select the optimal chromatography column sizes over a range of titres. The rules for column size selection result in multiple processing options with different costs and process durations. A process optimisation module within the framework was created to select the lowest cost configurations which maintain the operating schedule. In effect, the optimisation captures the tradeoffs between operating large columns with low cycles and high cost, and small columns with a greater number of cycles at a lower cost. A novel approach is outlined to visualise the robustness of the optimal configuration to both titre fluctuations and changes in scale over the lifecycle of a drug. Results Figure 4a shows the cost and time trade-offs for a selection of process configurations considered by the process optimisation module at a specific titre. Based on a fixed constant titre of 2g/l, configuration A would be selected as the schedule constraint is met at the lowest cost. Figure 4b shows how the process selection can be improved to account for expected titre fluctuations. Here the Pareto frontiers from several simulations running over a range of titres between 1.5g/l and 2.5g/l are shown. Points representing identical process configurations are connected by a series of straight lines (e.g. lines A, B and C). This diagram shows how configuration A, selected in the previous method, would start to run over the critical batch length with only a minor increase in titre and thus lead to a bottleneck in the facility. A better process selection would be configuration B which satisfies the time constraint for 95% of the titre range or ideally configuration C which satisfies it for 100% of the titre range.

Dynamic Simulation Framework for Design of Lean Biopharmaceutical Manufacturing

(a)

(b)

60

60

55

55

Batch Cost (Ł'000)

C

Batch Cost (Ł'000)

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50 45 C B A

40 35

B

A

2.5g/l

50 45

2g/l 40 35

30

1.5g/l

30 7

8

9

10

11

Batch Time (Days)

12

13

7

8

9

10

11

12

13

Batch Time (Days)

Figure 4: (a) Batch cost vs. batch time for a selection of process configurations investigated in the process optimisation module of the framework showing the Pareto frontier for a fixed titre of 2g/l. (b) Pareto frontiers compiled from several datasets generated using the process optimisation module of the framework.

5. Conclusions This paper has outlined the structure of a simulation framework that can be used to provide data to support decisions on the key issues concerning bioprocess manufacturing today. Storing the data independently from the simulation engine allows for data analysis and generation to happen simultaneously across multiple members of a process development team. Furthermore, determining the robustness of optimal configurations to uncertainties provides the opportunity to plan for such contingencies and highlight the importance of capturing risk when ranking different process configurations.

References [1] B. Kelley, Biotechnol. Prog. 23 (2007) 995. [2] D, Low, R. O'Leary and N. S. Pujar, J. Chromatogr. B Analyt. Technol. Biomed. Life Sci. 848 (2007) 48. [3] S. S. Farid, J. Washbrook and N. J. Titchener-Hooker, Biotechnol. Prog. 21 (2005) 486. [4] S. S. Farid, J. Washbrook and N. J. Titchener-Hooker, Comput. Chem. Eng. 31 (2007) 1141. [5] A. C. Lim, J. Washbrook, N. J. Titchener-Hooker and S. S. Farid, Biotechnol. Bioeng. 93(2006) 687. [6] S. Chhatre, R. Francis, K. O'Donovan, N. J. Titchener-Hooker, A. R. Newcombe and E. Keshavarz-Moore, Bioprocess. Biosyst. Eng. 30 (2007) 1.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1075

Global Sensitivity Analysis in dynamic metabolic networks Jimena Di Maggioa, Juan C. Diaz Riccib, M. Soledad Diaza a

Planta Piloto de Ingeniería Química-PLAPIQUI (UNS-CONICET), Camino La Carrindanga km 7, Bahía Blanca 8000, Argentina, [email protected] b Instituto Superior de Invetigaciones Biológicas-INSIBIO (UNT-CONICET), Chacabuco 461, San Miguel de Tucumán, Argentina

Abstract In this work, we have performed global sensitivity analysis through variancebased techniques to determine parameters to be estimated in a kinetic metabolic network. Sensitivity indices have been calculated for each parameter [1] to provide a proper measure for their influence on model outputs, regardless of model nonlinearity and non-additivity. The global sensitivity analysis has been carried out on a large-scale nonlinear differential algebraic system representing a dynamic model for the Embden-Meyerhof-Parnas pathway, the phosphotransferase system and the pentose phosphate pathway of Escherichia coli K12 W3110 [2]. As a result, sixteen parameters from the complex metabolic network under study have been selected to be estimated. Keywords: Global sensitivity analysis, Metabolic networks, DAE systems 1. Introduction The advances on experimental techniques and the consequent increase in the amount of accessible data on the dynamics of functioning cells allow the formulation of dynamic models for metabolic networks, which can predict the microbial behavior and constitute important tools in metabolic engineering. Dynamic models provide time profiles for the concentration of metabolites involved in the metabolic network under study. They comprise a nonlinear differential algebraic system of equations which arise from mass balances of extracellular and intracellular metabolites and co-metabolites, and have a large number of kinetic parameters that must be estimated for a specific growth condition. However, uncertainty in input parameters has different effects on model outputs. Thus, the first step to solve the inverse problem is to carry out a sensitivity analysis, which provides knowledge about the parameters that have the largest impact on model outputs. There are local and global sensitivity analysis techniques. Mauch et al. [3] proposed a local sensitivity method to determine stationary and time-dependent flux control coefficients and concentration control coefficients for a generic metabolic network and applied it to a metabolic network represented by two ordinary differential equations, with twelve parameters. Also Noack et al.[4] applied a local sensitivity

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analysis to a metabolic network. However, to our knowledge, there is no global sensitivity analysis report on metabolic networks in the literature. In this work, we have performed a global sensitivity analysis for a differential algebraic (DAE) system representing a complex metabolic network for glycolisis and pentose phosphate pathway of Escherichia coli. Sensitivity indices have been calculated for each parameter based on a variance-based method, proposed by Sobol’ [1], rendering a ranking of parameters to be estimated.

2. Mathematical modeling of metabolic networks The dynamic model for the Embden-Meyerhof-Parnas pathway, the pentose phosphate pathway and the phosphotransferase system of Escherichia coli K-12 W3110 [2] has been modeled with eighteen differential equations that represent dynamic mass balances of extracellular glucose and intracellular metabolites, thirty kinetic rate expressions and seven additional algebraic equations for co-metabolites and it involves one hundred and sixteen parameters. Equations 1 to 7 correspond to mass balances on main metabolites analyzed. The remaining mass balances are given in Chassagnole et al. [2]. ext dC glc

dt

dCg 6 p dt dC f 6 p

dt dC fdp dt dC pep dt dC pyr dt dC6 pg dt

a lim ext D(C glc  C glc ) f

pulso



C X rPTS ȡX

(1)

rPTS  rPGI  rG 6 PDH  rPGM  ȝCg 6 p

(2)

rPGI  rPFK  rTKb  rTA  2rMurSint  ȝC f 6 p

(3)

rPKF  rALDO  ȝC fdp

(4)

rENO  rPK  rPTS  rPEPCxylase  rDAHPS  rSynth1  PC pep

(5)

rPK  rPTS  rPDH  rsynth2  rMetSynth  rTrpSynth  PC pyr

(6)

rG 6 PDH  rPGDH  PC6 pg

(7)

Equations 8 to 12 show kinetic expressions for phosphotransferase system, pyruvate dehydrogenase, 6-phosphogluconate dehydrogenase, glucose-6-phosphate dehydrogenase, and phosphofructokinase respectively, which are involved in differential equations 1-7 max r PTS C

r PTS

§ ¨K ¨ ©

PTS , a 1

 K

C PTS , a 2

C

pep pyr

 K

PTS , a 3

C

extracelul glc

extracelul glc

lar

lar

C

pep

C

pyr

 C

extracelul glc

lar

N

C

pep

C

pyr

·§ C g 6PTSp , g 6 p ¸¨1  ¸¨ K PTS , g 6 p ¹©

· ¸ ¸ ¹

(8)

Global Sensitivity Analysis in Dynamic Metabolic Networks N PDH pyr

max r PDH C

r PDH

K PDH

(9)

N PDH pyr

C

, pyr

max rPGDH C 6 pg C nadp

rPGDH

C

§ § C nadph  K PGDH , 6 pg ¨ C nadp  K PGDH , nadp ¨ 1  ¨ ¨ K PGDH , nadph , inh © ©

6 pg

C

§ C nadph  K G 6 PDH , g 6 p ¨1  ¨ K 6 , nadph , g 6 pinh G PDH ©

g6 p

§ ¨C ¨ ©

B

§ ·§ Cnadph ¸¨ K G 6 PDH , nadp ¨1  ¨ ¸¨ K 6 , nadph , nadphinh G PDH © ¹©

max r PFK C

r PFK

1

1

·§ C ATP ¸¨ 1  ¸¨ K PGDH , ATP , g 6 pinh ¹©

(10)

·· ¸¸ ¸¸ ¹¹

rGmax 6 PDH CG 6 PDH C nadp

rG 6 PDH

A

1077

 K

atp

C pep

K PFK

PFK , atps

C adp



K PFK

, pep

C adp K PFK

, adpa

§ C adp ¨1  ¨ K PFK , adpc ©





, adpb

C amp

K PFK

· ·§ ¸ ¸¨ C ¸ ¸© ¹¹

f 6 p

atp

 K

C

PFK

f 6 p

, f 6 ps

A B

§ ¨ ¨ ·¨ ¸ 1 ¹¨ § ¨ ¨1  C ¨ ¨ © ©

L

PFK

B f 6 p

K

A PFK

, f 6 ps

· ¸ ¸ ¹

N

PFK

· ¸ ¸ ¸ ¸ ¸ ¸ ¹

(12)

(13)

, ampb

C amp K PFK

(11)

· · ¸  Cnadp ¸ ¸ ¸ ¹ ¹

(14)

, ampa

3. Global sensitivity analysis Sensitivity analysis methods can be classified into local and global ones. Local techniques may not be appropriate when handling nonlinear models, with interaction among parameters. Global sensitivity analysis is based on exploring the total range of variation of model parameters, sampling from the distribution function associated to each input parameter and on performing repeated simulations of the model, taking into account the sampled values of input parameters. As global methods do not require the assumption of linearity or additivity of the model, they are said to be modelindependent. In this work, we have performed global sensitivity analysis based on a variance-based method [1]. 3.1. Variance based methods: Sobol’ method Given a function Y=f(X), where Y is a model output and X is a vector of k model input parameters, if all the parameters vary over their entire range of variation, the uncertainty of the model output can be quantified by the unconditional variance V(Y), which can be written using conditional variances as follows V (Y )

V E Y xi  E V Y xi

(20)

The ranking of model parameters is carried out according to the reduction on the unconditional variance that is obtained when the true value of a given parameter, xi, is known, by means of their first order sensitivity index (Si): Si

V E Y xi V Y

Vi V (Y )

(21)

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The conditional and unconditional variances have been calculated according to Sobol’ [1], a straightforward Monte Carlo-based implementation, with a minimum amount of function evaluations. Main steps are: 1.' Two' different random sets of model parameters are generated:[ (K , ] ) and [ (K , ] .' ) Each matrix has dimensions N × k, where N is the sample size for Monte Carlo method and k is the number of parameters. In the previous nomenclature Ș is a vector of dimensions N × 1, which contains the N random values of the parameter xi whose sensitivity index is to be calculated. 2. Two new matrices are generated combining ȟ and ȟ’, which are required for the computation of the variances, as follows (f0 stands for E(Y|xi)) 1 N P (22) f0 ¦ f ([ i ) o N i1 N

1 N

¦f

1 N

¦

2

P ([ i ) o V  f 02

(23)

i 1 N

P f ([ i ) f (K i , ] i' ) o V i  f 02

(24)

i 1

3. Sensitivity indices are subsequently calculated by the corresponding definition given by equation 21.

4. Discussion of results We have implemented a kinetic model for a metabolic network model in g-PROMS [5], in which the differential algebraic system of equations is solved with DASSL [6]. In this environment, two different sets of random parameters, ȟ and ȟ’, have been generated for k=20 parameters, with sample size of N=2500 scenarios. Normal distribution has been assumed for each parameter, with mean equal to nominal values from the literature and 10% standard deviation. We have performed the N(k+1) Monte Carlo simulations in gPROMS and output temporal profiles for state variables have been exported for subsequent conditional and unconditional variances and sensitivity indices calculation within a Fortran 90 environment. KPTS1

1.0

KPTS,g6p

0.9

rPTS

1.0

NPTS,g6p max

KPGI,eq

0.8

0.8

KPFK,f6ps NPFK

0.7

max

rPFK KGAPDH,pgp

0.4

KPGK,eq

max

rGAPDH

0.4

KPGluMu,eq

0.3

KENO,eq NPDH

0.2

max

rPDH

0.1 0.0

0.6

KGAPDH,gap

0.5

Si

Si

0.6

0.2

KPepCxylase,fdp max

rG6PDH

0

50

100

150

Time (sec)

200

250

300

KPGDH,6pg max

rPGDH

Figure 1. Temporal profiles of Si for glucose-6-phposphate concentration.

0.0

0

50

100

150

200

250

300

Time (sec)

Figure 2. Temporal profiles of Si for pyruvate concentration.

Global Sensitivity Analysis in Dynamic Metabolic Networks

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1,0

0,8

Si

0,6

0,4

0,2

0,0

0

50

100

150

200

250

300

Time (sec)

Figure 3. Temporal profiles of S i for 6-phosphogluconate concentration.

We have studied the regulatory points in the metabolic network under study (phosphotransferase system, pyruvate kinase, phosphofructokinase and glucose-6phosphate dehydrogenase) and have analyzed which parameters are the most influential on the concentrations of substrates and products of the enzymes in regulatory points. Figures 1 to 3 show profiles for first order sensitivity indices for glucose-6-phosphate (Cg6p) concentration, pyruvate (Cpyr) concentration and 6-phosphogluconate (C6pg) concentration. Glucose-6-phosphate concentration is sensitive to all parameters, being the most influential ones rPFKmax, included in the kinetic expression for phosphofructokinase (Eqn 12) and NPTS,g6p, KPTS,g6p and rPTSmax, which are involved in the expression for phosphotransferase (Eqn 8) system, a regulatory point in the Embden-Meyerhof-Parnas pathway, as it can be seen in Fig. 1. Figure 2 shows that pyruvate concentration is affected by NPDH, which is involved in the kinetic expression of pyruvate dehydrogenase (Eqn 9), throughout the entire time horizon. Concentration of 6-phosphogluconate, the first metabolite involved in the pentose-phosphate pathway, is affected by four parameters, NPTS,g6p, rG6PDHmax, included in the kinetic expression for glucose-6-phosphate dehydrogenase (Eqn 11), KPGDH,6pg and rPGDHmax, being the last one the most influential on this metabolite concentration, as it can be seen in Fig. 3.

5. Conclusions Global sensitivity analysis has been performed on a kinetic metabolic network model, which comprises a differential algebraic system of equations. As a result, sixteen kinetic parameters have been selected as the most influential ones in the metabolic network. The input factor that produces the greatest effects on model outputs is NPTS,g6p, which is involved in the expression for the phosphotransferase system, a regulatory point in the glycolysis. Based on this analysis, the parameter estimation problem is currently being addressed.

6. Acknowledgments The authors gratefully acknowledge financial support from the National Research Council, Universidad Nacional del Sur and ANPCYT, Argentina.

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7. References [1] Sobol’ I.M.. Global sensitivity indeces for nonlinear mathematical models and their Monte Carlo estimates, Mathematics and Computers in Simulations 55, 2001, 271-280. [2] Chassagnole, C., Noisommit-Rizzi, N., Scimd, J.W., Mauch, K., Reuss, M.. Dynamic modeling of the Central Carbon Metabolism of Escherichia coli, Biotechnology and Bioengineering 79, 2002, 53-72. [3] Mauch, K., Arnold, S., Reuss, M.. Dynamic sensitivity analysis for metabolic systems, Chemical Engineering Science 52, No 15, 1997, 2589-2598. [4] Noack, S., Wahl, A., Haunschild, M., Qeli, E., Freisleben, B., Wiechert, W.. Visualizing regulatory interdependencies and parameter sesitivities in biochemical models, 2008, Mathematics and Computers in Simulations, In press. [5] g-PROMS, www.psenterprise.com [6] K. E. Brenan, S. L. Campbell, L. Petzold, The numerical Solution of Initial Value Problems in Differential-Algebraic Equations, Elsevier Science Publishing Co., (1989), second edition , SIAM Classics Series, 1996.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1081

Method for determination of the reaction kinetics of an enzymatic conversion in a heterogeneous system Przemyslaw Krausea, Roberto Maciasa, Georg Fiega, Bernhard Gutscheb a

Institute of Process and Plant Engineering, Hamburg University of Technology, Schwarzenbergstraße 95, 21073 Hamburg, Germany, [email protected] b Cognis GmbH, Duesseldorf, Germany

Abstract Within the development of a biotechnological production process for fatty acids from fatty acid methyl esters using packed bed catalysis the determination of the kinetics of the enzymatic reaction is essential. In this particular case immobilized lipase is applied as catalyst. This contribution presents a method for obtaining the reaction kinetics of the enzymatic hydrolysis of octanoic acid methyl ester and compares modelled and experimental results. Keywords: Hydrolysis, methyl esters, enzyme, packed bed

1. Introduction The most commonly used process for the production of short chain fatty acids is the hydrolysis of fats to fatty acids and glycerol and a posterior fractionation of the fatty acids [1]. The process alternative discussed herein consists of the hydrolysis of the desired fractions of fatty acid methyl esters, which are often available in excess in industrial practice [2]. The hydrolysis of such compounds applying traditional chemistry requires the use of relatively high temperatures, which might thermally degrade the products, and strong acids or bases as catalysts, which comes along with many disadvantages like catalyst residues in the product. From biotechnology it is known that methyl ester hydrolysis can also be catalyzed enzymatically, which takes place at mild operating conditions with temperatures up to 70 °C. However, the description of such systems requires a detailed analysis of the involved mechanisms as well as the selection of the appropriate catalyst and experimental setup. The enzymatic conversion follows a complex ordered ping pong bibi reaction mechanism [3]. Although this mechanism provides the most accurate description of the enzymatic reaction the number of model parameters is relatively high. Hence, a quasi steady state assumption can be used to simplify the mechanism, whereas still eight parameters remain. Within this work the enzymatic conversion of octanoic acid methyl ester with water performed in a batch experimental recycle packed bed reactor was investigated. The reaction system consists of two liquid and one solid catalyst phase, in which one liquid phase is formed mainly by the methyl ester and the produced fatty acid and the other by water. Early descriptions of comparable systems in regard to the number of involved reaction phases and the experimental setup were done for the so-called phase transfer catalysis [4]. Satrio et al. [5] developed a rigorous model for the nucleophilic substitution. In their model the catalyst is in contact with both phases. No comparable

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analysis of a reaction setup including a biotechnological catalyst could be found in literature for the investigated system. One major point of research for adequate modeling is to determine where the reaction takes place and which parameters affect the reaction kinetics. In particular the kinetic constants of the forward and backward reactions of the single reaction steps were determined.

2. Experimental section 2.1. Experimental conditions and setup The objective of the modeling and experimentation is to describe a new reaction system. The parameters which can be influenced are the ratios of water to methyl ester and enzyme to substrate, temperature and flow rate. Given that the variables are not expected to have a linear influence on the process at least 3 levels or values for each parameter have to be experimented. This results in 81 experiments for a 3k experimental design. For a pre-assumed model, it is known which parameters have a significant influence, as well as which interactions are to be expected. It becomes therefore possible to neglect interdependences of the altered parameters in the system. Therefore the number of required experiments can be reduced to 27. The resulting set of experiments provides measurements at water mass fractions of 0.25, 0.50, and 0.75 at 30, 40 and 50 °C for 0.019, 0.038 and 0.057 m s-1 superficial velocity. The experiments were performed in a recycle packed bed reactor, which is schematically shown in Fig. 1. In either case the same catalyst bed was used to warrant constant reaction conditions. Activity tests using 0.05 w/w 1-octanol in octanoic acid methyl ester solution were performed in regular intervals in homogeneous liquid medium to consider possible catalyst deactivation. In this reaction octanoic acid methyl ester is transesterified to octanoic acid octyl ester and methanol, which can be assumed as an irreversible conversion in regard to the high excess of methyl ester and the fact that the hydrolysis of octanoic acid octyl ester is hardly catalyzed by Novozym 435® [6].

Figure 1. Recycle packed bed reactor arrangement. 1. Mixing vessel. 2. Thermostatic bath. 3. Peristaltic pump. 4. Packed bed reactor

2.2. Materials and sample analysis N-Octanoic acid methyl ester (ME) and demineralized water were used as reactants to produce n-octanoic acid (FA) and methanol. For sample analysis n-octanoic acid methyl ester, n-octanoic acid and methanol were utilized as standards. For testing the enzyme activity 1-octanol was applied. All chemicals were analytical grade. As catalyst Novozym 435® was used.

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After withdrawal from the mixing vessel reaction samples were centrifuged to obtain two clear phases, from which samples were taken for gas chromatographic analysis. Samples from activity tests were analyzed the same way except prior centrifugation.

3. Mathematical modeling 3.1. Reaction model The experimental reactor followed the requirements of a differential reactor, thus the recycle packed bed arrangement can be simulated as a stirred tank reactor [7]. Hence it is assumed, that the compositions of both phases always correspond to the liquid-liquid equilibrium state. External mass transfer limitations were not considered since the experimental data used for evaluation was attained at flow rates at which no influence on the reaction rate could be observed. Furthermore water is available in large molar excess throughout the entire reaction. Assuming the reaction takes place in the organic phase the dynamic behavior of the courses of the concentrations can be described by a set of differential and algebraic equations which have to be solved simultaneously. The considered model is presented in Eqs. (1) to (5). The reaction mechanism includes two steps. By making a steady state assumption for the intermediate product the mechanism can be simplified resulting in the kinetic approach shown in Eq. (1). org org org org org ª k 2 k1C ME º dC FA C water C FA − k − 2 k −1C methanol org = C enzyme, 0 « org org org org » dt ¬ k −1C methanol + k 2 C water + k1C ME + k − 2 C FA ¼

(1)

The kinetic parameters in Eq. (1) are described using the Arrhenius approach. Eq. (2) and (3) represent the methanol concentration in the aqueous and the organic phase obtained from mass balances. It is assumed that the solubility of methyl ester and fatty acid in the aqueous phase can be neglected. aq C methanol =

(

total C methanol

total Worg K Pmethanol

)

−1

(2)

+ Waqtotal

(

)(

org total aq total C methanol = C methanol − Waqtotal C methanol Worg

)

−1

(3)

The concentrations of water and methanol at the liquid-liquid equilibrium were described by empirical models, which correspond to Eqs. (4) and (5).

(

Org Org Org CWater = f C Fatty Acid , C Methanol , T

K PMethanol =

(

)

Aq C Methanol Org = f C Fatty Acid , T Org C Methanol

(4)

)

(5)

3.2. Computation procedure The developed algorithm optimizes the kinetic parameters by minimizing the sum of squares of the error between the results of the mathematical model and the experimental data. The highest hierarchy within the programmed structure corresponds to the minimization algorithm. For the minimization the pre-existing function fmincon from

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Matlab® was used. At this level an initial guess is required. In the second hierarchy the objective function is defined as the sum of square values of the difference between the mathematical model and the experimental data. The calculated concentrations of fatty acid come from the next level. Using experimental data operating parameters and boundary conditions for the numerical evaluation are obtained. At the next lower level the evaluation is divided between specific time points. These points are obtained from the time values that correspond to the evaluation of the experimental data. The numerical solution of the differential equations is thus obtained between two time points corresponding to times at which samples were taken. The differential equations are solved using a TR-BDF2 integration scheme [8]. Two of the three steps involved in the solution are implicit, leading to a stable result for moderately stiff systems [9]. This integration scheme was chosen due to instabilities of the more common explicit schemes at near equilibrium regions. 3.3. Computation Results By reason of the simplifications made in the presented model the kinetic parameters used for the simulation presented below were obtained from parts of the experiments performed. Fig. (2) shows examples of measured data compared with the corresponding curves obtained with the mathematical model.

Figure 2. Reaction courses at two different water contents

As can be seen from the curves and experimental data, the model represents the behaviour observed in the experiments with sufficient accuracy. For an analysis of the entire concentration range a better description of the liquid-liquid equilibrium is required, e.g. activity coefficients for all components have to be considered, which is due to the strongly non-ideal thermodynamic behaviour of the reacting mixture. The computational algorithm did converge to values within expected limits for all the parameters. This shows that the chosen approach was correct. However, further research of the experimental system is required before all values can be conclusive.

Reaction Kinetics of an Enzymatic Conversion in a Heterogeneous System

1085

4. Conclusions With the developed computational procedure all experimental data can be used to obtain the final parameters. The final result should, provided enough experimental data are taken, give reliable values of the kinetic parameters. The advantages can be thus summarized as a more robust estimation of kinetic parameters. The mathematical algorithm developed is designed to look for local optima, therefore making an adequate initial estimate indispensable to obtain correct results. Furthermore, the evaluation of the differential equations may become instable during the optimization algorithm for some initial values of the parameters. Both factors lead to the contribution of a scientist being crucial for the final results of the procedure.

5. Acknowledgements The authors thank Cognis GmbH (Duesseldorf, Germany) for the generous gift of octanoic acid methyl ester.

References [1] Anneken, D. J.; Both, S.; Christoph, R.; Fieg, G.; Steinberner, U.; Westfechtel, A.: Fatty Acids, Ullmann's Encyclopedia of Industrial Chemistry, Wiley-VCH, Germany 2006. [2] Fieg, G.; Schörken, U.; Both, S.; Mrozek, I..; Klein, N.; Weiss; A.; Yüksel, L.; Otto, R.; Meyer, C.: Method for producing C4-C12 fatty acids, WO/2003/095596, 2003. [3] Paiva, A. L.; Balcao, V. M.; Malcata, X.: Kinetics and Mechanisms of Reactions Catalyzed by Immobilized Lipases, Enz Microb Tech, 27, 187-204, 2000. [4] Ragaini, V.; Verzella, G.; Ghignone, A.; Colombo, G.: Fixed-bed reactors for phasetransfer catalysis. A study of a liquid-liquid-solid reaction, Ind Eng Chem Des Dev, 25, 878-855, 1986. [5] Satrio, J. A. B.; Glatzer, H. J.; Doraiswamy, L. K.: Triphase catalysis: a rigorous mechanistic model for nucleophilic substitution reactions based on a modified Langmuir-Hinshelwood/Eley-Rideal approach, Chem Eng Sci, 55, 5013-5033, 2002. [6] Mori, T.; Kishimoto, S.; Ijiro, K.; Kobayashi, A. Okahata, Y.: A lipid-coated lipase as an efficient hydrolytic catalyst in the two-phase aqueous-organic system, Biotech Eng, 76, 2, 157-163, 2001. [7] Perego, C.; Peratello, S.: Experimental methods in catalytic kinetics. Chem Eng Sci, 56, 1-27, 2001 [8] Bank, R. E.: Numerical Methods Using Matlab, Pearson Education, USA, 2004. [9] Hosea, M. E.; Shampine, L.F.: Analysis and implementation of TR-BDF2, Appl Num Math, 20, 21-37, 1996.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1087

An Integrated Ontology for Operational Processes Ri Hai, Manfred Theißen, Wolfgang Marquardt AVT - Process Systems Engineering, RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany, {Ri.Hai, Manfred.Theissen, Wolfgang.Marquardt}@avt.rwth-aachen.de

Abstract Representing the knowledge of engineering work processes such as design or operational processes explicitly is vital for sharing and reusing knowledge. “Process knowledge” and “product knowledge” are considered in this paper. Whereas process knowledge is about a work process itself, product knowledge deals with the products of a work process. OntoCAPE is an integrated ontology, which allows the explicit representation of product and process knowledge for both design and operational processes in chemical engineering. This paper focuses on OntoCAPE´s partial ontology for operational processes. The integration of the product ontology and the process ontology facilitates a comprehensive representation of all relevant aspects of operational processes. Keywords: ontology, operational representation, task ontology

process,

chemical

engineering,

knowledge

1. Introduction During the lifecycle of chemical products, different types of work processes are performed by experts from various disciplines. The knowledge involved can be grouped into two types. The first type, called process knowledge, deals with the work process itself and includes the required input for a certain activity, the intention of an activity, etc. The second type of knowledge, called product knowledge, is about the result of the work process, e.g., a process flow diagram in case of a design process or the expected states of chemical substances during an operational process. Note that the meanings of the terms product and process can vary according to the concrete context. For instance, one product of a design process in chemical engineering is the specification of an operational procedure; an operational procedure, however, is a special type of a work process which, in contrast to the design process, is of particular interest from an operational perspective. It is economically attractive to share and reuse the valuable knowledge of engineering work processes. To this end, an ontology, i.e., a formal and explicit specification of a shared conceptualization, can play a significant role (Gruber, 1993). Task ontologies and domain ontologies are two important types of ontologies. Whereas a domain ontology deals with the factual, static knowledge of a given domain, a task ontology contains the knowledge about general problem-solving methods that can be applied in different contexts (van Heijst et al., 1997; Guarino, 1997). Separating the domain ontology from the task ontology permits to reuse domain knowledge across multiple tasks and to reuse task knowledge across several domains (Guarino, 1997). However, the efficient (re)use of a task ontology in a given domain across multiple applications

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requires the enrichment of generic task specifications with domain-dependent concepts (cf. Gómez-Pérez et al., 2004 ). We have developed a comprehensive domain ontology, called OntoCAPE, which originally only covered product knowledge of design processes in chemical engineering. More recently, OntoCAPE has been extended with process knowledge and it now covers domain knowledge as well as knowledge about generic and domain tasks. Two representative types of work processes are considered, i.e., design processes and operational processes. Both can be represented under a functional and a behavioral aspect. OntoCAPE is described in detail by Morbach et al. (2007). The following description focuses on the partial ontology for operational processes.

2. OntoCAPE - the Integrated Ontology OntoCAPE is implemented in the Web Ontology Language OWL (W3C, 2004), a formal language for knowledge representation. This section begins with a brief overview of OntoCAPE, followed by the introduction of concepts for representing work processes and generic tasks, as well as their further specification for operational processes. 2.1. An Overview of OntoCAPE The overall structure of OntoCAPE is given in Fig. 1. OntoCAPE is organized by layers which subdivide the overall ontology into different levels of abstraction. The Meta_model on the topmost Meta Layer introduces fundamental modeling concepts and states the design guidelines for the construction of the actual ontology. Further, the Upper Layer of OntoCAPE defines the principles of general systems theory according to which the ontology is organized. The fundamental concepts for work processes and for generic tasks are also introduced in this layer. Next, on the Conceptual Layer, different areas such as unit operations, plants, chemical process behavior as well as modeling concepts for operational processes are covered. Further, the Application-oriented Layer generically extends the ontology towards certain application areas, whereas the Application-specific Layer provides specialized classes and relations for concrete applications. Notation:

Meta Model Meta Layer

Meta_model

include

Module

OntoCAPE Upper_level System

Upper Layer

Suggested_ generic_WP

Work_process (WP)

Chemical_process_system (CPS)

Operational_process (OP)

CPS_realization Plant

Conceptual Layer Applicationoriented Layer Applicationspecific Layer

OP_function

Suggested_OP OP_behavior

Plant_equipment Fixture Applications Aspen_plus_model

Fig. 1: Overall structure of OntoCAPE

Batch_plus_model

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2.2. Work Processes Work processes are characterized under two different aspects (Fig. 2). Under the functional aspect, a work process is specified by its desired function, e.g., TemperatureChange in case of an operational process. Under the behavioral aspect, a work process can be represented in terms of sub-processes and their interrelations (e.g. sequence, iteration). To this end, modeling concepts such as Activity, Information, ControlFlow or InformationFlow are defined (Eggersmann et al., 2008). An activity within a work process can be described by a work process containing the sub-activities. This enables the decomposition of work processes. Work_process Notation:

isDescribedBy

Activity

contains

Suggested_ generic_WP

WorkProcessModel

hasBehavioral Aspect

WorkProcess

hasFunctional WorkProcessFunction Aspect

Operational_process_function

Generic_WP_function

OPFunction TemperatureChange

specialization relation

MixtureSeparation Diagnosis Process

Module_name module

Diagnosis

Plan

instantiation

Fig. 2: Modules Work_process, Suggested_generic_ WP, Operational_process_function, and Generic_WP_function (simplified)

2.3. Generic Task and Suggested Generic Work Processes In the literature, a task is defined according to the types of problem solving goals (Chandrasekaran et al., 1992). For example, the goal of a diagnosis task is to find explanations for abnormal observations. This definition of tasks is consistent with the “function” defined for work processes in our work. The corresponding concepts are defined in the partial module Generic_WP_function (Fig. 2). A task can be achieved by various methods, each of which may have some input, output and a list of subtasks (Chandrasekaran et al., 1992; Benjamins, 1995). In this sense, methods can be represented as work processes. Several libraries of generic tasks with the associated methods are given (e.g., Benjamins, 1995). In order to benefit from these libraries, we define the methods used in generic tasks as suggested generic work processes in Suggested_generic_WP. The generic work processes and their sub-processes are defined on the instance level, because OWL does not allow representing networks of interrelated elements (e.g., a work process containing interrelated activities) on the class level. These suggested generic work processes can be used as guidelines when conducting a corresponding work process. Additional alternatives to implement a function (e.g., best practice) can also be included in this partial model when necessary. 2.4. Operational Process An operational process can be considered as a work process conducted by a process control system or by human operators who act on a piece of equipment to achieve predefined functions. Consequently, the modeling concepts for both, the equipment involved and the desired functions are inevitable for representing operational processes. Concepts for plant equipment are defined on the product side of OntoCAPE (cf. Fig. 1). Typical functions of operational processes such as TemperatureChange or MixtureSeparation (Fig. 2) are defined on different levels of granularity. In this work, part of the well established IEC 61512 standard (IEC, 1997) has been adopted to describe the operation of batch processes in a structured manner. For example, operational processes are decomposed into Procedures, Operations, and Phases. Similarly, a plant is decomposed into Units, EquipmentModules, and Control-Modules.

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Relations between functional steps and pieces of equipment are also given on different levels of granularity. These structures are not depicted in Figure 2 for clarity. Besides the “common” functions, a real operational process also covers other functions including process monitoring or diagnosis of unexpected situations. Usually, the operators apply generic problem solving methods (i.e. one of the suggested generic work processes) to solve specific problems. To this end, the generic work processes need to be specified for operational processes. Suggested generic work processes Diagnosis ProcessModel

hasBehavioral Aspect

contains contains

Symptom Detection

Diagnosis Process

Suggested operational processes isA KindOf

FaultDiagnosis Process

contains

contains

...

Generate Hypothesis

hasInputhasOutput hasInput hasOutput

Observation

Symptom

hasBehavioral Aspect

HypothesisSet

FaultDiagnosis ProcessModel contains contains

OPSymptom Detection

Generate ProbableCause

hasInput hasOutput

hasInput hasOutput

MeasuredValue

AbnormalValue

...

ProbableCause

Fig. 3: An example for specifying the DiagnosisProcess

Obviously, not all generic work processes are relevant to a given domain. Therefore, an analysis of typical operational processes is needed to find out which generic work processes are appropriate for operational processes. For instance, a DiagnosisProcess can be used to support a FaultDiagnosisProcess during process operation since both share common features such as finding explanations for observations. Therefore, the FaultDiagnosisProcess isAKindOf DiagnosisProcess (Fig. 3). A simplified example for specifying a DiagnosisProcess for process operation is depicted in Figure 3. It is achieved by decomposing the FaultDiagnosisProcess in analogy to the structure of the generic DiagnosisProcess and mapping the product knowledge to the corresponding activities. For instance, MeasuredValue is mapped onto Observation; AbnormalValue is mapped onto Symptom. This way, the existing process knowledge and product knowledge are integrated and can be used to facilitate the FaultDiagnosisProcess. The partial ontology covering the FaultDiagnosisProcess and other specified operational processes is an important part of the process ontology, since they contain knowledge about domain tasks. All the specified operational processes are included in the module Suggested_OP (cf. Fig. 1).

3. Related work Numerous approaches have been reported to represent operational processes. They can be divided into three groups: (1) Some approaches do not consider domain task knowledge (e.g., Gabbar et al., 2004). (2) Approaches for knowledge-based systems cover both process and product knowledge, but most of them are merely for very special tasks, e.g., fault diagnosis. A review is given by Angeli (2008). (3) The last group includes approaches which consider both process and product knowledge for operational processes (as in this work). To our knowledge, only the research by Mizoguchi et al. (1992) belongs to this group. In this approach, the specified tasks (i.e., functions in our approach) related to operational process are introduced, but no generic tasks are defined.

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4. Conclusion and Outlook We have pointed out that product and process knowledge are two essential types of knowledge about engineering work processes. OntoCAPE is an integrated ontology covering both knowledge types. It enables to describe work processes – and operational processes in particular – under a functional and a behavioral aspect. The advantages of our approach are the following. (1) We use only one ontology to facilitate multiple applications. OntoCAPE can be used to model work processes, to support the document exchange between different software tools, etc. (2) We use only one ontology for different types of work processes. Introducing generic tasks and specifying them for specific work processes within one domain promotes reusability. Currently, generic tasks and their specification are still under development. Other important generic tasks such as scheduling, monitoring, or design tasks need to be considered. Moreover, the reusability of the generic tasks for various work processes needs to be further investigated. For this purpose, the representation of design processes in chemical engineering is currently under investigation.

5. Acknowledgements The authors acknowledge financial support from the German National Science Foundation (DFG) under grant MA 1188/29-1.

References C. Angeli, 2008, Online expert systems for fault diagnosis in technical processes, Expert. Syst., 25, 2, 115-132. R. Benjamins, 1995, Problem-solving methods for diagnosis and their role in knowledge acquisition, Int. J. Expert. Syst., 8, 2, 93-120 B. Chandrasekaran, T.R. Johnson, J.W. Smith, 1992, Task-structure analysis for knowledge modeling, Commun. ACM, 35, 9, 124-137. M. Eggersmann, B. Kausch, H. Luczak, W. Marquardt, C. Schlick, N. Schneider, R. Schneider, M. Theißen, 2008, Work process models, Collaborative and Distributed Chemical Engineering, LNCS 4970, Springer Berlin / Heidelberg, 126-152. H.A. Gabbar, A. Aoyama, Y. Naka, 2004, Model-based computer-aided design environment for operational design, Comput. Ind. Eng., 46, 3, 413-430. A. Gómez-Pérez, M. Fernández-López, O. Corcho, 2004, Ontological Engineering. Springer, Berlin. T.R. Gruber, 1993, A translation approach to portable ontology specifications, Knowl. Acquls., 5, 2, 199-220. N. Guarino, 1997, Understanding, building and using ontologies, Int. J. Hum.-Comput. St., 46, 23, 293-310. G. van Heijst, A.T. Schreiber, B.J. Wielinga, 1997, Using explicit ontologies in KBS development, Int. J. Hum.-Comput. St., 46, 2-3, 183-292. IEC– International Electrotechnical Commission, 1997, IEC 61512-1: Batch control – Part 1: Models and terminology. R. Mizoguchi, K. Kozaki, T. Sano, Y. Kitamura, 2000, Construction and deployment of a plant ontology, Knowledge Engineering and Knowledge Management, LNAI 1937, Spring-Verlag, 113-128. J. Morbach, A.D. Yang, W. Marquardt, 2007, OntoCAPE – A large scale ontology for chemical process engineering, Eng. Appl. Artif. Intel., 20, 2, 147-161. W3C– World Wide Web Consortium, 2004, OWL Web Ontology Language Reference. W3C Recommendation, online available at http://www.w3.org/TR/owl-ref/.

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Bulk Video Imaging for Nucleation Detection and Metastable Zone Determination of Pharmaceutical and Food Crystallization Processes Levente L. Simona, Zoltan K. Nagyb, Konrad Hungerbuehlera a

ETH Zurich, Institute of Chemical and Bioengineering, W. Pauli str. 10, Zurich 8093, Switzerland, [email protected], [email protected] b Loughborough University, Chemical Engineering Department, Loughborough, LE11 3TU, England, [email protected]

Abstract This work presents the comparison of bulk video imaging (BVI) approach with the focused beam reflectance measurement (FBRM) and ultra violet/visible spectroscopy. The BVI concept is presented on the caffeine and palm oil crystallization processes and it is shown that BVI is able to detect the nucleation onset with performance comparable to the other two sensors. Keywords: crystallization, FBRM, UV/Vis, video imaging, digital image

1. Introduction Metastable zone identification is the first step during the design of crystallization systems which provides important information that can be used to ensure reproducible crystal characteristics. The metastable zone width (MSZW) changes in function of several system characteristics such as: cooling rate, degree of stirring, solution history and presence of foreign particles with undesirable or desirable effects (impurities or additives). The accurate determination of the metastable zone allows improved supersaturation control policies, it helps to avoid secondary nucleation, ensures maximal productivity and the desired particle size distribution (PSD) at the end of the batch. The experimental determination of the MSZW is performed by heating and cooling the suspension at a constant rate until the clear point (solubility) and cloud point (nucleation phenomenon) are observed. In order to determine the MSZW several sensors have been used: turbidity [1], focused beam reflectance measurement (FBRM) [2, 3], spectroscopy [2, 3], ultrasonic velocity measurements [4], density [5] and electrical conductivity monitoring [6], hot stage microscopy [7], quartz crystal based monitoring [8], and by visual inspection [9] of the crystallizer content. The detection of the first nucleation events is a function of the used sensor, e.g. Fujiwara et al. [3] concluded that for the paracetamol system the FBRM provided the highest sensitivity towards nucleation detection, followed by the attenuated total reflection (ATR) – Fourier transform infrared (FTIR) spectroscopy and visual inspection. Marciniak compared the density, ultrasonic velocity and transparency signals for the MSZW identification of the fluoranthene in trichloroethylene [5]. The author concluded that the solution transparency was the most sensitive method. Calderon de Anda et al. observed that the fiber optic turbidity probe shows a time lag in detecting the onset of the nucleation [10]. Furthermore, Dharmayat et al. has confirmed the fact that the video microscopy based sensor is able to detect the polymorphic phase transition of the L-

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glutamic acid with as much as 30 minutes faster than the X-ray diffraction sensor (XRD) [11].

2. Problem statement Some of the measurement techniques detect the nucleation event directly by sensing the newly formed nuclei, e.g. FBRM and particle video monitoring (PVM) systems. In the case of these sensors in order to obtain a meaningful crystal the particles must be large enough to be detectable, they must cross the detection volume, and they need to be in high enough concentration to provide a significant number of measurements. The probability that the first nucleus passes the detection volume decreases as the crystallizer volume increases. The advantage of the FBRM and PVM type sensors is that these measure nucleation events (new particles) and not the property of the crystallizer bulk, and the signal and information provided by these instruments may provide detailed information related to shape, and size of individual particles and the size (chord length) distribution in various size bins. However the validity of the information will strongly depend on the assumption of well mixed system.

3. The BVI method Experimental setup and image processing strategies In this article we compare the FBRM, UV/Vis spectroscopy and bulk video imaging (BVI) for metastable zone identification and to detect the nucleation phenomenon. The studied crystallization systems are the caffeine and palm oil. Based on the BVI concept the liquid bulk is monitored using an external video camera. The experimental setup is located in the Pharmaceutical Systems Engineering Laboratory at Loughborough University (Figure 1).

Figure 1. Schematic representation of the experimental equipment.

The video data is processed using two strategies: robust and sensitive image processing. Based on the first strategy the average grey intensity value is calculated for each interrogation window cut out from the frames. The latter approach is based on several digital image processing algorithms and it aims to identify the first detectable crystal.

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The image processing steps are as follows: background subtraction using a moving window (size 2), thresholding, noise reduction using morphological operations, object identification and decision on the crystal presence.

4. Results & discussions The comparison of the BVI approach with the FBRM data for the caffeine (cooling rate 0.5 °C/min) is presented in Figure 2. The results show that the BVI and the FBRM probe detect the nucleation with comparable performance. 70

Crystallizer temperature [C] Set point temperature [C] 1000x # counts [-], range: 1-5.012 μ, no weight 1000x # counts [-], range: 1-1000 μ, no weight Grey average intensity [-]

60 50 40 30 20 10 0 0

50

100

150

200

250

300

Time [min]

Figure 2. Caffeine crystallization monitoring using the BVI and the FBRM data.

The comparison of the BVI approach with the UV/Vis data for the same crystallization system is presented in Figure 3. These results show that the BVI approach is comparable with the detection capability of the UV/Vis spectroscopy method. In both figures it can be noticed that the average grey intensity values have low noise level during the phase when all the crystals are dissolved.

120 110 100 90 80 70 60

Crystallizer temperature [C] Set point temperature [C] 1000 x UV Absorbance @ 274 nm [-] Grey average intensity [-]

50 40 30 20 10 0 66

70

74

78

82

86

90

94

98

102 106 110 114 118 122 126 130

Time [min]

Figure 3. Caffeine crystallization monitoring using the BVI and UV/Vis spectroscopy.

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The results obtained for the palm oil system are presented in Figure 4.

80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 180

Crystallizer temperature [C] Set point temperature [C] 200x # counts [-], range: 1-5.012 μ, no weight 200x # counts [-], range: 1-1000 μ, no weight Grey average intensity [-]

Nucleation point by BVI

185

190

Nucleation point by FBRM

195

200

205

210

215

220

225

230

235

240

Time [min]

Figure 4. Palm oil crystallization monitoring using the BVI and the FBRM data (2 °C/min cooling ramp).

The data acquired during this experiment shows that the BVI approach is able to detect the nucleation onset much sooner (15 min) than the FBRM probe. This is due to the fact that during the fast cooling of palm oil a large number of small crystals form, which are below the detection limit of the FBRM. These crystals are very large in number and provide a cloud formation in the bulk which can be detected by the BVI. Despite the visually observable cloudiness of the solution, the FBRM only detects nucleation after the large number of particles grew to the detectable size (about 0.5-1 micron). The faster the cooling rate is the smaller the crystals forming at nucleation are and the larger the delay between the moment when BVI and FBRM detect the nucleation events is. One of the main advantages of the BVI approach is that is a non-contact probe, can be installed externally (measurement through the observation window) and hence there are no contamination issues, which can be important in the food and pharmaceutical industries. Also being a bulk monitoring device it shows significantly lower sensitivity to the mixing conditions. The palm oil system for example becomes highly viscous shortly after nucleation, when measurements from FBRM are not reliable anymore, since it is not guaranteed that a representative sample reaches the measurement volume of the probe. The crystal detection capabilities provided by the digital image processing solution are shown in Figure 5 where it can be observed that the algorithm is able to detect the first crystal present in the liquid. This method provides great potential for early nucleation detection, for example in direct nucleation control schemes.

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Figure 5. Crystal detection using digital image processing technologies.

5. Conclusions In this work we have presented the proof of concept for the bulk video imaging (BVI) approach. It was shown that BVI has comparable performance in detecting the nucleation onset to the FBRM and UV/Vis probes. The BVI approach is proposed as a complementary approach to the existing process analytical monitoring methods, which can be mounted as an external sensor providing also significantly lower sensitivity to mixing conditions than other probes based on local measurements.

6. Acknowledgements The authors would like to acknowledge the help provided by E. Aamir, A. N. Saleemi and Dr. K. Patchigolla during the experimental work carried out at the Chemical Engineering department, Loughborough University, U.K. The second author acknowledges the financial support provided by the Engineering and Physical Sciences Research Council (EPSRC), U.K., (grant EP/E022294/1).

References [1] A. R. Parsons, S. N. Black, R. Colling, Chem. Eng. Res. Des., 81 (2003) 700. [2] D. O'Grady, M. Barrett, E. Casey, B. Glennon, Chem. Eng. Res. Des., 85 (2007) 945. [3] M. Fujiwara, P. S. Chow, D. L. Ma, R. D. Braatz, Cryst. Growth Des., 2 (2002) 363. [4] H. Gurbuz, B. Ozdemir, J. Cryst. Growth, 252 (2003) 343. [5] B. Marciniak, J. Cryst. Growth, 236 (2002) 347. [6] N. Lyczko, F. Espitalier, O. Louisnard, J. Schwartzentruber, Chem. Eng. J., 86 (2002) 233. [7] F. J. Kumar, S. G. Moorthy, D. Jayaraman, C. Subramanian, J. Cryst. Growth, 160 (1996) 129. [8] O. J. Joung, Y. H. Kim, K. Fukui, Sensors and Actuators B-Chemical, 105 (2005) 464. [9] O. Sohnel, J. W. Mullin, Chem. Eng. Res. Des., 66 (1988) 537. [10] J. C. De Anda, X. Z. Wang, X. Lai, K. J. Roberts, K. H. Jennings, M. J. Wilkinson, D. Watson, D. Roberts, AIChE J., 51 (2005) 1406. [11] S. Dharmayat, J. C. De Anda, R. B. Hammond, X. J. Lai, K. J. Roberts, X. Z. Wang, J. Cryst. Growth, 294 (2006) 35. [12]

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Design of environmentally friendly absorption cooling systems via multi-objective optimization and life cycle assessment Berhane H. Gebreslassiea, Gonzalo Guillén-Gosálbezb,Laureano Jiménezb and Dieter Boera a Department of Mechanical Engineering, University Rovira i Virgili b Department of Chemical Engineering, University Rovira i Virgili Av. Països Catalans, 26, 43007-Tarragona, Spain, [email protected]

Abstract This paper proposes a systematic approach for the design of environmentally conscious absorption cooling systems. The method presented relies on the development of a mathematical formulation that simultaneously accounts for the minimization of total cost and environmental impact at the design stage. The latter criterion is measured by the Eco-Indicator 99 methodology, which follows the principles of Life Cycle Assessment (LCA). The design task is formulated as a bi-criteria nonlinear programming (NLP) problem, the solution of which is defined by a set of Pareto points that represent the optimal trade-off between the two objective functions. The capabilities of the proposed method are illustrated in a case study problem that addresses the design of a typical absorption cooling system. Keywords: Absorption refrigeration, Multi-objective optimization, Life cycle assessment (LCA), Ammonia-water

1. Introduction In the last years, the air conditioning market has been growing very strongly, being most of the installed units still based on the mechanical vapor compression systems driven by electrical motors. As consequence, the electrical demand has been rising, which worsens the generation and distribution of electricity, along with the associated environmental burdens. In this challenging scenario, absorption refrigeration is gaining popularity in the air conditioning system, as they use refrigerants with zero global warming potential and do not contribute to ozone depletion. Absorption refrigeration systems use heat sources as energy input in order to produce cooling. The heat sources may be fossil fuel, renewable energy resources or even waste heat, which may be recovered from other thermal systems [1]. Unfortunately, despite their significant environmental benefits, their deployment in the market has been rather limited. The objective of this work is to provide a systematic method for the optimal design of environmentally conscious absorption cooling systems based on the combined use of life cycle assessment (LCA) and mathematical programming [2]. The methodology presented is intended to promote a more sustainable design of absorption cooling cycles. The capabilities of our method are illustrated using a typical absorption cycle.

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2. Problem statement We address the optimal design of absorption cooling cycles considering both, economic and environmental concerns. Given data are the cooling capacity of the system, the inlet and outlet temperatures of the external fluids, capital and operating cost data, and LCA related information (i.e. life cycle inventory of emissions and feed stock requirements, and parameters of the damage model). The goal is to determine the optimal design and associated operating conditions that simultaneously minimize the total annualized cost and environmental impacts.

Figure 1. Ammonia-water absorption cycle.

3. System description Figure 1 represents the absorption cycle in P-T plot. The system provides chilled water for cooling applications. The basic components are the absorber (A), condenser (C), desorber (D) and evaporator (E). The cycle also includes the refrigerant subcooler (SC), refrigerant expansion valve (RV), solution heat exchanger (SHX), solution pump (P), and solution expansion valve (SV). The high pressure equipments are the solution heat exchanger, desorber, and condenser, whereas the low pressure ones are the evaporator and absorber.

4. Mathematical formulation The mathematical formulation of the problem is next described in detail. 4.1. Variables The variables of the problem represent the temperatures of the flow streams, the high and low pressure levels, the areas of the heat exchangers, the minimum temperature differences, the concentration of the mixtures, the damage caused in each environmental impact category and the operational and capital costs.

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4.2. General constraints Our formulation includes some general constraints that impose limits on the working temperature as well as the temperature differences at the heat exchangers. Specifically, the model considers plate and frame heat exchangers and fixed overall heat transfer coefficients. 4.3. Mathematical model A computer code for simulating the cycle is developed using the generic algebraic modeling system (GAMS). The mathematical formulation takes the form of a bi-criteria nonlinear programming (NLP) problem, the solution of which comprises a set of tradeoff alternatives. The model of the absorption cycle is based on energy and materials balance that ensure the mass and energy conservation. These principles are applied to each unit of the cycle. Properties are estimated using correlations from Pátek et al. [3]. 4.4. Objective functions The model previously presented must attain two different targets: minimum total annualized cost and environmental impact. 4.4.1. Economic objective function The total annualized cost of the system, which is denoted by TC, includes the capital and operating costs (Cc and Cop, respectively). TC = C

c

+ C

(1)

op

The capital cost includes the cost of the heat exchangers, pumps and expansion valves, whereas the total operational cost includes the cost of the steam used in the desorber and the electricity consumed by the pump. 4.4.2. Environmental impact assessment based on LCA Our work follows the general LCA methodology, which comprises four steps: goal and scope definition, inventory analysis, impact assessment and interpretation. The environmental performance of the cycle is measured by the Eco-Indicator 99 [4]. Specifically, the life cycle inventory associated with each chemical b is calculated using eq. (2), and considering the emissions released in the generation of steam and electricity, which are both retrieved from the ecoinvent database. The damage in each impact category is calculated via eq. (3). Here, DMbi is the damage coefficient associated with impact category i and chemical b. These impacts are further translated into a set of damage categories (DAMd) caused to the environment by using eq. (4). Finally, the impacts in each damage category (human health, ecosystem quality and resources) are aggregated into a single metric (i.e. Eco-Indicator 99, ECO99). In our work, the Eco-Indicator 99 is determined based on the Hierarchist perspective and average weighting factors using eq. (5), in which nd and wd are given parameters. electricity LCIb = LCI steam + LCI = ms isb +W p ieb b b

∀b

(2)

B.H. Gebreslassiea et al.

1102

DAM

EC O

¦ b

=

IM P i

d

99

=

∀ i

D M bi L C Ib

¦ IM Pi i ∈ ID ( d )

= ¦ n d w d D AM d d

∀d

∀d

(3)

(4)

(5)

5. Solution method The ε-constraint method is employed in this work to calculate the Pareto solutions of the bi-criteria NLP problem. This method is based on formulating an auxiliary model, which is obtained by transferring one of the objective functions to an additional constraint. This model is then solved for different values of an auxiliary parameter ε, each of which provides a different Pareto solution to the problem. Each of these solutions represents an alternative process design, with a unique combination of environmental and economic performances.

6. Case study The capabilities of our approach are illustrated through a case study that addresses the design of a typical absorption cooling system. The system is driven by low grade heat and utilizes ammonia-water as working pair. 6.1. Result and discussions A bi-criteria nonlinear programming (NLP) simulation model was implemented in GAMS. The resulting optimization problem contains 206 continuous variables and 165 constraints. Each single iteration of the epsilon constraint method was solved with CONOPT. The Pareto points obtained by following this strategy are shown in Figure 2.

Figure 2. (a) Pareto solutions; (b) Breakdown of Eco-Indicator 99 in Pareto solutions A, B, and C.

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As shown in Figure 2a, there is a clear trade-off between both objective functions, since a reduction in the Eco-indicator 99 value can only be achieved at the expense of an increase in the total annualized cost. Points A and B are the optimal design solutions with minimum Eco-Indicator 99 and total annualized cost values, respectively. In the optimal solution A, the total cost is 25.9 % larger than in solution B, whereas in B, the Eco-Indicator 99 is 5.5% larger than in A. Point C represents a possible intermediate Pareto optimal solution in the middle of the extreme solutions. Note that each point in the Pareto set represents a different optimal design which operates under a set of specific conditions. The environmental impact is decreased along the Pareto curve by reducing the consumption of energy, which in turn decreases the environmental loads and, hence, the impact caused. This is accomplished by increasing the area of the heat exchangers of the cycle. Finally, Figure 2b shows a breakdown of the Eco-indicator 99 value into its single impact categories for the Pareto solutions A, B, and C. As can be seen, the most significant environmental impact is the depletion of natural resources (impact 11) followed by the damage to the ecosystem quality caused by ecotoxic emissions (impact 7). The third and fourth damages are the respiratory effects on human health caused by inorganic substance (impact 3) and the damage to human health caused by climate change (impact 4), respectively.

7. Conclusions A systematic approach for the design of sustainable absorption cooling systems has been presented. The method introduced relies on formulating a bi-criteria nonlinear programming (NLP) problem that accounts for the minimization of the total annualized cost and the environmental impact of the cycle. The latter criterion has been measured according to the principles of life cycle assessment (LCA). It has been clearly shown that significant reductions in the environmental impact caused by the cycle can be attained at a marginal increase in cost. The tool presented in intended to promote a more sustainable design of absorption cooling systems.

8. Acknowledgements B. H. Gebreslassie expresses his gratitude for the financial support received from the University Rovira i Virgili. Financial support received from the Spanish “Ministerio de Educación y Ciencia” (projects DPI2008-04099, PHB2008-0090-PC and BFU200800196) and the Spanish “Ministerio de Asuntos Exteriores” (projects A/8502/07, HS2007-0006 and A/020104/08) is also fully appreciated.

References [1] Herold, K., R. Radermacher, and K. SA, Absorption chillers and heat pumps. 1996, Boca Raton, Florida, USA: CRC Press. [2] Guillén-Gosálbez, G, Caballero J.A, Jimenez L, and Gadalla M. Application of life cycle assessment to the structural optimization of process flowsheets, in Computer Aided Chemical Engineering. 2007, Elsevier. 1163-1168. [3] Pátek, J. and J. Klomfar, Simple functions for fast calculations of selected thermodynamic properties of the ammonia-water system. International Journal of Refrigeration, 1995. 18(4) [4] PRé consultants, A., The Netherlands, The Eco-indicator 99, A damage oriented method for life cycle impact assesment and manual for designers. 2000.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Environmental Sustainability Normalization of Industrial Processes Ángel Irabien,a Rubén Aldaco,a Antonio Dominguez-Ramosa a

Universidad de Cantabria, Ingenieria Quimica y Quimica Inorgánica, Avda de los Castros s/n, Santander, 39005, Spain, E-mail:[email protected]

Abstract Sustainability indexes or indicators may be considered objective functions for industrial processes. They are based on different considerations; AIChE sustainability index [1] is based on seven components: Environmental Performance, Safety Performance, Product Stewardship, Social Responsibility, Value-Chain Management, Strategic Commitment and Sustainability Innovation; the Sustainable Development Progress Metrics developed by IChemE is based on three components: Environmental indicators, Economic indicators and Social indicators [2], but in all cases environmental variables play an important role in the sustainability evaluation. The Environmental Sustainability is based on two different variables: (1) Natural Resources Sustainability (NRS), and (2) Environmental Burdens Sustainability (EBS). The main components of EBS have been classified as atmospheric pollutants, water pollutants, soil pollutants and a fourth group including specific environmental burdens such as noise, etc. In this work normalization procedures for the environmental sustainability will be developed in order to get suitable objective functions for process optimization. Keywords: Normalization, Sustainability, Environmental impacts, LCA, Environmental Burdens

1. Introduction The competition on the chemical market has increased during the past decades and among the problems that the chemical and process industry has to face, the following can be mentioned: a) Many chemical plants for the production of bulk products were built based on a large margin of benefits; b) The globalization results in a great competitive pressure, on the operating companies. c) E-commerce based on the globalization leads to an increasing efficiency in the world market. Therefore, to be still competitive, most existing production processes need constant improvement through retrofitting while new processes need to satisfy stricter governmental regulations with concerns to pollution and social demands based on Corporate Social Responsibility (CSR). CSR (also called corporate responsibility, corporate citizenship, responsible business and corporate social opportunity) is a concept whereby organizations consider the interests of society by taking responsibility for the impact of their activities on customers, suppliers, employees, shareholders, communities and other stakeholders, as well as the environment.

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Á . Irabien et al.

One of the main challenges related to the environmental sustainability evaluation of industrial processes lies on the quantitative estimation of the environmental burdens, the normalization procedures and the impact evaluation. In order to compare results of different alternatives Life Cycle Assessment (LCA) has been assumed as the main technique, but it is very difficult to find normalization procedures to evaluate and compare different environmental impacts. Taking into account the Integrated Pollution Prevention Control (IPPC) policy [3] and the Integrated Product Policy (IPP) developed in the European Union, which includes a public information system based on the European Pollutants Release and TransferRegister (EPRT-R) [4] an initial classification and quantitative technical evaluation of the pollutants of concern has been considered for normalization purposes. Following these references; as first step a general normalized multi-objective function based on atmospheric pollutants, water pollutants, soil pollutants and transferred pollutants can be defined for environmental sustainability evaluation of the industrial chemical processes, which can be used for global LCA [5]. Increasing productivity based on the reduction of materials, water and energy consumption, leading to decrease the emissions the effluents and the industrial wastes all represent conditions (or constraints), which can be formulated as mathematical optimization problems. They also, formulate the conditions for a more sustainable process, which has been formulated for chemical transformations [6]. For many complex processing-systems, the techniques needed to solve these optimization problems may be time consuming or may even fail to give a solution. Also, for large and complex applications to chemical or biochemical processes, even when the problem is well defined and is solvable, there is no guarantee that the solution is the global optimum. Usually, the obtained solution is a trade-off between many of the above contradictory constraints (or conditions) as they may point towards opposite directions with respect to the performance criteria. The objective of this paper is to present a new generic and systematic methodology based on the European IPPC and IPP criteria in order to develop an objective function allowing the normalization procedure to different environmental constraints, related to the environmental sustainability.

2. Environmental Sustainability Variables Environmental Protection Agencies have been able to develop evaluation procedures, for example US EPA as part of their WAR algorithm [7]. The Institution of Chemical Engineers-UK has introduced for chemical process industries, the sustainability metrics to help engineers to address the issue of sustainable development. They also enable manufacturing companies to set targets and to monitor progress on a yearly basis. A lower metric indicates that either the impact of the process is less or the output of the process is more. In this work, the environmental sustainability metrics as proposed by the IChemE has been employed. From an environmental sustainability evaluation point of view, two main variables: X1, Natural Resources Sustainability (NRS) and X2, Environmental Burdens Sustainability (EBS) has been selected. These metrics should give a balanced view of the environmental impact of inputs– resource usage, and outputs– emissions, effluents and wastes and the products and services produced. Natural Resources Sustainability is based on the evaluation of four main variables: X1,1 Energy, X1,2 Material (excluding fuel and water), X1,3 Water, and X1,4 Land. These variables are related to economical considerations depending on the different markets.

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Environmental Burdens Sustainability, X2 is a very complex variable because an important number of chemical substances need to be taken into account. From a technical point of view: emissions, effluents and wastes have to be considered. The environmental impact categories chosen are a sub-set of those used internationally in environmental management, selected to focus on areas where the process industry’s activities are most significant. The environmental burden approach is a scientifically sound way to quantify environmental performance. It draws on developments in environmental science to estimate potential environmental impact, rather than merely stating quantities of material discharged. The Environmental Burden (EB) caused by the emission of a range of substances, is calculated by adding up the weighted emission of each substance. The weighting factor is known as the “potency factor”:

EBi = ¦WN ·PFi , N

(1)

where EBi = ith environmental burden, WN = weight of substance N emitted, including accidental and unintentional emissions, PFi,N = potency factor of substance N for ith environmental burden. Related to these variables an atmospheric impact X2,1 based on the emissions, an aquatic impact X2,2 based on the effluents and a land impact X2,3 based on the wastes can be assumed. The atmospheric impact can be related to five main environmental impacts: X2,1,1 Atmospheric acidification. EB is te/y sulphur dioxide equivalent; X2,1,2 Global warming. EB is te/y carbon dioxide equivalent; X2,1,3 Human health (carcinogenic) effects. EB is te/y benzene equivalent; X2,1,4 Stratospheric ozone depletion. EB is te/y CFC-11 equivalent; X2,1,5 Photochemical ozone (smog) formation. EB is te/y ethylene equivalent. The aquatic impact can be related to four environmental impacts: X2,2,1 Aquatic acidification. EB is te/y of released H+ ions; X2,2,2 Aquatic oxygen demand. EB is te/y oxygen; X2,2,3 Ecotoxity to aquatic life. EB is (i) X2,2,3,1 te/y copper equivalent, and (ii) X2,2,3,2 te/y formaldehyde equivalent; X2,2,4 Eutrophication. EB is te/y phosphate equivalent. The impacts to land can be described by: X2,3,1 Total Hazardous Solid Waste Disposal (where fourteen different hazardous characteristics, H1…H14 need to be considered) and X2,3,2 Total Non-Hazardous Solid Waste Disposal. 2.1. Normalization Procedure The E-PRTR Regulation [8] establishes an integrated pollutant release and transfer register at Community level in the form of a publicly accessible electronic database. It lays down rules for its functioning, in order to implement the UN-ECE Protocol on Pollutant Release and Transfer Registers and facilitate public participation in environmental decision making, as well as contributing to the prevention and reduction of pollution of the environment. The E-PRTR Regulation includes specific information on releases of pollutants to air, water and land and off-site transfers of waste and of pollutants in wastewater. Those data have to be reported by operators of facilities carrying out specific activities. Annex II of the E-PRTR Regulation lists the 91 pollutants that are relevant for reporting under the E-PRTR. Annex II to the E-PRTR Regulation also specifies for each pollutant an annual threshold value for releases to each relevant medium (air, water, land). The threshold values for releases to water also apply in respect of the off-site transfer of pollutants in wastewater destined for treatment. Where no threshold value is given, the parameter and medium in question do not trigger a reporting requirement.

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Á . Irabien et al. Table 1. Normalization procedure. Atmosphere

Variable

Reference

Number of substances [2]

X2,1,1

te/y dioxide te/y carbon dioxide te/y benzene te/y CFC-11 te/y ethylene

6

X2,1,2 X2,1,3 X2,2,4 X2,1,5

Reporting Dimensionless threshold (kg) variable [8] sulphur 150,000 X2,1,1 / 150 100,000,000

X2,1,2 / 100,000

23

1,000 1 1,000

X2,1,3 / 1 X2,1,4 / 0.001 X2,1,5 / 1

52 60 100

Table 1 shows the reduction of complexity in the environmental sustainability evaluation: near 250 different substances have been considered in the emissions to the atmosphere, which have been reduced to five dimensionless variables, which can be weighted in a standard indicator for atmospheric impact assessment: X2,1. Table 2. Normalization procedure. Aquatic Impact

Variable

X2,2,1 X2,2,2 X2,2,3

X2,2,4

Reference

Reporting Dimensionless threshold (kg) variable [8] X2,2,1 / 0,1 te/y of released 100 H+ ions te/y oxygen 50,000 X2,2,2 / 50 X2,2,3,1 te/y 50 X2,2,3 / 0,05 copper te/y 50 X2,2,3,2 formaldehyde te/y phosphate 5,000 X2,2,4 / 5

Number of substances [2] 4 14 11 18 8

Table 2 shows the main aquatic impacts, which can be also reduced to a weighted standard indicator X2,2. Table 3. Normalization procedure. Land Impact

Variable

Reference

X2,3,1

Hazardous Solid Waste Non-Hazardous 2,000 t/year Solid Waste

X2,3,2

Reporting threshold (t) [8] 2 t/year

Dimensionless variable X2,3,1 / 2

Number of substances [2] H1………H14

X2,3,2 / 2,000

Waste transfer is related to the hazardous properties H1…..H14, according to these considerations land impact can be evaluated by a weighted standard indicator X2,3, Table 3.

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3. Conclusions Environmental sustainability in industrial processes is a multiobjective optimization procedure due to the influence of the site location connected to the environmental vulnerability. It corresponds to a complex system optimization due to the increasing number of substances, which need to be controlled. In this paper a systematic normalization procedure has been developed based on the considerations of the European Integrated Pollution Prevention Policy (IPPC). Some examples will be given as case studies corresponding to the application of this methodology to the process optimization.

4. Acknowledgements This research was funded by the Spanish Ministry of Science and Technology (Project C- CTM2006-00317).

5. References [1] D Schuster, "Benchmarking Sustainability", Chemical Engineering Progress, Vol. 103, No. 6, June 2007. [2] Institution of Chemical Engineers, "The Sustainability Metrics. Institution of Chemical Engineers Sustainable Development Progress Metrics recommended for use in the Process Industries"Institution of Chemical Engineers, 2002. [3] Official Journal of the European Union L 24, "Directive 2008/1/EC of the European Parliament and of the Council of 15 Jan. 2008. concerning integrated pollution prevention and control (Codified version)", Jan. 2008. [4] Official Journal of the European Union L 33. "Regulation (EC) No 166/2006", Feb. 2006. [5] I. Grossmann, "Challenges in the new millenium: product discovery and design,enterprise and supply chain optimization, global life global life cycle assessment", Computers and Chemical Engineering, Vol. 29, pp29–39, Jul. 2004. [6] Anastas, P. T., Lankey, R. L., “Sustainability through green chemistry and engineering”, ACS Symposium Series, 823: 1-11, 2002. [7] Young, D., Scharp, R., Cabezas, H., “The Waste Reduction (WAR) Algorithm: Environmental Impacts, Energy Consumption and Engineering Economics”, Waste Management, 20: 605-615, 2000. [8] E-PRTR Regulation: Regulation (EC) No 166/2006 of the European Parliament and of the Council concerning the establishment of a European Pollutant Release and Transfer Register and amending Council Directives 91/689/EEC and 96/61/EC.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Sustainable resource consumption assessment on LCA’s basis Gennadiy Statyukha, Bogdana Komarysta, Iryna Dzhygyrey National Technical University of Ukraine, Department of Cybernetics of Chemical Technology Processes, Peremogy av. 37, 03056 Kyiv, Ukraine, [email protected]

Abstract This paper addresses the analysis of existing metrics of sustainable development for system application on the lower layers of hierarchy for enterprise management. Sustainable resource consumption coefficient is proposed which characterizes the ability of a system to regenerate resources used and compensate resources taken earlier. Sustainable resource consumption coefficient is obtained on the basis of data collecting within life cycle inventory that is second stage of life cycle assessment. Environment repairing stage is added to account for renewable resources regeneration. The approach was tested against the problems of the assessment of alternative sewerage systems. Keywords: system approach, sustainability, metrics, resource consumption, sewerage system

1. Introduction A number of the latest works aimed at the improvement of sustainable development estimation methodology open up promising opportunities of applying the natural capital theory. This theory is closely associated with the book of Hawken et al. (1999). The key element of the theory is an idea that economy moves from the emphasis on human productivity to radical increasing of resource productivity. This shift might provide more significant pay for the domestic work, better world life standards for the indigents and decreasing human impact on the environment. In the theory three main types of natural capitals are distinguished: supplies of renewable and non-renewable resources, land and ecosystems. Each of them contributes differently into the human development and influences differently the human activity.

2. Sustainable Development estimation based on the natural capital theory To estimate the interrelations of natural capital variables – those of reserves, flows and state one should have the idea how they are connected. One of the basic studies in this field belongs to Luri (1997) who developed the idea of resource cycles. Here, the resource cycle is a quasi-closed circle of man-used materials as “resource-wasteresource”. Luri considers two real ways of the nature and society relationship which replace each other regularly with an increase of the civilization material needs (see Figure 1 – interaction of nature and society in resource usage in technologies of “naturemother” type (A+B – resource renewal only by natural mechanisms) and “naturecompanion” type (A+B+C – resource renewal by natural and anthropogenic mechanisms).

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Fig. 1. Interaction of society and environment The anthropogenic intensification of resource regeneration although providing an increase of resource usage is accompanied by a decrease of its efficiency, i.e. every resource unit becomes more and more expensive. In his schemes Luri uses the notion of “resource usage efficiency” which is the ratio of volumes of resource usage (i.e. the whole amount of resources used by society – natural and caused by technological activities of people) to the total outlays (on production and regeneration). The higher is efficiency, the cheaper society obtains every resource unit and the more people get for personal and public consumption. The idea of quantitative estimation of resource usage efficiency deserves special attention from the point of view of solving the problem of sustainable development management. Taking into account considerable achievements of system research (Zgurovsky and Pankratova, 2007; Zgurovsky and Statyukha, 2007a, 2007b) the authors expect that the considered and proposed approach could be successfully used in engineering practice.

3. Resource cycle assessment by sustainable resource consumption coefficient 3.1. System approach to solving sustainability management problem System requirements for sustainable development estimation and management can be met on the basis of the natural capital theory and by use of resource cycles “consumption – natural resource regeneration”. From here it follows, first, the necessity to measure natural reserves and dynamics of their depletion rate and, second, the need for quantitative estimation of regenerating potential for ecosystems by including them into the renewal cycle of natural resources. It should be also pointed out that the cycles “consumption – natural resource regeneration” can be built at any society’s hierarchical level, which is especially efficient at lower levels: regional or company levels. Consideration of the society processes as “consumption – natural resource regeneration” cycles opens the prospect of designing an approximate but ideologically consistent cycle model for the natural resources components within some subsystem and the possibility of forming a sustainable development index for the sustainability process management. Here, technologies play the decisive role (Mulder, 2006).

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Finally, self-regeneration of nature should be pointed out by the inner natural mechanisms and acting with different dynamics (forest regeneration after fire – decades, land regeneration after radioactive contamination – centuries). As noted above, this flow does not require outlays (“nature-mother” system). The system’s flows balance can be easily estimated by the economic unified metric (outlays in terms of money). 3.2. Resource consumption coefficient Analyzing the explanations for Fig.1 and using the proposal is being made in the work Zgurovsky and Statyukha (2007a), there is the opportunity to build the Sustainability Resource Consumption coefficient (SRC or Ș). It will characterize the ability of system to regenerate the resources taken from nature now and compensate the resources used before, as shown in Eq. (1):

η = ¦ Quse ,ɿ i

¦j Qreg , j

(1)

where Quse,ɿ – costs for the raw materials usage (mining, transport etc), costs for the product manufacturing and delivery to consumers; Qreg , j – costs for the wastes treatment, product utilization, returned resources purification (technologies) and for correction of nature damaged earlier (resources regeneration at the expense of anthropogenic mechanisms). It is easy to notice that if SRC-coefficient value exceeds “1” then a system is unsustainable from the point of view of potential preservation: consumption of natural resources goes on more intensively then their regeneration. If SRC-coefficient value is equal to “1” then a system is on the sustainability borderline and if SRC-coefficient value less than “1” then a system is sustainable: the natural resources regeneration takes the lead over consumption. Obviously, all political decisions taken at the corresponding hierarchical levels should be such that η < 1 both at the expense of decreasing resources consumption and improvement of production technology and due to an increase of outlays for resources regeneration and replenishment. 3.3. LCA as a tool for SRC-coefficient calculation It is possible to calculate the coefficient of Sustainability Resource Consumption on the basis of life cycle assessment (LCA) for a product system. The best way is to build the product life cycle taking into account the resource regeneration including the anthropogenic mechanisms and detailed analysis of stock control in life cycle or using the inventory analysis (LCI). Last one is the second phase of LCA accordingly to ISO 14 040 – «Environmental management. Life cycle assessment. Principles and framework». LCI consist of several procedures including the collection and data treatment aiming the determination of input and output flows for product system. The process of LCI analysis is an iterative one. The new demands or restrictions can be formulated in proportion with data collection and system study. In turn, it will demand the correction in data collection procedures for the goals achievements. We sure the application of inventory analysis in the frame of full LCA can help us to get the Sustainability Resource Consumption coefficient for the system studied.

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4. SRC-coefficient calculation of alternative sewerage systems 4.1. Sewerage systems analysis Two alternative sewerage systems from Lindholm et al. (2007) are considered as test examples for SRC-coefficient estimation. These are hypothetical a conventional and a nature-based systems for treating wastewater. The conventional system consisted of a separate sewer system and a mechanical/chemical treatment plant using iron-chloride for precipitation. The nature-based system consisted of a composting toilet for black water and a septic tank and constructed wetland for grey water (see Fig. 2). Initial data for calculation are not presented in this work due to space limitations. The reader is referred to Lindholm et al. (2007) for detailed description of sewerage systems and data.

Fig. 2. The nature-based wastewater treatment system (Lindholm et al., 2007) Calculation of the alternatives bases on eq. (1) that is

η = (QR + QM ) (QWT + QDM + QNT + QAN )

(2)

where QR – outlays on mining, transportation etc; QM – outlays on production and product utilization; QWT – outlays on waste treatment; QDM – outlays on product destruction; QNT – outlays on natural treatment technology; Q AN – outlays on environment repairing (resource regeneration at the expense of anthropogenic mechanisms). Environment repairing stage is added to account for renewable resources regeneration, e.g. reforestation as component of repairing stage in cardboard life cycle. Outlays on water preparation and supply to the object are equal for both conventional and nature-based system:

QR + QM = 94 /y per cap. It should be noted that all outlays included are presented in terms of money, namely in hryvni per capita on an annual basis.

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Outlays on wastewater treatment, water purification, pumping etc. for conventional sewerage system is

QWT + QDM + QNT + QAN = 9793 /y per cap. So Sustainability Resource Consumption coefficient value is Șconv=0.01. Outlays on wastewater treatment, water purification, pumping etc. for nature-based sewerage system is

QWT + QDM + QNT + QAN = 16.4

/y per cap.

And Sustainability Resource Consumption coefficient value is Șnb=5.7. 4.2. Discussion Two different SRC-coefficients are obtained: Șconv=0.01 and Șnb=5.7. As it is pointed out above if Ș<1 then one can affirm that conventional sewerage system is sustainable (a lot of money is spent on resource regeneration) and natural-based system is not sustainable (Ș>1). Although it is obvious that nature-based scheme is much more profitable from pragmatic point of view since it is characterized by the lesser outlays. Classic economic approach does not take into account value of nature’s “investment” into waste treatment in fact actually. Today we accept this gift of the nature as a matter of course and we do not care about caused damage to the nature. It may be that ratio Șconv/Șnb§600 more completely characterizes nature’s contribution into waste treatment. Calculation of the ratio resolves uncertainty in outlays on water preparation, system operation etc., for example, impact of iron chloride production and utilization on human and natural environment or water losses within a sewerage system. Some additional parameters can be included in SRC-coefficient estimation like discharge of pollutants to water, air and soil or risks induced by infection potential in common units of DALYs, but still it is very difficult to assess the values in terms of money.

5. Summary and conclusions If suppose that our proposal to apply SRC for the sustainable development is sufficiently substantiated for the resource cycle control, the question arises how to calculate it for the product systems. The answer is the simple and complicate one simultaneously. It is simply to propose the deep monitoring of social, ecological and economical indicators for product system including the monitoring of resource state (reserves and rate of their consumption). It is also clear we are needed in monitoring of ecosystems participated in purification of wastes and regeneration of natural resources. Thus, the answer is simple one when it concerns of what we should do. However, the situation becomes very uncertain when we have to answer how it should be done. Here, the measure of natural indicators produces the special complexity. Despite the fact that part of them exists physically (for example, the natural resources stocks are estimated even in market values), the natural indicators are dispersed in different administrations and, hence, are difficulty accessible. Others, for example the ability of ecosystems to regenerate emissions are measured rarely and just in the special cases. In particular, between specialists do not exists the common opinion how to estimate the self-regenerating properties of ecosystems and hardly somebody knows how to measure such natural capital indicator as “aesthetic pleasure from nature”.

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Nevertheless, we hope that proposed approach opens the new perspectives in sustainable development estimation for product systems.

References P. Hawken, A. Lovins and H. Lovins, 1999, Natural capitalism: Creating the next industrial revolution, New York, 396 p. Ɉ. Lindholm, J. Greatorex and A. Paruch, 2007, Comparison of methods for calculation of sustainability indices for alternative sewerage systems – Theoretical and practical considerations, Ecological Indicators, Vol. 7, Iss. 1, pp. 71-78. D.I. Luri, 1997, Resource-usage development and ecological crises, Moscow, 172 p. (in Russian). K. Mulder, 2006, Sustainable Development for Engineers. A handbook and Resource Guide. Sheffield: Greenleaf, 288 p. M.Z. Zgurovsky and N.D. Pankratova, 2007, System Analysis: Theory and Applications (Data and Knowledge in a Changing World), Springer, 448 p. M. Zgurovsky and G. Statyukha, 2007a, The role of engineering science and practice in society’s sustainable development, System research and information technologies, No.1, p. 19-38. (in Russian). M. Zgurovsky and G. Statyukha, 2007b, A system approach to asessment and managment of society’s sustainable development, System research and information technologies, No. 3, p. 7-27. (in Russian).

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Accident Prevention by Control System Reconfiguration José Luis de la Mataa, Manuel Rodrígueza a

Autonomous System Laboratory-UPM, c/ José Gutiérrez Abascal, 2, 28006 Madrid, Spain, [email protected]

Abstract This paper presents the use of functional modeling for control system reconfiguration. An extension of the MFM methodology is presented; this extension provides the functionality that analyzes the control system status and provides possible reconfigurations in a semiautomatic and consistent way. Keywords: functional modeling, control reconfiguration, risks assessment.

1. Introduction While operating a plant there are many kinds of failures that could arise. It is a very important and complex task to identify their causes and their consequences. Functional modeling techniques make this identification easier and more accurate when combined with plant measurements. Many times problems arise because a part of the control system fails (sensor, actuator, controller and so on). If that happens, it is impossible to keep under control the part of the plant affected by the fail (and this can lead to an emergency shutdown or to an accident). But through control reconfiguration it is still possible to achieve certain goals and avoid some shutdowns (saving money) and even prevent accidents.

2. Multilevel Flow Modeling Extensions 2.1. Multilevel Flow Modeling Multilevel Flow Models (MFM) [1] are graphical models of goals and functions of technical processes [2]. The goals describe the purposes of a system and its subsystems, and the functions describe the system’s abilities in terms of flows of mass, energy and information. MFM also describes the relations between the goals and the functions that achieve those goals, and between functions and the subgoals that provide conditions for these functions. Mass and energy flow structures are used to model the functions of the plant and activity and information flow structures are used to model the functions of the operator and control systems. These flow function concepts and their associated symbols are shown in Fig. 1. Using these concepts it is possible to represent knowledge of complex process plants. The basic MFM functions were presented by Lind [1], the use of information functions was introduced by Larsson [2], finally, Petersen [3] presented causality considerations between functions.

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Fig. 1. Multilevel Flow Modeling Concepts.

In order to perform control reconfigurations some extensions are proposed, as shown in Fig.1. The first one, the control relation, links an information structure and a mass or energy function; the function linked is the manipulated variable of the control loop. The second one, the transport function extension, adds the set of controlled variables that can be influenced by the transport function considered (manipulated variable), adding a label to the transport function. The use of these extensions is shown in the following example.

Fig.2. Example Multilevel Flow Model.

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2.2. Example A hot stream (A) and a cold stream (B) are mixed in a vessel whose level must be controlled. Also the temperature must be controlled. The vessel level is controlled by the outlet stream flow and the outlet temperature is controlled by the cold stream flow. Considering the flowsheet it is possible to build its multilevel flow model as presented in Fig.2. The goal of keeping vessel level (L) is achieved by control in structure I1. The manipulated variable, represented by the control relation, is the transport function Tr03 in mass structure M1. The manipulated variable in keeping the vessel temperature (T) is the transport function Tr02 also in mass structure M1. The vessel level can be controlled with either stream flows and temperature can be controlled with both inlet stream flows. That is why the transport functions in mass structure appear with their labels, meaning what variables can influence each transport function.

3. Industrial Example: The Tennessee Eastman Process The Tennessee Eastman Process [4] consists of a reactor, condenser, separator, compressor and stripper with a gas recycle stream, as shown in Fig.3. This process was developed as an industrial plantwide control test problem. In the control structure considered (on-demand product) we assume that the flowrate of the product stream leaving the base of the stripper is set by a downstream customer [5].

Fig. 3. Eastman Process.

Considering the process description a set of goals and subgoals have been identified in order to guarantee a good plant behavior. All these goals are related with control objectives and safety. Each control goal has subgoals related with loop stability. The MFM model has eleven mass structures, three energy structures and ten information structures, all of them related and hierarchically ordered in the model in Fig.4. As it is a complex process, the resulting MFM model is also complex. But the objectives hierarchy and the different colors for the structures make it clearer than other functional models.

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Fig.4. Eastman Process MFM.

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The control reconfiguration analysis consists of the following steps: 1. Look for alternative manipulated variables (labeled transport functions). 2. Analyze the different alternatives available: 1.1. If the transport function is free (no related by the control relation to any control structure) the reconfiguration is done. 1.2. If the transport function is related to any control structure it is necessary to examine the hierarchy of both control goals so the less important (and that can be removed) is not achieved. Once the control reconfiguration is done the plant works with the new control structure until the fail is solved, at that point, the former control structure is used back. Note that the plant to operates without achieving certain objectives in order to achieve other goals that are more important. Following are some examples of different control reconfiguration analysis: 1. Failure in the reactor pressure (Pr) control loop (structure I3). If it is not possible to control the reactor pressure with the transport function in structure E223 there are three alternatives, two transport functions in M232 and one transport function in M211. No goal is unachieved because all of them are free (see Fig.5). 2. Failure in outlet product (Fo) control loop (structure I7). If outlet product control loop fails there is only one possibility as shown in structure M311, but the function is not free so the stripper level (control goal related to the transport function) wouldn’t be achieved (see Fig.6).

Fig.5. Fail 1, detail from MFM model in Fig.4.

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4. Conclusions and further work In this paper an extension of MFM has been presented. This extension introduces the possibility of analyzing the control system of a process plant. The extensions proposed provide a clear and simple visual way to define control dependences. Different extensions were presented by Lind in [6]. They have been tested in a control benchmark case like the Tennessee Eastman Process. The methodology works properly and introduces into the model additional information related to the control system of the plant, having more complete models. Further work will involve merging qualitative information (provided by the functional model) and quantitative information (provided by process sensors) in order to validate sensor signal and alarms firing.

Fig.6. Fail 2, detail from MFM model in Fig.4.

References [1] M. Lind, Modeling Goals and Functions of Complex Industrial Plant. Applied Artificial Intelligence, Vol 8 No. 2 , April-June 1994. [2] J.E. Larsson, Knowledge Engineering Using Multilevel Flow Models, Technical Report, Lund Institute of Technology, 2000. [3] J. Petersen, Knowledge based support for situation assessment in human supervisory control. Ph. D. Thesis. Technical University of Denmark. 2000. [4] J. J. Downs and E. F. Vogel, A plant-wide industrial process control problem. Computers and Chemical Engineering 17 (1993), pp. 245–255. [5] W. L. Luyben, B. Tyréus and M. L. Luyben, Plantwide Process Control. McGraw-Hill, 1998. ISBN: 0-07-006779-1. [6] M. Lind, Modeling goals and functions of control and safety systems – theoretical foundations and extensions of MFM. Nordic Nuclear Safety Research (NKS). 2005.

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Activity and Information Modeling of Comprehensive Assessment for Sustainable Process Design Yasunori Kikuchia,*, Masahiko Hiraoa a Department of Chemical System Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, *[email protected]

Abstract This study presents an activity model for sustainable process design with comprehensive assessment integrating risk assessment (RA) and life cycle assessment (LCA). The type-zero method of Integrated DEFinition language, or IDEF0 and the Unified Modeling Language for information system, or UML, were applied for enabling systematic and effective development of procedure and information infrastructure of such comprehensive assessment in process design. Integration of different assessment can be fulfilled by these modeling. In this study, to demonstrate the proposed model, a case study is performed on metal cleaning process where various chemical substances have been utilized. Keywords: Life cycle assessment (LCA), Risk assessment (RA), IDEF, UML, Metal cleaning 1. Introduction When we develop a sustainable process, local risk and global impact should be taken into account simultaneously, because sustainability has become the dominant concern of not only process owner but also the public [1]. The aspect of local risk such as ones in workplace and neighborhood are different from that of global impact. Risk assessment (RA) and life cycle assessment (LCA) can evaluate local risk and global impact attributable to processes [1]. The results of them should be interpreted comprehensively based on their meanings for process management and sustainability [1]. For the actual reduction of risk due to the use of chemicals under individual constraints, such evaluations should be practicable for each on-site decision maker. Activities and information assigned to a decision maker, which become massive and complicated, should be systematized to represent the way of collecting the required data, performing the evaluation, and interpreting the results as a clear procedure. The business modeling approach is useful for activating the smooth implementation of such new business activities [2]. Because the environmentally conscious design of processes needs systematically connected activities and information in process

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evaluation, simulation, and optimization [3], effective support from information technology is important for process engineers [4]. This study presents an activity model for sustainable process design with comprehensive assessment integrating RA and LCA. The procedure of the integrated application of them is visualized in the activity model with the requirements of information infrastructures. These models are developed on the basis of the definitions of system requirements towards the development of actual software system. A case study is performed on metal cleaning process to demonstrate the comprehensive assessment by a prototype tool, which is based on the developed activity and information models. 2. Activity and Information Modeling of Knowledge on Assessment The type-zero method of Integrated DEFinition language, or IDEF0 [5] and the Unified Modeling Language for information system, or UML [6], were applied to systematically describe the activities of comprehensive assessment. IDEF0 can visualize the required activities complexly intertwined with information on process design and evaluation systematically. It has been utilized for the modeling of the business model implementing the integrated process design [7, 8]. Required information for IDEF0 model was structured by UML. UML can specify the structure of required databases and the algorithm for designing processes with the databases. In business process reengineering field, IDEF0 and UML are applied for the design of novel business systems implementing new business procedure [2]. IDEF0 could visualize an integrated procedure of RA and LCA with required technical information such as hazard and process information, which are modeled by UML to clarify their data requirements and acquisitions. The knowledge and technology on process design and evaluation are divided into five knowledge units: mechanisms of risk specification (RSM), evaluation (EvM), alternative generation (AGM), process simulation (PSM), and risk interpretation (RIM) as shown in Fig. 1. The activities and information flows between them should be defined appropriately for the practicable risk-based decision making. Fig. 1 includes the activity analysis, decomposition, and redefinition for enhancing the practicability of risk-based decision making. In the analysis, the activities, which are difficult for actual decision maker to perform, are specified and retrieved from the activity on the viewpoint of researcher. This is the decomposition of no-practicable activities. Remained activities, which are practicable for decision makers, are redefined as a business model for them. Retrieved activities become ones of support mechanisms. These steps can convert the activities of researchers into practicable ones for actual decision makers. At the same time, the conceptual requirements of support mechanisms can be indicated. Among five knowledge groups, EvM might be the most important knowledge for implementing risk-based decision making in process design. This paper focuses on the modeling of EvM.

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Figure 1 Concepts of activity and information modeling for risk-based decision making

Figure 2 IDEF0 activity model of comprehensive assessment

Fig. 2 illustrates the activities of comprehensive assessment. These are defined as the sub-activities of process design on the viewpoint of actual decision makers. Evaluation activities consist of three main steps: definition of objectives and settings, evaluation, and data collection. Integration of assessment methodologies is achieved by combined definition of objectives and settings, comprehensive interpretation, and information share during a phase in

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both assessments. In objective settings and interpretation, the activities stay in close contact to share information for the avoidance of inadequate settings of redundant evaluation indices and ineffective interpretation on a narrow field of vision. Comprehensive interpretation needs the judgment of reducing candidates and deciding an alternative under evaluation results considering the difference of their meanings. The key points of the integration of LCA and RA are the assignment of evaluation indices to each methodology considering the matching of the features of evaluation indicators and actual adverse effects, and the appropriate screening with sufficient understanding of results [2]. For enabling such comprehensive assessment in practice, a software system can be regarded as a powerful mechanism. UML diagrams can play a role to define the requirements of software system implementing the comprehensive assessment. Fig. 3 shows one of the developed UML diagrams representing the activity relationship in the mechanism for EvM. This mechanism has interactive relationships with other knowledge on process design and assessment. Three call activities have important roles to facilitate each evaluation phase. In the first data input phase, EvM should take into account the alternative process settings, which requires the connections with AGM. Similarly, the objective settings and evaluation phases require the connections with RSM and PSM, respectively.

Figure 3 UML activity diagram for requirements definition of comprehensive assessment

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3. Case study on the design of metal cleaning process Case study on the design of metal cleaning process was performed to demonstrate comprehensive assessment based on developed IDEF0 and UML models. A prototype software system was developed for the assessment of a metal cleaning process on workers' and neighbors' health risk and environmental impact evaluated by RA and LCA, respectively. This case study also developed the requirements definition of such assessment tools for sustainable cleaning process design. For actual development of software system, detail calculations and sequences in mechanisms must be shown, which cannot be visualized in general models as shown in Figs. 2 and 3. For the detail requirements definition, UML sequence diagram can be applicable. The proposed mechanism for EvM is divided into several parts to fulfill the roles of assessing processes on LCA and RA. Graphical user interface (GUI) is one of the most important modules for enhancing the practicability of the integrated assessment, because it converts available information on site into required one for assessments. The conversion needs the calculation modules, which should be defined in detail. Fig. 4 shows one of the calculation module included in the software system supporting the assessment of metal cleaning process. It is the sequence of the estimation of utility use at cleaning process as an example. In this estimation, the available actual data is fully utilized to reduce the uncertainty of LCA results. Several sequence diagrams were developed for the requirements definition of a software system, and a prototype of assessment tool for metal cleaning process design was developed on them. The developed software tool can successfully execute LCA and RA with the inputted information, which is available on site.

Figure 4 UML sequence diagram of the heat duty calculation module required for the assessment in metal cleaning process design

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4. Conclusion This paper presents the models of activity and information implementing comprehensive assessment of local risk and global impact into actual process design. The models were visualized by IDEF and UML modeling languages developed in software system engineering. For an appropriate comprehensive assessment, the required activities and information flows should be carefully organized and connected each other as an integrated procedure. Using IDEF0, such activity and information relationships can be visualized systematically. At the same time, detail information processing required for process design and assessment is also important for the implementation of comprehensive assessment into practice. In this study, the mechanisms for process design and assessment were divided into five categories. Among them, evaluation mechanism is the most important to interconnect existing engineering knowledge on process design, because the evaluation results might be the objective functions in decision making. IDEF0 and UML models were developed for logically visualizing the activities and information in process design with comprehensive assessment. Based on the activity and information models, different assessment methodologies can be applied in decision making simultaneously. Actual case study of developing a system for the design of metal cleaning process demonstrated that the definition of system requirements should be able to define the important calculation in LCA and RA. In the case study, a prototype of assessment tool of metal cleaning process was developed. 5. Acknowledgements The authors would like to thank the Japan Industrial Conference on Cleaning for their cooperation on data collection through hearings with the engineers at metal degreasing sites and manufacturers of cleansing agents, washing machines and ventilation systems. Parts of this study were supported by the Japan Society for the Promotion of Science through a Grant-in-Aid for Research Fellowships (No. 1811314) and Scientific Research (B) (No. 18310052). References [1] Y. Kikuchi and M. Hirao, Environ. Sci. Technol., 42(12) (2008) 4527-4533 [2] Y. Naka (eds.), Introduction to Integration Engineering (original title in Japanese), Kogyo Chosakai, Tokyo, 2006 [3] H. Chen, D. R. Shonnard, Ind. Eng. Chem. Res., 43 (2004) 525-552 [4] R. Schneider, W. Marquardt, Chem. Eng. Sci., 57 (2002) 1763-1792 [5] D. T. Ross, IEEE T Software Eng., 3 (1977) 16-35 [6] Objective Management Group (OMG), Unified Modeling Language (UML) ® Resource Page. Available at http://www.omg.org/technology/documents/modeling_spec_catalog.htm#UML (Accessed November 2008) [7] Y. Kikuchi and M. Hirao, Proc.17th ESCAPE, (2007) 1223-1228 [8] M. Hirao, H. Sugiyama, U. Fischer and K. Hungerbühler, Proc.18th ESCAPE, (2008) 1065-1070

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A Goal Based HAZOP Assistant Netta Liin Rossinga, Morten Lindb, Niels Jensenc and Sten Bay Jørgensena a

CAPEC, Chemical and Biochemical Engineering, Technical University of Denmark, Lyngby, Denmark, E-mail: [email protected] b Electro Engineering, Technical University of Denmark,Lyngby, Denmark, Email:[email protected] c Safepark Consultancy, Kannikestræde 14, DK-3550 Slangerup, Denmark, E-mail: [email protected]

Abstract A goal based methodology for HAZOP studies in which a functional model of the plant is used to assist in a functional decomposition of the plant starting from the purpose of the plant and continuing down to the function of a single node, e.g. a pipe section. This approach leads to nodes with simple functions such as liquid transport, gas transport, liquid storage, gas-liquid contacting etc. From the node functions the selection of relevant process variables and deviation variables follow directly. The goal based methodology lends itself directly for implementation into a computer aided reasoning tool for HAZOP studies to perform root cause and consequence analysis. Such a tool will facilitate finding causes far away from the site of the deviation. The proposed Functional HAZOP Assistant is investigated in a HAZOP study which shows that the goal based methodology using a functional approach provides a very efficient paradigm for facilitating HAZOP studies and for enabling reasoning to reveal potential hazards in safety critical operations. Keywords: Risk Assessment, Systems Engineered HAZOP Analysis, Model based HAZOP

1. Introduction Hazard analysis provides a systematic methodology for identification, evaluation and mitigation of potential process hazards which can cause severe human, environmental and economic losses. Different methods are practiced at various stages during the plant life cycle. Most methods require considerable time and resources. Consequentially research has been stimulated to develop computer aided tools to assist in and even aiming at automating hazard analysis. A review of litterature on assisting HAZOP analyses revals [1-3] that it is desirable to develop a HAZOP analysis methodology based upon a model representation which can encompass the operational goal hierarchy for the plant. Such a functional model should represent the system using means-end concepts, where a system is described using goals/purposes in one dimension and whole-part concepts in another dimension. Such a functional modeling approach lends itself directly for implementation into a computer aided reasoning tool for HAZOP studies to perform cause and consequence analysis. The purpose of this paper is to present the development of a functional model based reasoning system for assisting in a goal based methodology for HAZOP analysis. The following section briefly introduces a traditional HAZOP, then the functional modeling methodology and the associated reasoning engine are described. Next the goal based HAZOP analysis methodology is presented based uopon a functional model which leads to the Functional HAZOP

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Assistant which is demonstrated on the case study. Finally the presented methodology is discussed and the conclusions are drawn.

2. Methods: Traditional HAZOP Procedure Since the development of hazard and operability (HAZOP) studies [4-they have been a cornerstone in risk assessment of process plants. The purpose of a HAZOP study is to investigate how a facility responds to deviations from design intent or from normal operation, i.e. to reveal if the plant has sufficient control and safety features to ensure, that it can cope with expected deviations normally encountered during operation. The HAZOP study is traditionally performed as a structured brainstorming exercise facilitated by a HAZOP study leader and exploiting the participants experience. A traditional HAZOP study has the following phases • Pre-meeting phase: The purpose and objective of the study is defined. The leader of the HAZOP study gathers information about the facility, and proposes a division of the plant into sections and nodes. For each node - or for the plant as a whole - the leader identifies relevant process variables and deviations from design intent or normal operation based on either past experience or company guidelines. The review participants in the different plant sections are identified. • Meeting phase: The team considers each P&ID or PFD in turn. The team leader ensures that process variables and deviations are considered in a rigorous and structured manner, that results are recorded, and that all areas meriting further consideration are identified by action items. • Post-meeting phase: All actions items are followed up by the assigned persons and the follow-up results are reported to the team leader. The team might call a review meeting to determine the status of all actions items, and decide if additional efforts are needed. Thus a HAZOP study requires considerable time and resources whenever it is carried out during the plant life cycle. Consequentially research has been stimulated to develop computer aided tools to facilitate HAZOP studies.

3. Functional Modelling Methodology In this paper Multilevel Flow Modeling (MFM) which is founded on fundamental concepts of action, is used to combine the means-end dimension with the whole part dimension, to describe the functions of the process under study and to enable modelling at different abstraction levels. MFM is a modeling methodology which has been developed to support functional modeling of process plants involving interactions between material, energy and information flows [8]. Functions are here represented by elementary flow functions interconnected to form flow structures representing a particular goal oriented view of the system. Each of the elementary flow functions can thus be seen as instances of more generic action types [8]. The views represented by the flow structures are related by means-end relations and comprise together a comprehensive model of the functional organization of the system. The basic modeling concepts of MFM comprise objectives, flow structures, a set of functional primitives (the flow functions) and a set of means-end relations and causal roles representing purpose related dependencies between functions. The functions, the flow structures and the relations are interconnected to form a hypergraph like structure. An MFM model builder has been implemented in MSVisio. Stencils implementing icons for the MFM

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concepts are used to build a model graphically. The model builder is interfaced with a reasoning system which can generate root causes and causal paths for a given fault scenario i.e. a top event (failed MFM function) and status information for selected flow functions. The reasoning system is implemented using the Java based expert system shell Jess. Rules for reasoning about function states in MFM models are implemented as a Jess rule base.

4. Results: A Functional HAZOP Assistant Traditionally the division of the plant into sections may be carried out by defining each major process component as a section. A section could also be a line between each major component with additional sections for each branch off the main process flow direction. Usually the function of a section or of a node is not directly specified, many HAZOP formats only identifies the part of the process considered by project number, P&ID number and line number. The design intent of the node may go unrecorded, even though the purpose of the HAZOP study is to consider deviations from design intent. Instead the goal based methodology for HAZOP analysis provides a structured approach where the study is divided into three phases, corresponding to the traditional approach described above. The first phase corresponds to the pre-meeting phase, the second phase to the meeting phase and the third phase to the post meeting phase. Phase 1: State the purpose of the plant. • Divide the plant into sections each of which has a clear sub-purpose or -aim in contributing to the overall purpose of the plant. • Divide each section into nodes, the function of which can be directly described by physical or chemical phenomena. Examples of such phenomena are: gas transport, liquid transport, liquid storage and gas-liquid contact. • At this point an MFM model may be directly developed using the model builder as described above (in case a model is not already available) provided that the physical and chemical phenomena are included in the existing model set. • For each type of node, i.e. each physical or chemical phenomenon, describe the process variable(-s), which identifies design intent or normal operation. For a node with the function 'gas transport' normal operation could be described by flow rate, temperature, pressure and number of phases. • For each process variable specify the relevant deviations. For flow rates typical deviations are qualitative, e.g. more, less and reverse. In this work the deviation 'no flow' is considered a limiting situation of 'less flow', and hence is not considered separately. Phase 2: Perform the diagnosis on the MFM workbench by working through the plant sections and nodes in sequence and analysing the deviations one by one facilitated by the qualitative reasoning capability in MFM Analyse the identified causes of hazardous conditions perhaps by refining the analysis through a more detailed study in case of a serious hazard or cause. Record the identified causes and the underlying reasoning for later reference. Phase 3: 1. For identified hazards then investigate and decide how to manage these, through a) definition of an alarm with a consequential response potential for the operator, b)

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Implementation of on line control of the plant, c) redesign of a part of the plant, or d) another action 2. Record the final decision and the underlying reasoning for later reference. Phase 1 may be carried out in a straightforward manner by using the functional approach. Using this approach to divide the plant all that is needed is a basic understanding of chemical unit operations, their purposes and the fundamentals on which these purposes are built, i.e. transport phenomena. This means that phase 1 of a HAZOP study may be efficiently performed by less experienced personnel, while phase 2 requires more experience. The above proposed three phase procedure clearly becomes a significant task even though the Functional HAZOP assistant enables consistent reasoning not only within the single nodes but also between nodes and sections and thereby facilitates revealing more complex causes of deviations than possible using the traditional approach.

5. Functional HAZOP of distillation pilot plant The indirect vapour recompression distillation pilot plant (IVaRDiP) at the Department of Chemical and Biochemical Engineering consists of a distillation column which is integrated with a heat pump. The purpose of the column is to separate a feed stream into two pure product streams while minimising energy used. To accomplish this the following subsystems with designated sub-goals are defined: 1. Column section. Purpose: Gas-liquid contact to facilitate separation. 2. Re-flux section. Purpose: Provide a liquid stream to the column and remove excess liquid as top product. 3. Feed section. Purpose: Provide a feed stream as close as possible to the conditions on the feed plate. 4. Re-boiler section. Purpose: Provide a gas stream to the column and remove excess liquid as bottoms product. 5. Low pressure heat pump section. Purpose: Transport energy from re-flux section to compressors. 6. High pressure heat pump section, including compressors. Purpose: Increase the heat pump fluid energy content by compression and transport energy from compressors to re-boiler. 7. Excess heat removal section. Purpose: Transport of excess energy from the heat pump to the environment. 8. Tank Park. Purpose: Provide storage for raw material and products.

6. Building an MFM model The IVaRDiP is divided into 8 sections in the above step 2 of the functional HAZOP approach. In the next step each section is further divided into nodes according to their function. For example the re-flux section, which consists of the piping from the top of the column through the condenser and accumulator back to the column with the piping from the accumulator to the top product storage tank, is divided into five nodes during step 3. From this subdivision of the section it is directly possible to construct the MFM in step 4 using the MFM workbench. The other sections of the distillation pilot plant are similarly divided into nodes, i.e. each node relates to a function described by physical or chemical phenomena. Having developed the MFM model for the different nodes these are directly concatenated to form the MFM model for the plant. In step 5 from the

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function of the node the variables necessary to describe design intent follows directly. Therefrom follows deviations relevant for the particular function directly. Having completed phase 1 it is now possible to enter phase 2, where the reasoning engine is used to perform the actual HAZOP study in step 7. During this step the Functional HAZOP Assistant is extremely helpful in providing the reasoning necessary to identify potential hazards. Initially it is recommended to perform the exhaustive evaluation for each variable in each node. Later as experience is accumulated it may be possible to facilitate also this step further. Below two analyses carried out on the IVaRDiP will be briefly described.

7. Traditional versus and functional HAZOP The result of a traditional HAZOP of the re-flux section of the distillation pilot plant is compared to the results of the Functional HAZOP Assistant. While the traditional approach provides 14 records in the HAZOP, then the Functional HAZOP Assistant only provides 8 records with the same information content. Hence the Functional HAZOP Assistant requires about half the effort in evaluating the causes of deviations, i.e. the number of lines in the HAZOP report. Clearly the time required to perform the HAZOP will be significantly shorter for the Functional HAZOP Assistant, when a MFM model is available, than for a traditional HAZOP. Furthermore the Functional HAZOP assistant directly can document the causes behind the deviations together with the underlying reasoning. In addition the availability of a scientifically based systematic approach to performing the HAZOP provides an interesting potential for the HAZOP study to cover the possible hazards in a plant which are foreseeable with the applied abstraction level in the MFM modelling. However a more detailed and systematic study of the different steps in the three phases of a HAZOP needs to be performed to further validate the relationship between the modelling abstraction level and the potential hazards. The ability of the Functional HAZOP Assistant also has been investigated for revealing more complex hazards in a plant. Here a very simplified functional model was developed for the IVaRDiP, where the mass flow of the distillation column is combined with a very simple energy flowstructure for the heat pump shown in the upper part of the figure. Using this model it was shown that the Functional HAZOP Assistant facilitates the discovery of root causes of deviations, which originate far from the node in which the deviation occurs. Some recent loss events in the chemical industry have involved such situations [9].

8. Discussion and Conclusions A goal based methodology for HAZOP analysis using a Functional HAZOP procedure is introduced, which allows even fresh chemical engineers to contribute meaningfully to a HAZOP study. The approach reduces the work involved in a HAZOP of a plant by dividing the plant along functional lines and analysing nodes with the same function once only. This approach significantly reduces the effort involved. Furthermore functional models of chemical plants are demonstrated to provide a useful basis for development of a Functional HAZOP Assistant. On a simple model of a part of an indirect vapour recompression distillation pilot plant the Functional HAZOP Assistant finds the same causes as a traditional HAZOP study. It is furthermore demonstrated, that the proposed Functional HAZOP Assistant is able to find causes far from the site of the deviation. This promising development calls for a more systematic study of the workflow involved in HAZOP studies to further enable design of efficient tools for

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supporting the important HAZOP studies for improvements in Safety Critical Operations in industry.

References [1] Bragatto, P., Monti, M., Giannini, F., Ansaldi, S. (2007) Exploiting process plant digital representation for risk analysis. Journal of.Loss Prevention in the Process Industris (20) p. 69-78. [2] Vaidhyanathan, R.; Venkatsubramanian, V.: Dyke, F.T. (1996): “HAZOPExpert: An Expert System for Automating HAZOP Analysis”, Process Safety Progress, (15 no.2) pp 80-88 [3] Venkatsubramanian, V.; Zhao ; Viswanathan (2000): “Intelligent Systems for HAZOP Analysis of Complex Process Plants”, Computers and Chemical Engineering (24) pp. 2291-2302 [4] Crawley, F. and Tyler, B. (2000): ” HAZOP: Guide to best practice”, The Inst. of Chemical Engineers, Rugby, UK [5] Crawley, F. and Tyler, B. (2003): “Hazard Identification Methods”, The Institution of Chemical Engineers, Rugby, UK [6] Swann, C.D.; Preston, M.L. (1995): “Twenty-five years of HAZOPs”, J.Loss Prev. Process Ind. 8(6), pp.349-353. [7] Lawley, H.G. (1974): “Operability Studies and Hazard Analysis”, Chemical Engng. Progress, (70 no.4) , pp. 45-56 [8] Lind, M. (1994): “Modeling Goals and Functions of Complex Industrial Plant”. Applied Artificial Intelligence, 8(2):259-283, 1994. [9] Mogford, J. (2005): "Fatal Accident Investigation Report", BP, Texas City.

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A Systematic Approach to Determine Economic Potential and Environmental Impact of Biorefineries Norman Sammons Jr.,a Wei Yuan,a Susilpa Bommareddy,a Mario Eden,a Burak Aksoy,b Harry Cullinanb a

Auburn University, Department of Chemical Engineering, 132 Ross Hall, Auburn University, AL 36849-5127, USA, [email protected] b Auburn University, Alabama Center for Paper and Bioresource Engineering, 242 Ross Hall, Auburn University, AL 36849-5127, USA, [email protected]

Abstract The integrated biorefinery has the potential to provide a strong, self-dependent alternative to the use of fossil fuels for the production of chemicals and energy, but difficulties arise in measuring the potential economic and environmental benefit of the biorefinery. A myriad of products and production pathways are possible in this growing field of biorefining, and the production path with maximum value and minimum environmental impact cannot be determined on heuristics alone. A framework is needed to determine the most optimal route based on measures of economic and environmental performance. Gross profit and net present value are used as economic metrics in the short term and long term respectively, and environmental impact is measured using the WAR algorithm developed by Young and Cabezas [1999]. Top candidates in economic and environmental performance are then subject to process integration techniques in order to minimize mass and energy usage, and these integrated biorefineries are once again analyzed for optimal performance. Keywords: Environmental impacts, Economic, Biorefinery, Product allocation, Optimization

1. Introduction The integrated biorefinery provides a unique opportunity for reinvigorating an entire manufacturing sector by creating new product streams from a renewable resource [Bridgwater, 2003]. Economic and environmental sustainability are achieved through the optimal use of renewable feedstocks, and a need exists for a process systems engineering (PSE) approach to ensure maximum economic and societal benefit through minimizing the usage of raw material and energy resources as well as the cost involved in supply chain operations intrinsic to biorefining. To maximize the applicability of such systematic methods and to integrate experimental and modeling work, a unique partnership has been established consisting of researchers, government entities, equipment vendors and industry stakeholders to procure the wide range of information necessary such as data needed for process models, capacity constraints, financial data, and optimization techniques. The overall goal of this work is to develop a system that will enable decision makers to evaluate production pathways in biorefining in order to maximize value while measuring and minimizing environmental impact.

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2. Development, Optimization, and Evaluation of Process Designs In biorefining, the large number of possible process configurations and products results in a highly complex problem that cannot be solved using simple heuristics or rules of thumb. Thus, it is necessary to develop a framework which includes environmental metrics, profitability measures, and other techno-economic metrics. Such a framework should enable policy and business decision makers to answer a number of important questions like: • • •

•

For a given set of product prices, what should the process configuration be, i.e. what products should be produced in what amounts? For a given product portfolio, how can process integration methods be utilized to optimize the production routes leading to the lowest environmental impact? What are the discrete product prices that result in switching between different production schemes, i.e. what market developments or legislative strategies are required to make a certain product attractive? What are the ramifications of changes in supply chain conditions on the optimal process configuration?

The introduction of PSE methods into biorefining research provides a systematic framework capable of seamlessly interfacing results generated in simulation studies as well as experimental work. Such a framework is imperative when attempting to combine knowledge and information from a variety of research areas and disciplines. The objective of this approach is to create a library of rigorous simulation models for the processing routes along with a database of corresponding performance metrics. Figure 1 shows a schematic representation of the strategy employed for identification of characteristic performance metrics of the individual subprocesses. An initial superstructure lists feasible technologies for a given feedstock, and basic simulation models are constructed for those corresponding processes. CAMD and property clustering techniques are employed to identify alternative solvents that minimize environmental and safety concerns [Eden et al., 2003; Harper and Gani, 2000]. Process integration techniques are then used to optimize the simulation models. This is an integral step in the model development as it ensures optimal utilization of biomass and energy resources. The optimized models are used to generate data for the economic as well as environmental performance metrics. The estimation of environmental performance is achieved through the use of the US-EPA Waste Reduction (WAR) algorithm [Young and Cabezas, 1999]. The end result of this strategy is a superstructure of biorefining simulation models and a database of corresponding economic and environmental performance metrics. As stated in previous work, this superstructure and database is then exported into a mathematical optimization program whose objective is to identify candidate solutions based on maximum profitability while measuring and ranking the environmental impact of these solutions [Sammons et al., 2007]. If a candidate solution satisfies both economic and environmental objectives, then the optimal production pathways have been identified. However, if none of the candidate solutions satisfy the environmental constraints, then the framework is then modified by relaxing economic performance constraints until one or more solutions will satisfy both criteria. Economic and environmental performance are decoupled in order to avoid the pitfall of identifying the

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zero production facility that will identify minimum environmental impact [Sammons et al., 2007]. It should be noted, that only the economic and environmental performance metrics are incorporated in the solution framework described below, thus decoupling the complex models from the decision making process. This approach allows for continuously updating the models as new data becomes available without having to change the selection methodology. Similarly, if new processes are to be included for evaluation, an additional set of metrics are simply added to the solution framework, thus making it robust and flexible. Initial Superstructure Generation No Data and Knowledge Extraction for Base Case Simulation Models Aspen Plus, HYSYS, Pro/II

Performance Validated?

Semi-empirical Data Published Data

Yes

INTERACTIVE PROCESS & MOLECULAR DESIGN Solvent-based Process ?

Yes

Process Synthesis Desired Properties of Solvents

Design Targets

Molecular Design PARIS, ProCAMD, Databases

No Alternative Solvents

Process Integration Pinch Analysis, Thermal Management & Resource Conservation Strategies

Optimized Simulation Models Minimum Utility Usage , Maximum Resource Utilization & Reduced Environmental Impact

Economic Data Cost Estimation Software & References Vendor Data

Model Library & Performance Metrics Database Relative Economic Potential Relative Environmental Impact

Environmental Impact Data PARIS, ProCAMD, Databases

Superstructure of Processing Routes Tree Structure Incorporating All Optimized Models

Figure 1 – Strategy for identification of performance metrics.

3. Generalized Biorefinery Model and Economic Optimization Strategy A generalized biorefinery model given in Figure 2 has been used to develop the structure of the optimization framework. The model structure was formulated to include a variety of basic complexities encountered in the decision making process, e.g. whether

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a certain product should be sold or processed further, or which processing route to pursue if multiple pathways exist for a given product. The objective function maximizing the overall gross profit of the biorefinery is illustrated in Equation 1, but this may be replaced with an objective function maximizing net present value as shown in Equation 2. 

Bioresource m

R 01,01 R 01,02

Product k = 1

R 02,01

R 01,04 R 01,03

Product k = 2

Product k = 3

R 02,02 TS 01

Product k = 4

R 02,03

TS02 Product k = 5 TS05

TS04

Product k = 6 TS03

TS 06

Market

Figure 2 – Generalized model to illustrate possibilities in decision making tree.

(1)

(2)

Using this nomenclature, the first set of terms in Eq. (1) represents the sales revenue from the products made from each bioresource m. TSmkt is a variable that denotes the production rate of product k from bioresource m that is sold to the market. Ckts is the sales price of product k which is a scalar and is determined through a survey of published prices and vendor quotes. The second set of terms represents the total processing cost incurred by the pathways pursued in production. Rmijt is a variable that represents the processing rate of route ij while CmijtP is a scalar that represents the cost of processing bioresource m through route ij and is determined through simulation models and process economics. The third set of terms represents the total cost of the biomass resource m, and this is broken down into the scalar purchase price of bioresource m in CmtBM and the combined rate of biomass processed by the plant in Rm1jt. Although both TSmkt and Rmijt are variables in the optimization program, they are not independent since the variables are related via mass balance constraints around the product points. This gross profit term may be maximized by itself or incorporated into an objective function that takes many more issues into account. Taxt represents the marginal tax rate, Hedget represents the expenses associated with hedging against catastrophic market actions, Govt is the net benefit realized through government incentives or penalties, and R is the expected rate of return, or cost of capital involved with the time value of

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money. The gross profit version of the model may be utilized for short-term decision making with existing equipment and market arrangements, while the net present value version is better suited for long-term planning that will involve extensive capital expenditure, anticipated government action, and supply chain considerations. Without including any constraints on capacity of the processing steps, the solution is a single-product configuration in which all available biomass is converted into the most profitable product. However, if constraints are imposed on the most profitable route, the framework identifies the additional products and processing routes required to maximize the overall profit, thus leading to a polygeneration facility [Sahinidis et al., 1989]. Approximate capacity constraints are based on a variety of sources, e.g. existing equipment, vendor data and qualitative process information provided by academic and industrial collaborators. In order to effectively address the strategic planning objectives of business decision makers, it is necessary to incorporate the total capital investment as a constraint in the formulation. Inclusion of capital cost constraints is crucial for practical application of the results, i.e. enabling evaluation of the potential benefits to be obtained for a given maximum investment through retrofit or new construction.

4. Case Study A case study was performed on a potential biorefinery involving the conversion of chicken litter to syngas, hydrogen, and electricity. Actual data on conversion rates were obtained from experimental work performed by the university and affiliated agencies as well as simulations constructed in ASPEN. Figure 3a shows the possible pathways for production and sale of these chemicals on the commodity market. The execution of the optimization code verified the results obtained from manual calculation; producing syngas from chicken litter and selling it on the market would maximize profit due to the high costs involved in converting the syngas to hydrogen or electricity. Figure 3b illustrates the active pathway chosen by the optimization program. This simple case study will be expanded to include a much wider range of products and feedstocks in order to become a crucial decision support tool in the emerging field of biorefining. Bioresource m Chicken Litter

Bioresource m Chicken Litter 12.56 kg/s Biomass

R 01,01 Product k = 1 Syngas R 02,01

0

R 02,02

Product k = 2 Hydrogen TS 02

Syngas (Conv. Ratio 1.057:1)

Product k = 3 Electricity TS 01

TS 03

0

Product k = 2 Hydrogen 0

Product k = 3 Electricity

13.28 kg/s Syngas

0

Market

Market (Optimal Profit = $1.922/s)

(a)

(b)

Figure 3 – (a) Unsolved decision making tree with variable designations. (b) Solved decision making tree with flowrate values and objective function.

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5. Conclusions and Future Work A general systematic framework for optimizing product portfolio and process configuration in integrated biorefineries has been presented. Decoupling the process models from the decision-making framework reduces problem complexity and increases robustness. The next phase of this work involves development of additional process models for the generation of performance metrics, specifically information on conversion, yield, and production cost for economic metrics. These additional process models will focus on a greater number of product streams (e.g. electricity, process steam, dimethyl ether, Fischer-Tropsch fuels, and mixed higher alcohols) as well as feedstocks (e.g. black liquor, forestry residues, crop and crop residues, animal byproducts). The EPA WAR algorithm will be incorporated into the mathematical optimization software, and data from the additional process models will be used to generate numerous time-based and mass-based measures of environmental impact. From there, process integration will be utilized to optimize these process models by reducing energy usage, material consumption, and waste streams. The framework will also become a stronger financial tool through the incorporation of various economic ideas and analyses. The further development of qualitative predictive models for capital investment and inclusion of capital amortization into the objective function will also increase the strength of the framework. Incorporation of options theory into the framework will allow management to develop financial strategies in response to events in the market or legislative environment. Optimization under uncertainty will be studied to quantify the effects on process configuration resulting from minute changes in product prices [Banerjee and Ierapetritou, 2003]. This, in combination with implementing superstructure generation techniques, will lead to increased robustness of the methodology and thus better recommendations [Chakraborty and Linninger, 2003].

6. References I. Banerjee and M. G. Ierapetritou. (2003). Parametric process synthesis for general nonlinear models. Computers and Chemical Engineering, 27, 1499-1512. A. V. Bridgwater. (2003). Renewable fuels and chemicals by thermal processing of biomass. Chemical Engineering Journal, 91, 87-102. A. Chakraborty and A.A. Linninger. (2003). Plant-wide waste management 2: Decision making under uncertainty. Industrial and Engineering Chemical Research, 42, 357-369. M. R. Eden, S. B. Jørgensen, R. Gani and M. M. El-Halwagi. (2004). A novel framework for simultaneous separation process and product design. Chemical Engineering and Processing, 43, 595-608. P. M. Harper and R. Gani. (2000). A multi-step and multi-level approach for computer aided molecular design. Computers and Chemical Engineering, 24, 677-683. N. E. Sammons, W. Yuan, M. R. Eden, H. T. Cullinan, B. Aksoy. (2007). A flexible framework for optimal biorefinery product allocation. Journal of Environmental Progress, 26(4), 349-354. N. V. Sahinidis, I. E. Grossmann, R. E. Fornari and M. Chathrathi. (1989). Optimization model for long range planning in the chemical industry. Computers and Chemical Engineering, 13, 1049-1063. D. M. Young and H. Cabezas. (1999). Designing sustainable processes with simulation: the waste reduction (WAR) algorithm. Computers and Chemical Engineering, 23, 1477-1491.

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Computer Aided Chemical Exposure Estimation in Process Design Mimi H. Hassim, Markku Hurme Helsinki University of Technology, P.O. Box 6100, FIN-02015 TKK, Finland, [email protected], [email protected]

Abstract Computer aided methods for comparing alternative processes in process design based on fugitive emissions and occupational exposures were developed. The fugitive emissions can be quantified and the inhalative exposure and risk to workers can be evaluated at an early stage of design. Information on local conditions such as the wind speed distribution data is utilized. A case study is presented to illustrate the approach. Keywords: process design, occupational health, fugitive emissions, flowsheeting.

1. Introduction Sustainability is nowadays a goal for many chemical companies. EU directives, such as IPPC and REACH, have entailed the inclusion of safety, health and environmental (SHE) analyses in process design. However, there has not been systematic computer based methods for conducting occupational health evaluations in process design. Such methods are in high demand, since more people die yearly from occupational diseases than get killed in industrial accidents. In fact there are good opportunities to implement occupational health efficiently in the early design phases in a similar way as inherent safety [1]. In oil and petrochemical industry, a major health risk to workers is the exposure to chemicals. From occupational health context, the main long-term effects to workers are resulting from the day-to-day inhalation based exposure to airborne chemicals released into air from a chemical process. The main release mechanisms are the fugitive emissions and manual batch or maintenance operations. This paper focuses on worker exposure to the fugitive emissions of chemicals. The approach extends the earlier work [1] by allowing a realistic computer based chemical exposure and occupational health risk evaluation, which takes into account the local meteorological conditions such as the wind conditions and the working arrangements (time spent in process area). The earlier conventional exposure models have not been process design oriented and were limited to certain type of indoor facilities only.

2. Fugitive Emissions Estimation The method has three levels of detail; preliminary simple flowsheet, detailed flowsheet and piping and instrumentation diagram (PID). The fugitive emissions are first estimated by the EPA average emission factor approach [2]. For PFDs the method is based on precalculated modules, which have been created for typical subprocess types (such as distillation, tubular reactor system etc.). For PFDs the modules were generated by counting the number of fugitive emission leak points (e.g. pump, valve, flange) from a 'typical' subprocess PID. For the simple PFDs the material

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balance is not fully known, therefore the emission from each module stream can be calculated based on the service type only (vapor, light liquid etc.) and the EPA emission factors. For detailed PFDs the material balance is known and the real stream compositions can be used. For PIDs, emission factors for more specifically defined component types (e.g. valve with rising stem or a certain type of exchanger head) are utilized. The actual PIDs of the process are used, which makes the estimation more accurate. The estimation methods can be integrated with flowsheeting programs, PID's, CAD and 3D design models [1].

3. Chemical Dilution by Wind Most of the large chemical plants are located outdoor and they depend on the natural wind for the dilution of chemicals. The local meteorological conditions affect the wind conditions, which are presented as a wind speed probability distribution measured typically at the height of 20-30 m. This wind speed variation can be best described by a Weibull distribution [3]. This wind speed has to be first corrected to the workers’ breathing level at about 1.5 m. This correction is done by the power law, where the exponent is the ground surface friction coefficient, which depends on the roughness of the surface. Here the exponent value of 0.20 was applied. [3]

4. Exposure Assessment in Process Design and Comparison During chemical process development and design, the worker exposure to chemicals can be estimated based either on; 1) chemical concentrations compared to the exposure limit values or 2) risks created by inhalation based intake of chemicals. This paper presents new methods and characteristic values for making more realistic evaluations in process development and design phase. Exposure Limit Value Based Assessment Concentration-based risk assessment is based on the standard hazard quotient (HQ), which is the ratio of the estimated concentration to the exposure threshold limit value. For noncarcinogens, generally HQs < 1.0 indicate acceptable risks. For carcinogens, a stricter benchmark could be applied. Even though the chemical concentration is below the threshold limit, there is still a small risk that some employees may be adversely affected when exposure is greater than one-tenth the limit [4]. Accordingly, 0.1 is used as a guideline to characterize exposure risk to carcinogens. For concentration-based approach a new measure called limiting wind speed can be defined representing the wind speed on which threshold limit concentration value is reached. In the same way a time can be defined which corresponds to the fraction of time, in which the concentration in air is above the threshold value in local wind conditions at the worker inhalation level. Risk Based Assessment In this approach the intake is expressed as a daily chemical rate, which is turned into a risk. The reference intake limits are however not available for all chemicals, which somewhat limits the applicability. The risk benchmark often used for public population is one in a million (10-6) and for occupational environment is one in a ten thousand (10-4) [5,6]. The method calculates first the average concentration of various chemicals from fugitive emissions in local wind conditions at worker inhalation level. Then based on the exposure time, which depends on the length of working hours and the fraction of time spent in process area vs. control room, the total yearly exposure to the main

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hazardous chemicals is calculated. The individual risks are calculated by slope factor. The risks are totaled. The total risk can be used for comparing process designs and for deciding (when comparing with benchmarks) whether the risk is acceptable or if the process should be improved. This risk based assessment is proposed here as a new method for process design, which allows more realistic estimation of the actual occupational risks to the worker.

5. Case Study A case study on benzene manufacturing is presented to demonstrate the approach. The process can be divided into four main stages of: pre-distillation, second-stage hydrogenation of pyrolysis gasoline, extractive distillation and benzene purification. Since benzene is the most dangerous compound present, the others are neglected. Fugitive Emissions Estimation Benzene fugitive emission rate in the plant is estimated based on the simple PFD, detailed PFD and the PID of the process. Simple PFD comprises of simplified process diagram and process descriptions only. Detailed PFD offers detailed mass and energy balances. Based on the estimation procedures described earlier [1], the estimated benzene emission rates are; simple PFD 3.29 kg/h, detailed PFD 2.26 kg/h and PID 1.2 kg/h. The reasons for the difference between values are the following: In simple PFD stage the mass balance is not known exactly. The most toxic chemical (here usually benzene) is used for representing the stream causing its emissions to be overestimated. In detailed PFD, the stream rate is corrected with the composition and therefore contributing to a smaller benzene emissions rate. Both PFD methods are based on uncontrolled equipment average emission factors. For the PID stage the right number of leak points is known. The monitored equipment emission factors are used resulting into a smaller but a more exact emission estimate. Concentration-Based Estimation of Exposure Risk The benzene concentration in the plant is estimated by using the benzene fugitive emission rate estimate, process module or real plot plan area and the annual wind speed distribution [1], which is corrected to the workers' breathing height. The average benzene concentration is found to be 0.33 mg/m3, which can be compared to the benzene exposure limit value of 3.25 mg/m3. Hence the hazard quotient (HQ) is 0.103, which is close to the benchmark of 0.1 used for carcinogens (see Fig. 1a). These values can be calculated for various process concepts based on the flowsheeting values and used for comparison of process concepts. Intake-Based Estimation of Exposure Risk The worker average daily benzene intake is quantified based on the yearly working hours, percentage of the worker being in the process area and the average respiration rate. The carcinogenic risk is calculated by multiplying the daily intake by the slope factor (SF). SF is the inhalative exposure intake limit for carcinogens (for benzene 0.029 kg day/mg). The average probability of carcinogenic risk as the function of wind speed is presented in Fig. 1b. The carcinogenic risk probability for benzene exposure is 7.7x10-4 calculated based on the average benzene daily intake of 0.0266 mg/kg day and the yearly wind distribution data in this case study. The estimated risk is somewhat higher than the benchmark (1x10-4) proposed by Chan et al. [6]. The exposure limit and risk based approaches do not directly correspond each other, since the benchmarks reflect different criteria. The exposure limit values are decided by

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public organizations and they do not only represent health aspects but also technical realities (i.e. which concentrations can be reached in practice) and political and social aspects. The risk-based values are indicators of the health risks only and they provide a quantitative value for the probability of harm as the result of exposure. Therefore this paper proposes the risk-based approach as a measure to combine several effects as a total risk. Yet the difficulty is to decide which size of risk can be tolerated.

Figure 1. Benzene exposure indicators based on a) limit concentration b) intake

Figure 2. Cumulative probability of the wind speed below a certain value

Critical Wind Speed Determination This paper defines a new indicator called the critical wind speed as the minimum air velocity necessary to maintain the level of chemicals below their exposure limits. For the purpose the wind speed is presented as a cumulative probability distribution (Fig. 1). The probability can therefore be expressed as the number of more risky chemical exposure hours in a year. Therefore the indicator gives quantitative information on the risky exposure time in a year. For this case study, based on the benzene fugitive emission rate, process area, and exposure limit value, the critical wind speed determined

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for benzene is 0.18 m/s, which corresponds to 0.35% of the working time based on the wind probability distribution as shown in Fig. 2. The critical wind speed is proposed here as a new indicator to be used for comparing process concepts in their actual location. The indicator can also take into account the local way of organizing the work; e.g. the number of working hours and the time spent in the process area.

6. Integration with Computer Systems The exposure estimation methods presented can be integrated with the existing computer systems used in process design. The fugitive emissions calculation for simple PFD stage requires a spreadsheet program with the process module database and database of boiling points of compounds. Detailed PFD stage requires integration with a flowsheeting program, which provides the material balance and the physical properties of compounds. For the PID stage connection to computer aided design (CAD) system is needed for acquiring the information on the exact number of piping components. Also information on the real plot area is needed. Both of these can be provided by the 3D design models. In addition a database of fugitive emissions factors for various pipe items etc. is needed. Finally, for characterizing the risk, chemical toxicity properties, such as the exposure limit values and slope factors are required as a database.

7. Conclusions The inhaled chemicals present the main occupational health risk to workers in petrochemical and related industry. Already in process development and design phases a computer aided occupational health evaluation can be done to estimate the fugitive emissions, to compare process concepts and to evaluate, whether a proposed process concept is acceptable from the health point of view. For instance the carcinogenic risk to workers can already be estimated in the process development phase based on flowsheeting calculations, if the program is extended with information on the health properties of chemicals and the database of standard process modules (e.g. distillation or reactor system). The local conditions can be taken into account early by considering the local wind velocity distribution and the local working arrangements such as working hours and residence time in process area. The information can be used in process development phase to evaluate a single process or to compare alternative design concepts based on the occupational health performance or fugitive emissions.

References [1] M. H. Hassim and M. Hurme, 2008, Computer Aided Design of Occupationally Healthier Processes, ESCAPE-18, Elsevier, 1119-1124. [2] EPA, 1988, Protocols for Generating Unit-Specific Emission Estimates for Equipment Leaks of VOC and VHAP, EPA-450/3-88-070. [3] M. R. Patel, 1999, Wind and Solar Power Systems, CRC Press, USA, pp. 58-70. [4] S. A. Roach, 1994, On Assessment of Hazards to Health at Work, Am. Ind. Hyg. Assoc. J., 55, 12, 1125-1130. [5] R. J. Watts, 1997, Hazardous Wastes: Sources, Pathways, Receptors, John Wiley & Sons, New York, pp. 530-531. [6] C-C. Chan, R.H. Shie, T.Chang and D.Tsai, 2006, Workers’ Exposures and Potential Health Risks to Air Toxics in a Petrochemical Complex Assessed by Improved Methodology, Int.Arch.Occup.Environ.Health, 79, 135-142.

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Fast response model for dense gas dispersion accounting for complex geometries Sara Brambilla,a Davide Manca,a Michael D. Williams,b Michael J. Brownb a

Politecnico di Milano, Dipartimento di Chimica, Materiali e Ingegneria Chimica “G. Natta”, P.zza Leonardo da Vinci, 32, 20133 - Milano (MI), Italy, [email protected] b Los Alamos National Laboratory, D-3 Systems Engineering Group, TA 52, Bldg. 43, Bikini Atoll Rd., SM 30, Los Alamos, NM 87545, United States of America

Abstract In the last thirty years, both theoretical and experimental investigations supported the analysis of the behavior of dense gases when released in the atmosphere. A few classes of models were developed, differing for the level of detail of the cloud description. For design purposes as well as operator training, we focused on a fast-running model, capable of dealing with complex environments, e.g., chemical facilities and urban areas. Consequently, we opted for the approach based on the shallow water equations, i.e. a system of partial differential equations describing the cloud height, and the spreading velocities in the horizontal directions. The cloud density is inferred from the cloud height and the entrained volume of air. The manuscript discusses the theoretical framework that was implemented to describe the dense gas behavior by means of the shallow water equations. Keywords: shallow water equations, dense gas, accident modeling, fast-response software

1. Shallow water equations for dense gas dispersion The models available in the literature for simulating the dense gas dispersion can be divided into three groups: • integral models that describe the bulk properties of the cloud; • models based on the shallow water equations (SWE) that consider depthaveraged quantities; • Computational Fluid Dynamics (CFD) models that solve the Navier-Stokes equations. The final use (e.g., emergency preparedness and response, accident investigation, operator training) and the typology of problems a model is called to solve, determine the choice of one of the aforementioned groups. For instance, CFD models are not appropriate for emergency response, when a prompt estimation of the accident consequences is necessary. Nonetheless, it is worth noting that the future improvements of both computer hardware and software will probably modify the suitability of models. At present, our aim is the implementation of a fast-running tool, capable of describing quantitatively the dispersion of a dense gas in either chemical facilities or urban areas, i.e. complex environments. Consequently, a model based on the SWE is the most appropriate choice. In fact, this set of equations not only models the ground slope but it also accounts for the presence of obstacles, such as buildings and process units.

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Conversely, the SWE cannot describe elevated releases. The use of an efficient numerical algorithm makes the computational time short enough to achieve fast-running simulations even on common personal computers. The SWE describe the dispersion dynamics of an incompressible fluid of constant density in terms of cloud height ( h ) and horizontal velocities ( u , v ):

­ ∂h ∂hu ∂hv + =0 ° + ∂y ° ∂t ∂x °° ∂u ∂u 2 ∂uv § ∂e ∂h · + + g ′ ¨ + ¸ + S fx = 0 ® + t x y ∂ ∂ ∂ © ∂x ∂x ¹ ° ° ∂hv ∂uv ∂v 2 § ∂e ∂h · ° + + + g ′ ¨ + ¸ + S fy = 0 ∂x ∂y °¯ ∂t © ∂y ∂y ¹

(1)

where g ′ is the reduced gravity, e is the ground elevation, Sfx and Sfy are the drag terms, and x and y are the spatial coordinates. It is worth underlining that all the dependent variables are depth-averaged, i.e. the model assumes they are constant throughout the cloud height. The original formulation of SWE can be modified to model a dense gas, whose density varies in time due to the dilution with air, by adding a partial differential equation for the density dynamics. SLAM (Ott and Nielsen, 1996), DISPLAY-2 (Venetsanos et al., 2003), and TWODEE-2 (Folch et al., 2007) add this additional equation to the original SWE (system (1)). However, our approach differs because we need an even faster tool for operator training simulation that requires real-time and faster than wall-clock simulations.

2. Modification of the SWE approach for modeling dense gases Both Fay and Ranck (1983), and Eidsvik (1980) claimed that the horizontal spreading of a dense cloud is almost independent from the air entrainment process for isothermal releases. Hanna and Drivas (1987) used this hypothesis to develop an integral (box) model. Consequently, for isothermal releases, it is possible to solve the SWE derived for fluids of constant density, and determine the dilution a posteriori. This feature differentiates our approach from other existing codes that modify the SWE framework to account also for the density variability, i.e. they solve an additional partial differential equation (PDE) for the density of the cloud. Our approach benefits from the simpler and faster numerical scheme to solve a system of three PDE instead than four PDE. In particular, we set up an algorithm for the solution of the PDE describing the cloud height, and the spreading velocities in the horizontal directions. The cloud density was inferred from the cloud height and from the air entrainment velocity (we) which is parameterized by the Eidsvik approach (1980). Our model accounts also for the difference between the velocities of the slumping cloud (wg) and the surrounding air (wa):

we =

a1 w* + a2 wa − wg 1 + a3 Ri

(2)

where the values of the constants are a1 = 0.65 , a2 = 1 , a3 = 0.2 (Hankin and Britter, 1999; Briggs et al., 2001), w* is the friction velocity, and Ri is the Richardson number.

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The PDE system is solved with the finite differences method on a rectangular grid of assigned dimensions. The solution algorithm is based on discretizing spatially the PDE into a system of ordinary differential equations, which are then numerically integrated by means of the Euler’s forward method. To get a stable solution, the time step should satisfy the Courant–Friedrichs–Lewy condition: dt = c ⋅ min ( dx u , dy v ) . We use the upwind scheme to discretize the spatial derivatives of system (1). 2.1. Accounting for Buildings The ground slope terms ( ∂e ∂x , ∂e ∂y ) in system (1) account for the topography of the domain of interest. Previous works (Venetsanos et al., 2003; Folch et al., 2007) did not explicit how to deal with the obstacles on the ground. We want to point out that obstacles are not considered in the evaluation of ground slope terms, since they have infinite slope and their effect on the cloud is captured by the following hypotheses on the fluid motion. (1) The cloud can flow on the top of an obstacle only if it is taller than the obstacle itself. (2) The obstacles are impenetrable. These conditions allow achieving a level of detail that is deeper than the box models by modeling realistically the flow around obstacles. Although not fully implemented at the time of writing this paper, the SWE model can benefit from the wind field evaluated with a diagnostic model, such as QUIC-URB (Pardyjak and Brown, 2003), which allows incorporating the complex wind patterns in presence of obstacles while having a more representative reference velocity to quantify the entrainment, i.e. the dilution of the contaminant. By doing so, the entrainment can differ in each portion of the dense gas cloud. In addition, it is also possible to use a Lagrangian random-walk model, as QUIC-PLUME (Williams et al., 2004), within the dense gas cloud and switch to the neutral gas simulation when the cloud density approaches the air density. 2.2. Accounting for Transition to Neutral Density The SWE approach for dense gas modeling is only valid during the early stages of dispersion before dilution makes the cloud almost neutral. Since the cloud is often still dangerous long after it has become a passive gas, the shallow water model must account for the transition or be linked to a passive gas dispersion model. Actually, we linked the SWE to QUIC-PLUME (Williams et al., 2004). In this approach, the random-walk marker particles are uniformly distributed inside the initial source volume and then they move with the dense gas slump velocities as computed by the SWE and the winds produced by the building-aware QUIC wind model. The turbulence within the dense gas cloud is reduced according to a term inversely proportional to one plus the cloud Richardson number. Marker particles can escape the dense gas cloud via the turbulent velocities or the vortices created by the buildings (e.g., an updraft on the back side of the building). Thus the model allows determining of material emitted from the dense gas cloud. Once outside the dense cloud, the marker particles are treated as passive neutral tracers. When the cloud is diluted enough to approach neutral conditions, i.e., the Richardson number approaches zero, a smooth transition is obtained since the same random-walk model continues to be used for the transport and dispersion but without the SWE input.

3. Verification The verification step is the process of checking that a numerical procedure solves the equations correctly. The verification process compares the model results with those of a standard model that was validated for some specific configurations of the system.

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To verify the dense gas dispersion model discussed in the previous sections, we compared its output with the box model of Hanna and Drivas (1987) for instantaneous releases. The purpose of this comparison was not quantifying the error of the model, instead, it allowed determining if the model reproduces the expected trends of the dependent variables. The future research activity will be focused on validating the model against experimental data and not box models. The case study involves the dispersion of a cloud of 9.3 m radius and 14 m height and 3 kg/m3 initial density. The wind speed at 10 m of height is 2 m/s. Figures 1 and 2 show the comparison between the cloud radius, height, and average density evaluated with the SWE modified model (discussed in this manuscript) and the box model of Hanna and Drivas (1987). These Figures show the dynamics of the cloud until the dilution makes it neutral. Henceforth, the dispersion mechanism changes and the cloud behaves as a passive contaminant. 180

14

160

SWE Model Box Model

12

140 10

120 ] m [ s ui d a R

] m [ t h gi e H

100 80 60

8 6 4

40

0 0

2

SWE Model Box Model

20 10

20

30 Time [s]

40

50

0 0

60

10

20

30 Time [s]

40

50

60

Figure 1: Dynamics of the radius (on the left) and the height (on the right) of a dense gas cloud 3 SWE Model Box Model

2.8 2.6 ] 3

2.4

m g/ 2.2 k[ yt 2 si n 1.8 e D 1.6 1.4 0

10

20

30 Time [s]

40

50

60

Figure 2: Average density of a dense gas cloud

Figures 1 and 2 show that the SWE modified model reproduces the expected behaviors. The radius increases in time due to the negative buoyancy of the cloud that makes it slump on the ground. Initially, the height decreases due to the slumping, and then it slightly increases because of the dilution with air. The density decreases monotonically due to the air entrainment and the consequent increase of the cloud volume.

Fast Response Model for Dense Gas Dispersion Accounting for Complex Geometries

1151

4. Gas dispersion in complex environments The model discussed in the previous section should be preferred to common box models because it is capable of describing the complex flow of a dense gas in presence of obstacles, as in real industrial plants or urban areas. Figure 3 shows the dispersion of a dense gas cloud in a complex environment.

Figure 3: Dispersion of a dense gas cloud in a complex environment

Initially, the cloud spreading is axisymmetric, i.e. a cylinder can approximate the cloud. Tall obstacles stop the cloud spreading and force it to disperse laterally. The cloud can spread behind obstacles and in the canopy. Figure 3 shows that the SWE modified model is capable of describing such a complex behavior, although it deserves an extensive and detailed validation.

5. Conclusions The SWE represent a suitable framework to simulate the dense gas dispersion in complex environments, i.e. either in industrial or urban areas, because they account for both the topography and the presence of obstacles. The entrainment can be parameterized for instance with the Eidsvik (1980) approach. By using a diagnostic model, as QUIC-URB (Pardyjak and Brown, 2003), it is possible to have a more representative reference velocity to quantify the air entrainment. Moreover, the horizontal velocities evaluated by solving the SWE can be used within a Lagrangian random-walk model, such as QUIC-PLUME (Williams et al., 2004) to switch to the neutral gas model when the cloud density approaches that of air. The verification procedure reported in Section 3 demonstrated that our modified model reproduced the expected trends of cloud height, radius, and average density that matched the standard box model of Hanna and Drivas (1987). Section 4 showed that the model reproduces reasonably well the expected behavior in presence of obstacles. Future improvements will be devoted to the verification of continuous releases and the validation of the model with experimental open air and wind tunnel data.

References Briggs G.A., R.E. Britter, S.R. Hanna, J.A. Havens, A.G. Robins, W.H. Snyder, “Dense gas vertical diffusion over rough surfaces: results of wind-tunnel studies”, Atmospheric Environment, 35, 2265-2284, 2001

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Eidsvik K. J., “A model of heavy gas dispersion in the atmosphere”, Atmospheric Environment, 14, 769-777, 1980 Fay J.A, D.A. Ranck, “Comparison of Experiments on Dense Gas Cloud Dispersion”, Atmospheric Environment, 17, 239-248, 1983 Folch A., A. Costa, R.K.S. Hankin, “TWODEE-2: A Shallow Layer Model for Dense Gas Dispersion on Complex Topography”, Computer and Geosciences, http://hdl.handle.net/, 2007 Hankin R.K.S., R.E. Britter, “TWODEE: the Health and Safety Laboratory’s Shallow Layer Model for Heavy Gas Dispersion. Part 1. Mathematical Basis and Physical Assumptions”, Journal of Hazardous Materials, A66, 211–226, 1999 Hanna S.R., Drivas P.J., Guidelines for use of Vapor Cloud Dispersion Models, AIChE Press, New York (NY - USA), 1987 Ott S., M. Nielsen, Shallow layer modeling of dense gas clouds, Risø-R-901(EN), Risø National Laboratory, 1996 Pardyjak E.R., M.J.Brown, QUIC URB v. 1.1 - Theory and Users Guide, LA-UR-07-3181, 2003 Venetsanos A.G., J.G. Bartzisa, J. Würtz, D.D. Papailiou, “DISPLAY-2: a Two-Dimensional Shallow Layer Model for Dense Gas Dispersion Including Complex Features”, Journal of Hazardous Materials, 99, 111-144, 2003 Williams M.D., M.J. Brown, B. Singh, D. Boswell, “QUIC-PLUME Theory Guide”, LA-UR-040561, 2004

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1153

Middle term optimal control problem in eutrophic lakes through advanced mathematical programming approaches Vanina Estrada a, Elisa R. Parodi b, M. Soledad Diaz a a

Planta Piloto de Ingeniería Química (PLAPIQUI), Universidad Nacional del SurCONICET, Camino La carrindanga Km 7, Bahía Blanca 8000, Argentina, [email protected], [email protected] b Instituto Argentino de Oceanografía (IADO), Universidad Nacional del SurCONICET, Camino La carrindanga Km 7, Bahía Blanca 8000, Argentina, [email protected]

Abstract In this work, we address lake biorestoration through the formulation of first principles models for water quality and advanced mathematical programming techniques. Dynamic mass balances have been formulated on main phytoplankton groups and nutrients, as well as other components available in lakes and reservoirs. Main parameters in the model have been estimated in previous work Estrada et al., 2008. The combined reductions in nutrient loading and inlake biorestoration strategies to control algae growth and reduce eutrophication have been formulated as an optimal control problem for a middle term time horizon (three years). The problem has been formulated within a simultaneous optimization framework and solving the large scale nonlinear program with an Interior Point method (Biegler et al., 2002). Numerical results give deep insight on the quantitative application of restoration strategies. Keywords: eutrophication, optimal control, dynamic optimization

1. Introduction Most water bodies in the world are becoming increasingly eutrophic due to anthropogenic activities. Eutrophication, characterized by enrichment of plant nutrients, is associated to excessive growth of phytoplankton expressed as algal blooms and loss of biodiversity. Main point sources for eutrophication are the discharges of agricultural, industrial and urban wastewater. Much research effort has been devoted in the chemical engineering community to address effluent treatment when dealing with point sources (Hostrup et al., 1999; Chachuat et al., 2001; San Ramón et al. 2007; Karuppiah and Grossmann, 2008). Non-point sources, which are mainly related to agricultural activities, are more difficult to deal with and have received little attention regarding modeling aspects. However, sustainable strategies to control eutrophication in water bodies, such as nutrient loading reduction and the application of the food-chain theory through inlake biomanipulation, requires the evaluation of the global effects on the ecosystem. Experimental analysis of this process is time-consuming and expensive. Therefore, the development of first principles-based rigorous models for water quality provides deep understanding of biogeochemical processes that take place within water bodies, which is a fundamental step when addressing lake restoration. Sagehashi et al. (2001), propose a water quality simulation model to study the long-term stability of the ecological system after biomanipulation in a hypothetical water ecosystem, through simulations. Krivtsov et al. (2001) and Gurkan et al. (2006) have applied simulation

V. Estrada et al.

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models to study the effects of two different restoration approaches, aeration of the hypolimnion and biomanipulation, to improve water quality in different lakes. Procopkin et al. (2006) have studied the effect of fish removal on cyanobacteria biomass though an eutrophication simulation model. In this work, we address lake restoration strategies through the formulation of first principles models for water quality combined with advanced mathematical programming techniques. We have formulated dynamic mass balances on main phytoplankton groups, nutrients, DO and BOD. The application of combined reduction in external nutrient loading to the lake and inlake biomanipulation strategies to control algae growth have been formulated as an optimal control problem for a time horizon of three years, considering two optimization variables corresponding to the fraction of tributary inflows through a wetland and the rate of fish removal along the time horizon. The problem has been formulated within a simultaneous optimization framework and solving the large scale nonlinear program with an Interior Point method Biegler et al., (2002). Numerical results provide useful information on the quantitative application of restoration strategies in the middle term, as well as dynamic behavior of the main components in the water body.

2. Mathematical model for water quality in lakes and reservoirs The application of restoration policies to improve the water quality requires modeling and optimization of major chemical and biological processes that take place within water bodies. The present case study is Paso de las Piedras Reservoir, which is located in the south of Buenos Aires Province (Argentina) at 38° 22´ S and 61° 12´ W. It was built in 1978 to supply drinking water to Bahía Blanca (population around 450,000) and for industrial purposes at a petrochemical complex. The lake has two tributaries, which run through an important agricultural area. This water body has a coastline perimeter of 60 km and a mean depth of 8.2 m, so it can be considered as a shallow lake. The high content of phosphorus and nitrogen in Paso de las Piedras Reservoir is consequence of agricultural activities. The trophic state of this water body is currently eutrophic. In previous work (Estrada et al., 2008b), we have addressed the application of restoration strategies throughout a time horizon of one year as an optimal control problem. However, the middle term effect of restoration is not well documented and has had different experimental results depending on the specific water bodies reported in the literature (Jeppesen et al., 1997). In this work, we have extended the time horizon in our dynamic optimization model, considering sinusoidal functions for representing input variables. A detailed description of the model equations can be found in Estrada et al. (2008a). We have considered averaged horizontal compositions and gradients along the water height. The partial differential equations system has been discretized into two layers and main equations are: Total mass balances

dhT dt

=

1 NIN 1 NOUT ¦ QOUTm +Qrain − Qevap ¦ QIN k − A m =1 A k =1

(Eqn. 1)

Component mass balances for horizontal layers (U: upper layer, L: lower layer: j: Cyanobacteria, Diatoms, Chlorophytes, Nitrate, Ammonium, Organic Nitrogen, Phosphate, Organic Phosphorus, Biochemical Demand of Oxygen, Dissolved Oxygen) Upper layer

Middle Term Optimal Control Problem in Eutrophic Lakes through Advanced Mathematical Programming Approaches

dCUj dt

=

IN

¦ N

k =1

QIN U,k CIN Ujk VU

NOUT

¦

−

m =1

QOUTU CUj VU

+ rUj -

1155

CUj dhU kdA (Eqn. 2) (CUj − C Lj ) − ǻhU hU hU dt

Lower layer NOUT QOUT dC Lj C Lj dh L L C + r + kdA (C − C = ¦ (Eqn. 3) Lj Lj Lj U,j ) − dt VL ǻh L h L h L dt m =1 Phytoplankton: Rate equations for phytoplankton groups take into account production and losses due to respiration, natural death, settling and grazing. rij = Rij,growth − Rij,resp − Rij,death − Rij,settling − Rij ,graz (Eqn. 4)

i = UL , LL ; j = cyano, diatom ,chlorophyte The growth rate of the three phytoplankton groups is a function of solar radiation, water temperature and nutrients availability. Rij,growth = k i,growth f(T)ij f ( I)ij f(N)ij C ij (Eqn. 5)

i = UL , LL ; j = cyano, diatom ,chlorophyte 2

f ( T )ij = −

( T j − Topti ) +1 T 2 opti

§ I exp¨1 − oi ¨ I opt j I opt j © C PO4 j f ( N ) ij = C PO4 j + K Pi

f ( I ) ij =

I oi

(Eqn. 6)

· ¸ ¸ ¹

(Eqn. 7)

(Eqn. 8)

Phytoplankton respiration, natural death and settling rates are given as: Rij ,resp = k j ,resp θr (T − 20)Cij Rij ,death = k j ,deathθm(T − 20 )Cij

Rij ,settling = k j ,settling

Cij

(Eqn. 9) (Eqn. 10) (Eqn. 11)

hi

i = UL , LL ; j = cyano, diatom ,chlorophyte The herbivorous zooplankton grazing rate is: Cij Rij,graz = k j,graz C Zooi Cij + K graz

(Eqn. 12)

Nutrients cycle in water bodies Phosphorus cycle: State variables describing phosphorus cycle are phosphate and organic phosphorus. Phosphorus is uptaken by phytoplankton in phosphate form. As phytoplankton biomass is composed of carbon, nitrogen and phosphorus, upon death, phytoplankton increases both phosphate and organic phosphorus pool. This latter goes through a mineralization reaction to phosphate, which is then available for phytoplankton generation again. Nitrogen cycle: Three state variables describe nitrogen cycle in the present model: ammonium, nitrate and organic nitrogen. Phytoplankton is able to uptake both ammonium and nitrate for growth. Ammonium is oxidized to nitrate and its concentration increases by organic nitrogen hydrolysis at a temperature-dependent

V. Estrada et al.

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mineralization rate. Due to internal nutrient recycle, reducing the external loading of nutrients to the lake is not enough for restoration. Detailed equations describing the described processes are presented in Estrada et al. (2008a).

3. Optimal control problem and optimization algorithm In this work, we formulate the application of inlake restoration strategies together with reduction of external loading of nutrients as an optimal control problem along a middle term horizon of three years, on a daily basis. Shapiro (Brezonic and Fox, 1975) suggested the term biomanipulation to refer to lake restoration techniques that are based on the food chain theory. This method is supported on a theory of top-down control on lakes. The basic idea is to perform zooplanktivorous fish removal or piscivorous fish stocking, or a combination of both, to keep a high grazing pressure on the phytoplankton community by the herbivore zooplankton Shapiro and Wright (1984). In this work, we have considered the application of biomanipulation by fish removal, considering zooplankton concentration as the optimization variable. This variable can be later associated to the rate of fish removal, based on fish biomass data from the specific lake. The objective function is the minimization of the offset between phytoplankton concentration and a tight desired value of 0.10 mg/l throughout the time horizon. 2

· § min ³0tf ¨ ¦ C j ( t ), − 0.25 ¸ dt ¸ ¨ j = phyto ¹ © st

(Eqn. 13)

DAE eutrophication model 0 싨 FWETLAND 싨 .5FDIVISORIO ( l / d )

0.01싨 Czoo 싨 1 ( mg / l )

The dynamic optimization problem is formulated within a simultaneous dynamic optimization framework by transforming it into a large-scale nonlinear program (NLP). Both state and control variables are represented as piecewise polynomials over finite elements in time and the differential-algebraic system is discretized by collocation on finite elements. We have used an Interior point method within program IPOPT Cervantes et al. (2000) with SQP techniques for solving the large-scale NLP. Extensions of this approach are described in Raghunathan et al. (2004), Kameswaran and Biegler (2006) and Zabala and Biegler (2009).

4. Discussion of results The DAE eutrophication model for Paso de las Piedras Reservoir has twenty one differential equations (plus an additional one for the objective function) and sixty algebraic ones, after spatial discretization into two layers. A time horizon of three years has been considered, on a daily basis. Input variables have been represented with sinusoidal functions, based on observed data for one year. The optimal control problem has two optimization variables corresponding to the fraction of inlet stream that is derived to a nearby wetland and the concentration of zooplankton in the lake to control phytoplankton growth, along the time horizon. The resulting nonlinear programming (NLP) problem for temporal discretization with eighty finite elements and two

Middle Term Optimal Control Problem in Eutrophic Lakes through Advanced Mathematical Programming Approaches

1157

collocation points with two optimization variables has 15383 nonlinear equations. It has been solved with program IPOPT (Biegler et al., 2002), which implements an Interior Point method with reduced Successive Quadratic Programming. Numerical results show that tributary deviation through a wetland for nutrient loading reduction is required throughout the entire time horizon, at its maximum allowed flowrate (50% of the inflows, with 50% nutrient retention). Figure 1 shows cyanobacteria concentration profiles before and after biomanipulation. It can be seen that the peak in the first year is reduced to 50% of its value without restoration, but still remains above the desired concentration (0.20 mg/l). However, during the following two years the peak in concentration is below the desired value. Figure 1 also shows that zooplankton concentration is required to be at its maximum value during the first year, with small increases before cyanobacteria peaks in the following years. Figure 2 shows phosphorus concentration before and after biomanipulation. It can be seen that nutrient loading reduction requires even longer time horizons to show noticeable effects on concentration due to nutrients recycle.

1.5

Cyanobacteria before restoration

Concentration (mgC/l)

Optimal zooplankton concentration Optimal cyanobacteria concentration

0.8

0.4

Phosphate concentration (mg/l)

1.2 1.2

0.9

0.6

After restoration Before restoration

0.3

0.0

0.0 0

200

400

600

800

1000

Time (Days)

Figure 1. Comparison between cyanobacteria concentration profiles before and after restoration and optimal profile for zooplankton conc.

0

200

400

600

800

1000

Time (Days)

Figure 2. Main nutrient concentration profiles before and after restoration

5. Conclusions In this work, we have formulated an optimal control problem to plan middle term restoration within a water body and analyze the ecosystem dynamic behavior under these strategies. Process systems engineering techniques have proved to be valuable tools for addressing control of ecological systems.

6. Acknowledgements The authors gratefully acknowledge financial support from the National Research Council (CONICET), Universidad Nacional del Sur and ANPCYT, Argentina.

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References V. Estrada, E. R. Parodi and M. S. Diaz, 2008a, Determination of biogeochemica parameters in eutrophication models with simultaneous dynamic optimization approaches, Comp. & Chem. Eng., submited. L. T. Biegler, Cervantes, A. and Waechter, A., 2002, Advances in simultaneous strategies for dynamic process optimization, Chem. Eng. Sci., 57, 575-593. M. Hostrup, P. M. Harper and R. Gani, 1999, Design of environmentally benign processes integration of solvent design separation processes synthesis, Comp. & Chem. Eng., 23, 13951414. B. Chachuat, N. Roche and M. A. Latifi, 2001, Dynamic optimization of small wastewater treatment plants including nitrification and denitrification process, Comp. & Chem. Eng., 25, 585593. F. M. San Ramón, E. Bringas, I. Ortiz and I. E. Grossmann, 2007, Optimal synthesis of an emulsion pertraction process for the removal of pollutants anions in industrial wastewater systems, Comp. & Chem. Eng., 31, 456-465. R. Karuppiah and I. E. Grossmann, 2008, Global optimization of multiscenario mixed integer nonlinear programming arising in the synthesis of integrated water networks under uncertainty, Comp. & Chem. Eng., 32, 145-160. M. Sagehashi, A. Sakoda and M. Susuki, 2001, A mathematical model of a shallow and eutrophic lake (The Keszthely Basin, Lake Balaton) and simulation of restorative manipulations. Wat. Res., 35, 1675-1686. V. Krivtsov, C. Goldspink, D. C. Sigee and E. G. Bellionger, 2001, Expansion of the model “Rostherne” for fish and zooplankton: role of top-down effects in modifying the prevailing pattern of ecosystem functioning, Ecol. Model., 138, 153- 171. Z. Gurkan, J. Zhang and S. E. Jørgensen, 2006, Development of a structurally dynamic model for forecasting the effects of restoration of Lake Fure, Denmark, Ecol. Model., 197, 89-102. I. G. Prokopkin, V. G. Gubanov and V. G. Gladishev, 2006, Modelling the effect of planktivorous fish removal in a reservoir on the biomass of cyanobacteria, Ecol. Model., 190, 419-431. V. Estrada, E. R. Parodi and M. S. Diaz, 2008b Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches, Comp. & Chem. Eng., (2008b) submited. E. Jeppesen, Ma. Søndergaard, Mo. Søndergaard and K. Christoffersen (eds.), 1997, Ecological studies, Springer, New York. P.L. Brezonik and J.L. Fox (eds.), 1975, Water Quality Management through Biological Control. Department of Environmental Engineering Science, Univ. Florida, Gainesville. J. Shapiro and D. I. Wright, 1984, Lake restoration by manipulation. Round Lake- the first two years, Freshwater biol., 14, 371-383. A. M. Cervantes, A. Waechter, R. Tutuncu and L. T Biegler, 2000, A reduced space interior point strategy for optimization of differential algebraic systems, Comp. & Chem. Eng., 24, 39-51. A. Raghunathan, M. S. Diaz and L. T. Biegler, 2004, An MPEC formulation for optimization of distillation operations Comp. & Chem. Eng., 28, 2037-2052. S. Kameswaran and L. T. Biegler, Simultaneous dynamic optimization strategies: Recent advances and challenges, 2006, Comp. & Chem. Eng., 30, 1560-1575. V. Zabala and L.T. Biegler, 2009, Optimization-based strategies for the operation of low-density polyethylene tubular reactors: Moving horizon estimation, Comp. & Chem. Eng., 33, 379-390.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1159

Numerical Comparison of Chemical Reactors Safety Criteria Eugeniusz Molga,a Michał Lewaka a

Warsaw University of Technology, Chemical and Process Engineering Department, ul. Warynskiego , 00-645 Warszawa, Poland, [email protected], [email protected]

Abstract The boundary safety criterion, which can be applied when the reaction kinetic information is scarce, has been compared to the model-based safety criteria: the divergence criterion and the criterion of derivatives, respectively. The results obtained for a homogeneous liquid reaction carried out in a semibatch stirred tank reactor fully confirm abilities of this boundary safety criterion to predict safe operating conditions. Keywords: Reactor modeling, safety of chemical reactors, safety criteria

1. Introduction A loss of temperature control in chemical reactors (thermal runaway) may occur for exothermic reactions, when for some reasons the rate of heat generation by chemical reaction exceeds the rate of heat removal by cooling. Then, a local or global increase of the reactor temperature can provoke an increase of the reaction rate, so also a further increase of the reactor temperature. Due to this auto-acceleration effect, the temperature of the reaction mixture may reach such a high value, at which dangerous side or decomposition reactions are triggered off, so a serious accident or even explosion may take place. Despite of a significant effort in research, design and management dedicated by chemical engineers in the filed of reactor safety, thermal runaway events in chemical reactors still occur. A numerous criteria for safe operating chemical reactors can be found in the literature [1]. From the industrial point of view an elaboration of robust and efficient safety criteria, which can be applied even in a case of scarce kinetic information, is crucial. In this paper predictions obtained with the boundary safety criterion [2], which can be applied even in a case of limited kinetic information, have been compared to the results provided with other model-based safety criteria – i.e. the divergence criterion [3] and the criterion of Hub and Jones (called also the criterion of derivatives) [4].

2. Reactor model Modeling of a stirred tank semibatch chemical reactor has been carried out for the second order homogeneous reaction taking place in the liquid phase. The stoichiometric equation of this reaction reads as follows:

ν A A +ν B B = ν CC +ν D D

(1)

In semibatch operating mode the compound B is loaded before starting of the reaction, while the stoichiometrically equivalent amount of the reactant A is slowly added into the reactor vessel at a constant volumetric feeding rate - ΦA. The considered reaction is

E. Molga and M. Lewak

1160

an exothermic one, the reactor content is perfectly mixed and the reactor vessel is equipped with the cooling jacket. The temperature of the cooling liquid - Tc is kept constant. This case is often met in industrial practice – e.g. in fine chemical industry where sophisticated temperature control systems are usually not in use and the cooling liquid is taken directly from the external reservoir. Assuming also, that for the considered reacting system each factor νi appearing in the stoichiometric equation is equal to 1, the reactor model equations (mass and heat balance equations) read as follows:

dV = ΦA , dt

(

dn A = Φ A c AD − r V , dt

d V ρ M c p, M T dt

)=Φ

A

dnB = −r V , dt

r=k

n A nB V V

(2-5)

ρ A c p , A TD + ΔH r r V − U A (T − Tc )

(6)

The presented set of model equations is valid during an addition period (0 < t < tD), while after completion of the addition (t > tD), model equations (Eqs. 2, 3 and 5) have to be slightly modified because the feeding rate ΦA becomes equal to zero. Before solving, this set of model equations can be transformed introducing dimensionless variables and process parameters as follows:

θ=

t , tD

β=

ε=

Φ A tD , VBo

RH =

T , TR

ª §

ρ A c p, A , ρ B c p,B 1 ·º

ζB =

nBo − nB , nBo

γ ad ,o =

ΔTad ,o , TR

ζA = γ=

nA n Ao

E R TR

(U A) t

o D κ = k k (T ) = exp «γ ¨¨1 − ¸¸» , Da = k (TR ) cBo t D , Co = R β ε ρ c © ¹ B p , B VBo ¬ ¼

(7-10)

(11-14) (15-17)

where TR = 300 K is the reference temperature. Solving a set of the presented model equations (Eqs. 2-6), the reactor temperature trajectory as well as the reactant concentrations can be determined as a function of time. So, the reactor performance at different operating conditions (i.e. at the feeding rate determined by the chosen dosing time – tD and at the cooling liquid temperature – Tc) can be easily investigated. Four typical reactor behaviors – obtained at conditions listed in Table 1 – are shown in Figs. 1a÷d, where the characteristic temperature trajectories are displayed for Runs A÷D, respectively. In these diagrams, each temperature trajectory is related to the socalled target temperature – Ta. This temperature is the reactor temperature trajectory obtained at such operating conditions, that all reactant A added into the reactor is immediately converted, so no significant accumulation of this reactant is present in the reacting mixture. Therefore, an operation of reactor along the target temperature trajectory is always safe and simultaneously efficient from a performance point of view. The target temperature is defined as follows:

Ta = Tc +

1.05 ΔTad ,o

ε [RH + Co (1 + ε θ )]

(18)

Numerical Comparison of Chemical Reactors Safety Criteria

1161

During the addition period (0 < t < tD or 0 < θ < 1), this target temperature slightly drops because of increase of the heat exchange area caused by an increase of the reacting mixture volume. Table 1. Reactor behavior for different reacting and at different operating conditions

Run Reactor behavior

Δγad,o RH Co Da ε

A B C D

[-] 0.197 0.600 0.672 0.690

Tc [K] insufficient ignition 292.88 marginal ignition 282.42 thermal runaway 288.61 safe, along Ta trajectory 298.31

380

[-] 2 2 2 2

[-] 10 10 10 10

TR [K] 300 300 300 300

380

Run B

Run A 360

360

340

340

T [K]

T [K]

γ [−] 40 40 40 40

[−] 0.3 0.3 0.3 0.3

[-] 2 2 2 2

320

Ta 320

Ta 300

TR

300

TR 280

280 0

1

2

3

4

5

6

0

1

2

θ [−]

3

4

5

6

4

5

6

θ [−]

380

380

Run C

Run D

360

360

Ta Ta

340

T [K]

T [K]

340

320

320

TR

TR 300

300

280

280 0

1

2

3

4

5

6

0

1

θ [−]

2

3

θ [−]

Figure 1. Dynamic behavior of the reactor at different operating conditions – details in Table 1

3. Criteria for safe operation of chemical reactors Boundary diagram safety criterion In industrial practice, due to a limited knowledge on the reaction kinetics, model-based simulations of the reactor performance are not possible. Particularly, in fine chemical industry costly investigations of the reaction kinetics are often omitted, because the time required for such studies is usually longer than a “product life-time” on the market. In this case the criterion based on the so-called safety boundary diagrams can be successfully used [1, 2]. To apply this criterion the reaction rate constant at the cooling temperature – kc as well as the reaction activation energy – E have to be only known. Runaway and non-runaway operating conditions can be predicted in the boundary safety

E. Molga and M. Lewak

1162

diagram, where a boundary line separating safe and dangerous regions is plotted in terms of the Reactivity and Exothermicity numbers. These dimensionless numbers are defined as follows:

Ry =

κ c Da

ε (RH + Co )

Ex =

,

Δγ ad ,o TR2 γ

Tc2 ε (RH + Co )

(19-20)

A typical safety boundary diagram is shown in Fig. 2. In this diagram the inherently safe region is clearly determined with the following relationships: Ex < Exmax and Ry > Rymin. Notice, that considered previously model-based reactor behaviors (see Table 1), fully confirm predictions supplied with use of the boundary safety diagram criterion. The boundary safety criterion is a typical off-line criterion, which helps to predict safe operating conditions in advance. 0.8

Co=10 RH=2

inherently safe region

0.7

Rymin

0.6

Ry

0.5

Run D

0.4 0.3

runaway region

Run A 0.2 0.1

Run C

Exmax

Run B

0.0 0

2

4

6

8

10

Figure 2. Safety analysis on the boundary diagram

12

14

16

18

20

22

Ex

Divergence criterion This criterion, which is based on the chaos theory techniques, states that the reactor is on the trajectory leading to runaway, when the divergence of the system becomes positive on a segment of the reaction path [3]. If the model-based solution is given, the appropriate values of divergence can be estimated as follows:

§ ∂β ∂¨ ∂θ div = © ∂β

· § ∂ζ · ¸ ∂¨ B ¸ ¹ + © ∂θ ¹ ∂ζ B

(21)

Predictions obtained with this criterion for Run C, where a significant thermal runaway is noticed, are given in Fig. 3a. It is visible that at time θ = 0.32 the divergence becomes positive, so the operator has enough time to undertake safety measures. This criterion fully confirms the predictions supplied with the boundary safety diagram, also for Runs A, B and D not shown in Fig. 3. Criterion of derivatives From a fundamental analysis of the reactor behavior it has been found, that for the detection of runaway, it is enough to observe the following expressions [4]:

d 2β >0, dθ 2

d (β − β c ) >0 dθ

(22-23)

Positive values of both derivatives indicate that the system is on the trajectory leading to runaway. Predictions obtained with this criterion for runaway case (Run C) are given in Fig. 3b. This method is very sensitive to the accuracy of derivatives estimation. In the

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considered case, both derivatives are positive just after starting the reaction, although significantly high value of the second derivative is noticed at θ = 0.62. Therefore, particularly for on-line indications an appropriate filtering of data is required. 400

(a) 300

15000

Run C

(b)

10000 θ = 0.62

2

200

100

2

d β/dθ

divergence

Run C

θ = 0.32

0

5000

-100

0

-200 0.0

0.5

1.0

θ [−]

1.5

2.0

0.5

0.6

0.7

0.8

Figure 3. Runaway detection with: (a) divergence criterion, (b) criterion of θderivatives

4. Conclusions A numerical comparison of safety criteria indicates that the boundary safety criterion gives sufficiently accurate predictions of safe operating conditions for semibatch reactors. This criterion has been directly verified with the results of the reactor model (Fig.2) as well as with the results supplied with use of the divergence criterion. The application of the derivatives criterion can be problematic, due to its sensitivity to experimental noise, which can cause triggering of false alarms.

5. Acknowledgements This work has been supported by the Ministry of Science and Higher Education (Poland) within a frame of the scientific grant.

6. References [1] [2] [3] [4]

K.R. Westerterp, E. J. Molga, Chem. Eng. Res. Des., 84 (2006) 543. E.J. Molga, M. Lewak, K.R. Westerterp, Chem. Eng. Sci., 62 (2007) 5074. J. Bosch, F. Strozzi, J. Zbilut, J.M. Zaldivar, Compt. Chem. Eng., 28 (2004), 527. L. Hub and J.D. Jones, Plant Oper. Prog., 5 (1986), 221.

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Sustainable reduction of dredging fleet emissions Renske Ytsma a, Zofia Lukszo a, Rick Maliepaard b Delft University of Technology, Jaffalaan 5, 2628 BX Delft, the Netherlands, [email protected] b Royal Boskalis Westminster, Rosmolenweg 20, 3350 AA Papendrecht, the Netherlands, [email protected] a

Abstract The research described in this paper presents a study done at Royal Boskalis Westminster – one of the largest dredging companies in the world. It was aimed at defining a practical approach for reducing the dredging-fleet emission of gases (CO2, SOx and NOx) by operational measures in a technologically, financially and socially feasible way. The designed experiments were carried out at one of Boskalis largest dredging vessels “The Queen of the Netherlands” during its operation. They resulted in understanding the influence factors of fuel consumption by dredging vessels and their relation to the amount and the type of emissions. Model-based process improvement including recommendations to realize the intended changes within the company concludes the paper. Keywords: Dredging, shipping, gaseous emission, fuel consumption, operational improvement

1. Introduction From uncontrollable outlier to the focus of all attention; environmental awareness, and especially gaseous emissions, are becoming more and more important in the shipping and dredging industry. Until recently, this enormous industry was scarcely affected by environmental issues. The estimations of CO2 emission from the shipping industry varies between 2% and 3% of the world’s total level, and for SOx and NOx around 15-17% [1]. Therefore, the research question is: how can the dredging-fleet emission of gases (CO2, SOx and NOx) be reduced by operational measures in a technologically, financially and socially feasible way? To answer this question the following approach aimed at improving environmental performance by operational measures is defined and executed: - Problem statement to learn what influences the performance indicators and how they can be changed by the problem owner - Defining a measurement method of actual emission during the dredging cycle (at this moment there is no generally available technology for measurements of emission onboard ships) - Performing field study (analyzing the ship’s operations): 1. Designing Experiments (reference experiments and experiments to identify relations between operational measures and the response, i.e. fuel consumption)

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2.

-

Modelling and Analysis (a quantitative analysis of the emission of the vessel) 3. Decision Making (an optimization model supporting operational improvement with respect to economic and environmental performance) Process changing (a framework with recommendations to realize the intended changes within the company).

2. Problem statement The propulsion of a dredging vessel by using fossil fuels is a large system with many different aspects. To be able to analyze whether the performance of the system will improve after intervention, the current performance needs to be known. To learn more about what influences the performance indicators and how they can be changed by the problem owner an analysis of the causal relations has been performed. Different types of factors can be identified from the causal-effect analysis: - steering variables; - uncontrolled (environment) or noise variables; variables that influence the outcome of the system without the possibility for the problem owner to interfere. - system variables; - output variables or performance indicators; variables that represent the objectives of the dredging contractor. The performance indicators identified here are: total costs company reputation Both performance indicators are influenced by the amount of emission or fuel consumed by the vessel. The factor identified to influence the amount of emission is the requested percentage of total pitch capacity. The pitch is the angle of the propeller blades. With this angle the speed of the vessel can be controlled. The power to be delivered by the engines is directly related to this angle.

3. Measuring emissions Different methods and materials exist or are in development to measure the emission of ships [2]. Nevertheless, at this time there is not yet one proven technique implemented widely in the industry that is capable of measuring all types of emission (NOx, SOx and CO2); costs are high and none of the techniques supports on-line measurement. To determine the amount of emission produced by a ship, the measurement of the fuel consumption of the ship is a suitable alternative. Emissions of SOx and CO2 can be determined directly based on fuel consumption and fuel specifications of the vessel. The NOx emissions can be calculated using engine specifications and combustion temperature. Wang et al. argue that a fuel based method is inferior to an activity based method because of inaccuracy [3]. Because at this moment there is no feasible alternative available, the fuel-based measurements can serve well for the purpose of comparing the effect of operational measures on the emissions.

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4. Field study With increasing attention to sustainability and fuel costs over recent times operational behaviour related to the vessel speed reduction and controlled acceleration have gained attention as emission abatement technologies. A three phase field study was performed to investigate the feasibility of operational improvements within dredging. The dredging contractor Royal Boskalis Westminster NV provided the possibility to do a field study for this research. On the trailing suction hopper dredger ‘Queen of the Netherlands’ the operational actions, the fuel consumption and the vessel speed had been monitored during a ten-day trial period.The research aimed at finding the relation between pitch, fuel consumption and vessel speed [4]. Design of Experiments To design experiments the experimental factors including the range of variations should be defined [5]. Firstly, reference measurements are executed to provide information about the fuel consumption of the vessel per phase of the dredging cycle during standard operation. Consequently, experiments were held to analyse what the effect of changes in operational behaviour are on the fuel consumption. Here the acceleration of the ship in phases between dredging and sailing loaded, and next between dumping and sailing empty was varied. Multiple repetitions of experiments for different uncontrollable factors (noise factors as e.g. water depth) are performed. Modelling and Analysis During this phase a quantitative analysis of the emission of the vessel was carried out. The total emission that a dredging vessel produces varies for each dredging phase. The data from the experiments have been inserted in a spread sheet model to enable standard translation from fuel consumption to vessel emissions as well as to estimate the vessel specific relation between vessel speed and fuel consumption. The reference measurements and experiments on board have provided information about the actual influence of operational changes on fuel consumption and emission production. With these results it is possible to “optimize dredging projects” and determine whether a feasible region for vessel speed reduction exists. The quantitative relation between pitch, fuel consumption and vessel speed is unique for each vessel and needs to be investigated for each vessel separately. Decision Making Using the experimental results an optimization model was developed to support operational improvement with respect to economic and environmental performance. The decision-making tool can support project optimization according to different scenarios, e.g. increasing price of crude oil, introduction of ship emission charging and changes in market price of dredging material. Furthermore, the optimization model can easily be adapted for changes in fuel specification, emission prices and environmentrelated variables as e.g. type dredged material or water depth. Since economic feasibility is the dredging contractor’s key-objective, the decision making tool minimizes the financial costs related to emissions, operation and fuel:

(1) whereby: S:

Pitch [%]

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The optimal solution of the model (1) giving an optimal financial setting for Pitch gives data to calculate the company reputation as a total amount of emissions and fuel consumed. It helps in finding a trade-off between two conflicting objectives. To enable fair comparison of performances it is desirable to express emission based on the performed production: emission per cubic metre of dredged material. This method is used in the Dutch NOx emission trading scheme, where quota for a region are set expost, based on the region’s effective production.

5. Process change The results of the scenario analysis show that certain combinations of fuel, emissions and dredged material price, vessel speed reduction and controlled acceleration can lead to more competitive project performances. However, in practice these operational improvements are not easily implementable within an organization where the mindset is aimed at maximal production rather than minimal emission. The independency of the vessel staff causes the agency problems: asymmetry in information, hidden characteristics and hidden actions. To assure that the vessel staff will carry out operational measures as suggested by the decision-making tool the classic categories of agency solutions ‘incentives’ and ‘monitoring’ can be used [6]. Furthermore, the company should attack the reason for the existence of the principal-agent relation: the difference in objectives between head office, project office and vessel staff. If the vessel staff becomes aware of the rationale for implementation of measures they will see the effect it can have on the company’s performances and thus their own salary or job assurance. The realization of this twosided commitment should go through solid communication; from vessel staff to head office but also vice versa. The following mechanism can be proposed to improve the communication between head office, project office and vessel staff: - Process rounds with the vessel staff during the project execution - Training and support - Expansion of the decision-making tool with a good trade-offs feasibility Next to the good relation between the head office and the vessel staff, it is important that the improvement measures are integrated throughout the whole dredging company to stimulate changing of the mind setting by addressing adequately environmental concerns. Moreover, communicating the operational measures aimed at reducing emissions and fuel consumption contributes to improving the visibility and reputation of the company.

6. Conclusion and recommendations for further research The proposed approach based on experimentation and process modelling including the organizational analysis of the company aimed at stimulating transition of mindset with respect to the environmental awareness was applied successfully at the Boskalis largest dredging vessel “The Queen of the Netherlands”. To make the research results presented in this paper applicable to other vessels or the complete fleet, additional experiments are needed to validate system and optimization models. The research approach as presented in Chapter 1 is generally applicable to any vessel. We would like to stress, that in order to ensure proper implementation of the operational measures, a decision making tool aimed at optimizing an economic criterion does not

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offer any guidance. A systematic analysis of the organizational complexity at the company is needed to formulate an implementation plan taking into account the dedication of employees. This way, the efforts that need to be taken to ensure the mindset transition is one step closer. The vessel staff needs to be motivated for the revised objectives by receiving information over the effect of their actions on performance indicators; and by “creating a sport” in minimizing emission. Moreover, providing a real-time visualization on board for the performance indicators ‘fuel consumption’, ‘emission’ and ‘costs’, will enable Officers to directly see the effect of their actions on the company objectives; without constraining their high level of autonomy.

References [1] Rees, W. E. (1992) Ecological footprints and appropriated carrying capacity: what urban economics leaves out, Environment and Urbanisation. 4 (2) [2] Duyzer, J. et al., Assessment of emissions of PM and NOx of sea going vessels by field measurements, TNO report 2006-A-R0341-B, 2007 [3] Wang, C.C., Firestone, J.J., Modeling Energy Use and Emissions from American Shipping, Environm. Science and Technology, 41 (9), 2007 [4] Ytsma, R.K., Limited emission dredging, Master Thesis, Delft Univ. of Techn, 2008 [5] Montgomery, D. C., Design and Analysis of Experiments, Wiley, 2004 [6] Rutherford, M.A., et al, Examining the Relation Between Monitoring and Incentives in Corporate Governance, J. Management Studies, 44 (3), 2007

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Systematic ontology development of accident databases R. Batres,a H. Muramatsu,a Y. Shimada,b T. Fuchino,c P. W. H. Chungd a

Toyohashi University of Technology, Toyohashi 441-8580, Japan National Institute of Occupational Safety and Health, Tokyo 204-0024, Japan c Tokyo Institute of Technology, Tokyo 152-8552, Japan d Loughborough University, Loughborough, LE11 3TU, England b

Abstract A number of accident databases have been developed including both public and commercial ones. However, these databases implement static data models that are used to classify each accident. It is then difficult to dynamically expand the underlying database schema if for example new causes are identified. In this paper we propose an approach for accident database development based on knowledge engineering techniques. In particular, we explore the use of ontologies and Formal Concept Analysis. Keywords: accident database, formal concept analysis, ontologies

1. Introduction Safety plays a very important role throughout the life cycle of a chemical plant. To ensure safety and minimize later plant changes, safety is evaluated during process and plant design stages. On the other hand, there is an enormous amount of information available on past accidents in the form of incident reports available as documents and managed by databases. Engineers who perform safety analysis can benefit from this information. However, existing incident reports and accident databases are written the form of textual natural language descriptions. Extracting knowledge directly from such sources has a considerable number of mismatches. False positives are reported when a word has the same spelling but a different meaning such as the word tank. Also, false negatives are obtained for the following reasons: 1. Some accident representations lack the ability to deal with types and subtypes of things. For example, a query for finding accidents that resulted in explosions may not show reports containing the word BLEVE (a kind of explosion involving vapors from boiling liquids). 2. Lack of semantic relations between two types of things. For example, querying the database to find accidents about “crude oil that leaks from distillation columns,” produces results of which only 40% are answers to the query. Accident databases are developed on models for a given domain. For example, Chung and Jefferson [1] describe a model for the domain of accidents in the process industries. In that work, keywords were extracted from over 5000 accident reports. Subsequently, these keywords were analyzed and organized into a hierarchy.

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A number of accident databases have been developed including both public and commercial databases. However, these databases implement static data models that are used to classify each accident. It is then difficult to dynamically expand the underlying database schema if for example new causes are identified. In this paper we propose an approach for accident database development based on knowledge engineering techniques. In particular, we explore the use of ontologies and Formal Concept Analysis. Ontologies define the structure of knowledge by defining types and subtypes of things and their relations. For example, search for the previous crude oil query can be improved by means of a location relation that associates the crude oil, the leaking process and the distillation column. The upper ontology defines basic classes and properties useful for defining concepts such as physical quantities, causality, substances, equipment, physical and chemical transformations, plant operations and personnel. Typically, domain ontologies are developed in an ad-hoc fashion, often without sound explanations of the class structure. To avoid this, we propose the use of FCA as way to assist the development of the domain ontology. Formal Concept Analysis (FCA) is an analysis technique for knowledge processing based on applied lattice and order theory. FCA works by processing a collection of objects and their properties to identify hidden relationships represented as concept lattice.

2. Methodology The proposed approach involves three steps: 1. Identify common objects (keywords) relevant to accidents in the process engineering domain 2. Use text processing techniques to identify attributes that are associated to the objects 3. Use FCA to evaluate the similarity of ontological objects, cluster the objects, eliminate redundancies and create class hierarchies 4. Merge and combine the hierarchies into the upper ontology For the identification of common objects, we are relying on the lower levels of the hierarchy of terms mentioned in [1] as well as books and Internet sources. Text processing includes the identification of terms and text parsing. Term identification is used to find a set of words that together constitute a term. For example, the words chemical reaction can be identified as a single term chemical_reaction using tools such as TextToOnto [2]. Text parsing converts natural-language sentences (such as fragments of a book) to representations that can be manipulated by computer programs. For example, the Stanford Parser [3] produces the following output when parsing the sentence “a chemical_explosion requires a chemical_reaction”. det(chemical_explosion-2, a-1) nsubj(requires-3, chemical_explosion-2) det(chemical_reaction-5, a-4) dobj(requires-3, chemical_reaction-5) where det, nsubj, and dobj are grammatical relations for determiner, nominal subject, and direct object, respectively. These grammatical relations can be utilized to extract

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attributes for the FCA step. There is still ongoing work for developing the rules that automate this step. FCA is used for finding a preliminary class hierarchy from a set of individuals, a set of properties and a binary relation defined on the Cartesian product of both sets stating that an object has or has not a given property. Subsequently, the class hierarchy obtained from the FCA is encoded in an ontology language and merged into an upper ontology. The upper ontology provides generic concepts that are domain independent.

3. Formal Concept Analysis Formal Concept Analysis (FCA) is a method that identifies implicit relationships between sets of objects and their attributes. FCA was originally developed by Wille et al. [4] based on applied lattice and order theory. The building block of FCA is called formal context. A formal context is defined as a set K := ¢O, A, R² where O is a set of objects, A is a set of attributes and R is a binary relation between O and A . The relation R is defined as the Cartesian product R ⊆ O × A consisting of all pairs ¢ o, a² ∈ R such that the object o has the attribute a as in (bicycle, has wheels). A formal concept is defined as the element of

K represented as the pair ¢Oi , Ai ² such

that: 1. Oi

⊆ O , Ai ⊆ A 2. Every object in Oi has every attribute in Ai . Conversely, Ai is the set of attributes shared by all the objects in Oi 3. For every object in

O that is not in Oi , there is an attribute in Ai that the object

does not have 4. For every attribute in

A that is not in Ai , there is an object in Oi that does not have

that attribute Formal concepts can be partially ordered into a lattice, such that a concept is a subconcept of another concept:

¢Oi , Ai ² ⊆ ¢O j , A j ² iff Oi ≤ O j which is equivalent to ¢Oi , Ai ² ≤ ¢O j , A j ² iff Ai ⊆ A j . Once the lattice is obtained, it can be visualized and analyzed. For example, it can be determined which concepts are redundant. In other words, some operations can be applied on the lattice so as to identify the concepts that can be obtained by the intersection of others. Contexts are easy to visualize when they are represented as a cross table, with the objects listed in the rows of the table and the attributes in the columns of the table. If an object o has an attribute a, which means that there is a binary relation between them, a

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checkmark is inserted in the cell (o, a). Table 1 shows the contexts associated to potential explosion classes. Table 1. Cross-table of contexts

JCUNKSWKF

KPXQNXGU UWDUVCPVKCNN[ VCMGU KPXQNXGU TCRKF CDQXGKVU RNCEGKP GPGTI[ RJCUG CVO QURJGTKE CXGUUGN TGNGCUG VTCPUKVKQP DQKNKPIRQKPV $.'8' ˜ ˜ ˜ ˜ GZRNQUKQP ˜ RJ[UKECNAGZRNQUKQP ˜ TCRKFARJCUGAVTCPUKVKQPAGZRNQUKQP ˜ ˜ EJGO KECNAGZRNQUKQP ˜ TWPCY C[ATGCEVKQPAGZRNQUKQP ˜ ˜ FGVQPCVKQP ˜ FGHNCITCVKQP ˜ XCRQTAENQWFAGZRNQUKQP ˜ ˜

TGCEVKQP KPXQNXGU TGCEVKQP

FQGUPQV

KPXQNXGU

KPXQNXGU KPXQNXGU

KPXQNXGU RTQRCICVGU RTQRCICVGU GZVTGO GN[ KPXQNXG TCRKF TGCEVKQP TCRKF CV EJGO KECN GZQVJGTO KE HNCO O CDNG CV EJGO KECN EJGO KECN RTQRCICVGU TGCEVKQP TGCEVKQP O CVGTKCN UWRGTUQPKE UWDUQPKE EJGO KECN TGCEVKQP TGCEVKQP TGCEVKQP URGGF URGGF ˜ ˜ ˜ ˜ ˜ ˜ ˜

˜ ˜

˜ ˜ ˜

˜

˜ ˜

˜ ˜

The lattice corresponding to the contexts in Table 1 are shown in Figure 1, which was obtained using the software Concept Explorer [5]. Each node in the lattice corresponds to a concept. An arc represents the superconcept-subconcept relation. Note that Table 1 includes the object explosion defined as “a sudden increase in volume and release of energy in an extreme manner”. From the lattice it can be verified that explosion is the most generic concept in the lattice from which all the other concepts are derived. When a concept has all the attributes that correspond to an object in the context table that concept is named after the object. However, there might be nodes in the lattice, such as A, B, and C in Figure 1, for which there is no object that contains all the attributes in the concept. Those nodes correspond to newly identified (but unnamed) classes. A close look at the attributes associated to those particular nodes, shows that A corresponds to those kinds of explosion that take place in a vessel, B corresponds to those chemical explosions that are exothermic and C denotes the classes of chemical explosions with chemical reactions that propagate.

D

C A

B

E A

B

C

Figure 1. Lattice of explosion-related concepts There is more that can be done with the lattice. Concept Explorer supports a function that identifies those objects and attributes that can be obtained by the intersection of other objects and attributes. The lattice obtained after such operation is shown in Figure 2. The attributes are shown in grey boxes. This means that it would have been possible

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to obtain the categories for explosion, rapid phase transition explosion and chemical explosion without explicitly adding those entries in the context table.

4. Ontology merging Ontologies define classes of things, their taxonomy, the possible relations between things and axioms for those relations. A class represents a category of things that share a set of properties. A relation is a function that maps its arguments to a Boolean value of true or false. Examples of relations are connected_to, and part_of. Class taxonomies are defined with the use of the subclass relation. Like in the concept-subconcept relation in FCA, a class is a subclass of another class if every member of the subclass is also a member of the superclass. Upper ontologies define top-level classes such as physical objects, activities, mereological (part-whole) and topological relations from which more specific classes and relations can be defined. Thus, specialized ontologies can be merged into the upper ontology by references to classes and relations in the upper ontology. Merging two ore more specialized ontologies into the upper ontology creates compatibility between their definitions.

5. Ontology-based accident database A prototype has been developed based on ontologies represented in the OWL language. In order to search the database, the user can construct composite queries each of which is formed by a relationship and two classes. For example, the query “crude oil that leaks from distillation columns” can be specified as (relative_location  leak distillation_column), (participation  leak  crude_oil).

6. Conclusions This paper presented an approach for accident-database development based on knowledge engineering techniques. Emphasis has been placed on the use of formal concept analysis (FCA) to identify hierarchies of classes. It must be noted that along with the class hierarchies FCA provides the rationale behind the class structure but also it provides knowledge about the attributes that must be or must not be presented for each of the classes. This knowledge would typically be represented as a series of axioms in the ontology. Such axioms would provide important benefits in the processing of accident information. For example, it would be possible to automate (at least partially) the classification of accident reports by identifying keywords that correspond to attributes which are use to identify relevant classes.

References [1] P. W. H. Chung and M. Jefferson. Applied Intelligence, 9 (1998) 129 [2] P. Cimiano and J. Völker. Procs. of the 10th Int. Conf. on Applications of Natural Language to Information Systems. Alicante, Spain (2005) 227-238 [3] M. C. de Marneffe, B. MacCartney, C. D. Manning. Procs of LREC-06 (2006) [4] B. Ganter and R. Wille. Springer-Verlag. (1999) [5] Yevtushenko, S., et al, Concept Explorer, Open source java software available at http://sourceforge.net/projects/conexp, Release 1.3 (2005)

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Effect of life cycle impact assessment on the design and scheduling of a recovery network for industrial polluted waste J. Duquea, A. P. F. D. Barbosa-Póvoa*b and A. Q. Novaisa a

Departamento de Modelação e Simulação de Processos, Instituto Nacional de Engenharia Tecnologia e Inovação, I.P., Lisboa, Portugal b Centro de Estudos de Gestão, CEG-IST, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

Abstract The present work uses a MILP model to optimise the design and operation of a generic recovery network for industrial polluted waste. The design is subjected to both economic and environmental targets, the latter being modelled based on the ecoindicator 99 method that aggregates the environmental assessment on a single index, the eco-indicator. The network’s optimal structure and operation is investigated with an example involving three types of entities (producers, transformers and clients) interconnected by two types of road transport that originate a high dimension superstructure. Results are presented for the two most extreme conditions – maximization of profit under no environmental restrictions and, conversely, the minimization of the eco-indicator under no profit restrictions – as well as for some intermediate scenarios. Subsequently, an analysis on the damage weights sensitivity is undertaken. It is shown that for the recovery network of polluted waste, even for the most adverse conditions, an acceptable environmental performance can be obtained and also that, more importantly, close-to-green scenarios can be reached at the expense of very small losses in profit. Keywords: Recovery networks, Environmental impacts, Eco-indicator.

1. Introduction The enforcement of legal regulations, the development of a pollutant emissions market, namely in Europe, and a public growing awareness, reinforce the need of including adequate environmental metrics at the initial stages of the optimal design and management of industrial processes. The need is even greater when dealing with geographically extended networks of collaborative industrial partners engaged in polluted waste recovery. Adequate environmental metrics are available [1] that take into account pollutant emissions, eco-system aggressions and resources depletion associated to all products, utilities and processing stages, involved in the Life Cycle Impact Assessment (LCIA) of the network. The optimal design and operation of a generic recovery network for industrial polluted waste, has been formulated by the authors as a MILP mathematical model, subjected to both economic and environmental targets [1]. The mathematical model employs the maximal State Task Network (mSTN) representation [2] and the eco-indicator 99 [3]. *

Corresponding author, Tel: +351-218419014. Fax: +351-218417638. E-mail: [email protected]

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This method aggregates into one single and comprehensive index, the information on the multiple aspects involved in an environmental impact assessment. The singularity of the eco-indicator, although dependent on a number of weights derived either from experiment or subjective choices, makes it very suitable for integration in the optimization work. The trade-off approach employed to account for the intrinsically conflicting economic and environmental targets, was based on a Pareto front, thus avoiding the resolution of a double-objective problem and allowing for the inspection of different alternatives by the decision maker. The optimal structure and operation of the network currently investigated involves three types of geographically distributed entities: 8 waste producers, 36 processing agents and 18 final consumers, all interconnected by two types of road transport. The superstructure of the resulting optimization model, given its inherent combinatorial nature, is of a very high dimension and hence the modelling of transports received special attention, given its marked influence on the tractability of the problem [1]. The results are presented in terms of the network structure, utilities and operating conditions, for the two most extreme conditions – the most adverse, i.e. maximization of profit under no environmental restrictions and, conversely, the most friendly or green, i.e. minimization of the eco-indicator under no profit restrictions. Some intermediate and more balanced scenarios (in terms of trade-off) located on the Pareto front were also obtained. In order to test the consistency of the most friendly scenario, sensitivity tests were subsequently conducted on the normalized damage weights that support the cultural perspective (i.e. hierarchical) selected for the eco-indicator.

2. Model characteristics The mSTN representation is used to model the general network superstructure, which is coupled with the Eco-indicator 99 methodology [3] to account for the pollution generation at the transformation, transportation and utility production stages. Since the recovery of hazardous products is being addressed, the system frontier for the environmental impacts is defined at the level of the feeds, including any type of utilities used. The amount of pollutants computed is used as input to an effect and damage analysis that is completed with some additional parameters for soil occupation/transformation and for the mineral and fossil resource balance (a full description of the model can be found in [1, 4]). The model considers all possible concurrent transportations and transformations, as well as all raw materials (i.e. the hazardous residual product) producers and re-users. The resulting pollutant materials emitted to the atmosphere, soil and water streams are then added up. The total pollutant’s upper limits emission is introduced in the form of vectors values normally derived from legal regulations and enter the model as additional constraints.

3. Example In order to study the economic/environmental trade-off, a close to real-life example, based on the optimization of a recovery route for Al-rich sludge, was used, which is a waste product to be found in the aluminium anodization and lacquering surface treatment industries. As an alternative to disposal, this sludge can be treated and employed as coagulant and flocculant for the treatment of industrial and municipal

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effluents. Since the locations of plants and of water treatment facilities do not in general coincide, suitable transports are needed. Two different types of sludge are considered that may be submitted to two different transformation processes (dilution and drying) which employ different relative proportions of each [1, 4] and originate stable storable final products. The transportation tasks can be done by two alternative transports (Tr1, Tr2), differing in costs and capacity. All possible connections are considered and the number of available trucks is limited to only one for each transport type. The transport is done on standard containers of 6, 10 and 20 cubic meters. Table 1 presents the costs and the typical diesel consumption of transports. The transit time is based on the distance between the entities connected, assuming an average speed of 80km/h and 66km/h, respectively, for types Tr1 and Tr2. This example contemplates the two mentioned types of transformation entities in every Portuguese district: older and more polluting but least expensive facilities (installation cost of 55k€) and new and less polluting but more expensive ones (installation cost of 70k€). The facilities’ capacity varies continuously between 7 and 150 tonnes. The example involves 8 waste producers, located in the northern and central Portugal, 18x2 processing agents and 18 final consumers. Consumers generate demands that are proportional to the district population with upper and lower bound values that are roughly 25% above and under the nominal values, respectively. Table 1. Typical monetary costs and fuel consumption for transport containers

Units Capacity Rental costs Diesel consumption

3

[m ] [€/month] [l/100km]

Values 6 40

10 40 30 to 35

20 85

For optimization purposes it is considered a production time horizon of 30 days with a 5-day periodic operation. The model was solved using GAMS/CPLEX (v22.7.2 for WINDOWS) software running in an Intel Core 2 Duo 6600 at 2.4 GHz and it is characterised by 77318 single equations, 61867 variables of which 31208 are discrete. Resource times used vary from 15 minutes to 6 hours, depending on the time it takes to obtain a solution that satisfies one of the termination criterions - a relative gap (between the obtained and the best possible solutions) of 2%, or alternatively up to a resource time limit of 22000 seconds (in such a case gaps of 5% or less were obtained).

4. Environmental versus economic trade-off To enable an analysis of the trade-off, the example is solved using a succession of economic and environmental (EI99 indicator) target values, leading to the Pareto front in Figure 1, to which an additional curve corresponding to the economic optimization for a succession of CO2 target limits was added.

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Fig. 1.

Economic and environmental optimization curves.

The three curves show the same general trend – with the exception of point A6, where the CO2 target is achieved by reducing the production of sludge, which in turn brings about a reduction in the environmental impact. A set of four solutions were chosen from Figure 1: two trade-off balanced solutions, G and S, and the extreme unbounded solutions, A and J. Table 2 presents the corresponding data which show that for the recovery network of polluted waste, by losing 2% on the maximum profit (A) it is possible to obtain a solution that differs from the greener solution (J) by only 2%, either for an economic (G) or environmental (S) optimization. Hence it is likely that close-togreen scenarios might, in general, be reached at the expense of very small profit losses. Table2. Comparison of the economic and environmental optimized solutions max Profit Case NIter Gen.+Exec. Time to [s] Profit [k€] EI99 [mPt] Solution Relative Gap Capital Cost [k€] Produced S3 quantities [t] S4 Electr. [kWh] Water [m3] Diesel [kl]

min EI99

A

G

S

J

7419 992.64 953.12 (100%) -1989 (51%) 1.84E-02 605.56 1892 1428

11519276 22989.135 935.38 (98%) -2900 (98%) 2.45E-02 632.19 1884 1424

10001582 22982.886 935.00 (98%) -2898 (98%) 2.35E-02 569.01 1892 1427

4596 1011.528 703.44 (65%) -2960 (100%) 1.66E-02 704.78 1431 1180

5906 4225 3452 95.556 94.848 95.428 5.310 1.330 1.398 *The bold values correspond to the imposed limit values

7 71.638 1.479

5. Sensitivity tests The damage eco-indicator considers the weighted contribution of three different damage types: to human health (Whh=40%), to eco system quality (Weq= 40%) and to natural, mineral and fossil resources (Wnr=20%). These individual weights aim to “measure” the perceived severity of the damage and are obtained from social studies [3]. The

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comparison of the environmental results, for different case studies is performed. The example used avoids mineral extraction and processing, thus diminishing the damage. The recovered aluminium is hence achieved essentially at the cost of the comparatively small damage generated by its recovering processes and transportation.

To ascertain the importance of the damage weights, a sensitivity analysis was performed in the case of unconstrained damage minimization. This is presented in Figure 2, where 3D plots were drawn with the optimal values obtained for the eco-indicator (EI99) and profit for a wide range of Wnr and Whh (the Weq value is the difference of their sum to 100). The results are depicted for Whh = 5 and 20 and Weq = 20, together with the estimated response for the lower limit on the eco system quality (Weq = 0). The coplanarity of the response, very marked for the environmental target, indicates that the optimal solution for this type of network is not sensitive to the weights variation. This is also partly confirmed by the optimized network structure (not shown) that is basically the same for all the points in Figure 1, except when the eco-system weighted quality damage exceeds the other types of damage. It can be then anticipated that for a case where the several types of damage values are more levelled the solution may depend on the weights used.

Fig. 2. Economic and environmental 3D plots for the damage weights sensitivity analysis. 6. Conclusions A general model was proposed to the design of waste recovery products where both economic and environmental aspects have been considered. For the current case it can be concluded that even for the most adverse conditions an acceptable environmental performance can be obtained and also that, more importantly, close-to-green scenarios can be reached at the expense of very small profit losses. Solutions vary from a centralized production with a few installed transformers, for the unconstrained economic optimization; to a more disperse production with transformers installed in the same location of the waste producers, for the unconstrained environmental optimization. Intermediate (close to green) scenarios were obtained that differed only in the choice of the type of transformation facilities. In the current example the sensitivity analysis allowed us to conclude that the solution is not sensitive to the variation of the damage weights. The possibility arose therefore that the reverse might occur, whenever the damage weighted values become more levelled. Additional work is therefore required to further explore this question.

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References [1] Duque J. (2007), PhD thesis, Instituto Superior Técnico, UTL, Lisbon [2] Barbosa-Póvoa and Macchietto, 1994, Comp. Chem. Engng., 18, 11/12, 1013-1042 [3] The Eco-indicator 99. “A damage oriented method for Life Cycle Impact Assessment”, Pré Consultants B.V.Amersfoort, Netherlands, available on-line at www.pre.nl [4] Duque J.; Barbosa-Póvoa, A.P.; Novais, A.Q. (2007), Computers & Operations Research, Volume 34, Issue 5, 1463-1490

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Artificial Neural Networks Modelling of PID and Model Predictive Controlled Waste Water Treatment Plant Based on the Benchmark Simulation Model No.1 Vasile-Mircea Cristea, Cristian Pop, Paul Serban Agachi Babes-Bolyai University, 11 Arany Janos Street, 400028 Cluj-Napoca, Romania, e-mail: [email protected]

Abstract The paper presents techniques for the design and training of Artificial Neural Networks (ANN) models for the dynamic simulation of the controlled Benchmark Simulation Model no. 1 (BSM1) Waste Water Treatment Plant (WWTP). The developed ANN model of the WWTP and its associated control system is used for the assessment of the plant behaviour in integrated urban waste water system simulations. Both embedded PID (Proportional-Integral-Derivative) control and Model Predictive Control (MPC) structures for the WWTP are investigated. The control of the Dissolved Oxygen (DO) mass concentration in the aerated reactors and nitrate (NO) mass concentration in the anoxic compartments are presented. The ANN based simulators reveal good accuracy for predicting important process variables and an important reduction of the simulation time, compared to the first principle WWTP simulator. Keywords: Artificial Neural Networks Model, PID Control, Model Predictive Control

1. Introduction Taking care of human waste products and waste disposal is becoming more and more important for the sustainable development of the modern society. The Waste Water Treatment Plant protects local ecosystems against increased load of waste products and waste disposal, preventing waste accumulation in lakes, rivers or underground waters. Degradation of organic material present in wastewaters consumes the oxygen inventory and the lack of oxygen may affect the living organisms. Therefore, the task of the WWTP is to remove the organic components and the suspended solids but also to reduce the nitrogen and phosphorous to an ecological safe content. The modern WWTPs consist in the mechanical treatment step, where filters remove large objects and particles, followed by the chemical-biological treatment stage where chemicals and microorganisms remove organic matter and reduce the nitrogen and phosphorous content. The activated sludge process is widely used by municipalities and industries as it treats wastewater containing organic chemicals, petroleum refining wastes, textile wastes, and municipal sewage. This treatment process converts dissolved and colloidal organic contaminants into biological sludge, further removed by settling. In order to perform nitrogen removal the activated sludge process consists in both aerated and non-aerated (anoxic) reactors. In the aerated reactors the bacteria oxidize ammonium to nitrate by the so-called nitrification process. In the anoxic reactors takes place the denitrification

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process where bacteria change nitrate into nitrogen, using oxygen present in the nitrate ions. The dynamic simulator proves to be a necessary and very useful tool for the cases of retrofitting the already operating WWT plants or for assessing the effect of the control system configuration on the design alternatives. Operating the WWTP in changing weather conditions with daily, weekly or seasonally periodic cycles requires an efficient dynamic simulator. The Benchmark Simulation Model No.1 is widely used as a standard model [1], based on the most popular mechanistic Activated Sludge Model No.1 (ASM1) and Takacs settler model [2]. It has been developed by the International Association on Water Pollution Research and Control, for modelling and for performance assessment of different the control strategies [3]. This first principle model, based on a set of nonlinear ODEs, is demanding long simulation time and considerable computer resources, especially when time-extended simulation scenarios are investigated. The paper presents the design of an Artificial Neural Networks model as an alternative to the mechanistic ASM1 model. ANN models are able to capture the complexity of the intrinsic processes featuring the global process behaviour. ANN are composed of simple elements, neurons, operating in parallel. The network operation is determined by the connections between its neurons. The weighted connection paths link every two neurons to each other, the weighting structure providing the total network performance. Statistical models developed by means of ANN and using process data are promising alternatives to the traditional analytical models [4].

2. Development of the ANN based dynamic simulator The schematic representation of the WWTP for which the ANN dynamic simulator has been developed is presented in Fig.1.

Figure 1: WWTP activated sludge process with PID/MPC control of DO and NO mass concentration

The mechanistic WWTP simulator has been used for generating the data further employed for the ANN training, based on a moving window approach. Both cases of the ANN WWTP simulators illustrating the WWTP controlled by the PID and by the MPC algorithms have been developed. Control configurations have been investigated where the DO mass concentration (measured with with SO sensor) in the third aerated reactor and the NO mass concentration (measured with SNO sensor) in the second anoxic reactor

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are controlled using PID and MPC [5-7]. The designed ANN inputs consist in a set of twelve variables; ten variables considered as WWTP influent values: soluble inert organic matter SI , readily biodegradable substrate SS, particulate inert organic matter XI, slowly biodegradable substrate XS, active heterotrophic biomass XB,H, NH4+ and NH3 nitrogen SNH, soluble biodegradable organic nitrogen SND, particulate biodegradable organic nitrogen XND, total suspended solids TSS, influent flowrate Q; two manipulated variables: oxygen transfer coefficient (air flow rate) KLa-5, and internal recycle flowrate Qa. All ANN input variables have been considered with their past values at 60 previous sampling moments (with the sampling time of 15 minutes). The output (controlled) variables are the DO mass concentration in the third aerated reactor and the NO mass concentration in the second anoxic reactor, both considered at the current (next) sampling moment. The ANN architecture for the WWTP simulators with PID/MPC control consists in a triple-layer feed-forward structure with the back propagation training algorithm used for computing the network biases and weights. Three layers of neurons have been considered. In the hidden layers 35 and respectively 25 neurons have been used and the output layer consists in 2 neurons. The number of nodes in the hidden layers has been set on the basis of a trial and error process. The tansig transfer functions have been used for the hidden layers and the purelin linear transfer function for the output layer. The quasi-Newton Levenberg-Marquardt algorithm was employed for training the ANN and overfitting has been avoided by the early stopping method which also improves generalization. Random initial conditions have been considered for the weights and biases, during the set of repeated sequence of training steps, in order to prevent convergence to undesired local minima. For improving the training procedure all inputoutput training data have been normalized using the maximum and minimum values of the input and output sets of data and principal component analysis has been used for reducing the dimension of the input vector. A set of input and output data, considered in this study for dry weather conditions and provided by the WWTP analytical simulator, has been used for training and testing the ANN. Under different weather conditions additional training is required. The entire data set has been divided into a set of data used for training the ANN (75 %) and the rest for testing the quality of the training process. The data set used for training has been chosen in correlation to the number of neurons in the hidden layers and covering the operating range of change of the input and output variables. The trained ANN is designed to predict one step ahead into the future the behaviour of the process variables. Applied repeatedly, the dynamic ANN predicts the time evolution of the state variables over a desired future time horizon. The testing set of data is completely different of the training one and not yet seen by the ANN. For the testing set of data a regression analysis between the network response and the corresponding targets was first performed, as the correlation coefficient (R-value) between the outputs and targets is a measure of how well the variation in the targets is explained by the ANN simulator outputs (predictions).

3. Training results of the ANN based dynamic simulator Results obtained for the testing set show the R-value close to unity for the two considered output variables (with both PID and MPC control), revealing a good correlation between targets and ANN outputs. This stands as a first evidence for proving the efficiency of the training process. In order to further asses the quality of the training process a second test has been performed. This second dynamic simulation test consists

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in generating randomly varying values for two influent mass concentrations, the readily biodegradable substrate SS and the active heterotrophic biomass XB,H (having a ±10 % span), and then comparing the simulation results of the analytical WWTP simulator with the ANN based WWTP simulator. Figure 2 presents the correlation between the results of this last test, for the case of the simulator using the PID control structure. Figure 3 presents detailed comparative simulation results (between the days 10 and 13 of the simulation) for the PID controlled WWTP, showing the same two controlled variables, i.e. DO and NO mass concentration. The results show an accurate ANN training, as the differences between the two simulators results are small. The same good fitness between the ANN based simulator and the analytical (mechanistic) simulator is also obtained when the MPC control of the two considered variables is performed. The results presented in figures 4 and 5 show again the valuable prediction of the ANN WWTP simulator using MPC control. R=0.99475, Linear Fit: Y=(1.049)X-(0.098)

R=0.99804, Linear Fit: Y=(0.9976)X+(0.000918)

2.006 O D r of ) s n oi cti d er P( st l u s e R r ot al u mi S N N A P T W W

1.5 Data Points Best Linear Fit Predictions =Targets

2.004

2.002

2

1.998

1.996

1.994

1.992 1.992

1.994 1.996 1.998 2 2.002 2.004 WWTP Analytical Simulator Results (Targets) for DO

Data Points Best Linear Fit Predictions=Targets

O N r of ) s n oi cti 1 d er P( st l us e R r ot al 0.5 u mi S N N A P T W W 0 0 2.006

0.5 1 WWTP Analytical Simulator Results (Targets) for NO

Figure 2. Correlation between analytical simulator results and ANN simulator results for the WWTP with PID controlled Dissolved Oxygen and nitrate mass concentration 2.004

1.5

ANN Predictions Analytical Simulation

ANN Predictions Analytical Simulation

2.002 ] L/ g m [ n oi t ar t n ec n o C O D

] L/ g m [ n oi t ar t n e c n o C O N

2

1.998

1.996

1

0.5

1.994

1.992

10.5

11

11.5 12 Time [days]

12.5

13

0

10.5

11

11.5 12 Time [days]

12.5

13

Figure 3. Comparison between analytical simulator results and ANN simulator results for the WWTP with PID controlled Dissolved Oxygen and nitrate mass concentration

1.5

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R=0.99804, Linear Fit: Y=(1.0316)X-(0.0326)

R=0.99332, Linear Fit: Y=(1.0469)X-(0.0952) 2.15 Data points Best Linear Fit Predictions=Targets

O 2.1 D r of ) s n oi 2.05 cti d er 2 P( st l us e 1.95 R r ot al 1.9 u mi S N 1.85 N A P T W 1.8 W 1.8

1.85 1.9 1.95 2 2.05 2.1 WWTP Analytical Simulator Results (Targets) for DO

Data Points Best Linear Fit Predictions=Targets

O N 1.1 r of ) s n 1.05 oi cti d er P( 1 st l u s e R 0.95 r ot al u mi 0.9 S N N A 0.85 P T W W 0.8 2.15 0.8

0.85 0.9 0.95 1 1.05 1.1 WWTP Analytical Simulator Results (Targets) for NO

1.15

Figure 4. Correlation between analytical simulator results and ANN simulator results for the WWTP with MPC controlled Dissolved Oxygen and nitrate mass concentration 1.15

2.15 ANN Predictions Analytical Simulation

2.1 ] L/ g m[ n oi t ar t n ec n o C O D

] L/ g m[ n oi t ar t n ec n o C O N

2.05 2 1.95 1.9

1.05 1 0.95 0.9 0.85

1.85 1.8

ANN Predictions Analytical Simulation

1.1

10.5

11

11.5 12 Time [days]

12.5

13

0.8

10.5

11

11.5 12 Time [days]

12.5

13

Figure 5. Comparison between analytical simulator results and ANN simulator results for the WWTP with MPC controlled Dissolved Oxygen and nitrate mass concentration

It is worthy to mention that good generalization capacity of the trained ANN is shown, as randomly changing test inputs of the WWTP are simulated by generating sets of WWTP input data not yet seen by the ANN during the training step. Compared to the analytical WWTP simulator, important reduction of the simulation time has been observed when the ANN based WWTP simulator was used. The reduction was evaluated to be of about one order of magnitude (i.e. 124 s simulation time compared to 11 s, for 14 days simulation of WWTP operation). The reduction in the simulation time is useful for the assessment of the WWTP behaviour, for large periods of time, when either PID or MPC control approaches are implemented. Emerged from the case of the WWTP operated under dry weather conditions, considered in this study, the training methodology of the ANN simulator may to be considered as a good choice for building models able to be used in real time control applications. The ANN models accurately reveal the dynamic behaviour of the plant while considerably reducing the computation effort. This feature has a favourable impact on the feasibility of the control strategies that imply an important amount of computation.

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4. Conclusions The presented results demonstrate the way and capability of the ANN based simulator to be efficiently trained for being further used in integrated urban waste water systems for rapid assessment of the plant behaviour with both PID and MPC control algorithms. The dynamic simulation test performed on random varying inputs proves the generalization potential of the ANN developed model and correlation coefficients close to unity confirm this appreciated feature. The reduction of the simulation time is important and this makes the ANN dynamic simulator an efficient tool for evaluating the WWT plant operation under changing conditions, while substantially sparing the computer resources. The presented training and testing methodology may be further extended and used for similar modelling cases where the real time implementation of first principle model based control is unfeasible or the computational burden my become overwhelming.

5. Acknowledgements Financial support from national projects CEEX 112 and PN 71-006 is gratefully acknowledged.

6. References [1] J. B. Copp (Ed.), 2002, The COST Simulation Benchmark-Description and Simulation Manual, Luxembourg: Office for Official Publications of the European Communities. [2] I. Takacs, G. G. Patry, D. Nolasco, 1991, A dynamic model of the clarification thickening process, Wat. Res., 25(10), 1263–1271. [3] H. Henze, C. P. L. Jr. Grady, W. Gujer, G. V. R. Marais, 1987, T. Matsuo, A general model for single-sludge Wastewater Treatment systems, 1987, Wat. Res., 21(5), 505–515. [4] V. M. Cristea, L. Toma, P. S. Agachi, 2007, Simulation and Model Predictive Control of the Fluid Catalytic Cracking Unit Using Artificial Neural Networks, Revue Roumaine de Chimie, 52(12), 1157–1166. [5] M. Yong, P. Yongzhen, U. Jeppsson, 2006, Dynamic evaluation of integrated control strategies for enhanced nitrogen removal in activated sludge process, Contrl. Eng. Prac., 14, 1269–1278. [6] U. Jeppsson, C. Rosen, J. Alex, J. B. Copp, K. V. Gernaey, M. -N. Pons, P. A. Vanrolleghem, 2006, Towards a benchmark simulation model for plant wide control strategy performance evaluation of WWTPs. Water Science and Technology, 53(1), 287–295. [7] B. Bernaud, J. -P. Steyer, C. Lemoine, E. Latrille, 2007, Optimization of WWTP control by means of multiobjective genetic algorithms and sensitivity analysis, In B. Braunschewig and X. Joulia (Eds.), 18-th European Symposium on Computer Aided Process Engineering Lyon, Elsevier, 539–544.

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Automated Targeting for Total Property-based Network Denny Kok Sum Ng,a Dominic Chwan Yee Foo,a Raymond R. Tan,b Mahmoud El-Halwagic a

University of Nottingham Malaysia, Department of Chemical and Environmental Engineering, Broga Road, 43500 Semenyih, Selangor, Malaysia, [email protected], [email protected] b De La Salle University-Manila, Chemical Engineering Department, 2401 Taft Avenue, 1004 Manila, Philippines, [email protected] C Texas A&M University, Chemical Engineering Department, College Station, TX 77843, United States of America, [email protected]

Abstract This paper presents an optimisation-based, automated procedure known as automated targeting to analyse a total property-based network that consists of the individual elements of material reuse/recycle, regeneration/interception and waste treatment. Due to the close interaction among these individual elements, simultaneous synthesis of a total network is considered. This optimisation-based approach provides the same benefits as conventional pinch analysis techniques, in yielding various network targets prior to detailed design. Besides, the flexibility in setting objective function is the major advantage of the automated targeting approach over the conventional targeting techniques. An industrial example is utilised for illustration. Keywords: Process integration, property integration, resource conservation, waste minimisation, optimisation.

1. Introduction Process industries have traditionally focused on conventional end-of-pipe waste treatment in order to comply with environmental legislation. However, there is a recent trend towards the use of pollution prevention instead. This is mainly due to the increase of public awareness of environmental sustainability, the rise in cost of manufacturing inputs and more stringent environmental legislation. One of the cost effective solutions is resource conservation where materials are reused/recycled within processes without adversely affecting the process performance. Process integration has been commonly accepted as an effective tool in evaluating various resource conservation alternatives. El-Halwagi (1997; 2006) defined process integration as a holistic approach to process design, retrofitting and operation which emphasises the unity of the process. In most cases, both fresh material consumption and waste generation are reduced simultaneously by carrying out resource conservation activities. Over the past decade, extensive works have been reported for the synthesis of water (Wang and Smith, 1994; Hallale, 2002; El-Halwagi et al., 2003; Manan et al., 2004) and utility gas (Towler et al., 1996; Alves and Towler, 2002) networks as special cases of mass integration. In most of these the characterisation of the streams and constraints on the process sinks are

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described in terms of the concentration of pollutants. However, there are many applications in which stream quality is characterised by physical or chemical properties rather than pollutant concentration. This led to the concept of property integration (Shelley and El-Halwagi, 2000). In this work, a recent developed automated targeting approach (Ng et al., 2009) is extended for a total property-based network that includes material reuse/recycle, regeneration/interception and waste treatment for final discharge. The automated targeting technique is formulated as a linear programming model.

2. Problem Statement The problem of a total network is stated as follows. Given a set of sources i that may be reused/recycled and/or regenerated/intercepted to be sent to the process sinks. Each source has a flowrate, Fi and is characterised by a single constant property, Pi. A set of water sinks j are specified. Each sink requires a flowrate of Fj and is restricted to complies with the predetermined allowable property constraints as follows: p min ≤ p j ≤ p max j j

(1)

and p max are the specified lower and upper bounds of the admissible where p min j j properties for sink j. External sources are readily available to supplement the flowrate required by the sinks (FFW,j). The unused sources are to be treated prior to discharge. In addition, environment legislation restricts the quality of waste to be discharged as follows: p discharge ≤ p environmen t

(2)

where p environment is the discharge limit of property. A linearised property mixing rule is needed to define all possible mixing patterns among the individual properties. The mixing rule takes the form (El-Halwagi, 2006): ψ ( p ) = ¦ xiψ ( pi )

(3)

i

where ψ(pi) and ψ ( p ) are linearising operators on source property pi and mixture property p , respectively; while xi is the fractional contribution of stream i in the total mixture flowrate. The objective of this work is to target the minimum total cost for a total property-based network.

3. Automated Targeting The automated targeting technique was originally developed for mass exchange network synthesis (El-Halwagi and Manousiothakis, 1990). It was extended by Ng et al. (2009) for property-based resource conservation network (RCN) based on water cascade analysis (Manan et al., 2004). However, the previous work did not consider waste treatment. This aspect is now included in this work. Following the previous approach, the first step is to construct a revised property interval diagram (PID) (Ng et al., 2009). The sinks and sources are arranged in ascending order based on the property operator (Ȍk). In cases where the property operator levels for fresh resource(s) and zero property operator level that do not exist within the process sinks and sources, an additional level is added. An arbitrary value is also added at the final level (highest among all property operators) of the PID to allow the calculation of

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residue property load. Next the flowrate and property load cascades are performed across all property operator levels based on Equations 4 and 5 respectively. δk = δk-1 + ( Σi FSRi – Σj FSKj )k

(4)

εk = εk–1 + δk (Ȍk+1 – Ȍk)

(5)

As shown in Equation 4, the sum of the net material flowrate cascaded from the earlier property operator level k – 1 (δk-1) with the flowrate balance (ΣiFSRi − Σj FSKj) at property operator level k form the net material flowrate of each k-th level (δk). Meanwhile, the property load at each property operator interval is given by the product of the net material flowrate from level k (δk) and the difference between two adjacent property operator levels (Ȍk+1 – Ȍk). The residue of the property load of each property operator level k (εk) is to be cascaded down to the next property operator level. The residual property load, ε must take a positive value:

εk ≥ 0

(6)

To incorporate waste treatment into automated targeting technique, modification is required on the original automated targeting model. In principle, waste is discharged from a process source when it is not being recovered. Hence, waste flowrate (FWWq) is added as a new sink at each property operator level where a source exists in the PID of RCN. Equation 4 is then modified to take the form of Equation 7: δk = δk-1 + ( Σi FSRi – Σj FSKj – Σi FWWi)k

(7)

These waste sources are then sent to the waste treatment network (WTN) to improve its property before discharge. In order to determine the minimum treatment flowrate, flowrate and property load cascades for WTN is added. The identified waste flowrates (FWWq) from RCN become sources in the WTN cascades. Besides, the individual treated flowrate (FTRr) exists as a sink in each operator level where a source exists, while their summed flowrate becomes a single source at the treatment outlet operator level (or calculated based on the removal ratio of the treatment units). Finally, the discharge flowrate (FD, sum of the individual waste flowrates, i.e. ΣqFWWq), is added as a new sink at the operator level of the final discharge limit. The flowrate balance at each level takes a similar form as Equation 7, with its load cascade and non-negativity given as in Equations 5 and 6, respectively. Since different sets of cascades are formulated for RCN and WTN, different properties can be used for network syntheses.

4. Case Study An industrial wafer fabrication process (Ng et al., 2009) is used to illustrate the application of the automated targeting technique. In this case study, the pre-treatment system is used to generate ultra pure water (UPW) for the process requirements. It is assumed that 70% of the inlet flowrate to ultra filtration (UF) is recovered as permeate, while the remainder is rejected. The same assumption applies for the reverse osmosis (RO) membrane unit. The effluent from RO unit is then sent to deioniser (DI) to produce the UPW. It is assumed that no water losses occur in the DI. In order to reduce fresh water consumption, the recovery of reject stream from the pre-treatment system should be considered. In this case study, the most significant water quality factor was determined to be resistivity (R), which constitutes an index of the total ionic content of aqueous streams. The general mixing rule for resistivity is given as (El-Halwagi, 2006):

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1 = R

¦R

xi

i

(8)

i

Note that the lowest resistivity also corresponds to the lowest quality level. Table 1 summarises the pertinent data for the sinks and sources. In this case study, the lower bounds of the resistivity are selected as the limiting property for process sink when water recovery scheme is considered, since these lower bounds correspond to the lowest stream quality that can be tolerated by the processes, and thus maximises the potential for water recovery. Besides, heavy metal content is chosen as the main property for final discharge, which is given as 2 mg/L. A fixed outlet concentration of 0.5 mg/L is assumed for the treatment effluent. In order to synthesise a cost effective total RCN, it is necessary to minimise the total operating costs (TOC) of fresh water, UPW and waste treatment. The unit costs for fresh water (COSTFresh), UPW (COSTUPW) and waste treatment (COSTT) are given as 1 $/t, 2 $/t and 0.5 $/t respectively. TOC = COSTFresh× FFresh + COSTUPW× FUPW + COSTT×FT

(9)

where FFresh and FUPW are flowrates of fresh water and ultra pure water respectively. The optimisation model is solved to minimise TOC (Equation 9), subject to the constraints in Equations 5-7, and resulted in the RCN and WTN cascades (Figure 1). The total annual cost is targeted as $1,122,970 (assuming 330 days/year). The optimal municipal fresh water, UPW and wastewater flowrates are determined as 3095, 1516.55 and 2205 t/h, respectively, with the minimum waste treatment flowrate as 739.68 t/h. An alternative RCN design that achieves the targets is shown in Figure 2. Table 1. Limiting data for wafer fabrication process (Ng et al., 2009). Process

Flowrate (t/h)

Resistivity, R (Mȍ.m) Operator, Ȍ ( [Mȍ.m]-1) Heavy metal Lower Upper Lower Upper content bound bound bound bound (mg/L)

(Sink) Wet (SK1) 500 7.000 18.000 Litography (SK2) 450 8.000 15.000 CMP (SK3) 700 10.000 18.000 Etc (SK4) 350 5.000 12.000 Cleaning (SK5) 200 0.008 0.010 Cooling tower makeup (SK6) 450 0.02 0.050 Scrubber (SK7) 300 0.01 0.020 (Source) UF reject (SR1/UFR) 30% of UF inlet 0.010 RO reject (SR2/ROR) 30% of RO inlet 0.005 Wet I (SR3) 250 1.000 Wet II (SR4) 200 2.000 Litography (SR5) 350 3.000 CMP I (SR6) 300 0.100 CMP II (SR7) 200 2.000 Etc (SR8) 280 0.500 Cleaning (SR9) 180 0.002 Scrubber (SR10) 300 0.005 Ultra pure water (UPW) ? 18.000 Municipal fresh water (Fresh) ? 0.020

0.143 0.125 0.100 0.200 125.000 50.000 100.000

0.056 0.067 0.056 0.083 100.000 20.000 50.000

100.000 200.000 1.000 0.500 0.333 10.000 0.500 2.000 500.000 200.000 0.056 50.000

1.50 10.00 5.00 4.50 5.00 10.00 4.50 5.00 15.00 10.00 0.00 0.50

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(a) RCN Cascade Operator, Ȍ 0 0.056 0.100 0.125 0.143 0.200 0.333 0.5 1 2 10 50 100 125 200 500 1000

Flowrate cascade (t/h) 0 Ø UPW = 1516.55 Ø -700 Ø -450 Ø -500 Ø -350 Ø 350 Ø 400 – 266.55 (FWW4) Ø 250 Ø 280 – 250.96 (FWW8) Ø 300 Ø -450 Ø -300 + 928.5 (FUFR) – 928.5 (FWW1) Ø -200 Ø 300 + 649.95 (FROR) – 578.99 (FWW2) Ø 180 – 180 (FWW9) Ø 0

Property load cascade

0 1516.55 816.55 366.55 -133.45 -483.45 -133.45 0 250.00 279.04 579.04 129.04 -170.96 -370.96 0 0

0 Ø 67 Ø 87 Ø 94 Ø 86 Ø 22 Ø 0 (PINCH) 0 (PINCH) 250 Ø 2482 Ø 2564 Ø 32096 Ø 27822 Ø 0 Ø 0 Ø 0

(b) WTN Cascade

Heavy metal content (mg/L) 0 0.5 1.5 2 4.5 5 10 15 100

Flowrate cascade (t/h) 0 Ø 739.68 (FT) Ø 928.5 (FWW1) Ø -2205 (FD) Ø 266.55 (FWW4) Ø 250.96 (FWW8) Ø 578.99 (FWW2) – 559.68 (FTR3) Ø 180 (FWW9) – 180 (FTR4) Ø 0

Heavy metal load cascade

0 739.68 1668.18 -536.82 -270.27 -19.31 0 0

0 Ø 740 Ø 1574 Ø 232 Ø 97 Ø 0 (PINCH) 0 (PINCH)

Figure 1. RCN and WTN cascades for wafer fabrication process.

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UPW 1516.55 t/h

Pre-treatment system Municipal fresh water 3095 t/h

UF

200 t/h (SR4) 354.66 t/h

RO

DI 125.62 t/h 337.54 t/h

UF reject, SR1 928.5 t/h (wastewater)

RO reject, SR2 649.95 t/h

Wet, SK1 Litography, SK2

250 t/h (SR3)

180.28 t/h (wastewater)

350 t/h (SR5)

112.46t/h 111.92 t/h 588.08 t/h

19.31 t/h (wastewater)

19.72 t/h

FAB

CMP, SK3

278.99 t/h

300 t/h (SR6) 200 t/h (SR7)

86.27 t/h (wastewater)

113.73 t/h 107.8 t/h

259.68 t/h

236.27 t/h

Etc, SK4

280 t/h (SR8) 29.04 t/h

Cooling tower makeup, SK6

63.16 t/h

121.06 t/h Wastewater Treatment

180 t/h (SR9)

Cleaning, SK5

300 t/h (SR10)

Scrubber, SK7

250.96 t/h (wastewater)

334.1 t/h

78.94 t/h 142.1 t/h

739.68 t/h (wastewater)

157.9 t/h

2205 t/h (Total wastewater) Heavy metal (2 mg/L)

Figure 2. Optimal water recovery scheme for wafer fabrication process.

5. Conclusion In this paper, the automated targeting approach is extended for total property-based network where the individual elements of reuse/recycle, regeneration/interception and waste treatment are considered simultaneously. The automated targeting has the advantages of both insight-based and mathematical optimisation approaches. An industrial case study is solved to illustrate the proposed approach.

References J. J. Alves, G. P. Towler, 2002, Analysis of refinery hydrogen distribution systems, Ind. Eng. Chem. Res., 41, 5759-5769. M. M. El-Halwagi, 1997, Pollution Prevention through Process Integration: Systematic Design Tools, Academic Press, San Diego. M. M. El-Halwagi, 2006, Process integration, Elsevier Inc., Amsterdam. M. M. El-Halwagi, F. Gabriel, D. Harell, 2003, Rigorous Graphical Targeting for Resource Conservation via Material Recycle/Reuse Networks, Ind. Eng. Chem. Res., 42, 4319-4328. M. M. El-Halwagi, V. Manousiothakis, 1990, Automatic Synthesis of Mass-Exchange Networks with Single Component Targets Chem. Eng. Sci., 9, 2813-2831. N. Hallale, 2002, A New Graphical Targeting Method for Water Minimisation , Adv. Env. Res., 6 (3), 377-390. Z. A. Manan, Y. L. Tan, D. C. Y. Foo, 2004, Targeting The Minimum Water Flowrate using Water Cascade Analysis Technique, AIChE J., 50 (12), 3169-3183. D. K. S. Ng, D. C. Y. Foo, R. R. Tan, Y. L. Tan, C. H. Pau, 2009, Automated Targeting for Conventional and Bilateral Property-Based Resource Conservation Network, Chem. Eng. J., (DOI:10.1016/j.cej.2008.10.003). G. P. Towler, R. Mann, A. J. - L. Serriere and C. M. D. Gabaude, 1996, Refinery hydrogen management: Cost analysis of chemically integrated facilities, Ind. Eng. Chem. Res., 35(7), 2378-2388. M. D. Shelley, M. M. El-Halwagi, 2000, Componentless design of recovery and allocation systems: A functionality-based clustering approach, Comp. Chem. Eng., 24, 2081-2091.

Automated Targeting for Total Property-Based Network Y. P. Wang, R. Smith, 1994, Wastewater Minimisation, Chem. Eng. Sci., 49 (7), 981-1006.

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19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Comparison of Control Strategies for Dissolved Oxygen Control in Activated Sludge Wastewater Treatment Process Evrim Akyurek,a Mehmet Yuceer,b Ilknur Atasoy,c Ridvan Berber a*+ a

Ankara University, Faculty of Enginering, Dept.of Chemical Engineering 06100 Tandogan/Ankara, Turkey, E-mail: [email protected], E-mail:[email protected] b Inonu University, Faculty of Enginering, Dept.of Chemical Engineering 44280 Malatya, Turkey, E-mail:[email protected] c Refik Saydam Hygiene Center, Department of Environment Health Research 06100 Ankara, Turkey, E-mail: [email protected]

Abstract Six control strategies; PID control, Model Predictive Control (MPC) with linear model, MPC with non-linear model, Nonlinear Autoregressive-Moving Average (NARMA-L2) control, Neural Network Model Predictive Control (NN-MPC) and optimal control with sequential quadratic programming (SQP) algorithm were evaluated via simulation of activated sludge wastewater treatment process. Controller performance assessment was based on rise time, overshoot, Integral Absolute Error (IAE) and Integral Square Error (ISE) performance criteria. As dissolved oxygen level in the aeration tank plays an important role in obtaining the effluent water quality, and in operating cost, it was chosen as the controlled variable. It was concluded consequently that NARMA-L2 controller and optimal control with SQP would outperform the others in achieving the specified objective. Keywords: Activated sludge process, MPC, Neural Network MPC, NARMA-L2, Optimal control

1. Introduction Effective control of wastewater treatment plants (WWTPs) has been receiving rising attention during the last decade due to increasing concern about environmental issues. In this sense, the importance of studies concentrating on control and operation of WWTP is remaining intact. Activated sludge process is commonly used in biological wastewater treatment. In this process, a bacterial biomass suspension is responsible for the removal of pollutants; depending on the design and the specific application, an activated sludge WWTP can achieve biological nitrogen removal and biological phosphorus removal, besides removal of organic carbon substances [1]. In the control of wastewater treatment plants, generally mechanistic models are used in simulating plant behavior over a wide range of operating conditions. The main activated sludge models were developed by the International Water Association (IWA). The Activated Sludge Model No.1 (ASM1) has been widely accepted as a reference model in activated sludge process [2]. There have been previous investigations attempting to tackle the control problem in activated sludge processes. Among the latest ones, one can mention the works by Caraman et al. [3] and Holenda et al. [4] who both tried MPC algorithm with a simplified model and ASM1 model. In one previous control study by Stare et al. [5],

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only two different controllers (namely PI and MPC) were applied on Benchmark simulation model 1. Therefore, thorough comparative study is thought to be needed. Dissolved oxygen control, ammonia control and nitrogen control are the most commonly used controlled variables in activated sludge processes. The growth rate of the microorganism and the concentration of effluent substrate are highly dependent on dissolved oxygen level in the process. For this reason dissolved oxygen concentration in the aeration tank was selected as controlled variable in this study. The objective was to maintain the effluent substrate concentration below a preset level dictated by environmental regulations. This goal was achieved by controlling effluent dissolved oxygen concentration at the set point by manipulating aeration rate. The proposed control strategies were evaluated in terms of set-point rise time, reliability of manipulated variable, IAE and ISE performance criteria.

2. Model and Methods 2.1. Plant Layout and Process Model The wastewater treatment process whose schematic representation is shown in Figure 1 is considered. Simplified mathematical model and kinetic parameters were taken from the literature [3, 6]. Prior to the closed loop control simulations, the process was brought to the steady state, and in the course of simulations it was assumed that there was no substrate or dissolved oxygen in the recycled sludge flow of the bioreactor. Equations of biological reactions in aeration tank and settler were extracted from previous studies [3, 6]. 2.2. Applied control strategies The state-space model for the controllers was generated by linearization of the activated sludge process using Jacobian at the steady-state operating point obtained from openloop simulations of the wastewater treatment plant. Having applied constant concentration values for the influent for 42 days, the steady-state operating points were reached in start-up simulations. Obtained operating points were used as initial values for proceeding control simulations. Trial and error method was used for the identification of tuning parameters for obtaining the possible best performance out of the controller. Boundaries of manipulated variables were the same for all control algorithms. The maximum aeration rate was limited to 80 1/h and the minimum aeration rate was limited to 40 1/h, while the dissolved oxygen values were maintained between 0 and 7 mg/L.

Figure 1. Wastewater treatment process

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2.2.1. PID control In this control strategy state-space linear model was used. Parameters of PID controller were tuned using Ziegler-Nichols method. Tuning parameters of the PID controller were found to be as Kp=46, τi=115, τd=4.6. 2.2.2. Model Predictive Control MPC is by far the most commonly applied advanced control strategy in the wastewater treatment process. In this control strategy two approaches were applied with using MATLAB MPC toolbox; MPC with linear model and MPC with non-linear model. During the simulations aeration rate was taken as manipulated variable with constant dilution rate. Parameters of MPC controller were tuned by trial and error. The prediction horizon and control horizon were determined as 60 and 20 interval, respectively, and the sampling time was taken as 0.25 h. 2.2.3. NN-MPC & NARMA-L2 Control Neural network model predictive control and Nonlinear Autoregressive-Moving Average control were applied successfully in the identification and control of dynamic systems. Rather than attempting to survey the many ways in which multilayer networks have been used in control systems, we concentrated on two typical neural network controllers: model predictive control [7, 8], and NARMA-L2 control [8]. They are based on standard linear control architectures like other neural controllers. Using neural networks for control purposes, two steps are critical; system identification and control design. In the system identification stage, a neural network model of the plant was developed to control, and in the control design stage, the neural network plant model was used to design and train the controller [9]. Table 1 shows the parameters used in these controllers.

2.2.4. Optimal control with sequential quadratic programming algorithm Sequential quadratic programming (SQP) method is an iterative method, which solves at each iteration a quadratic programming problem to investigate the best operational strategy for manipulated variable sought to catch the set point. In this control strategy, firstly state variables and manipulated (optimized) variable (x(0) and u(0)) were initialized, and upper and lower bounds of manipulated variable (u) were defined. Then model was solved up to tfinal with 0.25 h sampling time and obtained state variables in each interval were used as an initial value for the next interval. The difference between the controlled variable values obtained from the model and desired set point values for each sampling time were squared and their sum was used as objective function to minimize. As soon as the desired criteria had been obtained, optimization ended and manipulated variable profile was obtained for 20 sampling intervals (i.e. control horizon). The first value of the obtained manipulated variable profile was implemented on the model as an actual control effort and the procedure was repeated for the next interval until the final operation time was reached. Table 1. Parameters for NN-MPC and NARMA-L2

Parameters Size of hidden layer Training function Training data Cost horizon (N2) Control horizon (Nu) Control weighting factor(ρ) Search parameter (α)

NN-MPC 3 Levenberg-Marquardt normalized 20 2 0.1 0.1

NARMA-L2 5 Levenberg-Marquardt Normalized -

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3. Results and Discussion In this study, the performances of six different control strategies were comparatively evaluated for an activated sludge process through model simulations in MATLAB environment. Dissolved oxygen level in the aeration tank was used as controlled variable whereas the manipulated variable was the aeration rate. This decision was based on the fact that the growth of biomass in the aeration tank is highly dependent on dissolved oxygen concentration. Selected set-point of dissolved oxygen concentration of the controller strongly influences the performance of the plant. High DO levels in the aeration tank will cause high energy consumption. On the other hand, substrate will not convert to biomass in low DO concentration. In order to find the impact of the controller set points on plant performance, a number of simulations with different set point values were performed. During these simulations, effluent substrate concentration was taken as process constraint. By the environmental regulations it must be below 30 mg/L. An optimal setpoint value of dissolved oxygen concentration was selected as 4 mg/L. Figure 2 shows the comparison of the performances of the control strategies for a step change around this optimal set point value. To determine the performance of the controllers, dissolved oxygen set point value was changed from 3.43 to 4 mg/L. The obtained value of IAE, ISA and rise time values are shown in Table 2. The PID control strategy gives the largest overshoot (OS) value, 13.2 % as expected. PID controller catches the set point in 12 hours. MPC controller with linear model gives better response than the MPC controller with non-linear model. The rise time of these controllers are 10 and 20 hours, respectively. NN-MPC’s rise time is 9 hours. NARMAL2 controller and SQP algorithms give much better responses than the others in terms of rise time and overshoot. Both of these controllers employed non-linear model. Dissolved oxygen concentration in NARMA-L2 controller and SQP algorithm reaches the set point in 0.6 and 1 hour, respectively. Optimal control with SQP algorithm and NARMA-L2 controller exhibit most adequate responses compared to other controllers in terms of IAE and ISE performance criteria (Table 2).

Figure 2. Comparison of control strategies at optimal set-point value

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Table 2. Comparison of Controllers in terms of IAE, ISE and Rise Time

Controller NARMA-L2 SQP PID NN-NMPC Linear MPC Nonlinear MPC

IAE 0.1018 0.1820 0.3188 0.7546 0.8668 1.0046

ISE 0.0346 0.0812 0.1241 0.2508 0.3663 0.3801

Rise time (h) 0.6 1.0 12.0 9.0 10.0 20.0

4. Conclusions Six control strategies; PID control, MPC with linear model, MPC with non-linear model, NARMA-L2 control, NN-MPC and optimal control with SQP algorithm were evaluated for dissolved oxygen control in an exemplary activated sludge system. The control objective was to keep effluent dissolved oxygen concentration at a certain value by manipulating the aeration rate. Results were indicative of the conclusion that NARMA-L2 controller and optimal control with SQP would outperform the others in achieving the specified objective.

5. Acknowledgements This work has been partially supported by the European Union FP6 project INNOVA-MED (Contract No. INCO-CT-2006-517728), for which the authors are grateful.

References [1] K.V. Gernaey, M.C.M.Van Loosdrecht, M.Henze, M.Lind, B.S.Jorgensen, Environmental Modelling and Software. 19(2003) 763. [2] M. Henze, W. Gujer, T. Mino, M. Loosdrecht, Scientific and Technical Report No. 9 (2002). [3] S. Caraman, M. Sbarciog, M. Barbu,. International Journal of Computers, Communications and Control. 2 (2007) 132. [4] B. Holenda, E. Domokos, A. Redey, J. Fazakas, Computers and Chemical Engineering. (2008) 1270. [5] A. Stare, D. Vrecko, N. Hvala, S. Strmcnik, Water Research. 41 (2007) 2004. [6] F. Nejjari., A. Benhammou, B. Dahhou and G. Roux, Int.J. Adaptive Control Signal Process. 13 (1999) 347. [7] K. S. Narendra and S. Mukhopadhyay, IEEE Transactions on Neural Networks. 8 (1997) 475. [8] K. S. Narendra and K. Parthasarathy, IEEE Transactions on Neural Networks. 1 (1990) 4. [9] I. Atasoy, M. Yuceer, E. Oguz Ulker and R. Berber, Chemical Engineering & Technology 30(2007) 1525.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Metal ions sorption equilibrium on chitosan foamed structure W. KamiĔski, E. Tomczak, U. Wilicka Faculty of Process and Environmental Engineering, Technical University of Lodz, WólczaĔska 215, 93-005 ŁódĨ, tel. +48 (42) 631 37 08, [email protected]

Abstract In this study, experiments were carried out to estimate sorptivity of a chitosan foamed structure and its selectivity towards Cu+2, Zn+2 and Cr+6 ions. In the case of single ions it was found that in the whole range of concentrations, experimental data were well described by the Langmuir-Freundlich equation which is a relationship between the amount of adsorbed metal per adsorbent mass unit and equilibrium concentration of the solution. A mathematical description of sorption isotherms of the analyzed ions in the presence of one or two additional ions in the solution is complicated from the theoretical point of view. In this case the application of a neural MLP network was proposed. The network consisted of three inputs corresponding to equilibrium concentrations of particular components, a hidden layer and an output layer. On the basis of available experimental data in the so-called process of network training, the number of hidden neurons and weights of neurons combinations were given. Calculations with the use of MLP enabled description of sorption isotherms for one ion, for selected two and for three ions present at the same time in the solution. The network enabled also an analysis of sorption of the selected ion, taking into account the effect of its concentration on the sorption of other ions. This assessment would not be possible in an experimental way only. Keywords: heavy metals ions, adsorption, artificial neural network

1. Scope of experiments Formation of chitosan foamed structure Glycerin, 0.2% glutar aldehyde and sodium bicarbonate were added to 2% acetic acid. The releasing carbon dioxide caused foaming of the mixture, while the formed OHshowed a coagulating action. The process was carried out while stirring vigorously. After formation, the chitosan foam was washed in distilled water. Stable foam with moisture content ca. 90% was obtained. The formed structure, with high porosity was used as a sorption material to remove heavy metal ions. Experimental setup About 10 g of wet chitosan foam was placed in conical flasks and 250 cm3 of the tested solution or mixture of the tested salt solutions in the concentration range from 20 to 100 mg/dm3 was added. A source of ions were water solutions of copper (II) (CuSO4×5H2O), zinc (II) (ZnSO4×7H2O) and chromium (VI) (K2CrO4) – chromium occurred in the form of chromium (VI) anions. Ion concentrations in the mixtures were the same as for individual ions. Next, the samples were placed in a thermostat and stirred continuously. Experiments were carried out at pH = 5 to 6. Samples for analysis

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were taken every 30 min until the state of equilibrium was reached. The samples were analyzed by atomic absorption spectrometric method (AAS) in a Solar M6 spectrophotometer (Unican). Tests were carried out at the temperature 30°C, 40°C, 50°C and 60°C.

2. A mathematical description of sorption equilibrium Prediction of sorption kinetics is one of important issues in the design of process equipment. Adsorption rate is the highest in the moment when fluid contacts the adsorbent for the first time. Then, the rate decreases with time until equilibrium is reached. When sorption equilibrium is described for a solution which contains a single cation, the Langmuir-Freundlich equation can be used successfully:

qe K FL ⋅ CenFL = qm 1 + K FL ⋅ CenFL

(1)

where: KFL, qm and nFL are constants in this equation for a given system. Further on, experiments with mixtures of the tested metals were performed in multicomponent systems. Sorption of metal ions in such systems is a complex problem. Several approaches to this problem have been proposed [Juang & Shao, 2002; Vold et al., 2003; Becker et al., 2000; Petrus & Warchol, 2005]. However, results appeared to be not fully satisfying. So, it was decided to apply artificial neural networks in the description of sorption equilibrium in multi-component systems. Artificial neural networks and techniques of their training and verification are nothing more than only a method to describe relations between independent and dependent variables when the explicit form of mapping is not known. In studies devoted to ANN it was proven that a MLP-type network (Multilayer Perceptron) is a universal approximator, i.e. it can map any function with a predetermined accuracy. The MLP network was applied to describe the sorption equilibrium. The network consisted of an input, hidden and output layer. The layers are composed of neurons. The neurons from one layer are combined to the neurons from a consecutive layer on the each-to-each principle. The task of a neuron is to sum up received signals and non-linear transformation. Usually this is a sigmoid function which was used in Kaminski et al., 2008 paper. Training of a network consists in a selection of weights attributed to the connections between neuron layers. This usually proceeds according to second-order methods. An analysis showed that the best results from the point of view of the accuracy of calculations and possibilities of extrapolation and interpolation were given by the following MLP input/output system: network input was initial concentration Ci and network output was the amount of adsorbed metal ions qe [mg/g d.m. chitosan]. Figure 1 illustrates a schematic diagram of the MLP network. The isotherm equation can be obtained by the simple formula:

qe = f MLP (C1 , C 2 , C3 )

(2)

3. Results and discussion Figure 2 shows some experimental data and results calculated according to the Langmuir-Freundlich equation. It is observed that the equation well describes sorption

Metal Ions Sorption Equilibrium on Chitosan Foamed Structure

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equilibrium from a single-component solution in the whole range of concentrations. Similar results were obtained for three analyzed heavy metal ions and different process temperatures. Modeling of sorption equilibrium for one-component solution is quite easy and has been described extensively in literature [Bodu et al., 2003; Ng et al., 2002]. In the case of ANN, training data were experimental results for single- and multicomponent systems. If on any of the three inputs to the network the value of zero appeared, it meant that the component was not present in the analyzed solution. After the network training results could be obtained for a single-component, binary and ternary system, respectively.

q

OUTPUT LAYER b1

w2

HIDDEN LAYER b1

w11

1 INPUT LAYER

f Ȉ

C1

f Ȉ

w12

w13

2

C2

3

C3

Figure 1. Schematic diagram of MLP neural network

Below, results calculated for Cr(VI) single-component solution and in a ternary mixture are shown (Fig. 3). Figure 4 shows a comparison of experimental data and values calculated by means of MLP for copper and zinc (results are similar for chromium). In the case of ideal accuracy, the points which represent calculation and experimental sorptivity of chitosan should be exactly on the diagonal. It can be seen that for most cases good and very good correctness was obtained. Table 1 gives weighs and biases for all metal ions and measuring temperatures. A statistical estimation of the network operation quality was presented by means of the square correlation coefficient (0.94÷0.99) and the mean relative error (0.05÷0.19).

4. Conclusions The chitosan foam is a new material applied to sorption processes which characterize stable structures with good mechanical properties. High porosity promotes sorption processes. When modeling sorption equilibrium of Cu(II), Zn(II) and Cr(VI) ions for singlecomponent solution on foamed chitosan, the Langmuir-Freundlich equation can be used as it well describes equilibrium in the whole concentration range. When two or three ions occur in the solution simultaneously, modeling is more complicated and should reflect the interactions between ions and their mutual effect on sorption efficiency. This knowledge is not necessary in the case of ANN. A method to

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describe sorption equilibrium with the use of MLP structure is presented in the paper. Good agreement was obtained between experimental and ANN-predicted results.

2

R = 0,954 qm=61,22

80 70

80

KFL=0,015

60

qe [mg/g]

qe [mg/g]

40

o

Cu(II)

40 C

Experimental data Langmuir-Freundlich equation

30 20

T=30 C

Experimental data Langmuir-Freundlich equation

60

50

O

Zn(II)

70

50 2

R = 0,989 qm=-81,91

40 30

KFL=-0,18

20

10

10

0

0 0

10

20

30

40

50

0

3

10

20

30

Ce [mg/dm ]

40

50

3

60

70

80

90

Ce [mg/dm ]

Fig. 2. Sorption equilibrium for Cu(II) and Zn(II) in a single-component solution 60

a)

b)

50

50

40

40

qe [mg/g]

qe [mg/g]

60

30

30

o

o

T=40 C

20

T = 40 C

20

EXP CAL

10

EXP CAL

10 10

20

30

40

50

3

Ce [mg/dm ]

60

70

80

90

5

10

15

20

3

Ce [mg/dm ]

25

30

35

Fig. 3. Sorption isotherm of Cr(VI) for a single-component solution (a) and for a mixture with copper (II) and zinc (II) (b) 80

80

70

70 60

50 40 30

Cu(II) 20 10

SINGLE ION o 30 C o 40 C o 50 C o 60 C MIXTURES o 30 C o 40 C o 50 C o 60 C

0

Calculated data

Calculated data

60

50 40

Zn(II) 30 20 10

SINGLE ION o 30 C o 40 C o 50 C o 60 C MIXTURE o 30 C o 40 C o 50 C o 60 C

0 0

10

20

30

40

50

Experimental data

60

70

80

0

10

20

30

40

50

Experimental data

60

70

80

Fig. 4. A comparison of experimental and calculated data for copper and zinc

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Table 1. Comparison of weighs and biases in MLP

Ion

Cu

Zn

Cr

Temperature [°C] 30 40 50 60 30 40 50 60 30 40 50 60

w1 w11 0.305 0.512 -0.242 0.080 -0.017 -0.034 -0.095 -18.957 -0.014 -0.022 -0.197 0.014

w12 -0.028 -0.011 -0.113 0.014 0.019 0.023 0.024 -1.619 0.000 -0.005 -0.037 -0.011

w13 0.040 0.070 0.001 0.080 0.002 -0.003 0.021 3.374 -0.008 -0.016 -0.115 -0.017

b1

w2

b2

-1.850 -3.061 6.717 -6.031 -4.900 -5.220 -3.945 86.051 1.914 3.876 5.571 4.319

4.859 4.937 -3.319 60.127 0.015 0.019 54.954 -2.866 57.910 -0.011 -3.626 -140.81

2.154 -2.485 2.136 -1.335 -2.584 -2.560 -2.527 2.043 48.333 105.437 2.519 137.228

5. Acknowledgements Research project no. N207 031/1436 was financed by funds for science in the years 2006-2009.

References [1] Becker T., Schlaak M., Strasdeit H., Adsorption of nickel(II), zinc(II) and cadmium(II) by new chitosan derivatives, Reactive & Functional Polymers, vol.44, 289-298, 2000. [2] Boddu V.M., Abburi K., Talbott J., Smith E., Removal of hexavalent chromium from wastewater using a new composite chitosan biosorbent, Environ. Sci. Technol. vol.37, 4449-4456, 2003. [3] Juang R.S., Shao H.J., A simplified equilibrium model for sorption of heavy metal ions from aqueous solution of chitosan, Water Research, vol.36, 2999-3008, 2002. [4] KamiĔski W., Tomczak E., Jaros K., Interactions of metal ions sorbent on chitosan beads, Desalination, 218, 281-286, (2008). [5] Ng J.C.Y., Cheung W.H., McKay G., Equilibrium studies of the sorption of Cu(II) ions onto chitosan, Journal of Colloid and Interface Science, vol.255, 64-74, 2002. [6] Petrus R., Warchol J.K., Heavy metal removal by clinoptilolite. An equilibrium study in multi-component system. Water Research, vol. 39, 819-830, 2005. [7] Vold, 2003; Vold I.M.N., Varum K.M., Guibal E., Smidsrod O., Binding of ions to chitosan – selectivity studies, Carbohydrate Polymers, vol.54, 471-477, 2003.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Optimization of Wastewater Treatment Network Grzegorz Poplewski, Jacek M. JeĪowski Rzeszow University of Technology, Department of Chemical and Process Engineering, ul. W. Pola 2, 35-959 Rzeszow,Poland, [email protected]

Abstract A simultaneous method has been developed to solve wastewater treatment network design problem with wastewater treatment technology choice. The approach consists in solving optimization model of a superstructure. Adaptive random search (ARS) method has been used as optimization technique. The approach accounts for various objectives. Structural issues such as forbidden connections can be taken into consideration. The tests proved that this approach is able to solve all the literature case studies reaching the results similar or even better than those from complex approaches with the use of sophisticated optimization algorithm. Keywords: design, superstructure optimization, wastewater treatment network, technology choice

1. Introduction Wastewater treatment network (WWTN) is one of two basic elements of total water network consisting of water using processes and wastewater treatment operations. Though a problem of designing a network of water using processes drawn greater attention also that on WWTN has been addressed in several papers. Seminal paper of Wang and Smith [1] formulated the problem and proposed pinch technology tools. The approach has been extended and improved by Kuo and Smith [2]. Systematic approaches have been proposed in references [3-8] to name a few. They all used superstructure concept but employed different optimization strategies to cope with difficult nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) formulation. For instance, Galan and Grossmann [3] used multi-start procedure to increase the chance of location of the global optimum. Statyukha et al.[7] employed water pinch approach as the initialization scheme for a simple NLP solver. Bergamini et al. [5] applied the method which was claimed to be a global optimization algorithm. As we will show by an example even this complex method was not able to find the global optimum. In this paper we will show the use of a simple stochastic optimization approach to solve WWTN superstructure model. The method does not guarantee the global optimum. However, it was able to calculate, for all literature case studies, the solutions which are similar are even better than those considered to be the optima.

2. WWTN Problem Formulation Given are: • Wastewater streams from various sources with concentrations of contaminants and total flow rates • Treatment processes with available treatment technologies for each treatment process • Removal ratios of contaminants for each treatment process/technology

G. Poplewski and J.M. Jez owski

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•

Final discharge sites for water streams after treating with environmental limits on concentrations. • Technical and technological conditions on operations/technologies and structure (mainly on connections). The constraints on a structure include forbidden and must-be connections, upper limits on number of branches from a splitter and so on. • Cost parameters for calculating economic goal function The objective is to design WWTN that minimizes / maximizes certain performance index. The objectives in the approach can differ from the simplest one such as total flow rate to more complex such as total cost of treatment technologies and expenses on pipelines.

3. Superstructure and its optimization model The superstructure consists of main building elements: mixer-wastewater treatment process – splitter. Each splitter can redistribute outlet stream from a process to other processes including recycle to the same process and a stream to the disposal site. There is also a splitter for each wastewater stream that redistribute the effluents to mixers of processes and to the disposal site. Finally, there are the mixers of the disposal sites (we use one disposal site in the following for simplicity sake). Hence, all possible structures are embedded in this superstructure. It is important to note that treatment technologies are not included explicitly into the representation but are accounted for in the model. Namely, one technology can be chosen for a process. It is assumed, similarly to other papers, that one unit is used for one technology. The selection of technology causes the use of binary variables defining existence of the technology. Binary variables are also applied to define existence of connections between basic elements of the superstructure. The constraints of the superstructure model are as follows: 1. Overall mass balances for splitters of wastewater streams. 2. Overall mass balances of treatment operations. 3. Mass balances of contaminants of treatment processes with removal ratios. 4. Mass balances of contaminants for mixers of treatment processes. 5. Mass balances of contaminants for mixer of the disposal site. 6. Logical conditions, which force flow rates to zero if appropriate binaries are zero. Also, they are used to eliminate non-optimal technology from a structure. 7. Inequality constraints on contaminant concentrations to the disposal site. They ensure that the concentrations are not higher than the given environmental limits. 8. Other technological case specific constraints such as for instance lower limits on flow rate via piping sections. The overall model is of MINLP type. The main source of nonlinearity (except of the goal function) are bi-linear terms: a concentration times a flow rate.

4. The solution approach To solve this optimization problem we applied adaptive random search (ARS) optimization. This is a modified version of basic Luus-Jaakola algorithm [9]. It was successfully applied to optimal water usage network design in JeĪowski et al. [8]. The detailed algorithm with tests is illustrated elsewhere [12]. Here we will present some enhancements that we have developed to solve WWTN problems with large number of variables. They concerned the methods of dealing with equality constraints and with

Optimization of Wastewater Treatment Network

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binary variables. Also, an initialization procedure was used to generate a feasible starting point. In regard to constraints we applied the direct solution of equalities within optimization procedure. They were transformed into linear equations by proper division into two subsets: dependent variables and decision ones and, also, by appropriate sequencing the equalities. The decision variables are the flow rates of all streams except of those sent to the disposal site and, also, auxiliary variables for selection of treatment technology. All other variables are calculated from equality constraints, that is, these variables are dependent variables. In regard to the initial starting points for the solver we have used all possible centralized treatment networks for the given technologies. The networks differ as for the combination of treatment technologies assigned to the operations. The binary variables for connections were treated as dependent parameters calculated in a solution procedure on the basis of decision variables – flow rates through the connections. The simple statements were used in the ARS method: IF flow rate through connection < minimum value THEN flow rate through connection :=0 and binary for the connection :=0

(1)

The value of the minimum flow rate was assumed at 2 t/h. Binary variables for technology selection are generated randomly via auxiliary continuous variables. The continuous variable associated with a technology is generated from the uniform distribution by Monte Carlo generator. The upper bound on the variable is the number of available technologies for the process – the lower bound is zero. Let x denotes the auxiliary variable and tt – technology number (i.e. integer number). The scheme of selection of the binary Y(tt) is as follows: IF x∈(tt-1 , tt) THEN Y(tt) := 1 ELSE Y(tt) := 0

(2)

5. Example of application The example is taken from Galan and Grossmann [3] and it was also solved in Bergamini et al. [5]. The data for wastewater sources together with the environmental limits on the concentrations of contaminants A, B and C to disposal site are given in Table 1. Parameters of available treatment technologies for three treatment processes are gathered in Table 2. Table 1. Data for wastewater sources and environmental limits on contaminants’ concentrations for the example

Concentrations of contaminants [ppm] Source

F [t/h]

1 2 3

20 15 5

Cei ,in ,max

A 1100 300 500 100

B 300 700 1000 100

C 400 1500 600 100

Authors [3] calculated the optimum network for the example of the goal function of 1.69 106 [$/year]. The technologies selected were as follows: technology no. 1 for process 1 and technology no. 3 for processes 2 and 3. The network, i.e. structure and parameters, had not been given in [3]. Bergamini et al. [5] presented the optimal

G. Poplewski and J.M. Jez owski

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solution shown in Fig. 1 but failed to give the goal function and we calculated it as 1 692 760 [$/year]. With control parameters of the optimization algorithm that result in CPU time of 66 CPU seconds per run at PC with processor Intel Centrino 1.5 GHz, we obtained the better solution with the goal function equal to 1 650 578 [$/year]. Table 2. Removal ratios and costs for treatment processes and technologies in the example

Treatment processes

ψ (%)

Treatment technology

A 90 50 0 0 0 50 80 0 0

1 2 3 1 2 3 1 2 3

1

2

3

12.74

Costs

B 0 70 80 90 99 99 0 0 0

C 40 0 0 0 0 80 60 80 40

investment [$] 3840 F0.7 469 F0.7 26 F0.7 726 F0.7 1260 F0.7 5000 F0.7 320 F0.7 58 F0.7 10 F0.7

operation [$/h] 0 10 F F 0.0089 F 0.018 F 5.8 F 6F 15 F F

t3 tt3 37.6

t1

20

s1

40

tt1 7.26

e

2.4

15

s2

t2 tt3 24.86 5

s3

Fig.1. Optimal solution to the example from Bergamini et al. [5]

s3

t2

5

tt3 27.262

s2

t1

15 7.263

tt1

40

e

19.44

s1

20

12.737

t3 tt3 32.177

Fig.2. Optimal solution to the example calculated by ARS-based approach with goal function of 1 647 392 [$/year]

For larger CPU time we were able to calculate the network shown in Fig. 2 with the cost of 1 647 392 [$/year]. Both solutions use the same treatment technologies as those in the network calculated in [3, 5]. The analysis reveals that the improvement has been

Optimization of Wastewater Treatment Network

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achieved due to recycle P1→P3→P1, which does not exist in the solution from method of Bergamini et al. [5].

6. Summary The ARS based solution method for WWTN design problem has been developed. The approach accounts for various goal functions and various technical and economical conditions. For instance, cost of pipelines and/ or structural constraints can be accounted for. Also, the choice of optimal treatment technology is possible. The method is easy to use and does not require sophisticated (commercial) optimizers. The example showed that this simple stochastic approach was able to find the better solution than the sophisticated global optimization algorithm applied in reference [5]. Several other problems from the literature were also calculated with this simultaneous method. Only in one case we haven’t reached the global optimum network though the solution obtained differs only slightly from the optimum.

7. References [1] Y.-P. Wang and R. Smith, Design distributed effluent treatment systems. Chem. Eng. Sci., 49 (1994) 3127-3145. [2] W.-C. J. Kuo and R. Smith, Effluent treatment system design. Chem. Eng. Sci., 52 (1997) 4273-4290. [3] B. Galan and I. E. Grossmann, Optimal design of distributed wastewater treatment networks. Ind. Eng. Chem. Res., 37 (1998) 4036-4048. [4] R. Hernández-Suárez, J. Castellanos-Fernández and J. M. Zamora, Superstructure decomposition and parametric optimization approach for the synthesis distributed wastewater treatment networks . Ind. Eng. Chem. Res., 43 (2004) 2175-2191. [5] M.L. Bergamini, P. Aguirre and I. Grossmann, Logic-based outer approximation for globally optimal synthesis of process networks. Comput. Chem. Eng., 29 (2005) 19141933. [6] C. A. Meyer and C. A. Floudas, Global optimization of a combinatorially complex generalized pooling problem. AIChE J., 52, 3 (2006) 1027-1037. [7] G. Statyukha, O. Kvitka, I. Dzhygyrey and Jacek JeĪowski, A simple sequential approach for designing industrial wastewater treatment networks. Journal of Cleaner Production, 16 (2008) 215-224. [8] J. JeĪowski, R. Bochenek and G. Poplewski, On application of stochastic optimization techniques to designing heat exchanger- and water networks . Chemical Engineering and Processing: Process Intensification, 46 (2007) 1160-1174. [9] R. Luus and T.H.I. Jaakola, Optimization by direct search and systematic reduction of the size of search region. AIChE J., 19, 4 (1973) 760-766. [10] J. JeĪowski, R. Bochenek and G. Ziomek, Random search optimization approach for highly multi-modal nonlinear problems. Advan. Eng. Software 36, 8 (2005) 504-517.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Water Network Synthesis for Mixed Batch-Continuous Processes Hella Tokos and Zorka Novak Pintariþ University of Maribor, Faculty of Chemistry and Chemical Engineering, Smetanova 17, SI-2000 Maribor, Slovenia, [email protected]

Abstract This paper presents a mixed-integer nonlinear programming (MINLP) mathematical model for optimizing water re-use and regeneration re-use in batch-continuous processes. This model is based on a design method developed by Kim and Smith (2004) and performs efficient integration of discontinuous water-using operations, and continuous wastewater streams with low contaminant concentrations (with or without storage tanks for continuous streams). In addition, synthesis of batch and/or continuous local wastewater treatment system can be performed simultaneously. The developed model was applied on industrial case study, at a Brewery. Keywords: water, wastewater, re-use, regeneration, MINLP

1. Introduction In the literature, studies on the design of water re-use and wastewater treatment networks in industry are mainly concerned with continuous processes (Bagajewicz, 2000; Karuppiah and Grossmann, 2006), while very little attention has been directed towards the development of water conservation strategies for batch operations or combinations of batch-continuous processes. Two main approaches are generally used to address the issue of freshwater demand minimization in batch processes, i.e. the graphical approach (Wang and Smith, 1995; Foo et al., 2005; Majozi, 2006; Chan et al., 2008), and the mathematically-based optimization approach with different options for storage tank installation (Almato et al., 1999; Kim and Smith, 2004; Majozi, 2005). One of the advantages of mathematical models is the possibility of incorporating several optimization problems, e.g. batch scheduling, water re-use network, and wastewater treatment network, into a single model, in order to generate an integrated water network in batch processes (Cheng and Chang, 2007). This paper presents a mathematical model for the integration of continuous and discontinuous water-using operations with or without storage tanks for continuous streams, as well as the extended model with local treatment units operating in batch or continuous modes. The model is based on the design method developed by Kim and Smith (2004), because of its straightforward formulation, and because the required input data can be obtained with relative ease on the production site.

2. Mathematical formulation The superstructure of the developed model involves all possible direct connections between batch operations, batch and continuous operations, and indirect connections of operations throughout the local treatment unit. The objective function of the original model (Kim and Smith, 2004) was extended in order to account for the treatment costs

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of discharged wastewater, f4, and the investment costs of local treatment units, f5, in addition to the freshwater cost, f1, annual investment costs for the storage tank, f2, and piping installation, f3: min FObj = f 1 + f 2 + f 3 + f 4 + f 5

(1)

Only a brief description of the model’s constraints is given in the continuation, while the complete model will be presented elsewhere (Tokos and Pintariþ, 2008). Mathematical model extended with continuous streams In the first step, the basic formulation was modified in order to integrate continuous and discontinuous operations. The continuous streams are treated as limited water sources, defined by the water flow rates of the continuous units. The set of water sources, w, includes freshwater sources, fw, and continuous water-using operations, ww. Additional equations for water re-use between continuous and discontinuous operations are given in the continuation. The limited water mass of the continuous stream ww over time interval j is defined by equation:

(

C E S mww , j = q m ,ww ⋅ t j − t j

)

0 0 j = j ww , j ww + 1, , J ww

(2)

where the set j represents time intervals where a continuous stream ww is present, C mww , j /t represents the limiting water mass of the continuous stream over the time interval j, q m ,ww / (t/h) is the mass flow rate of the continuous stream ww, t Sj /h and t Ej /h are starting and ending times of the time interval j. The outlet water mass from the continuous water stream over time interval j is given by equation: C, OUT C mww = m ww ,j ,j −

¦m

0 0 j = j ww , j ww + 1, , J ww ,

W ww ,n

∀n : t nS = t Sj

(3)

n

C,OUT where mww . j /t is the water mass from the continuous unit discharged over the interval W j, mww ,n /t is the water mass from continuous water source ww to batch operation n (re-

use). Mathematical model with storage tanks for continuous streams This model is further extended by the option of installing intermediate storage tanks for the collection of unused continuous wastewater streams, which enables water re-use during subsequent time intervals in which a continuous process does not operate. The mass of wastewater from the continuous operation discharged, m C, FOUT /t, is defined by equation: C, FOU T mww =

¦m

C, OUT ww , j

j

−

¦m

W ww ,n

0 0 j = j ww , j ww + 1, , J ww , ∀n : t nS ≥ t JEww

(4)

n

The existence or non-existence of a storage tank for continuous operation ww is obtained by a logical constraint: W C, ST Yww ≤ 0 ,n − Yww

∀n : t nS ≥ t JEww

(5)

W where Yww ,n is the binary variable for water mass from water source ww to operation n, C,ST Yww is the binary variable for a storage tank of continuous wastewater source ww. The

Water Network Synthesis for Mixed Batch-Continuous Processes

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C,ST capacity of a storage tank for the continuous wastewater stream, mww /t is defined by equation: C, ST m ww =

¦m

∀ n : t nS ≥ t JEww

W ww ,n

(6)

n

Mathematical model with batch local treatment units Additional reduction in the overall water consumption, as well as in the contaminant load of discharged water, can be achieved by water regeneration re-use. The water network is extended by local treatment units operating in batch mode. The option of storage tank installation before and after treatment is included in the model, in order to store wastewater and/or purified water if the time schedule of the treatment unit requires storage. The capacity of the local treatment unit, mtrTRC /t, is obtained by the inequality:

mtrTRC ≥

¦¦ m nc

S ∀nc ∧ ∀j : t nc = t Sj

TR nc ,n ,tr

(7)

n

TR where mnc ,n ,tr /t represents the re-used water mass from operations nc within the same

time interval j to subsequent operations n, purified in a local treatment unit tr. The purification of wastewater from operation nc in treatment unit tr can start anytime after the termination of process nc. Time constraints on the treatment unit are expressed by those disjunctive expressions which hold for selected connections, whilst for unselected they are redundant:

(

)

t LB − M ⋅ 1 − YncTR,n ,tr

(

S, TR E UB ≤ t nc + M ⋅ 1 − YncTR,n ,tr ,tr − t nc ≤ t

)

(8)

S, TR where t nc ,tr /h is the starting time of the wastewater treatment from operation nc in

local treatment unit tr, YncTR,n ,tr is the binary variable of treatment, t LB , t UB are the lower and upper bounds of time difference, and M is a large constant. The ending time of the E, TR purification, t nc ,tr , is defined by: E, TR S, TR TR t nc ,tr = t nc ,tr + Δt tr

(9)

where Δt trTR /h is the treatment time in the local treatment unit tr. The purification of wastewater from process nc in treatment unit tr has to be completed before process n starts:

(

t LB − M ⋅ 1 − YncTR,n ,tr

)

E, TR ≤ t nS − t nc ,tr

(

≤ t UB + M ⋅ 1 − YncTR,n ,tr

)

(10)

If the treatment time is shorter than the difference between the ending time of process nc and the starting time of process n, the waiting times before and after treatment are defined by equations:

(

− M ⋅ 1 − YncTR,n ,tr

)≤t

S n

(

E B, TR TR A, TR TR − t nc − t nc ,n ,tr − Δt tr − t nc ,n ,tr ≤ M ⋅ 1 − Ync ,n ,tr

)

(11)

B, TR A, TR where t nc ,n ,tr /h is the waiting time before treatment and t nc ,n ,tr /h is the waiting time

after treatment in the unit tr.

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The following constraint is used to identify those processes that require the installation of a storage tank for wastewater before treatment: TR, IN B, TR UB TR, IN t LB ⋅ YtrST, ≤ t nc ⋅ YtrST, ,nc ,n ,tr ≤ t ,nc

(12)

TR, IN is the binary variable for the storage tank before the treatment unit. where YtrST, ,nc

Those processes that require the installation of a storage tank for purified water after treatment are identified by the following constraint: TR, OUT A, TR UB TR, OUT t LB ⋅ YtrST, ≤ t nc ⋅ YtrST, ,nc ,n ,tr ≤ t ,nc

(13)

TR, OUT is a binary variable for the storage tank after treatment unit tr. where YtrST, ,nc

Mathematical model with continuous local treatment units The scheduling of the continuous treatment unit only differs from that of the batch treatment unit, when defining the treatment's ending time: E, TR S, TR t nc ,tr = t nc ,tr

(14)

3. Illustrative example Application of the mathematical model is firstly illustrated by Example 2 from Kim and Smith (2004). The example is extended by a continuous operation, with an acceptable purity level. Continuous operation produces a wastewater stream with an average flow rate of 100 t/h and contaminant concentration of 50 g/m³. The continuous stream is available within time intervals from 0 to 3 h. The freshwater consumption of optimally integrated batch units without the integration of a continuous stream amounts to 490.62 t. Figure 1 represents the optimal water network obtained by the extended mathematical model, which includes the integration of continuous operation and installation of on-site wastewater treatment. Wastewater purification is carried out in a continuous treatment unit (TR3), while batch units (TR1, TR2) are not selected. Process P1 uses fresh water, process P2 the continuous wastewater stream, while processes P3, P4, P5 and P6 use purified wastewater.

Figure 1. Optimal water network for illustrative example.

Water Network Synthesis for Mixed Batch-Continuous Processes

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Note that piping costs and the overall costs of wastewater treatment are reduced (Table 1). The overall cost of the final water network is 29 % lower than the cost of the optimal solution without integration of a continuous stream. Table 1. Results of illustrative example (all costs are in £/a)

No integration Integrated solution

Fresh water cost

Storage tank cost

Piping cost

Waste water treatment cost (CT)

Waste water treatment cost (LT)

Overall cost

785,000

13,568

123,637

249,600

0

1,171,805

512,000

0

80,340

188,081

2,403

830,757

CT-central treatment unit (off-site), LT-local treatment unit (on-site)

4. Industrial case study The possibilities of water re-use were analyzed in the packaging area of the brewery, where several continuous wastewater streams with low contaminant concentrations are available for re-use in batch operations with lower purity requirements. The possibilities for regeneration re-use were analyzed in the brewhouse, and the cellar, where the concentration of wastewaters is unacceptable for direct re-use. Water re-use in the packaging area Processes in the packaging area operate mostly in batch mode. The freshwater consumption per week is 2,000 t. There are two continuous streams available: the outlet stream of the rinser for non returnable glass bottles (K1), and the wastewater from the can rinser (K2). According to the results of process integration, the wastewater from the continuous process, K2, can be reused during the pasteurization processes. Wastewater from the pasteurizers can be reused in the bottle washer for returnable bottles, while the resulting outlet stream could be reused for washing crates. The freshwater consumption per week is reduced from 2,000 t to 1,126 t. The common costs of freshwater and wastewater treatment would decrease by 42 %. No storage tank installation is needed. The net present value of water network reconstruction is positive at 10 % discount rate and a payback period is 5 years. Water regeneration re-use in the production area Opportunities for regeneration re-use were analyzed in the brewhouse and the cellar because of high COD values of water streams. The daily consumption of freshwater is 886 t. In the integrated solution, the condensate from wort boiling can be re-used after regeneration as CIP rinsing water and partially to pour the batch material from one vessel into another. The water used for pouring the batch material can be collected, clarified, and re-used in the CIP system. Wastewater from filtration can be directly reused for pouring the batch material. A continuous treatment unit (nanofiltration) is selected for wastewater purification as an optimal design, while the batch unit is not selected. The freshwater consumption would reduce to 552 t. The freshwater and wastewater treatment costs together would decrease by 41 %. The net present value of the proposed water network reconstruction is positive, and the payback period is 2,8 years.

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H. Tokos and Z. Novak Pintaric

5. Conclusions An MINLP mathematical model is presented for the minimization of freshwater consumption and wastewater contaminant load in batch-continuous processes, by re-use and regeneration re-use. The mathematical formulation of the model is based on the design method developed by Kim and Smith (2004) for water re-use in batch processes. The original mathematical model was modified in order to suit specific industrial requirements. The developed model was applied to an industrial case study of a Brewery Plant. By applying the proposed re-use and regeneration re-use connections the brewery could save about 42 % of the current freshwater demand and reduce the costs of freshwater and wastewater treatment by 41 %.

References M. Almato, A. Espuna, L. Puigjaner, 1999, Optimisation of water use in batch process industries, Comp. Chem. Eng., 23, 10, 1427–1437. M. Bagajewicz, 2000, A review of recent design procedures for water networks in refineries and process plants, Comp. Chem. Eng., 24, 9–10, 2093–2113. J. H. Chan, D. C. Y. Foo, S. Kumaresan, R. A. Aziz, M. A. A. Hassan, 2008, An Integrated Approach for Water Minimisation in a PVC Manufacturing Process, Clean Technologies and Environmental Policy, Clean Technologies and Environmental Policy, 10, 67–79. K. F. Cheng, C. T. Chang, 2007, Integrated Water Network Designs for Batch Processes, Ind. Eng. Chem. Res., 46, 4, 1241–1253. C. Y. Foo, Z. A. Manan, Y. L. Tan, 2005, Synthesis of maximum water recovery network for batch process systems, Journal of Cleaner Production, 13, 15, 1381–1394. R. Karuppiah, I. E. Grossmann, 2006, Global optimization for the synthesis of integrated water systems in chemical processes, Comp. Chem. Eng., 30, 4, 650–673. J. K. Kim, R. Smith, 2004, Automated design of discontinuous water systems, Trans IChemE, 82, B3, 238–248. T. Majozi, 2005, Wastewater minimisation using central reusable water storage in batch plants, Comp. Chem. Eng., 29, 7, 1631–1646. T. Majozi, 2006, A graphical technique for wastewater minimisation in batch processes, Journal of Environmental Management, 78, 4, 317–329. H. Tokos, Z. N. Pintariþ, 2008, Design of Water Re-use and Regeneration Re-use System for Batch-Continuous Processes, Manuscript submitted to Chem. Eng. Technol. Y. P. Wang, R. Smith, 1995, Time pinch analysis, Trans IChemE, 73A, 905–914.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1221

Wastewater Storage Minimisation through the Exploitation of Inherent Storage Jacques F. Gouwsa,b, Thokozani Majozia,c a

Department of Chemical Engineering, University of Pretoria, Lynnwood Rd, Pretoria, 0002, South Africa b Logistics and Quantitative Methods, CSIR Built Environment, P. O. Box 395, Pretoria, 0001, South Africa c Department of Computer Science, University of Pannonia, Egyetem u. 10, Veszprém, H-8200, Hungary

Abstract The need for wastewater minimisation in batch processes is gaining importance as environmental pressures are forcing industry to seek means to reduce effluent. One of the most economical means of reducing effluent is through wastewater recycle/reuse. Wastewater recycle/reuse in batch processes is either done in the form of direct reuse, from unit to unit, or indirect reuse through intermediate storage. The reuse of wastewater through intermediate storage allows for the bypassing of the inherent time dimension present in batch processes. Intermediate storage, however, occupies a substantial amount of space. This is undesirable in batch operations since these operations are usually undertaken in limited spaces. In general, a trade-off exists between the size of wastewater storage and the savings achieved through wastewater reuse. However, an unexplored wastewater storage option exists in form of idle processing units. In any batch process there are processing units that are idle for most of the time within the time horizon of interest. These units are those units that are not the bottleneck in the process recipe. The fact that the processing units are idle means that the full return on investment is not being realised. Furthermore, any processing unit is in essence a storage vessel. Therefore, idle processing units can be used as wastewater storage vessels. In doing this the utilisation of the idle processing units increases, thus increasing the return on capital investment. The size of the required intermediate storage vessel also decreases and in certain cases, the usage of inherent storage increases reuse possibilities. This concept was first considered by Majozi et al.[1]. The authors considered the usage of inherent storage in their graphical wastewater minimisation technique. The mathematical method presented in this paper deals with wastewater minimisation in batch processes through the usage of inherent storage in idle processing vessels. The method proposed determines the minimum wastewater target and the corresponding minimum size of the central storage vessel through the usage of inherent storage. Keywords: Wastewater storage, inherent storage batch process

J.F. Gouws and T. Majozi

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1. Introduction Mounting environmental and legislative pressures are forcing industry to seek economic means to reduce the amount of effluent discharged from an operation. This need is further driven by the fact that the amount of freshwater available is limited. Wastewater minimisation techniques in batch processes have, therefore, been gaining interest in the past few years. Wastewater minimisation in batch processes can roughly be divided into two main groups, namely graphical and mathematical techniques. Graphical techniques [3,4,1] have their roots in pinch analysis and, therefore, have the advantage of giving insight into the problem. However, graphical techniques are inherently restricted to single contaminant problems. Mathematical techniques [5,6,7,8] are based on mathematical programming and optimisation and can deal with the multi-dimensionality of the wastewater minimisation problem. Mathematical techniques, however, have the drawback of a “black box” type approach where the interaction with the problem ends after problem formulation. Common in all the methods, is the usage of intermediate storage to allow for effective wastewater minimisation. Storage for wastewater takes up space which, in most batch operations, is problematic due the fact that these operations are undertaken within small areas. Apart from this is the fact that generally there are processing units that are idle for portions of a time horizon. These processing units can, in essence, function as storage vessels. Therefore, one could use idle processing units for the storage of wastewater, thereby reducing the size dedicated wastewater storage and increasing the utilisation of idle processing units. This concept has been explored by Majozi et al. [1], however, the method was based on a graphical approach in which the schedule is known beforehand. The inherent storage opportunities were identified using an inherent storage availability diagram. Presented in this paper is a method in which idle processing units are used for wastewater storage to minimise the size of the central reusable storage vessel and the amount of effluent generated. The methodology is based on the scheduling technique proposed by Majozi and Zhu [2], and thus the optimum schedule that allows for minimum wastewater generation is determined at the same time as the wastewater target and size of storage vessel. It is important to note that the method is not limited to operations where the main source of wastewater is from processing unit cleaning.

2. Problem Statement The problem addressed can be stated as follows: Given the following data, 1. 2. 3. 4. 5.

the maximum inlet and outlet concentration for each process in the plant, the mass load in each operation, the average task duration of each operation, the number of processing units and the capacity of each, and the time horizon of interest,

Wastewater Storage Minimisation through the Exploitation of Inherent Storage

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determine the minimum size of the central storage vessel that is concomitant with the minimum wastewater generation.

3. Mathematical Formulation The proposed mathematical formulation involves the following sets, variables and parameters. Sets P = {p | p = time point} J = {j | j = unit} Sin,j = {sin,j | sin,j = input state into unit j} Sout,j = {sout,j | sout,j = output state from unit j} Variables

qu ( j, p ) t u (s in , j , p )

t p (s out , j , p )

amount of water stored in unit j, at time point p time at which unit j starts operating at time point p time at which unit j finishes operating at time point p

tstu in ( j ,′ j , p )

time at which water goes to unit j, operating in inherent

tstu out ( j ′, j , p )

storage mode, from unit jƍ at time point p time at which water leaves unit jƍ, operating in inherent

y ( s in , j , p )

storage mode, to unit j at time point p binary variable showing usage of unit j at time point p

ystu in ( j ′, j , p)

binary variable for the transfer of water into unit j,

ystu out ( j ′, j , p)

operating in inherent storage mode, from unit jƍ binary variable for the transfer of water from unit jƍ, operating in inherent storage mode, to unit j

Parameters

Qu ( j )

maximum storage capacity of unit j

H

time horizon of interest

Mass balance constraints The mass balance constraints are derived around a unit for both the case where the unit is processing raw material and acting as a wastewater storage vessel. Further constraints are also derived around the central reusable storage vessel. Both water and contaminant balances are derived in each case. Constraint (1) ensures that the amount of wastewater

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J.F. Gouws and T. Majozi

stored in a unit is less than the capacity of the unit. This constraint also ensures that if a unit is processing raw material the unit cannot store wastewater.

qu( j , p ) ≤ Qu ( j )(1 − y (sin , j , p )), ∀ , j ∈ J , sin , j ∈ S in , j , p ∈ P

(1)

Scheduling constraints The scheduling constraints derived can be divided into five groups. The first group deals with task scheduling and are similar to those presented by Majozi and Zhu [2]. The second group deals with direct wastewater recycle and reuse. These constraints ensure the correct timing of direct wastewater recycle and reuse. The third group deals with the scheduling of wastewater storage in a processing unit. Constraint (2) ensures that the time at which water is sent for storage in a processing unit is after the finishing time of the previous task in the processing unit. Constraint (3) ensures that the time at which stored wastewater leaves a processing unit is before the start of the next task in the processing unit.

§ · tstu in ( j ′, j , p ′) ≥ t p (sout , j , p ) − H ¨ 2− ystu in ( j ′, j , p ′) − y (sin , j , p − 1)¸ , © ¹ ∀ j , j ′ ∈ J , p ∈ P , p ′ ≥ p , p > p1

(2)

§ · tstu out ( j , j ′, p ′) ≤ t u (sin , j , p ) − H ¨ 2− ystu out ( j , j ′, p ′) − y (sin , j , p )¸ , © ¹ ∀ j , j ′ ∈ J , sin , j ∈ S in , j , p ∈ P , p ′ ≤ p

(3)

The fourth group of constraints deal with scheduling of wastewater reuse through the central reusable storage vessel. These constraints ensure water moving to and from the central reusable storage vessel occurs at the correct time in the time horizon. The final group of constraints is comprised of the time horizon constraints and a number of feasibility constraints.

4. Solution Procedure To find a solution, a two step procedure is adopted. The first step involves the determination of the minimum wastewater target. This is done without considering inherent storage and a central storage vessel with unlimited capacity. The objective function in this step is the minimisation of wastewater. The objective of the second step is to determine the minimum size of the central storage vessel, whilst achieving the minimum wastewater target identified in the previous step. In this step inherent storage, in addition to central storage, is included. The objective function in this step is the minimisation of central storage, i.e. the minimisation of the sum of storage throughout the time horizon of interest.

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5. Literature Example[7] The plant considered in the example comprises of 5 operations, each producing wastewater containing a single contaminant, namely NaCl. The required concentration data and starting and finishing times are given in Table 1. The capacity of each unit is 2000kg. In operation A water is used to absorb the NaCl by-product. In operations B and D, water is used as the reaction solvent. Finally, operations C and E water is used to extract any remaining NaCl in the product. Operations C and E are polishing steps, and therefore, there is relatively little mass transferred to the water. The contaminant mass in operations C and E was ignored, due to the small mass transferred to the water. In operations C and E a minimum and maximum mass of water is defined. These limits are defined based on operational considerations. Table 1. Data for the literature example Operation

Max inlet conc.

Max outlet conc.

Start

(kg salt/ kg water)

Mass water (kg)

time (h)

End time (h)

(j)

(kg salt/ kg water)

A

0

0.1

1000

0

3

B

0.25

0.51

280

0

4

C

0.1

0.1

[300,400]

4

5.5

D

0.25

0.51

280

2

6

E

0.1

0.1

[300,400]

6

7.5

The resulting models, from step one and two, were solved in GAMS/DICOPT solution algorithm. In the first step a minimum wastewater target of 1285.5kg was identified, which relates to a 45% reduction in the amount of wastewater. The solution found in the second step had no storage vessel, which means that there is sufficient capacity in idle processing vessels to ensure the minimum wastewater target is met. It is important to note that the minimum wastewater target from the first step, namely 1285.5kg, was met in the second step. The resulting Gantt chart is given in Figure 1. Constraints (1) - (3) form part of the model for the second step only, due to the fact that inherent storage is not considered in the first step of the method. The constraints used in the first model in the first step are similar to those presented by Majozi [7] and do not take wastewater reuse through inherent storage into account. As can be seen from Figure 1 the processing units in which operations A and E occur are both used to store wastewater.

J.F. Gouws and T. Majozi

1226 Processing

Storing

E 142.75 D Unit 400 C

300

400 142.75

B

300 1000

A

1

2

3

4

5

5.5

6

7

7.5

Time (h)

Figure 1. Resulting Gantt chart for the literature example

6. Conclusions A method has been presented that determines the minimum wastewater target and the corresponding minimum size of the central reusable storage vessel. The method makes use of inherent storage opportunities within idle processing units. The solution procedure is a two step procedure in which the first step determines the minimum wastewater target and the second step the minimum size of the storage vessel. In the literature example presented the resulting solution decrease the amount of effluent produced by 45% and required no central storage vessel to achieve this target.

References [1] [2] [3] [4] [5] [6] [7] [8]

Majozi, T., Brouckaert, C. J., Buckley, C. A., 2006, J. Environ. Manage., 78, 317 Majozi, T., Zhu, X. 2001, Ind. Eng. Chem. Res., 40, 5935 Wang, Y. P., Smith, R., 1995, Trans IChemE, 73a, 905 Foo, D. C. Y., Manan, Z. A., Tan, Y.L., 2005, J. Clean. Prod., 13, 1381 Almató, M., Sanmartí, E., Espuña, A., Puigjaner, L., 1997, Comp. Chem. Eng., 21, s971 Kim, J. K., Smith, R., 2004, Proc. Safe. Environ. Prot., 82, 238 Majozi, T. 2005, Comp. Chem. Eng., 29,1631 Gouws, J.F., Majozi, T., 2008, Ind. Eng. Chem. Res., 47, 369

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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Water-efficiency as Indicator for Industrial Plant Sustainability Assessment Gennadiy Statyukha, Olexander Kvitka, Arcadiy Shakhnovsky, Iryna Dzhygyrey National Technical University of Ukraine, Department of Cybernetics of Chemical Technology Processes, Peremogy av. 37, 03056 Kyiv, Ukraine, [email protected]

Abstract Water-efficiency indicator is proposed for water management system sustainability assessment that can be used as a component of sustainable development indicators system of company’s estimation for reporting on sustainability. Assessment approach bases on water usage and wastewater treatment networks optimization. The systems approach for finding the minimum freshwater consumption rate and wastewater treatment capacity in water usage and treatment systems is used. Mathematical models of water usage and water treatment networks components and models of networks as a whole have been worked out. Keywords: sustainability assessment, system approach, water consumption

1. Introduction The necessity of sustainability indicators development is emphasized in Agenda 21 (1992) approved at United Nations Conference on Environment and Development (Rio de Janeiro, 1992). The Agenda 21 Global Program denotes importance of “Treatment and safe reuse of domestic and industrial waste waters …” (§50) in sustainable development aspect. Implementation of the key sense of sustainable development “… development that meets the needs of the present without compromising the ability of future generations to meet their own needs” (Brundtland et al., 1987) is impossible without sustainable management of water resources. A decrease of water usage means a decrease of wastewater generation. A substantial reduction of both freshwater and wastewater flow rates can be achieved by wastewater reuse and regeneration. Therefore researches for development of support decision-making procedures in design of optimal water supply, consumption and purification systems providing sustainable water use within company are topical. This paper is an attempt to develop an economic indicator for measuring the progress of industrial plant to sustainable water utilization. The systematic approach for the estimation and comparison of industrial companies in specific sub-branches regarding water systems sustainability performance are proposed.

2. Indicators utilization for measuring industrial systems sustainability A lot of sustainability assessment methods focused on companies’ performance have been proposed by now. One can marks out estimation approaches by range, by object and by purpose. Among single indicator approaches for industrial systems sustainability assessment exergy analysis, economic analysis, life cycle assessment (LCA) and system analysis can be accented. Exergy analysis is straightforward approach for processes efficiency determination but it can not help with environmental impacts. Economic analysis bases on economic theory and uses a variety of instruments (LCC, CBA etc.)

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but again environmental costs are difficult to quantify within the approach. LCA is good methodology for environmental impacts assessment but tells us nothing about sustainability of whole considered system only its units and components. In contrast system analysis allows to capture whole system and to make assumption about its sustainability. Here process integration techniques (Dunn and Bush, 2001) can be used for analysis, optimization and decision-making on sustainability aspect. Systems of indicators and indices are widely used not only for countries and regions estimation but for measurement of objects sustainability at lower levels – company, industrial plant, system, technology. Krajnc and Glavic (2005) proposed a model for designing a composite sustainable development index that depicts performance of companies along all the three dimensions of sustainability – economic, environmental, and societal. The procedure of calculating the index that would enable comparisons of companies in specific sector regarding sustainability performance is presented. Similar approach based on aggregating of single indicators was proposed by Muga and Mihelcic (2007) for sustainability assessment of wastewater treatment technologies. Also it must be noted that researches deal with urban wastewater treatment systems (Balkema et al., 2002, Boer and Boer, 2007) excite interest on possibility of utilization of proposed concepts within industrial plants level. For example, Balkema et al. (2002) proposed system analysis approach for decision-making on sustainability assessment of wastewater treatment systems based on multidisciplinary set of indicators. Different organizations work at sustainability metrics development for industry (e.g. IChemE Metrics, 2004); such metrics can be used with some modifications for industrial water systems sustainability estimation. It is obviously that set of selected indicators depends strongly on industrial branch and features of the object. Necessity of such dependence is clear and reasonable for different companies but interferes with sustainability assessment at bottom level of systems, components and units of the company. The attempts of practical implementation of recommendations developed at the upper level leads to significant distortions and finally to the appearance of some new methodology for creating and managing technologies which is not consistent with the initial one. Single indicator based on system approach is proposed for water consumption and wastewater treatment systems estimation of an industrial plant in this paper. Following reasons are our guide: (1) Single indicator eliminates weighting and grouping of subcomponents. The individual importance (weight) of indicators in aggregated one (index) is very difficult to determine with sufficient accuracy. Aggregation method influenced on the result significantly. (2) Single indicator eliminates selection of components therefore, e.g., can be used for any company regardless of industrial sector. (3) System analysis has significant advantage over other single indicator approaches – environmental limits and impacts can be included; object system can be considered as a whole; clear and consistent results can be obtained.

3. The approach to water usage and wastewater treatment networks optimization The Agenda 21 (1992) emphasizes “Promotion of water conservation through improved water-use efficiency and wastage minimization schemes …” (§12). Optimization of water usage and wastewater treatment networks of industrial plant that leads to water use minimization and is key component of the research belongs to cleaner production area. It is reasoned that reaching a significant progress in all cases demands to find flow rates of streams and their composition in a system consisting of water using operations and treatment processes. Note that this also means determining of system topology. This complex problem is commonly formulated as water network (WN) optimization. Total

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water network design is very complex and, thus, commonly divided into two parts – designing of network of water usage processes (water usage network – WUN) and designing of wastewater treatment network (WTN). We have investigated both problems – partially separately but usually in close cooperation since developed approaches to both problems are from the category of systematic, optimization based methods (Zgurovsky et al., 2007; Jezowski et al., 2008). 3.1. Water usage network optimization Due to other purpose of the paper we address here a simplified WUN, i.e. with wastewater reuse only (wastewater reuse network – WWRN). Thus, the network does not contain regeneration processes. WWRN design problem can be formulated as designing WWRN that minimizes certain performance index. Usually freshwater consumption is employed as the goal function, however, we used also more complex index involving structural features. Optimization-based techniques have been applied to deal with the task. More precisely, superstructure optimization concept was applied (Shakhnovskij et al., 2004). The major difficulty is that superstructure optimization model is nonlinear, and, additionally may contain both discrete and continuous variables – mixed-integer nonlinear programming (MINLP). To cope with the problem two main strategies have been investigated: using meta-heuristic/stochastic optimization approaches and applying deterministic solvers, sometimes with some problem modification. The main achievements were presented in journals and conference papers, e.g. in JeĪowski et al. (2006), Wałczyk et al. (2007) to list a few. The linear programming model for calculating the minimum attainable freshwater usage at targeting stage was developed (JeĪowski et al., 2006). After all we managed in developing systematic approach for designing optimal WWRN, see for instance (Shakhnovskij et al., 2004). Nonlinear model has been developed with some valid relaxation that allows robust and efficient solution with existing optimization solvers for medium scale cases. Also, the approach allows accounting for costs of pipelines. More recently the method was proposed for analysis of data under uncertain conditions (Shakhnovsky et al., 2007). This increases potential for industrial applications. Finally, we have also developed robust and efficient optimization approach for WUN consisting of processes that are modeled as non-mass transfer operations (Wałczyk et al., 2007). 3.2. Wastewater treatment network optimization In addition to the reduction of wastewater generated in WUN the decrease of cost of water treatment can be achieved by proper design of treatment plant. A segregation or combination of separate wastewater streams in treatment systems is a crucial mean to reach the aim. We have developed an efficient, robust and designer controlled systematic approach for designing optimal WTN. The designing method is sequential and applies insight-based techniques followed by mathematical programming. The foundations of the method and results of tests for typical literature examples were presented in (Statyukha et al., 2008). It is important that in some cases savings leading to cleaner production were substantial (Klemes and Huisingh, 2008). Then, the method has been largely extended to account for more rigorous models of processes. Also, operating and piping costs have been included into goal function. The design procedure is automated so it can be used for retrofitting WTN of various industrial plants. The applications of the extended and modified approach for various industrial cases have been shown in (Kvitka et al., 2007, Statyukha et al., 2007).

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4. Water-efficiency The term “water-efficiency” is utilized for water management system sustainability assessment of an industrial plant. Here water-efficiency is ratio of minimum possible outlays (in terms of money) on the water management system after implementation of water savings, energy savings, increasing of water consumption and wastewater treatment processes effectiveness, innovations etc. to total expenses on water conditioning, wastewater treatment and disposal (including ecological penalties) that industrial plant bears within production by now.

I WE = C MIN C

(1)

where I WE is water-efficiency indicator; C MIN – minimum possible outlays on water conditioning, wastewater treatment and disposal, grn./y; C – outlays on water conditioning, wastewater treatment and disposal by now, grn./y. Minimum possible outlays value can be obtained by proposed system approach to WUN and WTN analysis and synthesis. Numerator and denominator in eq. 1 have to meet water quality requirement and environmental limits of contaminants before disposal; mass load of contaminants as environmental impact factor may be also included. If resulted value is close to “1” than water management in the company can be characterized as close to optimal and sustainable. In contrast, if water-efficiency indicator value is close to “0” than water conditioning, water consumption, wastewater treatment system of the industrial plant can be refer to ineffective, uneconomical and unsustainable. Water-efficiency also can be ratio of minimum possible fresh water consumption to fresh water consumption for the product (service) manufacture by now without changing of the product quality.

I WE = F MIN F *

(2)

* is water-efficiency indicator; F MIN – minimum possible water consumption, where I WE 3 m /d; F – water consumption by now, m3/d. Water-efficiency indicator does not aspire to universality as single indicator of industrial plant sustainability. This indicator can be used as a component of sustainable development indicators system for company’s sustainability estimation, e.g. proposed by Krajnc and Glavic (2005).

5. Case studies The analysis of the pharmaceutical company by considered system approach shows that implementation of water saving measures, restructuring of water consumption and wastewater treatment networks allow decreasing fresh water consumption from 3.9Â106 m3/y to 3.1Â106 m3/y. Benefit from implementation of optimal water management system can be 18-20% depending on the market (Shakhnovsky, 2006). It means that water-efficiency indicator value is about 0.8 for existing water consumption and wastewater treatment systems. Analogous assessment was carried out for breadbaking plant. Complex of measures are proposed to optimize existing system: (1) implementation of the regulation practice of water flow rate on compressors’ cooling; (2) increasing of condensate return ratio from steam loads; (3) implementation of recycling system connecting waste heat boilers; (4) substitution of some water cooling units by air cooling units. Optimization of water consumption network allows substantiating possibility of water reuse after brew chilling processes in brewing

Water-Efficiency as Indicator for Industrial Plant Sustainability Assessment

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machine and in yeast section for washing of equipment, forms, vats and implements. Average monthly fresh water consumption (F) is presented on Fig. 1 for 2003 year (before optimization – dash line) and for 2004 year (after modernization – solid line).

Fig. 1. Fresh water consumption for bread-baking plant in 2003-2004 years, m3/month Comparison of the existing water system to proposed one gives the water-efficiency indicator value of 0.9 and tells about higher level of company’s water-efficiency than in previous case study of the pharmaceutical company. It must be noted that development of production technologies, water conditioning, water purification, appearance of new products and services, new technical means influence on the value of water-efficiency indicator for object (company, industrial plant). But this value for the company contributing sustainable development, satisfying environmental limits, implementing innovations will be always close to “1”.

6. Summary and conclusions Water-efficiency indicator is proposed for water management system sustainability assessment that can be used as a component of sustainable development indicators system of company’s estimation for sustainability reporting. Assessment approach bases on water usage and wastewater treatment networks optimization. The systems approach for finding the minimum freshwater consumption rate and wastewater treatment capacity in water usage and treatment systems is used. Models of water usage and treatment networks components and models of networks as a whole have been worked out.

References Agenda 21, 1992, UNEP, downloadable from: www.un.org/esa/sustdev/agenda21.htm. A.J. Balkema, H.A. Preisig, R. Otterpohl and F.J.D. Lambert, 2002, Indicators for the sustainability assessment of wastewater treatment systems, Urban Water, Vol. 4, Iss. 2, pp. 153-161. J.E. Boer and J.J. Boer, 2007, LCA-IWM: A decision support tool for sustainability assessment of waste management systems, Waste Management, Vol. 27, Iss. 8, pp. 1032-1045. G. Brundtland et al., 1987, Our common future, Report of the World Commission on Environment and Development, downloadable from: www.un-documents.net/wced-ocf.htm. R.F. Dunn and G.E. Bush, 2001, Using process integration technology for CLEANER production, Journal of Cleaner Production, Vol. 9, Iss. 1, pp. 1-23. IChemE Metrics, 2004, Sustainable Development Progress Metrics recommended for use in the Process Industry, IChemE, downloadable from: www.icheme.org/sustainability/metrics.pdf. J. JeĪowski, Wałczyk K., Shakhnovsky A., 2006, Systematic methods for calculating minimum flow rate and cost of water in industrial plants, Chemical and Process Engineering, Vol. 27, pp. 1137-1154.

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J. Jezowski, G.Statyukha, A. Jezowska, A. Shakhnovsky and I. Dzhygyrey, 2008, Minimization of water usage and wastewater treatment cost by systematic approaches, 1st Science and Applied Conference “Computer Modelling in Chemistry and Tecnology”, 12-16 May, Cherkasy – Ukraine, p. 135-137. J. Klemes and D. Huisingh, 2008, Economic use of renewable resources, LCA, cleaner batch processes and minimising emissions and wastewater, Journal of Cleaner Production, Vol. 16, Iss. 2, pp. 159-163. D. Krajnc and P. Glaviþ, 2005, How to compare companies on relevant dimensions of sustainability, Ecological Economics, Vol.55, Iss. 4, pp. 551-563. O. Kvitka, I. Dzhygyrey and J. JeĪowski, 2007, Optimal Design of Wastewater Treatment Network for Glass Container Plant, Chemical Engineering Transactions, Vol. 12, pp. 327-332. H.E. Muga and J.R. Mihelcic, 2007, Sustainability of wastewater treatment technologies, Journal of Environmental Management, Vol. 88, Iss. 3, pp. 437-447. A. Shakhnovskij, J. Jezowski, A. Kvitka, A. Jezowska and G. Statiukha, 2004, Optymalizacja sieci wody procesowej przy zastosowaniu programowania matematycznego, Inzineria chemiczna i procesowa, Vol. 25, ɪp. 1607-1612. A. Shakhnovsky, 2006, The analysis and design of industrial water usage networks: synopsis of PhD thesis (in Ukrainian). A. Shakhnovsky, A. Kvitka, G. Statiukha, J. JeĪowski and A. JeĪowska, 2007, On the statistical analysis of data for the water usage network design, Chemical and process engineering. Vol. 28, pp. 493-503. G. Statyukha, O. Kvitka, I. Dzhygyrey and J. JeĪowski, 2007, Optimal Design of Wastewater Treatment Network – Case Study of Synthetic Organic Dye Manufacturing Plant, Chemical and Process Engineerin, Vol. 28, pp. 505-514. G. Statyukha, O. Kvitka, I. Dzhygyrey and J. Jezowski, 2008, A simple sequential approach for designing industrial wastewater treatment networks, Journal of Cleaner Production, Vol. 16, Iss. 2, pp. 215-224. K. Wałczyk, G. Poplewski, J. JeĪowski, A. JeĪowska and A. Shakhnovsky, 2007, Optimization of Water Network with Models of Non-Mass Transfer Processes, Chemical and Process Engineering, Vol. 28, pp. 515-525. M. Zgurovsky, G. Statyukha, O. Kvitka, A. Shakhnovsky and I. Dzhygyrey, 2007, The Systems Approach to Design of Optimal Water Usage and Wastewater Treatment Networks, International Conference on Environment: Survival and Sustainability, Nicosia – Northern Cyprus – Cyprus, 19-24 February, MT-14, pp. 623-624.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

A Simulation Program for Modelling Pollutant Dispersion for Educational Applications Elena Skorzinski,a Mordechai Shacham,b Neima Braunera a b

Faculty of Engineering, Tel-Aviv University Tel Aviv, Israel Dept. Chem. Eng., Ben-Gurion University, Beer-Sheva, Israel

Abstract Simulation programs are widely used in engineering education for numerical, modelbased and virtual experimentation, analysis of cause-effect relationships in complex systems, and visualization of challenging concepts. We have developed a pollutant dispersion simulation program applicable in environmental engineering education. The simulation models are implemented in MATLAB and the user interface is provided in the form of a MATLAB GUI. Three types of simulations can be carried out: oxygen sag model for predicting oxygen deficit in a river, Gaussian model for predicting pollutant dispersion in air from a continuous point source, and pollutant dispersion in ground water from a point source. The benefits of using simulation programs for “virtual experimentation” in environmental engineering education and practice are demonstrated and discussed.

Keywords: Environmental engineering, virtual experimentation, pollutant dispersion, air pollution, water pollution 1. Introduction Simulation programs are widely used in engineering education for numerical, modelbased and virtual experimentation, analysis of cause-effect relationships in complex systems, and visualization of challenging concepts (Shacham et al. [1]). The earliest use of virtual (simulated) experiments is documented for process control laboratory courses. The Advanced Control System (ACS) of IBM was used in the early nineteen eighties in several Universities for carrying out simulated laboratory experiments [2]. In the 1990 PC based simulation programs have replaced the main frame based ACS program [3]. The use of virtual (simulated) experiments can reduce considerable the cost of a laboratory course, increase the number of experiments included and enable carrying out experiments that otherwise would require working with dangerous materials and/or working in dangerous conditions.

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1234

Shacham et al. [4] and Eizenberg et al. [5] advocated the use of dynamic simulation program in courses dealing with process safety for learning to anticipate and prevent chemical process hazards, and demonstrated the successful use of this approach in teaching process safety. Unfortunately, only a few simulation programs applicable to environmental engineering education are presently available ([6], [7]). We have developed a pollutant dispersion simulation program for environmental engineering education. The simulation models are implemented in MATLAB and the user interface is provided in the form of a MATLAB GUI (Graphical User Interface, MATLAB is a trademark of The Math Works, Inc. http://www.mathworks.com). Three types of simulations can be carried out: use of the oxygen sag model to predict oxygen concentration and deficit in the river [6]; prediction of pollutant dispersion in air from a continuous point source using the Gaussian model [8]; and prediction of pollutant dispersion in ground water from a continuous point source [9]. In the following the individual programs will be described in some detail.

2. Predicting oxygen concentration and deficit in the river using the oxygen sag model The oxygen-sag model is a classical problem, used for demonstration of various subjects in the basic course of "Water Pollution Control". The model consists of several differential equations that describe the processes of de-oxygenation and re-oxygenation as a function of time or distance (related to the river velocity), assuming ideal plug-flow conditions in the flowing river. The natural oxygen balance in the river is disturbed by oxygen depletion (de-oxygenation) due to the sewage BOD which is biodegraded aerobically by natural bacteria. Oxygen replenishment in the river (re-oxygenation) is caused by absorption of atmospheric oxygen stimulated by the turbulent flow. The main parameters involved in this kind of a problem are shown in Table 1. The oxygen balance along the river can be expressed by:

dC dt

dC re dC de  dt dt

r (C s  C )  kLa exp(kt )

Table 1. The Main Variables of the Oxygen Sag Model

Q – Flow rate [m3/d] V – River velocity [m/d] BOD – biochemical oxygen demand [mg/L] L – Ultimate BOD [mg/L] C – Oxygen concentration [mg/L] Cs – Oxygen saturation concentration [mg/L] D – Oxygen deficit [mg/L] k – First order BOD degradation rate coefficient (de-oxygenation constant) [d-1] r – Atmospheric oxygen dissolution rate coefficient (re-oxygenation constant) [d-1]

t – Time [d] T – Temperature [oC] Subscripts: r – River sw – Sewage (wastewater) a – Dilution point cr – Critical point de – de-oxigenation re – re-oxygenation

(1)

A Simulation Program for Modelling Pollutant Dispersion

1235

Using the definition of the oxygen deficit with respect to the saturation concentration (D=Cs-C), and integrating the differential equation dD / dt kLa exp(  kt )  rD , yields a simple algebraic solution of the deficit as function of time:

Dt

kLa >exp(kt )  exp(rt )@  Da exp(rt ) (r  k )

(2)

The expressions for the critical (maximum) deficit and the related time correspond to

dD / dt

Dcr

0 , ( d 2 D / dt 2  0 ) and are given by:

La exp( ktcr ) ; tcr r/k

­° r 1 ln ® ( r  k ) °¯ k

ª ( r / k  1) Da º °½ «1  »¾ La ¬ ¼ °¿

(3)

The parameters that need to be introduced into equations (1) through (3) are: the initial BOD (La), and the oxygen concentration (Ca), or oxygen deficit (Da), at the sewage discharge (dilution) point. The definitions of these parameters are shown in Table 2. The equations for the temperature dependence of the kinetic and mass transfer coefficients k, r and of Cs are also shown in Table 2. The graphical interface for the river pollution simulation program is shown in Figure 1. A typical assignment for the students, which involve the use of the simulation program, includes the calculation of the critical oxygen deficit and the consequent minimum oxygen concentration that endangers aquatic life, as a function of the discharged sewage organic load, which is determined by the flow-rate and the BOD concentration. The manipulated input parameters of the problem include the river flow-rate, the sewage flow-rate, raw sewage ultimate BOD; unpolluted river ultimate BOD, ambient temperature and the raw sewage oxygen concentration. The corresponding calculated initial values for La , Da and Ca are shown on the r.h.s. column. All the parameters have default values so that the user need only change the ones that differ from the default values. Upon pressing “OK” the simulation is carried out. The results presented include the critical values of the oxygen deficit, oxygen concentration and the time when these values are reached. A graph of one of the following variables versus time is also presented: BOD biodegradation (L), Rate of oxygen consumption (DEOX), Reoxygenation (REOX), oxygen deficit (D) and oxygen concentration (C). All the variables can be put on the same graph by rerunning the simulation with a different plot variable selected.

E. Skorzinski et al.

1236 Table 2. Parameters of the Oxygen Sag Model

Parameter BOD at dilution point (mg/L)

Oxygen concentration at the dilution point (mg/L)

La Ca

Definition (Qr Lr  Qsw Lsw ) (Qr  Qsw ) (Qr C r  Qsw C sw ) (Qr  Qsw )

Oxygen deficit at the dilution point (mg/L) Temperature effect on k

Da = (Cs-Ca)

k (T )

k(To )1.047(T To )

Temperature effect on t r

r (T )

r(To )1.024(T To )

Oxygen saturation concentration (mg/L)

Cs= 14.126 exp(-0.0202T)

Figure 1. GUI for the River Pollution Simulation Program

The solution presented in Figure 1 demonstrates how the rates of the two main processes (i.e., de-oxygenation and re-oxygenation) change with time, due to the residual organic matter L (first order kinetics for de-oxygenation) and due to the oxygen concentration driving force Cs-C (re-oxygenation rate by oxygen dissolution). This information is shown clearly in Figure 1, which demonstrates the higher rate of oxygen consumption (DEOX curve, parallel to the L depletion curve) at the beginning of the combined process (i.e., close to the dilution point). The trend is affected also by the relative values of k and r. The result is an initial gradual decrease of the oxygen concentration (C) and a mirror-shape increase of the oxygen deficit (D). At the critical point, the combined effects of the high mass transfer coefficient r and the reduced driving force (low L) for the first order BOD degradation (and for the consequent

A Simulation Program for Modelling Pollutant Dispersion

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oxygen depletion) results in a gradual increase of the oxygen concentration to the saturation level Cs, and a mirror-shape decrease of the oxygen deficit to zero. It should be noted that in addition to the use of the simulation program the student can ask for explanations which includes presentation of all the model equations with a brief explanation regarding the role of the various equations in the model. This further enhances the educational value of the program.

3. Additional simulator options The additional options of the simulation program include the prediction of pollutant dispersion in the air from a continuous point source using the Gaussian model [8]; and prediction of pollutant dispersion in ground water from a continuous point source [9]. In both cases graphical user interfaces, similar to the one presented in Figure 1 are used. For the case of the pollutant dispersion in the air the changeable input parameters of the problem include the effective stack height; atmospheric stability conditions; wind velocity; rate of pollutant emission; distance from the emission source; horizontal distance from the center of the plume and vertical distance from the ground. The results presented include the concentration of the pollutant in a pre-specified point, maximum concentration at the ground level and distance from the source of the maximum concentration point. Graphical results can be presented for ground concentration of the pollutant as function of the distance from the source and vertical concentration profile of the pollutant at a given point. For pollutant dispersion in ground water two cases are considered: the pollution is related to absorption and it is related to radioactive radiation. The changeable input parameters of the problem include the distance from the source; concentration of the pollutant in the sewage; ground water velocity; diffusion coefficient and retardation coefficient. In case of radioactive waste the half life of the material should also be provided. The results presented include the time when the concentration of the pollutant (C) in the selected point is 95% of the initial concentration (C0), the time when C = 0.5 C0. Graphical results are presented for the pollutant concentration at a particular distance from the source as function of time.

4. Conclusions It has been shown that the use of simulation programs for “virtual experimentation” can be beneficial in environmental engineering education and practice. They show the variation in time and space of the various variables instead of their point values as usually obtained by analytical solutions. Seeing the profiles considerably contributes to the understanding of the processes involved. The use of the simulation encourages the students to ask "what if" questions (such as what is the effect of organic load and/or of the temperature) and to carry out parametric studies (change of oxygen concentration, oxygen deficit and biochemical oxygen demand with time or with distance) because of the speed and the simplicity in which the answers to those questions can be found. Thus, the simulation enables learning by "discovery" instead of the traditional learning techniques, which are much less exciting.

E. Skorzinski et al.

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It is important, however, that the computer program used is simple to understand and use and the results are easy to interpret. This way the learning effort is concentrated on the subject matter of the course, not on the technical details of the program being used. Using the techniques presented in this paper to use the MATLAB GUI for the user interface enables the use of simulators presented, with short learning curves and only minimal user intervention in the technical details of the solution process. We can envision that this technique will lead to rapid introduction and effective use of simulations in environmental, chemical and biotechnology engineering education and practice.

5. References [1] M. Shacham, N. Brauner and M. B. Cutlip, pp. 32 - 35 in F. Scura, M. Liberti, G. Barbieri, and E. Drioli (Eds), 5th Chem. Eng. Conference for Collaborative Research In Eastern Mediterranean Countries (EMCC5), May 24-29, 2008, Cetraro (CS) – Italy [2] Corripio, A. B., Academic Computing, 1 (1987), pp. 30-31, 60-62. [3] Cooper, D. J., Chemical Engineering Education, 27(1993) 176. [4] Shacham, M., N. Brauner and M. B. Cutlip, Computers chem. Engng, 24(2000), 415. [5] Eisenberg, S., M. Shacham and N. Brauner, Journal of Loss Prevention in the Process Industries 19 (2006) 754–761. [6] Brenner, A., M. Shacham and M. B. Cutlip, Environmental Modeling and Software, 20 (2005) 1307. [7] E. Fatehifar, E., A. Elkamel and M. Taheri, Comput. Appl. Eng. Educ. 14 (2006) 300. [8] E. Boeker and R. van Grondelle, Environmental Physics, 2nd Ed, Wiley, 2000 [9] C. W. Fetter, Contaminant Hydrogeology, Macmillan, N. Y. 1993

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1239

Heat and power integration for hydrogen-fuelled Combined Cycle Gas Turbine (CCGT) Calin-Cristian Cormos,a Ana-Maria Cormos,a Serban Agachi a a

Babes – Bolyai University, Faculty of Chemistry and Chemical Engineering 11 Arany Janos Street, RO-400028, Cluj – Napoca, Romania Tel: +40264593833, Fax: +40264590818 E-mails: [email protected]; [email protected]; [email protected]

Abstract Integrated Gasification Combined Cycle (IGCC) is a technology for power generation in which the feedstock is partially oxidized to produce syngas (a gas mixture containing mainly hydrogen and carbon monoxide). In a conventional IGCC design, the syngas is purified for dust and hydrogen sulphide (H2S) removal and then sent to a Combined Cycle Gas Turbine (CCGT) for power generation. Carbon capture technology is expected to play a significant role in the coming decades for curbing the greenhouse gas emissions. IGCC is one of the power generation technologies having the highest potential to capture CO2 with low penalties in efficiency and cost. In a modified IGCC design for carbon capture, syngas is shifted to maximize the hydrogen level in the syngas and to concentrate the carbon species as CO2 than can be later captured. After CO2 and H2S capture in a pre-combustion arrangement, the hydrogen-rich syngas is used in a CCGT for power generation. This paper investigates the main differences in term of heat and power integration between a syngas-fuelled CCGT and a hydrogen-fuelled CCGT. The coal and biomass-based IGCC case study investigated in the paper produces around 400 MW electricity with 90 % carbon capture rate (main design data). The cases were simulated using ChemCAD to produce input data for heat and power integration study of the CCGT section (integrated with rest of the plant units). The combined cycle configuration considers the use of one gas turbine (M701G2 type of Mitsubishi Heavy Industries) and one steam turbine with a steam cycle having three pressure levels and one reheat (for MP steam). Heat and power integration analysis optimizes the steam flows generated in HRSG for maximizing the power production. Influence of ancillary power consumption in the both cases (hydrogen and syngas-fuelled CCGT) is discussed for evaluation of efficiency penalty associated with carbon capture and storage (CCS). Keywords: Gasification, Heat and Power, CCGT, Carbon Capture and Storage

1. Introduction The introduction of hydrogen in the energy system as a new energy carrier complementary to electricity and conventional fuels (e.g. natural gas, oil derived products, coal etc.) is raising much interest, as this offers significant advantages including reduction of greenhouse gas emissions at the point of end use, enhancement of the security of energy supply and improvement of economic competitiveness [1]. In term of proven reserves, solid fossil fuels (coal and lignite) give a much bigger energy independence compared with liquid and gaseous fossil fuels [2], but coal utilization is regarded with concern because of bigger greenhouse gas emissions

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C.C. Cormos et al.

associated with it. Also, utilization of biomass (e.g. sawdust, agricultural waste, energy crops etc.) and other different solid wastes (e.g. municipal waste, sewage sludge etc.) in energy conversion processes is become more and more significant and its use is predicted to increase sharply. In this context, European Commission has set as a target for the whole community block that until 2020, 20 % from the energy mix should be covered by renewable energy sources [3]. Gasification is a thermo-chemical conversion process in which the solid feedstock is partially oxidized with oxygen and steam (or water depending on the technology to be used) to produce a combustible gas called syngas (mainly a mixture of H2 and CO). Syngas can be used for chemical conversion into different valuable compounds (e.g. hydrogen, methanol, ammonia, liquid fuels) or to generate power in a Combined Cycle Gas Turbine (CCGT). Integrated Gasification Combined Cycle (IGCC) is one of the power generation technologies having the highest potential to capture CO2 with the low penalties in efficiency and cost [4-5]. In a modified IGCC designed for carbon capture, syngas is catalytically shifted to maximize the hydrogen level and to concentrate the carbon species in form of CO2 that can be later capture in a pre-combustion arrangement. After CO2 and H2S capture in a double stage Acid Gas Removal (AGR) system, the hydrogen-rich gas is used in a CCGT for power generation. However, the use of hydrogen in gas turbines rises significant issues compared with the situation when syngas is used: different combustion properties of hydrogen compared with syngas, significant difference between hydrogen higher heating value HHV and lower heating value – LHV, (difference is about 18 %), the need to dilute the hydrogen with nitrogen or steam for decreasing the flame temperature (and subsequently NOx emissions) and for power augmentation [6-8]. This paper investigates two cases of power generation based on IGCC technology using a mixture of coal and sawdust as feedstock. The first case is a conventional IGCC scheme without carbon capture in which the syngas is burnt in CCGT for power generation (syngas-fuelled gas turbine). The second case considers a modified IGCC scheme in which power generation unit (CCGT) is fuelled with hydrogen-rich gas (hydrogen-fuelled gas turbine). The two case studies investigated in the paper generate about 400 MW electricity with 90 % carbon capture rate (for second case). The paper will identify the main differences in term of heat and power between these two cases and also will quantify the energy penalty imposed by carbon capture process.

2. Plant configuration and design assumptions A conventional Integrated Gasification Combined Cycle (IGCC) uses the syngas resulted for the solid fuel gasification (after removing the ash and hydrogen sulphide) for power production by burning in a gas turbine [9]. The flue gases coming from the gas turbine are used to raise steam (in HRSG) which by expansion in a steam turbine generates extra electricity in addition to the one produced by the gas turbine. Compared with the conventional IGCC design, introduction of carbon capture stage by pre-combustion capture involves some changes in the plant configuration. The conceptual layout of a modified IGCC scheme for power generation with carbon capture is presented in Figure 1 [5,9-11].

Heat and Power Integration for Hydrogen-Fuelled Combined Cycle Gas Turbine (CCGT)

Coal & Biomass +Transport gas (N2)

Air Air Separation Unit (ASU) & O2 Compression

Water N2

1241

O2 Gasification

Syngas Quench & Cooling

Steam

Slag

O2 Water – Gas Shift

Claus Plant & Tail gas Treatment

Sulphur

Acid Gas Removal (AGR)

CO2

Combined Cycle Gas Turbine

Power

Figure 1. Layout of IGCC scheme for power generation with carbon capture

The main differences of this scheme compared with a conventional IGCC scheme without carbon capture is the presence of shift conversion of carbon monoxide (water – gas shift), a bigger Acid Gas Removal (AGR) system which captures, in addition of hydrogen sulphide as in the conventional technology, also carbon dioxide and a combined cycle gas turbine running on hydrogen [5,10]. For the two case studies analyzed in this paper, a mixture of coal and sawdust in the ratio or 80 to 20 was considered as feedstock. As gasification reactor considered in the paper, the option was in favor of entrained flow type operating at high temperature (slagging conditions) which give a high conversion of solid fuel (~99 %). From different gasification technologies available on the market, Siemens technology (formerly known Future Energy) was chosen, the main factors for consideration were dry feed design and water quench which ensure the optimal condition for shift conversion of CO [9-10]. Because the main focus of the article is on the heat and power integration of the combined cycle in two cases (syngas and hydrogen-fuelled gas turbine), Table 1 presents major design assumptions of the power island [7,11]. Table 1. Main design assumptions of the power island - CCGT Stream / Unit Undiluted syngas (Case 1)

Undiluted hydrogen-rich fuel gas (Case 2)

Parameters Pressure: 31.7 bar (ex. AGR) Coposition (% vol.): 58.94 % CO; 28.45 % H2; 6.32 % CO2; 5.34 % N2; 0.92 % Ar; 0.03 % H2O Lower heating value (LHV): 10.49 MJ/Nm3 Pressure: 28 bar (ex. AGR) Composition (% vol.): 1.83 % CO; 88.92 % H2; 2.95 % CO2; 5.41 % N2; 0.87 % Ar; 0.02 % H2O Lower heating value (LHV): 9.45 MJ/Nm3

Table 1. Main design assumptions of the power island - CCGT (continuation) Stream / Unit Gas turbine

Parameters Gas turbine type: M701G2 (MHI)

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1242

Heat recovery steam generation (HRSG) and steam cycle

Heat exchangers

Net power output: 334 MW Electrical efficiency: 39.5 % Pressure ratio: 21 Turbine outlet temperature (TOT): 588oC Nitrogen dilution of fuel gas to 6.5 MJ/Nm3 Three pressure levels: 118 bar / 34 bar / 3 bar Reheat of MP steam Steam turbine isoentropic efficiency: 85 % Steam wetness ex. steam turbine: max. 10 % ΔTmin. = 10oC Pressure drop: 1 % of inlet pressure

3. Heat and power integration analysis The energy conversion processes were modeled and simulated using ChemCAD to produce input data for heat and power integration analysis. Table 2 presents the overall plant performance indicators for the two analyzed cases: Case 1 – Conventional IGCC scheme without carbon capture, syngas-fuelled gas turbine and Case 2 – Modified IGCC scheme (see Figure 1) with carbon capture, hydrogen-fuelled gas turbine. Table 2.Overall plant performance indicators Main Plant Data Coal and biomass flowrate (a.r.) Coal / Biomass LHV (a.r.) Feedstock thermal energy – LHV (A)

Units t/h MJ/kg MWth

Case 1 161350 25.353 / 16.057 1053.00

Case 2 180455 25.353 / 16.057 1177.68

Thermal energy of the syngas (B) Cold gas efficiency (B/A * 100) Thermal energy of syngas exit AGR (C) Syngas treatment efficiency (C/B *100)

MWth % MWth %

835.34 79.33 831.95 99.59

934.26 79.33 831.95 89.05

Gas turbine output (1 x M701G2) Steam turbine output (1 ST) Expander power output Gross electric power output (D)

MWe MWe MWe MWe

334.00 183.6 1.48 519.08

334.00 200.14 0.78 534.92

ASU consumption + O2 compression Gasification island power consumption AGR + CO2 drying and compression Power island power consumption Total ancillary power consumption (F)

MWe MWe MWe MWe MWe

40.37 6.8 7.48 20.53 75.18

45.13 8.27 40.54 19.05 112.99

Net electric power output (G = D - F) Gross electrical efficiency (D/A * 100) Net electrical efficiency (G/A * 100) Carbon capture rate CO2 specific emissions

MWe % % % kg/MWh

443.9 49.29 42.15 0.00 826.05

421.93 45.42 35.82 92.83 71.19

As can be noticed from the Table 2, comparing IGCC scheme with and without carbon capture (Case 2 vs. Case 1), the penalty in overall plant energy efficiency of the carbon capture process is about 6.33 %. The main reason of this fact is the significant increase in ancillary power consumption of the AGR system and captured CO2 compression for Case 2 compared with Case 1 (in this case AGR system only separate the hydrogen sulphide form the syngas). From the point of view of greenhouse gas emission, implementation of carbon capture technology for an IGCC scheme is resulting in a substantial reduction of the specific CO2 emission (71.19 vs. 826.05 kg CO2/MWh). IGCC technology has also

Heat and Power Integration for Hydrogen-Fuelled Combined Cycle Gas Turbine (CCGT)

1243

other benefits from environmental point of view: very low SOx and NOx emissions, possibility to process lower grade coals or other types of solid fuels which are difficult to handle by conventional energy conversion process (e.g. steam plant). Also it has to be mentioned the fact that, although, the carbon capture rate of the scheme evaluated in the paper is about 90 % in fact the overall capture rate is higher considering also that the renewable energy source used in addition to coal (sawdust) can be considered CO2 free (green CO2) since the wood „captured” the CO2 from the air during the normal photosynthesis process. The simulation results of both cases were used to make a heat and power integration study of the Combined Cycle Gas Turbine (power island) for optimization (maximization) of power generation. In both cases, the steam generated in the gasification island and syngas conditioning (LP steam for Case 1 and HP and LP steam for Case 2 were integrated in the steam cycle of the CCGT). Also, the heat duties (steam) for various units in the plant (gasification island, AGR system, power island) were extracted from the steam cycle. The optimized steam flows generated in the plant in two cases were as follow: Case 1: 339.2 t/h HP steam; 67 t/h MP steam; 301 t/h LP steam; Case 2: 437 t/h HP steam; 69 t/h MP steam; 180 t/h LP steam. Hot and cold composite curves (HCC and CCC) of syngas-fuelled gas turbine and hydrogen-fuelled gas turbine are presented in Figure 2 and respectively Figure 3. COMPOSITE CURVES

700

Temperature (°C)

600 500 400

HCC CCC

300 200 100 0 0

50000 100000 150000 200000 250000 300000 350000 400000 450000 50000 Enthalpy (kW)

Figure 2. Composite curves for syngas-fuelled CCGT COMPOSITE CURVES

700

Temperature (°C)

600 500 400

HCC CCC

300 200 100 0 0

50000 100000 150000 200000 250000 300000 350000 400000 450000 50000 Enthalpy (kW)

Figure 3. Composite curves for hydrogen-fuelled CCGT

The main difference for which Case 2 generates more power from the steam turbine (with approximate 8.7 %) is the fact that it uses more efficiently the heat generated from CO shift conversion for raising HP steam (HP and LP steam generate in

C.C. Cormos et al.

1244

the gasification island and syngas treatment line is integrated with the steam cycle of the combined cycle). In term of heat transfer area for HRSG, there is no much difference between the two designs, Case 2 having less than 2 % heat transfer area compared with Case 1.

4. Conclusions This paper analyze from technical point of view the main differences in term of energy efficiency and heat and power integration between a conventional IGCC scheme without carbon capture (syngas-fuelled gas turbine) compared with an IGCC scheme with carbon capture (hydrogen-fuelled gas turbine). Modeling and simulation techniques were used to quantify the energy penalty of capturing carbon capture and for evaluate the main differences in term of heat and power between the analyzed systems.

5. Acknowledgements This work has been supported by Romanian National University Research Council through grant no. 2455: “Innovative systems for poly-generation of energy vectors with carbon dioxide capture and storage based on co-gasification processes of coal and renewable energy sources (biomass) or solid waste”.

References [1] F. Müller-Langer, E. Tzimas, M. Kaltschmidtt, S. Peteves, Techno-economic assessment of hydrogen production processes for the hydrogen economy for the short and medium term, Int J Hydrogen Energy 2007; 32:3797-810. [2] Statistical Review of World Energy BP 2008, www.bp.com. [3] European Commission, DG Energy and Transport (DG TREN), 2009, http://ec.europa.eu/energy. [4] E. Tzimas, A. Mercier, C. Cormos, S. Peteves, Trade-off in emissions of acid gas pollutants and of carbon dioxide in fossil fuels power plants with carbon capture, Energy Policy, 35, 2007, 3991 – 3998. [5] International Energy Agency – Greenhouse Gas Programe (GHG), Potential for improvement in gasification combined cycle power generation with CO2 capture, Report PH4/19, 2003. [6] F. Starr, E. Tzimas, S. Peteves, Critical factors in the design, operation and economics of coal gasification plants: The case of the flexible co-production of hydrogen and electricity. International Journal of Hydrogen Energy 2007; 32: 1477 - 1485. [7] C. Cormos, F. Starr, E. Tzimas, S. Peteves, Innovative concepts for hydrogen production processes based on coal gasification with CO2 capture, International Journal of Hydrogen Energy, 33, 2008, 1284 – 1294. [8] K. Jordal, Benchmarking of power cycles with CO2 capture - The impact of the selected framework, International Journal of Greenhouse Gas Control, 2, 2008, 468 – 477. [9] C. Higman, M. Van Der Burgt, Gasification, Elsevier Science, Second edition, 2008. [10] C. Cormos, F. Starr, E. Tzimas, S. Peteves, A. Brown, Gasifier concepts for hydrogen and electricity co-production with CO2 capture, Third International Conference on Clean Coal Technologies, Cagliari, Sardinia, Italy, 2007. [11] P. Chiesa, S. Consonni, T. Kreutz, R. Williams, Co-production of hydrogen, electricity and CO2 from coal with commercially ready technology. Part A: Performance and emissions. International Journal of Hydrogen Energy 2005;30: 747 – 67.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

1245

A heat exchanger model to increase energy efficiency in refinery pre heat trains Francesco Coletti and Sandro Macchietto Department of Chemical Engineering, Imperial College London South Kensington campus, London SW7 2AZ, UK, [email protected]

Abstract Crude oil fouling in pre-heat train heat exchangers has been a major problem in oil refining for decades. The operating problems, increased energy requirements and greenhouse gases emissions which arise from the inefficiencies caused by fouling are discussed. A mathematical model capable of predicting the dynamic behavior of a shell and tube heat exchanger undergoing fouling is used to assess the costs and the environmental impact of the crude distillation unit. Using the model, retrofit options were proposed for an existing industrial unit leading to improved energy efficiency. Keywords: energy efficiency, fouling, crude oil, modeling, refinery

1. Introduction Refinery operations use about 6% of the crude oil throughput (ESDU 2000), i.e. ~5 million barrels per day worldwide. An extensive network of heat exchangers, the preheat train (PHT), recovers energy from the hot streams of the crude distillation column (CDU). A furnace supplies the remaining energy before distillation to a typical coil inlet temperature (CIT) of ~300 °C, accounting for ~ ½ of refinery energy demand. The deposition of low thermal conductivity material (fouling) by the crude in the heat exchangers decreases the PHT energy recovery efficiency, lowers the CIT and requires extra fuel in the furnace, with increased costs and CO2 gases release. Current design practice of heat exchangers use fouling factors or area margins and has received several critics (Epstein 1983; Rabas and Panchal 2000). It fails to account for the dynamics of the fouling process leading to over-design of the unit which can be counterproductive. An improvement in the current heat exchanger design methodology would be greatly beneficial. A detailed mathematical model would help in predicting the fouling trends and assisting scheduling decisions for maintenance. Several dynamic models for shell and tube heat exchangers have been proposed (Fryer and Slater 1985; Pataknar and Spalding 1974; Roetzel and Xuan 1999). Some are single-pass only and none specifically addresses crude oil fouling. Here, a detailed mathematical model (Coletti and Macchietto 2008; Coletti and Macchietto 2009) of a multi-pass shell and tube heat exchanger undergoing crude oil fouling is used to calculate the impact of heat exchanger design on energy requirements and CO2 emissions, and to assess retrofit options so as to reduce fouling and related costs.

2. Heat exchanger and cost models The mathematical model for a TEMA type AET heat exchanger undergoing crude oil fouling on the tube side proposed in (Coletti and Macchietto 2008) is summarised in Table 1. The distributed model considers 4 control volumes (Figure 1): (i) the tube side domain (ŸT,n); (ii) the deposit layer domain (ŸL,n) between Rflow and the inner radius of

F. Coletti and S. Macchietto

1246

Ωs L

Ωw

Wall

ΩL

Deposits Fouling layer

δ

Ro

Ri

Ωt

R flow

r z

Figure 1 Domains definition and reference system.

the tube, Ri; (iii) the tube wall domain (Ÿw,n); and (iv) ŸS, the shell side domain. A local thermal balance in each domain is calculated. The classical Ebert-Panchal (1995) model is used to calculate the fouling resistance as function of process conditions and time. The fouling layer thickness is function of this fouling resistance and is simulated as a moving boundary domain. The cost model considers the impact of the reduced thermal and hydraulic performance as the sum of extra furnace fuel cost, Cfurnace, the electricity cost due increase in pumping power, Cpump and costs associated to the CO2 emission, Cemissions: C = C furnace + C pump + Cemissions (1) The extra furnace energy cost is calculated as the integral of the difference between the total heat duty in clean (Qclean, ) and fouling (Q )conditions. The extra pumping costs are the integral of the difference between pumping power in clean (Wclean) and fouled (W) conditions: t

t

EQloss = ³ ( Qclean − Q ) dt ;

E pump = ³ (Wclean − W ) dt

0

(2)

0

Table 1 Summary of main model equations. Ÿ is the domain considered.

Ÿ

Equation ∂

ΩT

(A

∂t

flow

ρe) +

∂ ∂z

(A

flow

∂T º

dR ªA k + Ph ( T − T ) ; = α Re « » ∂z ¬ ∂z ¼ dt ∂

ρ ue ) =

flow

f ,n

t

§ ρu · ¸; © 2 ¹

dδ n ( z )

2

T f , n ( z ) = Tn ( z ) + 0.55 (TL , n ( z , R flow ) − Tn ( z ) );

ΩL ρ

L

c p , L ∂TL , n

kL

Ωw ρ

w

c pw ∂Tw , n

kw

ΩS

∂t

∂t

=

=

1 ∂TL , n

r ∂r 1 ∂Tw , n

r ∂r ∂ ∂t

τ = Cf ¨

dt

Pr

−0.33

= kL

+r

∂r

2

∂ Tw , n

p,S

∂r

2

TS ) =

;

qL , n = − k L

;

qw , n = − k w

∂ ∂z

(ρ c S

p,S

TS u S ) +

∂

§k ¨

∂z ©

∂TS S

∂z

·+ ¸ ¹

1

AS

dt ∂TL , n ∂r ∂Tw , n

Np

¦P

S ,i

i =1

−E

dR f , n ( z )

2

+r

§

exp ¨

© RTf , n

2

(ρ c S

∂ TL , n

−0.66

w

hS (TS − Tw , i )

∂r

· ¸ − γτ ¹

A Heat Exchanger Model to Increase Energy Efficiency in Refinery Pre Heat Trains

1247

Table 2 Cost model parameters.

Parameter Fuel C content (CC) Energy content (Ef) CO2 Price (PCO2) Electricity Price (Pelec)

Units kg C/kg kWh/kg $/ton $/MWh

Value 0.7 11.7 30 50

Parameter Fuel price (Pfuel) Furnace efficiency (Ș) Pump efficiency (Șpump)

Units $/MWh -

Value 27 90% 80%

The energy loss calculated above, EQloss, is for a single heat exchanger in the network. Assuming that all the heat duty lost in the one heat exchanger considered has to be compensated for at the furnace and that the heat capacity of the crude, Cp, is constant, Equation (1) then becomes:

C=

EQloss

η

× Pfuel +

E pump

η pump

× Pelec +

EQloss

η

× mCO × PCO + Cemissions 2

(3)

2

where Șpump is the pump efficiency and Ș is the overall furnace efficiency. The cost due to the CO2 emissions is calculated by: Cemissions = E fuel × mCO2 × PCO2 (4) where PCO2 is the price of CO2 and mCO2 the carbon emission produced in the furnace, calculated via the greenhouse gas conversion factor for fuel oil (kg CO2/kg fuel) and the energy content of the fuel, Ef (J/kg fuel). Prices and cost parameters used are given in Table 2. In practice, unless the heat exchanger considered is the last before the furnace, the presence of other units will reduce the effect on the coil inlet temperature. To properly calculate the overall energy loss in this case, a simulation of the whole network would be required which is beyond the purpose of this paper.

3. Application - Retrofit options assessment Table 3 gives a summary of geometries of an industrial heat exchanger (1 pass on the Table 3 Summary of main model parameters.

Parameter Density Viscosity Heat capacity Thermal conductivity Inlet temperature Tube length Tube diameters Shell diameter Mass flowrate Activation energy Deposition constant Suppression constant Tube count Heat transfer coeff.

Symbol ȇ Ȃ Cp K Tin L d o/ d i DS m E ǹ ī NT H

kg m-3 Pa s J K-1 kg-1 W m-1 K-1 °C m mm m Kg s-1 J mol-1 m2K kW-1 h-1 m2K kW-1 h-1Pa-1 W m-2K-1

Tube 850 2.68 × 10-4 2200 0.125 190.1 6.1 19.05/13.51 57.2 28000 4100 2.63 × 10-5 calc

Shell 800 2.05 × 10-4 2300 0.110 273.4

0.990 13.4

630 560

Wall 7850 502 38

F. Coletti and S. Macchietto

1248 5.8

1.4

5.6

1.2

EQloss

5.2 Q [MW]

ΔP [bar]

5.4

1.0 0.8

5.0 4.8

0.6

4.6

0.4 4.4

0.2

0

50

100

150

200

250

300

350

4.2

0

50

100

Time [d]

150

200

250

300

350

Time [d]

(a)

(b)

Figure 2 Total pressure drops across the unit (a) and heat duty (b) over time. The dashed area in part b of the figure shows the additional energy requirement at the furnace due to fouling.

shell side, 2 passes on the tube side) and physical properties used in a Base Case model. The hot shell side fluid is the bottom pump-around stream from the crude distillation column, with desalted, pre-flashed crude in the tube side. Literature parameters (Yeap et al. 2004) were used for the fouling model (Table 3). The model allows us to track the effects of fouling along the heat exchanger over time, in particular the complex interactions between deposit layer, hydrodynamics and thermal exchange. After a year of operation, the total pressure drop is increased to a value above 1.3 bars (Figure 2.a) generating an extra cost of approximately 9000$ for the increased pumping power required over the year. The thermal performance of the unit is shown in Figure 2.b in terms of total heat duty. The dashed area, calculated using Equation(2), shows the energy loss due to fouling that must be compensated in the furnace. The heat transferred to the crude oil decreases from 5.6 MW to 4.3 MW (a 23% drop) after a year of operation because of the increased resistance to heat transfer given by the deposition of the fouling material. One option to mitigate fouling is to reduce the internal diameter of the tubes so that, for 4

45

1'' Gauge 12 3/4'' Gauge 16 3/4'' Gauge 12

Tube side inlet Tube side outlet

40 35

ΔP/ΔPclean

Area reduction [%]

3

2

30 25 20 15 10 5

1

0

0

50

100

150

200

Time [d]

(a)

250

300

350

1''

Gauge 12

3/4'' Gauge 16

3/4'' Gauge 12

Tube type

(b)

Figure 3 Increase in pressure drops (ǻP/ ǻPclean) over time (a) and area reduction at the tube inlet and outlet (b) for the three cases considered.

A Heat Exchanger Model to Increase Energy Efficiency in Refinery Pre Heat Trains

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50 1.4

1'' Gauge 12 3/4'' Gauge 16 3/4'' Gauge 12

1.2

40 Qclean - Q [MW]

Pumping power [kW]

45

35 30 25

1.0 0.8 0.6

20

10 5

0.4

1'' Gauge 12 3/4'' Gauge 16 3/4'' Gauge 12

15

0.2 0.0

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

Time [d]

Time [d]

(a)

(b)

Figure 4 Pumping power (a) and decrease in heat duty (b) due to fouling in the three cases considered.

constant mass flowrate, the oil velocity increases thus reducing fouling deposition. The Base Case geometry (1 inch do, gauge 12) was compared with two tube diameter retrofit options: Case B: ¾ inch tubes gauge 16 (di = 15.75 mm) and Case C: ¾ inch tubes gauge 12 (di =13.51mm). For consistency, all configurations have the same overall heat transfer area, i.e. for smaller tube diameters, the number of tubes is increased. All cases start from a clean heat exchanger (cleaning is not performed during the one year operation time considered). The smaller tubes (Cases B and C) result in higher pressure drops compared to Base Case. However, the pressure drop increase due to fouling (i.e. ǻP/ǻPclean) is smaller (Figure 3.a) as the higher pipe velocity reduces depositions. Figure 3.b shows the substantial decrease in cross-sectional area caused by fouling at the inlet and the outlet of the heat exchanger. Case C gives the smallest reduction, which explains the smaller ǻP/ǻPclean ratio in Figure 3.a. but requires the greatest pumping power (Figure 4.a). The small ¾ inch gauge 12 tubes give a clear thermal benefit (Figure 4.b). The total costs associated with fouling over time are shown in Figure 5.a. with breakdown given in Figure 5.b. The figures show the significant economic impact of fouling in the Base Case, the effectiveness and value of retrofit options in increasing energy efficiency, the major role played by the additional fuel cost 400,000

400,000 1'' Gauge 12 3/4'' Gauge 16 3/4'' Gauge 12

Cemissions

350,000

300,000

300,000

250,000

250,000 Cost [$]

Cost [$]

350,000

200,000 150,000

Cpump Cfurnace

200,000 150,000 100,000

100,000 50,000

50,000 0

0

0

50

100

150

200

250

300

350

1'' Gauge 12

3/4'' Gauge 16 Tube type

3/4'' Gauge 12

Time [d]

(a)

(b)

Figure 5 Total cost due to fouling and break down of the different sources of cost if the unit is not cleaned for a year.

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in the furnace and the importance in economic terms of the extra CO2 released. Other geometries and limitations (e.g. on allowable velocity) will of course have to be considered.

4. Conclusions and future work The model of a multi pass shell and tube heat exchanger presented captures the severe energy inefficiency due to fouling in refinery PHT. The distinctive feature of the model is that it allows capturing in a quantitative way the complex interactions between flow dynamics and fouling deposit growth over time, and establishing the trade-off between costs and benefits. It allows calculating more quantitatively than so far possible the additional energy requirements and consequent economic and CO2 release impacts due to fouling, and assessing various mitigation options at the design stage. This goes well beyond current practice which relies on the use of very aggregate, averaged and highly empirical fouling factors. The results show that such analysis will allow an important reduction in the energy requirements of refinery crude oil preheat.

5. Acknowledgements The authors gratefully acknowledge ExxonMobil for the data provided.

References Coletti, F. and Macchietto, S. (2008). Minimising efficiency losses in oil refineries: a heat exchanger fouling model. Sustainable Energy UK: Meeting the science and engineering challenge”, St Anne’s College, Oxford. Coletti, F. and Macchietto, S. (2009). "A dynamic, distributed model of shell and tube heat exchangers undergoing crude oil fouling." In preparation. Ebert, W. A. and Panchal, C. B. (1995). Analysis of Exxon crude-oil-slip stream coking data. Fouling Mitigation of Industrial Heat-Exchange Equipment, San Luis Obispo, California (USA), Begell House inc. Epstein, N. (1983). "Thinking about Heat Transfer Fouling: a 5x5 matrix." Heat Transfer Engineering 4(1): 43-56. ESDU (2000). Heat exchanger fouling in the pre-heat train of a crude oil distillation unit, Data Item 00016. London, ESDU International plc. Rabas, T. J. and Panchal, C. B. (2000). "Fouling Rates, Not Fouling Resistances, editorial." Heat Transfer Engineering 21(2): 1-3. Yeap, B. L., Wilson, D. I., Polley, G. T. and Pugh, S. J. (2004). "Mitigation of crude oil refinery heat exchanger fouling through retrofits based on thermo-hydraulic fouling models." Chemical engineering research & design 82(1): 53-71.

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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CAPE Contribution to Availability and Reliability of Waste to Energy László Sikos, Jiří Klemeš EC Marie Curie Chair (EXC) “INEMAGLOW”, Research Institute of Chemical and Process Engineering, FIT, University of Pannonia, Egyetem u. 10, 8200 Veszprém, Hungary, [email protected]; [email protected]

Abstract The role of CAPE tools is crucial for the analysis of failure data in Reliability, Availability, Maintainability and Safety (RAMS). In waste management a variety of failures influences the process. Scheduled outages as cleaning, supervision, avoidance of fatigue need to be considered as well. Some data are difficult to collect and rather sensitive. An efficient CAPE approach in this field is to cover the combination of reliability and waste management software tools for the related analyses, calculations and predictions, considering the specificities of waste management failure data.

Keywords: waste to energy, availability, reliability, RAMS, optimisation 1. Introduction The paper studies software tools supplying reliability data analysis of waste to energy systems. It is an advanced method for extracting the required data from life test and field data to make appropriate and realistic decisions.

2. Problem statement Let us briefly describe and discuss the basic concepts and software modelling techniques used for analyses and optimisation. The availability of a waste management chain represents the capability to manage waste continuously in a usual and regular way. On-site pollution management and treatment economics depend on the location and the availability of off-line facilities, e.g. regional sewage treatment, off-site hazardous waste treatment plants [1]. The availability of waste management chains depends on the frequency of system component breakdowns and the time taken to repair them. Reliability is the probability that the waste management system will perform satisfactorily for at least a given period of time [2]. Reliability is typically 90-95 % as the periodic shutdowns caused by scheduled maintenance [3]. Unreliability might be eliminated through preventive maintenance, and should be considered. An important factor is the operational reliability of the incinerator grate, considering the specific features and varying quality of waste [4].

3. Input data requirements and data sources Reliability engineering requires failure rates and mean times for calculations. Although the time duration between downtimes and uptimes, as well as operation hours can be measured, there are many problems. Unlike products of factories the measuring of waste flow is difficult. There are several components and products of treatment processes that are complicated to measure, e.g. ashes, burning gases, liquids and waste water,

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L . Sikos and J. Klemeš

especially poisons and toxics. In waste management systems, data source varies. The data provided by the company could be measured or fixed, while others are estimated, predicted, or calculated. 3.1. Wide variety of input data A wide variety of failures includes feeder failures, leakages, waste supply problems, breakdowns, stoppages, overflows, pressure problems, equipment fallouts etc. Reliability event data cover the work events, the type of tasks, current conditions, schedules and the associated costs. Subsystems are repairable or non-repairable. Input data should be handled by their types: quantitative (numbers) and qualitative (words, pictures) data. Further categories of life data need to be well separated: complete (all data are available) and censored (some data are missing or failure occurrence is uncertain). Data can be grouped or non-grouped, all failed or not all failed, exact or interval. Experimental data can provide a good model. Data dependency, accuracy and precision are some of the further factors that need to be taken into account. 3.2. Reliability data collection Reliability calculations require failure data obtained from the system performance or from planned reliability tests (life tests). Reliability data collection is the process of identifying and acquiring data to support reliability analysis at the subsystem, component, product and system levels. The waste management plan data sheet should contain the quantity of inert, active and hazardous materials for re-used onsite and offsite, recycled for use onsite and offsite, sent to recycling facility, as well as the disposal to landfill. 3.3. Data analysis Data analysis involves (1) converting data to common measures/formats and (2) performing statistical analyses to identify trends; develop models and tools; and create reports, handbooks and documents that are capable to support the product throughout its life cycle.

4. Calculation and modelling efficiency The efficiency of calculations and modelling can be compared via statistical simulation experiments. The main steps of the investigation of efficiency are (1) model development, (2) verification/validation, (3) statistical experimentation and results analysis. There are several statistical indicators, including mean, mode and parameters (location, scale and shape [5]), that tell important information about the distribution of random values. Mean-value analysis models are processed by their average output. To consider idle state and waste flow disruptions is a limitation and simulation is required in some cases for accurate predictions. The failure properties of components are best described by statistical (probability) distributions, commonly used life distributions of RAMS software packages, including but not limited to normal, beta, binomial, exponential, gamma, lognormal, uniform and Weibull distribution. Standard distributions can be examined visually for different combinations of input parameters. ReliaSoft Weibull++ is one of comprehensive software in this field.

5. Cost efficiency It is always important to find the right balance of reliability, availability and costs. Life Cycle Cost analysis tools enable the expert selection of the most appropriate scenario (the project variants) considering cost and reliability parameters simultaneously. It should be determined, based on Weibull parameters, if the system will survive until the

CAPE Contribution to Availability and Reliability of Waste to Energy

1253

next scheduled outage. Is equipment replacement more cost-effective than to wait until the next outage?

6. A suggested methodology Reliability engineering reports should contain results based on predictions and analyses that are supported by various comprehensive software tools (Fig 1). Figure 1. Availability and reliability tasks supported by various software tools RAMS software

Specific waste management software

Mathematical packages / optimisation software

D E J

F

K

L

G A

H

C

B

I Statistical software

The combined use of reliability and waste management software has a significant advantage due to various comprehensive features. Specific waste management software gather, store and organize all required data (A). Their data handling is automated, which saves time, increases controllability, and decreases fault occurrence. Waste data can be exported to spreadsheets or other software tools (B). Examples are: ESS hazardous waste management software, Soft-Pak, WIMS. Several features of RAMS software support waste management modelling (D-H) and optimisation (L), including cohesive modelling modules, simultaneous analyses, combining series and parallel subsystems, independent computation modes, approximation, prediction, and reliability optimisation via structure analysis, failure analysis (C) and total system approaches. They have the capability to model various tools simultaneously considering the relationship between data, equations, diagrams, input data, failure tree, and RBD. They can use field/test data for analysis requires qualification and summarisation. RAMS tools are capable to consider economical aspects. Such software modules are ReliaSoft Weibull++ and BlockSim, Relex Reliability Studio, Item ToolKit. A more detailed description was introduced by Sikos et al. [6] An example of special analyses methods is the Alternate Ranking Method (ReliaSoft) transforming the input data into a table of exact and interval failures, by obtaining a weighted midpoint [7]: βˆ

β −1 ⎛t⎞ −⎜ ⎟ βˆ ⎛ t ⎞ ηˆ ˆ ˆ ∫LI t f t; β ,η dt LI∫ t ηˆ ⎜⎝ ηˆ ⎠⎟ e ⎝ ⎠ dt tˆn βˆ ,ηˆ = TF = βˆ βˆ −1 ⎛t⎞ TF ˆ −⎜ ⎟ ˆ ∫LI f t; β ,ηˆ dt ∫ β ⎛⎜ t ⎞⎟ e ⎝ ηˆ ⎠ dt ηˆ ⎝ ηˆ ⎠ LI TF

( )

(

(

)

TF

)

based on the β and η Weibull parameters.

ˆ

(1)

L . Sikos and J. Klemeš

1254

There are several simulation tools (I), e.g. ASPEN Plus, ChemCAD, HYSYS, Pro II, TDW [8], suitable for waste management systems. For thermal processing of waste own software tools proved to be the right solution in many cases [9]. Data can be processed using statistical software packages such as ADSTAT or STATGRAPHICS. They are capable to evaluate regression parameters, perform dispersion variance, residue and reliability analyses. General purpose mathematical or optimisation software can be used if further optimisation needed (e.g., Maple, Matlab). A failure analysis can be conducted by (1) identifying the failure location, (2) observing the failure, (3) analysing equipment. Quantitative methods of data analysis are: univariate or bivariate descriptive analysis, explanatory analysis, and inferential analysis. The trend test (J) can be graphic and analytical. The trend free data are further analysed (K) to determine the characteristic of failure time distributions of crushing plant subsystems for estimating the reliability. Some data cannot be analysed by standard distribution models and nonstationary models should be used, e.g. the Non-Homogeneous Poisson Process (NHPP).

7. Case study A modern waste thermal treatment plant is selected as a demonstration case study. It has 65 different types of equipment units and subsystems (Fig 2). The measured failure data have been inserted into the spreadsheets of Relex Reliability Studio. After data completion the failure data were calculated. The fault tree diagram includes 7 OR gates and 20 kinds of basic events (Fig 3). Failure analyses of the last three years were used. Several measurements have been calculated or predicted, including mean time values, availability and reliability. System reliability problems have been identified. As a result, the location of weak points and the achievable reliability values in the different reliability problem groups have been shown (Table 1).

Figure 2. The structure of the plant [10] 14

32

2

1

40

31

3

39

4

42

41

5

21 23

22

21

38

30

43

6

M

M

26 M

20

M

M

14

46

M

M

14

M

44

45

47

48

M

33

9

7

14

M

M

24

M

M

49

M

53 M

54

45

M

M

M

14

19

4

25

10

29

36 37

50

51

26

27

35

3

15

3

17

56

14

3

59 M

60 M

61

16

28

34

57 62

58 M

12 13

55 3

52 M

M

15

11

50

18

17

8

M

63

64 65

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1255

Figure 3. Fault tree diagram 1 Top event OR

6

5

4 OR

18

19

8

7

2

3

OR

OR

9

21

12

22

23

14

13

15

16

17

OR

OR

OR

20

11

10

24

25

26

27

Table 1. Reliability improvement possibilities of the plant by origin

Origin Tank, silo or trap Mechanical treatment Equipment units Chemical treatment Supply

Existing reliability 92.05 % 92.41 % 92.68 % 93.96 % 92.41 %

Achievable reliability 95.31 % 95.24 % 95.49 % 95.86 % 95.24 %

8. Conclusions Failure factors in waste treatment can be effectively optimised by the combination of reliability and waste management software, including (1) specific waste management software, (2) RAMS software, (3) statistical packages, (4) modelling and optimising tools. The main advantage is that comprehensive predictions and efficient calculations can be performed.

9. Acknowledgements The support from the EC project MEXC-CT-2003-042618 “Integrated Waste to Energy Management to Prevent Global Warming” is gratefully acknowledged.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

G.J. Celenza. Vol 1, CRC Press (2000) 2 W.G. Ireson, C.F. Coombs, and R.Y. Moss. McGraw-Hill (1996) U.S. Congress, Office of Technology Assessment. Diane Publishing Co. (1989) 219 T. Rand, J. Haukohl, and U. Marxen. No. 462, World Bank Publications (2000) 56 A.M. Law, and W.D. Kelton. McGraw-Hill (2000) L. Sikos, and J. Klemeš. Proceedings of EMINENT 2, Hungary (2008) 263-272 ReliaSoft Corporation. www.reliasoft.com P. Stehlík, R. Puchyr, and J. Oral. Waste Management 20 (2000) 435-442 P. Stehlík. Applied Thermal Engineering 27 (2007) 1658-1670 P. Michalec. MOZAIKA – Liberec (block diagram). REME spol.s r.o. (2003)

19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. JeĪowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.

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A disjunctive programming model for the optimal design of cooling water systems José M. Ponce-Ortega,a Medardo Serna-González,a Arturo Jiménez-Gutiérrezb a

Universidad Michoacana de San Nicolás de Hidalgo, Morelia Mich, Mexico, 58060, [email protected], [email protected] b Instituto Tecnológico de Celaya,Celaya Gto, Mexico,38010, [email protected]

Abstract This paper presents a disjunctive programming formulation for the optimal design of integrated cooling water systems. The model considers different alternatives for the design parameters and construction materials for the cooling tower; in addition, a superstructure for cooling networks is included, which allows for configurations in series and in parallel, as well as the bypass of fresh and previously-used cooling water. The model includes the detailed design of cooler exchangers, taking into account different alternatives for construction and incorporating pumping considerations. Operational and geometrical constraints given by standard codes to get feasible designs are included. The objective function is set as the minimization of the total annual cost. The solution to an example shows that the maximum allowable temperature of the cooling water should be obtained as part of the optimal solution, which also helps to provide a suitable energy management for these systems. Keywords: Cooling water system, cooling tower, cooler network, detailed design

1. Introduction Cooling water systems are used to treat hot process streams in the process industry. Traditional strategies reported to design cooling water systems have decomposed the problem to optimize separately the design of the cooling tower [1, 2], the cooler exchanger network [3, 4, 5] and the pumping system, typically using some simplifications. These components, however, have strong interactions among each other. In addition, the synthesis methods for cooler networks generally use estimations of constant heat transfer coefficients. Therefore, there is a clear motivation to develop a systematic method for the simultaneous optimization of integrated cooling water systems. This paper presents a simultaneous optimization model for the synthesis and detailed design of re-circulating cooling water systems. The model is based on generalized disjunctive programming, and it is optimized with an MINLP reformulation to determine the cooling water system design that minimizes the total annual cost. In addition to the optimal cooling network, the proposed approach also generates the detailed design of the individual units, including mechanical and thermal-hydraulic variables.

2. Problem statement and system superstructure The problem addressed in this work is stated as follows: given a set of hot process streams with their inlet and target temperatures, flow-rates, and physical properties, find

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the cooler network configuration, the operating conditions, the design parameters of each network heat exchanger and the cooling tower that achieve the required cooling service at a minimum total annual cost. The proposed superstructure for the cooling water systems considers the interactions among the cooling tower, the cooling water network and the pumping system, as shown in Fig. 1.

Fig. 1 Superstructure for the integrated cooling water system

A Disjunctive Programming Model for the Optimal Design of Cooling Water Systems

1259

3. Model development The objective function consists of the minimization of the total annual cost for the cooling water system, which includes the capital costs for the tower, coolers, and pumps, plus the operating costs for the fan of the tower, pumps and water make up (Eq. 1).

min TAC = kF ª¬CVCT ACT L fi + CGCT mamean + C0CT º¼ β ª § Ai , k · º exc exc » + k F « ¦ ¦ CFi zi , k + ¦ ¦ Nsi ,k Ci ¨ ¨ Ns ¸¸ » «i∈HPS k∈ST i∈HPS k∈ST i ,k ¹ © ¬ ¼ γ ª § ΔPTOT Fi h · º + k F « ¦ CFi pump + ¦ Cipump ¨ i ¸ » ρi «¬i∈HPS i∈HPS © ¹ »¼ γ ª § ¦ ΔPcuSTAGE ¦ ( FFk ) · º k « ¨ ¸ » k∈ST + k F «CFcupump + C cupump ¨ k∈ST ¸ » ρcu « ¨ ¸ » © ¹ ¼» ¬«

(

)

(1)

+ C pow H Y 3600ΔPCT

(

)

ª ΔPcuSTAGE ¦ ( FFk ) º» k § ΔPiTOT Fi h · k¦ HY « ∈ST k∈ST + C pow ¸+ ¦¨ » η pump «i∈HPS © ρi ρcu ¹ «¬ »¼ + Cwater HY 3600 Lmakeup w The model includes a set of constraints that relate the cooling tower, the cooling network and the pumping system. Because of space limitations, the equations are not reported here, only a description of the major components. Cooling network constraints: They include total heat balances for the hot process streams and heat balances for each stage of the superstructure, mass and heat balances for the cooling water in the network, and temperature feasibility constraints. Also included are equations for the velocities of the fluids, the log-mean temperature difference, the global heat transfer coefficient and the heat transfer area. Pumping effects: When a cooler exists in the network, the heat exchanger detailed design is carried out as a function of the pumping requirements. The equations used for the detailed heat exchanger design include two compact relationships that relate pressure drops and film heat transfer coefficients for the shell and the tube side. The compact expression for the shell side is based on the Kern method. As part of the problem, a selection must be made for the tube layout, the tube size and the fluids location for each cooler of the superstructure. The following disjunction is used to model this situation,

J.M. Ponce-Ortega et al.

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zi,k ª º « » Apply exchanger design equations « » layout layout « » ª YTRI º ª º Y SQUi ,k i ,k « » « »∨« » « » «¬( triangular ) »¼ «¬( square) »¼ « » i ∈ HPS (2) « »∨ª ªY1tube º ∨ ... ∨ ªYittube º ∨ ... ∨ ªYITtube º ¬ z , º i ,k ¬ i ,k ¼ ¬ i,k ¼ ¬ i ,k ¼ « » « » k ∈ ST «ª » loc loc Set design variables as zero¼ ¬ º ª º Y1i ,k Y2i ,k «« »∨« »» « «hot fluid in the tubes» «hot fluid in the shell» » ¼ ¬ ¼» «¬ Npass1 Npass 2 «ª º ª º» Yi,k Yi,k «« »∨« »» ¬«¬Single pass exchanger ¼ ¬Multipass exchanger¼»¼ Cooling tower constraints: They include mass and heat balances, the Merkel method for the design of the tower, and empirical correlations for the air pressure drop and for the loss and overall mass transfer coefficients in the packing section of the tower. Additional disjunctions are used to select the type of packing and the type of draft.

4. A numerical example The model was applied to a problem of three hot process streams that need to be cooled to given target temperatures. Table 1 shows the stream data. The following economic scenario was used. The operation time was taken as 8,500 hr/year, the annualization factor was 0.23 year-1, and the coefficients for the capital cost function for the coolers were $30,800, $1,650 and 0.65 for CFexc, Cexc and β , respectively. The capital costs for the pumps were estimated assuming CFpump as $2,000, Cpump as $5 and γ as 0.68. The coefficients for the capital cost of the cooling tower were $1,097.5 for CGCT, and $31,185 for CoCT. The electricity cost was $0.00005/W-hr and the efficiency for the pumps 70%. The unit cost for the cold makeup water was taken as $1.5949 x 10-5/kg. The efficiency for the fan of the cooling tower was 75% and the number of cycles for the cooling water system was set as 4. Table 1. Stream data for the Example Stream

H1

H2

H3

TIN [°C]

76.60

82.00

100.00

TOUT [°C]

40.00

60.00

60.00

FCP [kW/(m2 K)]

100.00

45.00

400.00

Cp [J/(kg K)]

2,454

1,670 -4

2,680 -4

2.1 x 10-4

ȝ [kg/(m s)]

2.4 x 10

k [W/(m K)]

0.114

0.23

0.14

634

780

890

0.00015

0.00017

0.00016

3

ȡ [kg/m ] 2

Rd [(m K)/W]

2.3 x 10

The model for this example included 1,367 constraints, 1,046 continuous variables and 176 discrete variables. The problem was solved with a PC system with a Pentium 4

A Disjunctive Programming Model for the Optimal Design of Cooling Water Systems

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processor in 445.05 s using the DICOPT solver. The cooling water system shown in Fig. 2 was obtained, with a total annual cost of $251,122/year. Notice that the network configuration includes a combination of coolers in series and in parallel. It can also be observed that the maximum allowable temperature for the cooling water is reached to get a good performance of the cooling tower. For comparison purposes a sequential optimization approach was implemented, which resulted in a total annual cost of $269,030/year (7.13% higher that the optimal solution obtained with the simultaneous model). The main reason for the higher annual cost of the sequential solution is that the consumption of water make up increased by 118%. A typical parallel arrangement for the coolers was also considered; in this case, the total annual cost for the system was $256,709, or $2.22% higher than the optimal configuration. This result is mainly explained from a higher capital investment required for the coolers.

Fig. 2. Optimal configuration for the Example

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5. Conclusions We have proposed a simultaneous optimization model that includes the three major components of cooling water systems, i.e. a cooling water network, a wet-cooling tower, and a pumping system. The operating conditions and design parameters of the units are considered as optimization variables. Disjunctive programming formulations are used to model the discrete decisions of the problem, which are then transformed into to an MINLP problem. Since the model is highly non convex, no optimal solution can be guarantied with a local optimization algorithm. However, with a suitable initialization process a satisfactory solution for many practical purposes can be obtained. The solution of the example presented here shows the incentive to carryout an integrated solution with respect to two simplifications typically used to solve these types of systems (i.e. consider arrangements in parallel for the coolers, or implement a sequential solution for each component of the cooling water system).

References [1] M.S. Soylemez, Energy Conversion and Management, 7 (2001) 783. [2] M.S. Soylemez, Energy Conversion and Management, 15-16 (2004) 2335. [3] J.K. Kim, and R. Smith,. Chemical Engineering Science, 12 (2001) 3641. [4] X. Feng, R.J. Shen and B. Wang, Energy & Fuels, 4 (2005) 1723. [5] J.M. Ponce-Ortega, M. Serna-González and A. Jiménez-Gutiérrez, Chemical Engineering Science, 21 (2007) 5728.

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A MultiObjective Genetic Algorithm Framework for Electricity / Hydrogen Co-Production From Generation IV Nuclear Energy Systems Adrien Gomez a,c, Catherine Azzaro-Pantel a, Luc Pibouleau a, Serge Domenech a, Christian Latgé b, Patrick Dumaz c, David Haubensack c a

Université de Toulouse, Laboratoire de Génie Chimique, CNRS UMR 5503, 5 rue Paulin Talabot, 31106 Toulouse Cedex 1, France, {Adrien.Gomez, Catherine.AzzaroPantel, Serge.Domenech, Luc.Pibouleau}@ensiacet.fr b CEA Cadarache, DEN/CAD/DTN/DIR Bât 710, 13108 St Paul Lez Durance, France, [email protected] c CEA Cadarache, DEN/CAD/DER/SESI, Bât 212, 13108 St Paul Lez Durance, France, {Patrick.Dumaz, David.Haubensack, Adrien.Gomez }@cea.fr

Abstract One of the great motivations of studying and developing Generation IV (Gen IV) reactors of VHTR (Very High Temperature Reactor) design is their capacity to efficiently produce both electricity and H2 (hydrogen). This study aims at developing an optimization methodology for cogeneration systems of hydrogen and electricity, with respect to energy constraints, economics and conjuncture in terms of demand. It lies within the scope of a collaboration between the Laboratoire de Génie Chimique (LGC Toulouse, France) and the French Atomic Energy Commission (CEA, Cadarache, France) in order to compare various cogeneration systems from both energy and economics viewpoints.This paper describes the different steps of the technico-economic methodology for H2 and electricity cogeneration systems. Keywords: Hydrogen, Electricity, multiobjective optimization

cogeneration,

Gen

IV

nuclear

systems,

1. Introduction Hydrogen is currently viewed as one of the energetic vectors that will replace traditional fossil fuels in the XXIth century. Although the transition is assumed to be progressive, innovative technologies for a massive production of H2 have to be investigated. The VHTR (Very High Temperature Reactor) concept, considered as the nearest-term reactor design, can indeed be coupled on the one hand, with innovative electricitygenerating cycles and, on the other hand, with massive H2 production processes. Thus, due to a high exit core temperature (at least 950°C) reached by helium used for cooling, VHTR is dedicated to the cogeneration of electricity and hydrogen by Sulphur-Iodine (S-I) thermochemical cycle or by High Temperature Electrolysis of steam water. Globally, these processes require the simultaneous supply of electricity and heat at high temperature. The optimal design of these process configurations constitutes an important challenge. In this perspective, simulation tools for thermal systems were previously developed by the CEA (French Atomic Energy Commission, Cadarache, France), i.e., CYCLOP for thermodynamic cycle modelling. This code allows to model innovative energy

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production systems for given operating conditions while taking into account the influence of classical variables: exchanger efficiency, pressure ratio and isentropic efficiency (compressor, turbines …), pressure loss… This paper first describes the three steps of the technico-economic optimization methodology implemented for the selection of cogeneration systems. The first one is based on a bicriteria optimization with total life cost and exergy losses minimization. The second one implies exergetic production cost evaluation of any energy form. The last step provides decisional data, as hydrogen production cost for different scenarios for electric market corresponding to a given plant, to make possible the choice between different systems. Finally, the methodology is applied successfully to two different systems dedicated to electricity and hydrogen production, taking into account various scenarios of the electricity market.

2. Technico-economic optimization methodology for H2 and electricity cogeneration The choice of the best strategy for electricity and H2 massive production systems is a technico-economic concern. The cogeneration system considered here (Fig. 1) consists in coupling a VHTR nuclear reactor with an electrical generator (that is a Brayton cycle) in direct cycle, on the one hand, and, with a hydrogen production plant (Iodine-Sulphur cycle) for which the thermal and electrical demand is known. It involves a site of 4 autonomous sections, each one including a VHTR reactor, an electrical generator and n H2 production plants operating in parallel.

VHTR 600 MW

H2 Storage IHX Heat Distribution

H2 Plant

Electric Generator

Fig. 1. Configuration of electricity and H2 cogeneration site (example)

Bicriteria optimization by exergetic losses and lifespan cost minimization of the production plant The first step of the methodology implies a bicriteria optimization, by simultaneous minimization of the total exergetic losses and of the total costs of the production sites over their lifespan. The choice of a criterion based on the minimization of the exergetic losses was justified in [1]: it represents the lost “available work” during the energy conversion. The thermodynamic model of the cogeneration system is implemented in the CYCLOP simulator [2]. The economic criterion takes into account both construction costs of the site (nuclear reactors, electricity generators, H2 plants) and operating costs (nuclear fuel, maintenance of VHTR and H2 plants) for 60 years life (Eqn. 1):

A MultiObjective Genetic Algorithm Framework for Electricity/Hydrogen Co-Production from Generation IV Nuclear Energy Systems

TCSite = ¦ [Ca Nucl.Fuel (t ) + Ca O & M (t ) + Ca Invest (t )]× (1 + i ) D

−t

t =1

1265

(Eqn. 1.)

Where: TCSite: Total Cost (M€), CaNucl. Fuel: nuclear fuel annual cost, CaO&M: operating & maintenance costs, CaInvest.: investment annual cost (including end of life costs), i: discount rate (%), D: Cogeneration Site Life (years) The economic model, based on the so-called SEMER code [3], was extended for H2/electricity cogeneration case and cost models for innovative components were also developed specifically. The multiobjective optimization procedure was performed via genetic algorithms, that have proven to be particularly well-fitted for such problems and have the advantage to lead directly to the so-called Pareto front. The bicriteria optimization step was carried out with MULTIGEN library [4], as a master procedure, connected to CYCLOP and SEMER codes (Fig. 2). MULTIGEN Algorithm(NSGA II) Global Optimisation Variables Flows, pressure , ratio,…exchanger efficicency

CYCLOP

SEMER

Thermodynamic Model

Economic Model of Cogeneration Site

Component Cost Models

Optimization Criterion Exergy Losses Of Cogeneration Site

Total Life Cost Over lifespan

Fig. 2. Integration of the different models in the methodology

Typical results are presented in Fig. 3 and exhibit different sets of compromise solutions, called Pareto fronts corresponding to various H2 production levels represented by one or several H2 production plants. The objective of the following step of the methodology is to reduce this set to assist the decision maker in selecting the preferred or best compromise solution from among the whole set of solutions.

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8000 Confidential Values

Total Life Cost(M€ 2007)

8500

7500 7 H2 Plants / Reactorr

7000

6 H2 Plants / Reactor

6500

5 H2 Plants / Reactor

6000

4 H2 Plants / Reactor 3 H2 Plants / Reactor

5500

2 H2 Plants / Reactor 5000 4500 120

1 H2 Plant / Reactor 130

140

150

160

170

180

190

200

210

220

230

240

250

260

Exergetic Losses / Reactor (MW)

Fig. 3. Bicriteria optimization results: Pareto fronts for cogeneration systems.

Global production cost evaluation The production cost evaluation is classical for electricity production (Eqn. 2), and has been performed for the solutions identified at the first step of the methodology (Fig. 3).

CPr od (∈ / kWh ) =

TC Site D ª Pa (t ) (1 + i )−t º» ¦« t =1¬ 1000 ¼

(Eqn. 2.)

Where: CProd: production cost (€/kWh), Pa: annual production of energy (MWh/year). For cogeneration systems, the annual production of energy involves the contribution of both electricity and exergetic power of H2:

Pa = H × [Welec + m H 2 × PEx (H 2 )]

(Eqn. 3.)

Where: H: production period (hours/year), Welec: electric production (MW), m H 2 : H2 production (mol/s), PEx: Exergetic Power of H2 (235.3 MJ/mol). Let us mention that the electrical and hydrogen production cost is identical in value (€/kWh) from an exergetic point of view. According to Fig. 4, solutions with minimum exergetic production costs can be highlighted: they correspond to minimal production costs of electricity. But, at this level, H2 and electricity are undifferentiated from the production cost point of view.

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0,142

7 H2 Plants / Reactor 6 H2 Plants / Reactor

0,132

5 H2 Plants / Reactor

Confidential Values

Exergetic Production Cost (€/kWh)

0,152

4 H2 Plants / Reactor

0,122

3 H2 Plants / Reactor 2 H2 Plants / Reactor 1 H2 Plant / Reactor

0,112 0,102

Selected: Minimum Production Cost solutions

0,092 0,082 0

50

100

150

200

250

300

Electric Production / Reactor (MW)

Fig. 4. Production cost evaluation for bicriteria optimization results

Fixing the cost of electricity As abovementioned, the use of the exergy concept implies that the production costs of both forms of energy are undifferentiated, i.e. the overcost related to the production of H2 is reflected on the cost of electricity. The production cost of electricity (€/kWh) is then fixed to deduce the production cost of hydrogen (€/kg). For a given H2/electricity production ratio, an optimum of H2 production costs exists for a given electricity cost, as displayed in Fig. 5. These results constitute a decisional map for the selection of cogeneration systems. Each optimal solution is related to a simultaneous electricity/hydrogen production: optimal production costs can be deduced from Fig 5.

400

4,5

300

3,0 250

2,5 200

2,0

150

1,5 1,0

100

0,5

50

0,0 0,00

0,05

0,10

Electricity Production Cost (€/kWh)

0 0,15

1200

1000

4,0 Confidential Values

3,5

H2 Cost (€/kg) Electric Production

3,5

800

3,0 600

2,5 2,0

400

1,5 1,0

200

Electric Production of Site (MW)

5,0

350

Confidential Values

H2 Production Cost (€/kg)

4,0

450

H2 Production Cost (€/kg)

H2 Cost (€/kg) H2 Production

4,5

H2 Production of Site (Tons/Day)

5,0

0,5 0,0 0,00

0,05

0,10

0 0,15

Electricity Production Cost (€/kWh)

Fig.5. Final optimal cogeneration solutions for decision makers

3. Conclusions The proposed methodology, based on classical evaluation criteria, makes it possible to visualize clearly and quickly the economic interest of cogeneration systems (electricity & H2). From the application of exergetic theory, the overall production cost can be deduced. When fixing the cost of electricity, different scenarios can be proposed to the decision maker to assist him for cogeneration system selection. This methodology is

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intended to be applied to any system, implying different modes of production for electricity and hydrogen.

References [1] A. Gomez et al., Optimization of electricity / hydrogen cogeneration from generation IV nuclear energy systems, ESCAPE 17, Elsevier, 2007. [2] D. Haubensack et al., The COPERNIC/CYCLOP Computer Tool: Pre-conceptual Design of Gen IV Nuclear Systems, Proceedings, Conf. on High Temperature Reactor, Beiging, IAEA, 2004. [3] S. Nisan et al., SEMER: a simple code for the economic evaluation of nuclear and fossil energy-based power production systems, Nucl. Eng. and Design 221 (2003) 301. [4] A. Gomez et al., Teaching Mono and Multi-objective Genetic Algorithms in Process Systems Engineering: an illustration with the MULTIGEN environment, ESCAPE 18, Elsevier, 2008.

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Energy Efficiency Advancements in Wastewater Treatment – Study of Autothermal Thermophilic Aerobic Digestion Jaime Rojas and Toshko Zhelev Charles Parsons Initiative on Energy and Sustainable Environment, University of Limerick, National Technological Park, Plassey. Co. Limerick, Ireland, [email protected]

Abstract Several researchers have identified the need to and the optimum operating conditions (OCs) of autothermal thermophilic aerobic digestion (ATAD). Our main hypothesis is that the optimum operating conditions have the potential to significantly improve the specific energy requirements of ATAD systems, and perhaps even to increase their capacity. The aim of the present ongoing study is to minimize the specific energy requirement of existing ATAD designs by altering the operating conditions. The methodology selected to achieve this is dynamic parameter optimization. The mathematical ATAD reactor model needed to solve the optimization problem is currently being extended and built in MATLAB. Keywords: wastewater

energy efficiency,

dynamic

optimization, thermophilic, digestion,

1. Introduction Autothermal thermophilic aerobic digestion is a sludge treatment process developed in the 1970s. The main goals of the treatment are to reduce both the organic matter content (stabilization) and the amount of pathogens (pasteurization) present in the sludge. Several review papers are available on this subject [5] [6] [7]. There has been a substantial development of ATAD technology since the first generation of ATAD systems was built. While first generation ATAD systems are characterized by the use of aspirating air systems, 2 or 3 reactors operated in series, short hydraulic retention times (HRT) of less than 10 days, the use of foam cutters, and the use of invariable air supply without any aeration control, some second generation ATAD systems are characterized by single stage operation with a HRT of 10-15 days, the use of pressurized jet aeration, variable air supply and aeration control, and foam control [12]. Despite the numerous technological advancements, there are some contradicting reports in current literature regarding the cost and energy efficiency of ATAD [7]. Some researchers suggest that ATAD is costly and energy inefficient [8], while others have

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Figure 1: Typical oxygen demand and supply curves for a conventional ATAD system.

pointed out that ATAD is competitive on an economic base [3] [2] [11]. Several researchers suggest that more research is needed so as to identify the optimum operating conditions of ATAD systems [5] [6]. We hypothesize that the energy efficiency of existing ATAD systems can be significantly improved by altering the OCs. This ongoing study seeks to minimize the energy requirement of established ATAD designs by altering the OCs while complying with treatment goals.

2. Problem Statement The variables defining the OCs considered in this study are the oxygen concentration, temperature, and charging procedures. Oxygen concentration and temperature are two fundamental (and perhaps the most important) variables affecting the process performance [5]. The charging procedures have being identified as having a direct influence on the specific energy requirements for removal of organic matter [10]. The OCs of ATAD systems have not been exploited. This can be seen in the fact that conventional ATAD systems (i) use invariable air supply without aeration control, regardless of the level of bacterial activity; (ii) have no temperature regulation and are subject to strong temperature fluctuations as a result of the thermal shock; (iii) use one single volume change per day, therefore not allowing a complete exploitation of the thermophiles' efficiency. 2.1. Oxygen Due to the huge oxygen uptake rates of the thermophiles (several times higher than in the mesophilic case), there is a relatively high energy consumption in relation to the aeration of the reactors. As a result, ATAD is an energy intensive process. Conventional ATAD systems use invariable-speed aerators which operate continuously. Researchers have suggested that ATAD is more expensive to operate in terms of electricity consumption, because of this continuous aeration mode [6]. The typical oxygen demand and supply curves of conventional ATAD systems are illustrated in Figure 1. When supply exceeds demand, there is waste of electricity and aeration; foam is generated as a result, and there is excessive loss of heat through the exhaust gas. When demand

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Figure 2: (a) Flow diagram of case study ATAD facility in Killarney, Co. Kerry, Ireland. (b) Temperature-dependent growth rate of thermophiles

exceeds supply, microaerophilic conditions lead to oxidation underperformance, and odours are generated. It is clear that the oxygen supply as shown in Figure 1 is far from optimized. 2.2. Temperature The main issue related to the reactors' temperature is the so-called thermal shock. Figure 2a illustrates the flow diagram of the case study ATAD facility, while Figure 2b represents the temperature dependence of the thermophilic microorganisms. The latter shows how the thermal shock caused by daily charging of the reactors shifts the whole system into low-activity regions, therefore causing carbon oxidation to underperform. It takes an average of 14 hours for the reactors to reach their initial temperature. 2.3. Charging Procedures As stated earlier, conventional ATAD systems use one single volume change per day, and this does not allow a complete exploitation of the thermophiles efficiency [9]. The volume change frequency influences the sludge oxidation rate, the specific energy requirements, the overall capacity of the system, and the magnitude of the thermal shock [9] [10] [1].

3. Methodology The methodology selected to minimize the specific energy requirement of established ATAD designs by altering the OCs is dynamic optimization. Dynamic optimization is a type of problem that belongs to the branch of Calculus of Variations. The main idea is to and the state- and control variables' histories that minimize a specified cost functional. In our particular problem the control variables are the aeration rate, temperature, and charging procedures, and the specific energy requirement is the cost functional to be minimized. There are a number of constraints involved: Firstly, the dynamic constraint, dx(t)/dt = f(t), imposed by the differential equations which describe the time-dependent behavior of the ATAD reactors' system. Secondly, the (inequality) constraints necessary to satisfy both stabilization and pasteurization requirements (the two goals of the treatment). In the case of stabilization, the constraint is given by the time needed to achieve a minimum volatile solids (VS) reduction of 38% with regard to the feed sludge. In the case of pasteurization, the constraint is given by the time needed

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to achieve pathogen-free product. The temperature-dependent pasteurization time is given by the expression

tP =

50070000 10 0.14⋅TP

(Eqn. 1)

where tP is the pasteurization time, and TP the pasteurization temperature. The cost functional can be calculated by integrating the following equation: tf

& & & 1 J= P[ x (t ), u (t ), p(t )] ⋅ dt ³ V L ti

(Eqn. 2)

where J (the cost functional) represents the specific energy requirement, VL the liquid volume, ti and tf the initial and final time, P is the power, x(t) are the state variables, u(t) the control variables, and p(t) the time dependent parameters. The control variables considered here, that is u1(t), u2(t), and u3(t), are the aeration rate, the reactors' temperature, and the charging procedures, respectively. The parameters p(t) are all the kinetic parameters contained in the mathematical model (such as growth and decay rates) which are in general temperature dependent and therefore time dependent. As mentioned earlier, one of the constraints is the dynamic constraint imposed by the differential equations' system. That means that a mathematical ATAD reactor model is necessary in order to solve the optimization problem. The chosen model has to include both energy and mass balances. For this purpose the model proposed in [4] was selected. It has been shown to describe well the behavior of well-mixed ATAD systems for constant temperatures. The model includes a mass balance but lacks an energy balance. For the purpose of this study, the mentioned model has to be extended with a detailed energy balance in order to allow for prediction of temperature fluctuations inside the reactors and the effect which such fluctuations would have on the oxidation rate and the overall performance of the process. The problem of finding the minimum of the cost functional is to be achieved numerically by applying the Gradient Method.

4. Future Work The next step will be to extend the model proposed in [4] with an energy balance and to verify the results of the extended model with data from our case study ATAD facility and from the literature. The following step is to appropriately formulate both necessary and sufficient conditions for optimality, and finally to numerically apply the gradient method to find the optimizing state- and control histories.

References [1] Zs Csikor, P Mihaltz, A Hanifa, R Kovacs, and M F Dahab. Identification of factors contributing to degradation in autothermal thermophilic sludge digestion. Water Science and Technology, 46(10):131{8, 2002. [2] H G Kelly. Comparing biosolids treatment of thermophilic digestion, thermal-chemical and heat drying technologies. In Proceedings of the 4th European Biosolids and Organic Residuals Conference, pages 1-13, Wakefield, UK, November 1999. Chartered Institution of Water and Environmental Management. [3] P W Keohan, P J Connelly, and A B Prince. Engineering and economic assessment of autoheated thermophilic aerobic digestion with air aeration, project summary. Research

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and development report, USEPA, Municipal Environmental Research Laboratory, Cincinati, Ohio, October 1981. [4] R Kovacs and P Mihaltz. Untersuchungen der kinetik der aerob-thermophilen klaerschlammstabilisierung - einfluss der temperatur. May 2005 2005. [5] Timothy M. LaPara and James E. Alleman. Thermophilic aerobic biological wastewater treatment. Water Research, 33(4):895{908, 1999. [6] N M Layden, H G Kelly, D S Mavinic, R Moles, and J Barlet. Autothermal thermophilic aerobic digestion (atad) { part i: Review of origins, design, and process operation. Journal of Environmental Engineering and Science, 6(6):665{678, 2007. [7] N M Layden, H G Kelly, D S Mavinic, R Moles, and J Barlet. Autothermal thermophilic aerobic digestion (atad) { part ii: Review of research and full-scale operating experiences. Journal of Environmental Engineering and Science, 6(6):679{690, 2007. [8] S M Le. Thermophilic biological pre-treatments for mads. In AquaEnviro Workshop: Advances in Technology for the Anaerobic Digestion of Municipal Sludge, Manchester, UK, 14 June 2006. [9] Charly Ponti, Bernhard Sonnleitner, and Armin Fiechter. Aerobic thermophilic treatment of sewage sludge at pilot plant scale. 1. operating conditions. Journal of Biotechnology, 38(2):173{182, 1995. [10] Charly Ponti, Bernhard Sonnleitner, and Armin Fiechter. Aerobic thermophilic treatment of sewage sludge at pilot plant scale. 2. technical solutions and process design. Journal of Biotechnology, 38(2):183{192, 1995. [11] D W Riley and C F Forster. An evaluation of an autothermal aerobic digestion system. Process Safety and Environmental Protection, 80(B2):100{104, March 2002. [12] J P Jr Scisson. Atad, the next generation: Design, construction, start-up and operation of the first [13] municipal 2nd generation atad. In WEF/AWWA/CWEA Joint Residuals and Biosolids Management Conference and Exhibition 2003, Baltimore, MD, February 2003.

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Evaluation of energy vectors poly-generation schemes based on solid fuel gasification processes with Carbon Capture and Storage (CCS) Calin-Cristian Cormos,a Ana-Maria Cormos,a Victoria Goia,a Serban Agachi a a

Babes – Bolyai University, Faculty of Chemistry and Chemical Engineering 11 Arany Janos Street, RO-400028, Cluj – Napoca, Romania Tel: +40264593833, Fax: +40264590818, E-mails: [email protected]; [email protected]; [email protected]; [email protected]

Abstract Energy issue is very important and actual for the modern world giving the double significance of the problem: security of energy supply, environmental protection and climate change prevention by reducing the greenhouse gas emissions (mainly carbon dioxide). This paper investigates the innovative ways for transforming the coal in addition with renewable energy sources (biomass), through gasification into different energy vectors (power, hydrogen, heat etc.) simultaneous with carbon dioxide capture and storage (CCS). Lately, solid fuel gasification is extensively evaluated being one of the energy conversion technologies having the highest potential to capture CO2 with low penalties in efficiency and cost. Also, gasification, compared with other technologies, has very good potential to generate by thermo-chemical conversion various energy vectors apart from power (e.g. hydrogen, substitute natural gas, liquid fuels etc.). The innovative energy conversion processes investigated in the paper were modeled and simulated using commercial process flow modeling software (ChemCAD) for technical evaluation of poly-generation processes (focused on poly-generation processes of power, hydrogen and heat) based on gasification with carbon capture and storage. The case studies investigated in the paper will produce a flexible ratio between power and hydrogen (in the range of about 400 MW electricity and 0 – 200 MW hydrogen) with more than 90 % carbon capture rate (design assumptions). A particular accent is put in the paper on thermal and power integration of plant sub-systems, flexibility analysis of the energy conversion process (ability to change plant generated energy vectors over time), carbon dioxide capture and storage and discussing the quality specifications for hydrogen and carbon dioxide considering the potential use of hydrogen in the transport sector (fuel cells) and for carbon dioxide storage in geological formation or using for Enhanced Oil Recovery (EOR). Keywords: Gasification, Coal and Biomass, Carbon Capture and Storage

1. Introduction The introduction of hydrogen in the energy system as an energy carrier complementary to electricity and other conventional fuels (e.g. natural gas) is exciting much interest, as this offers significant advantages including reduction of greenhouse gas emissions at the point of end use, enhancement of the security of energy supply and improvement of economic competitiveness.

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Hydrogen can be produced from different feedstocks, such as natural gas, oil derived products, coal and water [1]. Usually it is used in the chemical and petrochemical sectors but in the future there is hope than it can be largely used in transport sector (e.g. Proton Exchange Membrane – PEM fuel cells). It is known that solid fossil fuels reserves (mainly coal and lignite) give a much bigger energy independence compared with liquid and gaseous fossil fuels [2] but coal utilization is regarded with concern because of bigger greenhouse gas emissions associated with it. Also, utilization of biomass (e.g. sawdust, agricultural waste) and other different solid wastes (e.g. municipal waste, sewage sludge etc.) in energy conversion processes is become more and more significant. In this context, European Commission has set as a target for the whole community block that until 2020, 20 % from the energy mix should be covered by renewable energy sources [3]. In the future, solid fuel gasification is likely to play a key role in large-scale hydrogen and electricity production [4]. These processes will be based on entrained flow gasification as this type of gasifier maximizes hydrogen production and facilitates the capture of carbon as CO2, whereby it can be stored in geological reservoirs or used for enhanced oil recovery (EOR) [5]. Gasification is a technology in which the solid feedstock is partially oxidized with oxygen and steam (or water depending on the technology to be used) to produce syngas. Syngas (mainly a mixture of hydrogen and carbon monoxide) can be used for chemical conversion into different valuable compounds (e.g. methanol, ammonia, liquid fuels) or to generate power in a Combined Cycle Gas Turbine (GGCT). Integrated Gasification Combined Cycle (IGCC) is one of the power generation technologies having the highest potential to capture CO2 with low penalties in efficiency and cost [6]. In a modified IGCC design for carbon capture, syngas is catalytically shifted to maximize the hydrogen level in the syngas and to concentrate the carbon species in the form of CO2 that can be later capture in a pre-combustion arrangement. After CO2 and H2S capture in a double stage Acid Gas Removal (AGR) system, the hydrogen-rich syngas is used in a CCGT for power generation of for production of purified hydrogen (using a Pressure Swing Adsorption unit) which can be used in (petro)chemical industry or for transport sector in hydrogen-fuelled fuel cells. This paper investigates co-generation of hydrogen and electricity from gasification of coal and sawdust mixture with carbon capture and storage. The case studies investigated in the paper will produce a flexible ratio between power and hydrogen in the range of about 400 MW electricity and 0 – 200 MW hydrogen (considering hydrogen lower heating value - LHV) with 90 % carbon capture rate.

2. Plant configuration and design assumptions A conventional Integrated Gasification Combined Cycle (IGCC) uses the syngas resulted from the solid fuel gasification (after removing the ash and hydrogen sulphide) for power production by burning in a gas turbine. The flue gases coming from the gas turbine are used to raise steam (in Heat Recovery Steam Generator - HRSG) which by expansion in a steam turbine generates extra electricity in addition to the one generate by the gas turbine. Compared with the conventional IGCC design which is designed for power production, modification of the design for poly-generation of various energy vectors as well as introduction of carbon capture stage by pre-combustion capture involves some changes in the plant configuration. The conceptual layout of a modified IGCC scheme

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for poly-generation of different energy vectors (electricity, hydrogen and heat) with simultaneous carbon capture is presented in Figure 1 [7-10]. Coal & Biomass +Transport gas (N2)

Air Air Separation Unit (ASU) & O2 Compression

Water

O2 Gasification

Steam

Syngas Quench & Cooling

Slag

O2

N2

Water – Gas Shift

Sulphur

Claus Plant & Tail gas Treatment

Acid Gas Removal (AGR)

CO2

Pressure Swing Adsorption (PSA) Combined Cycle Gas Turbine

Heat (steam)

Power

H2 compression

Purified hydrogen

Figure 1. Layout of IGCC scheme for poly-generation of power, hydrogen and heat with carbon capture

For the case studies analyzed in this paper, a mixture of coal and sawdust in the ratio or 80 to 20 (wt.) was considered as feedstock, considering the wide distribution of this biomass sort in Romania, mainly coming from wood industry [11]. The characteristics of both fuels are presented in Table 1. Table 1. Feedstock (coal and sawdust) characteristics Parameter

Coal

Sawdust

Proximate analysis (% wt) Moisture Volatile matter Ash

8.10 28.51 14.19 Ultimate analysis (% wt dry) Carbon 72.04 Hydrogen 4.08 Nitrogen 1.67 Oxygen 7.36 Sulphur 0.65 Chlorine 0.01 Ash 14.19 Lower heating value - LHV (MJ/kg a.r.) 25.353

10.00 80.05 0.98 49.20 5.99 0.82 42.98 0.03 0.00 0.98 16.057

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As gasification reactor considered in the paper, the option was in favour of entrained flow type operating at high temperature (slagging conditions) which give a high conversion of solid fuel (~99 %). From different commercial gasification technologies available on the market, Siemens technology (formerly known Future Energy) was chosen, the main factors for consideration were the dry feed design and water quench which ensure the optimal condition for shift conversion (pre-condition for capturing the carbon dioxide) [10]. Other main sub-systems of the plant for poly-generation of various energy vectors and theirs design assumptions used in the mathematical modelling and simulation are presented in Table 2 [5,7-9]. Table 2. Main design assumptions Unit Air separation unit (ASU)

Gasifier (Siemens)

Shift conversion (WGS)

Acid gas removal (AGR)

CO2 compression and drying

Claus plant & tail gas treatment

Pressure Swing Adsorption (PSA)

Gas turbine

Heat recovery steam generation (HRSG) and steam cycle

Heat exchangers

Parameters Oxygen purity: 95 % (vol.) Delivery pressure: 2.37 bar Power consumption: 225 kWh/ton O2 Pressure: 40 bar Pressure drop: 1.5 bar Temperature: >1400oC Water quench Sulphur tolerant catalyst Two adiabatic beds Pressure drop: 1 bar / bed Solvent: Selexol® Separate capture of CO2 and H2S Solvent regeneration: pressure flash Delivery pressure: 100 bar Compressor efficiency: 85 % Solvent used for drying: TEG (Tri-ethylene-glycol) Oxygen-blown H2S-rich gas composition: > 20 % (vol.) Tail gas recycled to H2S absorption stage Purified hydrogen: > 99.95 % (vol.) Purification yield: 85 % Tail gas pressure: 1.5 bar (recycled to the power island) Gas turbine type: M701G2 (Mitsubishi Heavy Industries) Net power output: 334 MW Electrical efficiency: 39.5 % Pressure ratio: 21 Turbine outlet temperature (TOT): 588oC Three pressure levels: 118 bar / 34 bar / 3 bar Reheat of MP steam Steam turbine isoentropic efficiency: 85 % Steam wetness ex. steam turbine: max. 10 % ΔTmin. = 10oC Pressure drop: 1 % of inlet pressure

The two gas products of the plant (hydrogen and captured carbon dioxide) have to comply with certain quality specification considering the use of these streams. Hydrogen produced by the plant is intended to be used in PEM fuel cells (for transport sector) which imply very strict quality specification (> 99.95 % H2 and virtually no CO and H2S) due to the possibility of poisoning. Regarding CO2, considering that this stream will be transported to the storage sites (EOR or aquifers) via pipeline network, it will have to have very low concentration of water (<500 ppm) and hydrogen sulphide (<100 ppm) as these components could give corrosion problems along the pipeline network.

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3. Simulation of energy conversion scheme and discussions The energy conversion process presented in Figure 1 was modeled and simulated using ChemCAD. The case study was simulated in different situation (only electricity or various modes of hydrogen and electricity co-production). Table 3 presents the overall plant performance indicators. For electricity only mode, the gas turbine (GT) is running full load and for co-production modes on part load operation. Table 3.Overall plant performance indicators Main Plant Data Coal & biomass flowrate (a.r.) Coal / Biomass LHV (a.r.) Feedstock thermal energy – LHV (A)

Units t/h MJ/kg MWth

Power

Power + hydrogen 180455 25.353 / 16.057 1177.68

Thermal energy of the syngas (B) Cold gas efficiency (B/A * 100) Thermal energy of syngas exit AGR (C) Syngas treatment efficiency (C/B *100)

MWth % MWth %

Gas turbine output (1 x M701G2) Steam turbine output (1 ST) Expander power output Gross electric power output (D) Hydrogen output – LHV (E)

MWe MWe MWe MWe MWth

334.00 200.14 0.78 534.92 0.00

312.59 190.78 0.72 504.09 50.00

292.57 181.51 0.67 474.75 100.00

286.93 172.10 0.61 459.64 150.00

ASU consumption + O2 compression Gasification island power consumption AGR + CO2 drying & compression H2 compression Power island power consumption Total ancillary power consumption (F)

MWe MWe MWe MWe MWe MWe

45.13 8.27 40.54 0.00 19.05 112.99

45.13 8.27 40.54 0.66 18.37 112.97

45.13 8.27 40.54 1.33 17.72 112.99

45.13 8.27 40.54 2.01 17.02 112.97

Net electric power output (G = D - F) Gross electrical efficiency (D/A * 100) Net electrical efficiency (G/A * 100) Hydrogen efficiency (E/A * 100) Cumulative efficiency (G+E/A * 100) Carbon capture rate CO2 specific emissions

MWe % % % % % kg/MWh

421.93 45.42 35.82 0.00 35.82 92.83 71.19

391.12 43.05 33.21 4.24 37.45 92.83 76.61

361.76 40.31 30.72 8.49 39.21 92.83 82.61

346.67 39.02 29.43 12.73 42.16 92.83 85.98

934.26 79.33 831.95 89.05

As can be noticed from the Table 3, for power only case, overall plant efficiency is decreased with about 7 – 8 % compared with a conventional IGCC scheme without carbon capture [6,8]. This efficiency decrease is the penalty of capturing the carbon dioxide and can be noticed compared the specific CO2 emission figure compared with about 700-800 kg/MWh without capture [6]. It worth to be mentioned the fact that, although, the carbon capture rate of the plant is about 90 %, the overall capture rate is higher considering also that the biomass (sawdust) used in addition to coal can be considered CO2 free (green CO2) since the wood „captured” the CO2 from the air during the normal photosynthesis process (no new CO2 in the ecosystem). The carbon flow coming from the sawdust is about 14 % (the rest coming from coal) which come to the conclusion that the plant concepts evaluated in the paper can be considered as zero emission power plant (ZEPP concept). Another fact that has to be mentioned is that for co-production mode, the overall efficiency of the plant is increasing in the situation in which the ancillary power consumption is remaining virtually constant (see Table 3). This fact is very important and attractive for plant cycling (modification of the power generated by the plant according to the demand of the national grid) considering that for low electricity

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demand the plant can produce mostly hydrogen which compared with power can be stored to be used either for covering the peak loads or for other applications (transport sector, petro-chemical sector etc.). It is worth mention the fact that the plant concept can also be used in combined heat and power (CHP) mode by simply use subtracting steam from Rankine cycle. Also, the syngas can be used for production of other energy vectors (e.g. methanol, substitute natural gas, liquids fuels by Fischer-Tropsch synthesis etc.).

4. Conclusions This paper analyze from technical point of view an innovative energy conversion process based on gasification of solid fuels (mixture of coal and sawdust) for poly-generation of different decarbonised energy vectors (power, hydrogen, heat etc.) with simultaneous carbon capture and storage (CCS). Modeling and simulation techniques were used to quantify the energy penalty of capturing carbon capture and to evaluate the main overall performance indicators among the different operation modes (power only or hydrogen and power co-generation).

5. Acknowledgements This work has been supported by Romanian National University Research Council through grant no. 2455: “Innovative systems for poly-generation of energy vectors with carbon dioxide capture and storage based on co-gasification processes of coal and renewable energy sources (biomass) or solid waste”.

References [1] F. Müller-Langer, E. Tzimas, M. Kaltschmidtt, S. Peteves, Techno-economic assessment of hydrogen production processes for the hydrogen economy for the short and medium term, Int J Hydrogen Energy 2007; 32:3797-810. [2] Statistical Review of World Energy BP 2008, www.bp.com. [3] European Commission, DG Energy and Transport (DG TREN), 2009, http://ec.europa.eu/energy. [4] European Hydrogen and Fuel Cell Technology Platform. Hydrogen Energy and Fuel Cells – A vision for our future. Report EUR 20719, https://www.hfpeurope.org/ ; 2005. [5] C. Cormos, F. Starr, E. Tzimas, S. Peteves, Brown A., Gasifier concepts for hydrogen and electricity co-production with CO2 capture, Third International Conference on Clean Coal Technologies, Cagliari, Sardinia, Italy, 2007. [6] E. Tzimas, A. Mercier, C. Cormos, S. Peteves, Trade-off in emissions of acid gas pollutants and of carbon dioxide in fossil fuels power plants with carbon capture, Energy Policy, 35, 2007, 3991 – 3998. [7] P. Chiesa, S. Consonni, T. Kreutz, R. Williams, Co-production of hydrogen, electricity and CO2 from coal with commercially ready technology. Part A: Performance and emissions, Int J Hydrogen Energy 2005;30: 747 – 67. [8] International Energy Agency (IEA) – Greenhouse Gas Programe (GHG), Potential for improvement in gasification combined cycle power generation with CO2 capture, Report PH4/19, 2003. [9] C. Cormos, F. Starr, E. Tzimas, S. Peteves, Innovative concepts for hydrogen production processes based on coal gasification with CO2 capture, Int J Hydrogen Energy 2008; 33: 1286 - 1294. [10] C. Higman, M. Van Der Burgt, Gasification, Elsevier Science, Second edition, 2008. [11] I. Habil, The potential of biomass in Romania, Integrated European Network for Biomass Co-firing, NETBIOCOF, 2006.

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Using Process Integration for Steam System Network Optimization with Sustained Boiler Efficiency T. Pricea and T. Majozi a,b a

Department of Chemical Engineering, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa, [email protected] b Department of Computer Science, University of Pannonia, Veszprém, Hungary.

Abstract The traditional steam system comprises of a steam boiler and the associated heat exchanger network (HEN). Most research published in literature tends to address both the elements of the steam system as separate entities instead of analyzing, synthesizing and optimizing the overall system in a holistic manner. This paper presents a process integration technique using conceptual and mathematical analysis without compromising boiler efficiency. It was found that the steam flowrate could be reduced whilst maintaining boiler efficiency by utilizing sensible heat from the high pressure steam leaving the boiler. In the event of too little sensible energy being available a compromise in either minimum steam flowrate or boiler efficiency must be made. Keywords: steam system, heat exchanger network, boiler efficiency

1. Introduction Pinch analysis has found numerous applications in a wide range of process integration areas, most specifically mass and heat integration. In heat integration, pinch analysis has the ultimate goal of reducing external utilities by maximizing process to process heat exchange but can also be used in the optimal placement of utilities (Linnhoff and Hindmarsh, 1983). The work on steam network synthesis by Coetzee and Majozi (2008) encompasses finding a minimum steam flowrate for the steam system and designing the corresponding HEN. The authors presented two methods, the first involved a graphical targeting technique as well as a mathematical LP model for the network design. The second method constituted an MILP model that targeting minimum flowrate and designing the network simultaneously. However, the effects of minimising the steam flowrate on the entire steam system have not been considered. The efficient operation on the steam boiler is dependent on the condensate return flowrate and temperature. Reducing the steam flowrate affects both of these areas. The advantages of reducing the steam flowrate in steam systems include decreased water consumption in retrofit operations and a smaller boiler for the grassroot design of plants.

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2. Problem Statement The problem addressed in this investigation can be formally stated as follows. Given: a steam boiler with known efficiency, a set of heat exchangers directly connected to the boiler with limiting temperatures and fixed duties, steam turbines with fixed power output and background heat exchangers directly connected to the steam turbine exhaust, determine the minimum steam flowrate and corresponding HEN while maintaining boiler efficiency. In the event that the minimum steam flowrate cannot be achieved without compromising the boiler efficiency two situations arise. Firstly the boiler efficiency is maintained whilst the minimum steam flowrate is compromised slightly or secondly the minimum steam flowrate is achieved at the expense of the boiler efficiency.

3. Paper Approach Figure 1(a) shows a typical steam system. Superheated high pressure steam is produced inside the steam boiler. A portion of this steam is sent to a high pressure steam turbine where energy is recovered in the form of shaft work. The rest of the steam from the boiler is sent directly to a process through a let down valve for pressure reduction and to remove the sensible heat. 3.1. Boiler Efficiency Equation (1) relates boiler efficiency, Șb, to the effects of changing steam load, capacity and operating conditions as would be encountered in a realistic situation (Shang and Kokossis, 2004).

ηb =

(c

p

ΔTsat

( [

)

q M M max + q ) (1 + b ) M M max + a

(

) ]

(1)

In Equation (1), q is the heat load of the steam (i.e. the latent and sensible heat), M is the steam load raised by the boiler which consists of the condensate return from all the steam using processes in the system and Mmax is the capacity of the boiler. The parameters a and b are taken from a study by British Gas in work done by Pattison and Sharma (1980). 3.2. Methodology The first part of the objective is to reduce the steam flowrate to the HEN. The model from Coetzee and Majozi (2008) forms the basis of the work presented in this study. The model comprises simple mass and energy balances based on a supersturcture found in the work by Coetzee and Majozi (2008).

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To calculate the boiler efficiency as defined in Equation (1) several variables are required. The outlet temperature of the process must be known and can be calculated by Equation (2). The return flowrate to the boiler form any heat exchanger i is represented by the two terms, FRSi and FRLi, the first being saturated condensate and the other subcooled condensate form the process. The total mass flow to the boiler, TS and Mturb, must be considered by Equation (3), where the temperature before preheating, Tpump, is also calculated. Using these variables the total return temperature to the boiler, Tboil can then be calculated with Equation (4). Then the efficiency can be calculated using Equation (5).

Ws

Ws Let Down Valve

Preheater

Ws

Ws

Process 1

MILP Network Layout

Preheater (Candidate for steam reduction)

Process 2

Process 2

Preheater using HP sensible heat

Process 3

Process 3

Condenser to Prevent Pump Cavitation

(a)

(b)

Figure 1: Steam system layouts.

¦ FRS Tsat + ¦ FRL Tout i

T proc =

i

i∈I

L i

i∈I

(2)

TS

In Equation (2), Tproc is the process outlet temperature.

T pump =

(T

proc

TS ) + (Tturb M turb )

(3)

(TS + M turb )

In Equation (3), Tturb and Mturb are the turbine outlet temperature and mass flowrate respectively.

Tboil = T pump +

Q preheat

(4)

(TS + M turb )c p

In Equation (4), Qpreheat is the heat added by the preheater.

ηb =

(c (T p

(

sat

)

q (TS + M turb ) M max − Tboil ) + q ) (1 + b ) (TS + M turb ) M max + a

[

(

) ]

(5)

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Since the steam flowrate reduction causes a decrease in the return boiler temperature a means of reheating the boiler feed must be found. It is suggested that the boiler return condensate be heated by the sensible heat of the superheated steam from the boiler. In most instances this energy is lost during the pressure let down. Thus the energy can be reclaimed and used to maintain the boiler efficiency. Figure 1(b) shows a simple diagram of this alteration. The new boiler return condensate temperature is calculated using Equation (6):

Tboil = T pump +

TS (hsup − hsat )θ

(TS + M turb )c p

(6)

In Equation (6), hsup is the enthalpy of the superheated steam leaving the boiler, hsat is the enthalpy of saturated steam at the boiler outlet conditions and ș is the fraction of this energy that can be used safely without the risk of condensation. Equations (2) to (6) can be used to create a second part to the mathematical model, the first part being the formulation by Coetzee and Majozi, (2008). Two cases can be considered, each focusing on different objectives. 3.2.1. Case 1:Maintain boiler efficiency with slight compromise in minimum flowrate Firstly the primary objective can be to maintain boiler efficiency. This may mean that the minimum steam flowrate may not be reached if there is not enough sensible heat available. The method of Coetzee and Majozi, (2008) is first used to find the minimum steam flowrate. The boiler efficiency is then fixed while the deviation from the minimum steam flowrate is minimised. 3.2.2. Case 2:Maintain minimum flowrate with slight compromise in boiler efficiency Secondly the minimum flowrate must be achieved with the smallest possible decrease in boiler efficiency. The method of Coetzee and Majozi, (2008) is once again used to find the minimum steam flowrate. With this value fixed the deviation in boiler efficiency is then minimised. 3.3. Case Study The case study presented by Coetzee and Majozi, (2008) is used here to show how boiler efficiency is affected by a reduction in steam flowrate and how the formulations above can be used to maintain the original efficiency. Using Equation (5) the boiler efficiency was calculated as 0.6349. The HEN was a parrallel configuration. After steam reduction the steam flowrate was reduced from 10.90kg/s to 7.69kg/s. Figure 2(a) shows the network layout using this flowrate. This reduction in flowrate and consequently outlet temperature corresponds to a new boiler efficiency of 0.5991, a 5.6% reduction.

Using Process Integration for Steam System Network Optimization with Sustained Boiler Efficiency

Saturated Steam

Saturated Condensate

1285

Sub-Cooled Condensate

1

1

6

2

2

3

7

4

3

4

Sub-cooled Condensate Return to Boiler

4 2

5 4

7

5 Saturated Condensate Return to Boiler

(a)

(b)

Figure 2: Network layouts obtained using the formulation.

Using the first premise it was found that the boiler efficiency could be sustained without compromising the steam flowrate by using 79.2% of the available sensible heat. With the reduction in steam flowrate, the return temperature had to be increased from 113°C to 117.7°C. Given that the steam flowrate was not changed the heat HEN remains as Figure 2(a). Both formulations gave the same result since there was enough sensible energy available. If the amount of sensible energy was reduced the models may show how they compromise either efficiency or flowrate. For this purpose the amount of sensible heat available was reduced to 30% of the original available amount. To maintain boiler efficiency the minimum steam flowrate was indeed compromised. The solution resulted in a flowrate of 8.32kg/s, which still yielded a 23.7% reduction from the original, parallel HEN. This new flowrate did require a new HEN to shown in Figure 2(b). Using the second objective the new boiler efficiency was calculated as 0.6130, a decrease of 3.5%. The network required for this flowrate is the same as that of Figure 1(a), since there is no change in flowrate.

4. Conclusions The following conclusions can be made about reducing steam flowrate while maintaining boiler efficiency: Preheating the return flow to the boiler can maintain efficiency for a reduced steam flowrate. In the event of there not being enough sensible heat available a compromise in either the boiler efficiency or the minimum flowrate must be made.

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References [1] Coetzee, W.A. and Majozi, T. (2008) Steam System Network Design Using Process Integration, Ind. Eng. Chem. Res 2008, 47, 4405-4413. [2] Shang, Z. and Kokossis, A. (2004), A transshipment model for the optimisation of steam levels of total site utility system for multiperiod operation, Computers and Chemical Engineering 28, pages 1673-1688. [3] Linnhoff, B. and Hindmarsh, E. (1983) The pinch design method for heat exchanger networks, Chemical Engineering Science 38, No. 5, pages 745-763. [4] Pattison, J. R. and Sharma, V. (1980) Selection of boiler plant and overall system efficiency. Studies in energy efficieny in buildings, British Gas.

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Flexible Separative Reactors for Biodiesel Production Anton A. Kiss AkzoNobel Research, Development & Innovation, Process & Product Technology, Arnhem, The Netherlands, [email protected]

Abstract This study proposes an integrated biodiesel production via a two-step process that combines the advantages of using solid acid and base catalysts with the integration of reaction and separation. Such an integrated separative reactor is flexible to treat any range of free fatty acids present in the fatty raw material. Computer aided process engineering tools such as AspenONE are used for process design and simulation of a plant producing 10 ktpy biodiesel from animal fat and bio-ethanol. Keywords: reactive distillation, green catalysts, solid acid / base, biofuels

1. Introduction The recent steep increase in fossil fuel prices associated with governmental restrictions on discharge of green-house gasses shifted the worldwide trend to focus on renewable energy sources. Biodiesel is a very popular renewable fuel, currently produced from vegetable oils, animal fat or even recycled waste cooking-oil from the food industry.1,2 Due to its properties similar to petrodiesel, biodiesel can be used in pure form, or may be blended with petroleum diesel at any concentration, in most modern diesel engines. Biodiesel is a mixture of fatty esters, currently produced by (trans-)esterification of triglycerides and free fatty acids, followed by several neutralization and purification steps. However, all the traditional methods suffer from drawbacks related to the use of liquid acid/base catalysts, heading to major economical and environmental penalties, especially considering the recent boost of the international biodiesel production rate. Worldwide, the production of biodiesel increased tremendously during the past 10 years, mostly in Asia, US, and Western Europe with Germany, France, Austria, Spain and UK among top consumers (Figure 1). This work proposes a novel two-step biodiesel production process bases on reactiveseparation using solid acid/base catalysts, thus simplifying the overall process and bringing significant benefits: high conversion and selectivity, elimination of conventional catalyst-related operations, no waste streams, as well as reduced capital investment and operating costs. The process design of the 10 ktpy fatty acid ethyl esters plant described here is based on experimental results, integrated in rigorous simulations performed using AspenTech AspenONE as computer aided process engineering tool.

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Figure 1. Biodiesel production per region (left), and biodiesel consumption in EU (right).

2. Problem statement All conventional biodiesel production methods have associated optimal operating parameters and downstream processing steps, although much of the available literature emphasizes the base catalyzed route.1-3 Traditional biodiesel processes employ liquid catalysts, such as H2SO4 or KOH.3 The problem is that such catalysts demand neutralization, separation, washing, recovery, and salt waste disposal operations with serious economical and environmental consequences. Nowadays, the surplus of waste oil available at industrial scale would allow production of very cheap biodiesel – a key benefit in the energy market. For example, in Brazil alone, more than 350 millions litres of biofuel are produced annually from animal fat. The problem with the animal fat or waste-oil, is that it becomes useless within 24 hours since it turns so acidic due to the increased free fatty acids (FFA) content, that it is more appropriate for making soap than for biodiesel. To solve these problems, we propose a sustainable two-step process based on the esterification of FFA’s in a separative reactor using solid acids,4,5 followed by trans-esterification of the remaining tri-glycerides (TG) using conventional or solid base catalysts. 1: R-COOH + EtOH ↔ R-COO-Et + H2O (esterification) 2: TG + 3 EtOH ↔ 3 RCOO-Et + Gly

(trans-esterification)

The integrated reactive distillation equipment proposed in this work is able to shift the chemical equilibrium and drive the esterification reaction to completion by continuously removing the fatty esters products and water by-product.6,7 The raw materials consist of waste-oil or animal fat – mainly a mixture of free fatty acids – and a light alcohol, such as methanol or (bio-)ethanol. A key feature of this work is the replacement of anhydrous ethanol by its hydrous azeotrope, thus leading to further reduction of production costs. Table 1 presents an overview of the available solid acid and base catalysts for biodiesel production by (trans-)esterification.4-6 In this work we selected the metal oxides as solid acid catalysts for FFA esterification (first step) and calcium ethoxide as solid base catalyst for the trans-esterification of the remaining tri-glycerides (second step).

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Table 1. Advantages and disadvantages of the acid/base catalysts tested for (trans-)esterification.

Catalyst type Ion-exchange resins (Nafion, Amberlyst) TPA (H3PW12O40) TPA-Cs (Cs2.5H0.5PW12O40) Zeolites (H-ZSM-5, Y and Beta) Sulfated metal oxides (zirconia, titania, tin oxide) Niobic oxide (Nb2O5) Calcium oxide / CaO Calcium methoxide / Ca(OMe)2 Calcium ethoxide / Ca(OEt)2 Li-dopped zinc oxide / ZnO KF loaded on Eu2O3

Benefits Very high activity Easy regeneration Very high activity Super acid sites Controlable acidity and hydrophobicity High activity Thermally stable Water tolerant Low temperatures High yield, reusable High yield, short times Low temperatures Short reaction times

Drawbacks Low thermal stability Possible leeching Soluble in water Low activity per weight Small pore size Low activity Deactivates in water, but not in organic phase Average activity Long reaction times High reactants ratio High reactants ratio Long reaction times Incomplete yields

3. Simulation methods The simulation methods available are given in Table 2. Each method has important benefits but also certain drawbacks and the requirements can differ significantly. The amount of data required by the rigorous method is practically not feasible in practice while the shortcut method leads to low-fidelity models only, with limited applications. For practical reasons, the hybrid approach gives the best results. In this work the experimentally determined kinetic parameters were used 5,6 but the fatty components were lumped into one fatty acid/ester compound, according to the reaction: R-COOH + EtOH ↔ R-COO-Et + H2O

Drawbacks

Benefits

Requirements

Table 2. Simulation methods for biodiesel production: requirements, benefits and drawbacks.

Rigorous method

Shortcut method

Hybrid method

Properties for all species. VLL data and BIP’s for all pairs of components. Kinetic parameters for all reactions possible.

Properties for single fatty acid/ester/tri-glyceride. VLL data for the system ester/glycerol/alcohol. Asumed conversion (no kinetic parameters). Simple model. Fast simulations. Easy-to-build mass and energy balance. No data needed for all species present. No comparison possible for various feedstocks. Low-fidelity model. Less ability to use RTO.

Single or reduced list of fatty acid/ester/TG. Short list of VLL data and BIP’s for components. Reduced list of kinetic parameters, few reactions. Optimization possible for reaction and separation. Certain ability to compare various feedstocks. Better model fidelity. Fast simulations for RTO. More effort to build component list and get kinetic parameters. More work to find VLL data and regress BIP’s.

Easy optimization of reaction and separation. High fidelity model. Usable for many plants. Easy comparison for various feedstocks. Slow simulations and convergence problems. Expensive measurements. Limited RTO and model based control usage.

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4. Results and discussion The properties of the fatty components were determined experimentally, or estimated using state-of-the-art contribution methods such as UNIFAC – Dortmund modified.5-9 Figure 2 (left) shows the residue curve map (RCM) for the ethanol-water-glycerol ternary mixture. The presence of the ethanol-water azeotrope does not hinder the biodiesel production process, since ethanol is a reactant and not a high purity product. Moreover, as water by-product from the esterification reaction further dilutes the ethanol, its hydrous azeotrope can be used directly as a lower-cost feedstock. Vapor pressure is perhaps one of the most important properties with a critical effect in modeling reactive separations. Figure 2 (right) shows the vapor pressure of most common fatty acids and esters. At ambient pressure the boiling points are relatively high, exceeding 300 °C. Although high purity products are possible by reactive distillation, the high temperature in the reboiler – caused by the high boiling points, is in conflict with the thermo-stability of the biodiesel product. However, this problem can be avoided by working at lower pressure or by allowing ethanol in the bottom product. Figure 3 presents the flowsheet of a two-step biodiesel production process based on a reactive distillation column (RDC) as the key unit for esterification or pre-treatment of free fatty acids (FFA). The process proposed here was rigorously simulated and optimized using AspenTech AspenONE. The production rate considered for the plant designed in this work is 10 ktpy fatty acid ethyl esters (FAEE). Note that the kinetic parameters used in the simulation were previosly reported in the open literature.5,6 The RDC is operated in the temperature range of 100–250 °C, at ambient pressure. Out of the 15 stages of the integrated unit, the reactive zone is located in the middle of the column (10 stages). The fatty acid is pre-heated then fed as hot liquid on top of the reactive zone while a stoichiometric amount of alcohol introduced in the bottom of the reactive zone, thus creating a counter-current V-L flow regime over the middle reactive section. The reflux ratio is very low (RR=0.1) as returning water to the column is detrimental to the chemical equilibrium. Water by-product is removed in top, then separated in a decanter from which only the fatty acids are recycled to the column while water is recovered at high purity and hence reusable as industrial water on the same site. 10

Residue Curve Map: ethanol-water-glycerol

Vapor pressure / bar

Mole fraction ethanol

1

0.8

0.6

0.4

1

0.1

E-LAURIC E-MYRISTIC E-PALMITIC E-STEARIC E-OLEIC E-LINOLEIC E-LINOLENIC TG-LAURIC TG-MYRISTIC TG-PALMITIC TG-STEARIC TG-OLEIC TG-LINOLEIC TG-LINOLENIC

Fatty esters

Tri-glicerides

0.01

0.2

0 0

0.2

0.4

0.6

Mole fraction water

0.8

1

0.001 100

200

300 Temperature / C

400

500

Figure 2. RCM ethanol-water-glycerol (left), Vapor pressure of fatty esters vs temperature (right).

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Figure 3. Flowsheet of biodiesel production by catalytic reactive distillation.

The fatty esters are delivered as high-purity bottom product of the RDC. The hot product is flashed first to remove the traces of ethanol, then it is send to the transesterification reactor to further convert the remaining tri-glycerides to fatty esters. In this work we considered the worst case scenario, with 100% FFA in the feedstock. The mass and energy balance is given in Table 3. High purity products are possible, the purity specifications exceeding 99.9%wt for the final biodiesel product (FAEE stream). Note that the total amount of the recycle streams (REC-ACID and REC-ALCO) is not significant, representing only ~0.5% of the total biodiesel production rate. Figure 4 (left) shows the liquid composition profiles in the reactive distillation column. The concentration of fatty acids decreases while the concentration of fatty esters increases from the top to bottom. Similarly, the ethanol concentration decreases while water concentration increases from bottom to top. The temperature and reaction rate profiles in the RDC are presented in Figure 4 (right). As expected, the reaction rate exhibits a maximum in the middle of the column, in the reactive zone. Moreover, the concentration of water is low in the reactive zone, hence the catalyst activity is not affected. Nevertheless, the concentration of reactants is relatively high and the temperature is sufficiently high to allow high reaction rates and complete conversion. Table 3. Mass and energy balance of a 10 ktpa biodiesel production process, based on RD. F-ACID Temperature K Pressure atm Vapor Frac Mass Flow kg/hr Volume Flow l/min Enthalpy Gcal/hr Mass Flow kg/hr ETHANOL ACID WATER ESTER-E Mass Frac ETHANOL ACID WATER ESTER-E

F-ALCO

BTM

TOP REC-ACID

REC-ALCO

FAEE

WATER

372.6 1 0 7.312 0.154 -0.006

303.1 1 0 1250 23.774 -1.035

303.1 1 0 109.094 1.839 -0.413 0 0.008 109.086 0

418.1 1.036 0 1094.918 22.986 -0.892

352.2 507.9 1.036 1.017 0 0 264.202 1257.312 6.156 28.953 -0.394 -0.886

372.7 0.987 0 109.246 1.983 -0.405

303.1 1 0 0.152 0.003 0

0 1094.918 0 0

253.568 2.622 0 0 10.635 0.029 0 1254.661

0 0.115 109.089 0.043

0 0.107 0.003 0.042

0.857 1.765 0 0 0.013 0.016 6.442 1248.219

0 0.001 0.999 0

0 0.702 0.02 0.278

0.117 0 0.002 0.881

0 1 0 0

0.96 0 0.04 0

0.002 0 0 0.998

0.001 0 0 0.999

0 0 1 0

A.A. Kiss

1292 Molar fraction 0

0.2

0.4

0.6

Temperature / °C 0.8

1

0

0

50

100

150

200

250

0

3

Temperature

3

Water Acid

6

6

Stage

Reaction rate

9

9

12

Alcohol

12

Ester

15

15 0

0.2

0.4

0.6

Molar fraction

0.8

1

0

1 2 3 4 Reaction rate / kmol/hr

5

Figure 4. Profiles in RDC: liquid composition (left), temperature and reaction rate (right).

5. Conclusions An innovative two-step biodiesel process based on separative reactors using solid catalysts was developed in this study using computer aided engineering tools such as AspenTech AspenONE. The novel two-step process proposed here improves considerably the biodiesel production and reduces drastically the number of downstream processing steps. The major benefits of this sustainable process are: • Flexible integrated reactor suitable for a large range of fatty raw material with up to 100% FFA content, such as: frying oils, animal tallow, tall oil, waste vegetable oil. • Straightforward and robust process with no soap formation, no catalyst-related waste streams, and sulfur-free biodiesel as solid acids do not leach into the product. • Effective use of the integrated reactor volume leading to high unit productivity. • Efficient use of the raw materials: complete conversion and high selectivity, stoichiometric reactants ratio, FFA conversion to esters and not to soap waste. • Reduced equipment costs, with up to ~40% savings on the total investment costs. • Competitive operating costs due to the integrated design and the elimination of conventional steps: handling of homogeneous catalyst and corrosive solutions, separation and disposal of salts, waste water treatment, excess alcohol recovery.

References [1] [2] [3] [4] [5] [6] [7] [8] [9]

M. Balat, H. Balata, 2008, Energy Conversion and Management, 49, 2727. M.G. Kulkarni, A. K. Dalai, 2006, Industrial & Engineering Chemistry Research, 45, 2901. K. Narasimharao, A. Lee, K. Wilson, 2007, J. Biobased Materials & Bioenergy, 1, 19. T. Okuhara, 2002, Chemical Reviews, 102, 3641. A. A. Kiss, A. C. Dimian, G. Rothenberg, 2006, Advanced Synthesis & Catalysis, 348, 75. A. A. Kiss, G. Rothenberg, A. C. Dimian, F. Omota, 2006, Topics in Catalysis, 40, 141. A. A. Kiss, A. C. Dimian, G. Rothenberg, 2008, Energy & Fuels, 22, 598. S. Steinigeweg, J. Gmehling, 2003, Ind. Eng. Chem. Res., 42, 3612. A. C. Dimian, F. Omota, A. Bliek, 2004, Chem. Eng. & Proc., 43, 411.

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Graph-theoretic approach to the catalytic-pathway identification of methanol decomposition Yu-Chuan Lin,a L.T. Fan,a, Shahram Shafie,a Botond Bertók,b Ferec Friedlerb Department of Chemical Engineering, Kansas State University, KS, USA, 66506-5102, a [email protected] Department of Computer Science, University of Pannonia, Veszprem, Egyetem u. 10, b H-8200, Hungary

Abstract Catalytic partial oxidation of methanol (MD) plays a key role in hydrogen production, which is the desirable fuel for both proton exchange membrane and direct methanol fuel cell systems. Thus, the catalytic mechanisms, or pathways, of MD have lately been the focus of intense research interest. Recently, the feasible independent pathways (IPi’s) have been reported on the basis of a set of highly plausible elementary reactions. Nevertheless, no feasible acyclic combined pathways (APi’s) comprising IPi’s have been reported. Such APi’s can not be ignored in identifying dominant pathways.

Keywords: methanol decomposition, graph-theory, reaction pathways, independent pathways, acyclic combined pathways 1. Introduction The graph-theoretic approach resorting to various formal graphs is increasingly being deployed in identifying and representing catalytic or metabolic pathways because of its distinctive efficacy [1-7]. The current contribution represents the latest effort towards such a trend. P-graphs (process graphs) [4, 5, 8-12] have been extensively adopted in exploring the mechanisms of catalytic [7] as well as metabolic reactions [6, 13]. Redundancy can be largely circumvented prior to the follow-up investigation, e.g., the derivation of mechanistic rate equations [7], by determining only the feasible networks of elementary reactions algorithmically and rigorously. It is worth noting that the efficacy of the graph-theoretic method based on P-graphs has been increasing recognized through its wide-ranging applications [14-16]. Fishtik and his collaborators have identified via their reaction-route (RR) graph approach [17-21] the independent pathways for water-gas shift [22, 23] and methanol decomposition (MD) [24]. Nevertheless, revisiting the identical example [23] with our graph-theoretic method based on P-graphs [25] has indicated that their approach or results might not be totally valid. Moreover, the RR graph approach apparently lacks the capability to identify acyclic combined pathways that are no less essential than some of the independent pathways in determining the dominant or ultimate ones, as to be elaborated later. The current study explores the sets of both independent and acyclic combined pathways of MD by resorting to the graph-theoretic method based on P-graphs. This is followed

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by the identification of the dominant, or ultimate, pathway via Kirchhoff’s law of current (KLC) or Kirchhoff ’s law of potential (KPL).

2. Methodology The graph-theoretic method based on P-graphs is detailed elsewhere [4, 5]. The maximum structure corresponds to the super-structure containing exclusively all combinatorially feasible catalytic pathways, which are solution-structures. Stoichiometrically feasible pathways generated include independent pathways (IPi’s) and acyclic combined pathways (APi’s). Any APi is a stoichiometrically feasible combination of IPi’s, not containing a cycle; therefore, it is highly probable that such a pathway can potentially be dominant under some circumstances. Any pathway containing a cycle, i.e., cyclic pathway, is excluded in view of the principle of microscopic reversibility. A cyclic pathway is formed when two IPi’s giving rise to the identical overall reaction in opposite directions, and thus, it does not experience any free energy change [5, 26-29].

3. Results and discussion Table 1 lists 13 available elementary reactions for MD on Pt (1 1 1) [24, 30]. From these elementary reactions, the graph-theoretic method based on P-graphs has yielded stoichiometrically feasible IPi’s as well as APi’s in the current work. 3.1. Independent pathways Table 2 summarizes the six IPi’s identified; Figure 1 illustrates P-graphs of IP2 and IP3 among them. For clarity, the arcs of IP2 are drawn in solid line, and those of IP3, in dash lines. These six IPi’s are identical to those reported by Vilekar and his coworkers [24]. Table 2 also contains the overall resistances of the six IPi’s identified. They have been estimated by resorting to KLC and KLP based on the resistances of individual reaction routes from the literature [24]. Since the overall resistance of IP3 is the lowest among the six IPi’s, it can be regarded as the most dominant; this is in accord with what has been reported [24].

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Table 1. Elementary Reactions for Decomposition of Methanol on Pt (1 1 1) [24] s1 s2 s3 s4 s5 s6 s7 s8 s9 s 10 s 11 s 12 s 13

Elementary reactions CH3OH + Ɛ ↔ CH3OHƐ CH3OHƐ + Ɛ ↔ CH3OƐ + HƐ CH3OƐ + 2Ɛ ↔ CH2OƐ2 + HƐ CH2OƐ2 ↔ CHOƐ + HƐ CHOƐ + Ɛ ↔ COƐ + HƐ CH3OHƐ+ Ɛ ↔ CH2OHƐ + HƐ CH2OHƐ+ Ɛ ↔ CHOHƐ + HƐ CHOHƐ+ Ɛ ↔ COHƐ + HƐ COHƐ+ Ɛ ↔ COƐ + HƐ CHOHƐ + 2Ɛ ↔ COƐ+ 2HƐ CH2OHƐ+ 2Ɛ ↔ CH2OƐ2 + HƐ COƐ ↔ CO + Ɛ 2HƐ ↔ H2 + 2Ɛ

Table 2. Feasible Independent Pathways (IPi’s) for Decomposition of Methanol on Pt (1 1 1)

Designation (IPi) IP1 IP2 IP3 IP4 IP5 IP6

Pathway s1 + s2 + s3+ s4 + s5 + s12 + 2s13 s1 + s6 + s7 + s8 + s9 + s12 + 2s13 s1 + s6 + s7 + s10 + s12 + 2s13 s1 + s2 + s3 + s7 + s8 + s9 - s11 + s12 + 2s13 s1 + s2 + s3 + s7 + s10 - s11 + s12 + 2s13 s1 + s4 + s5 + s6 + s11 + s12 + 2s13

Estimated resistance (ȍ) 8126.03 44.61 13.71 15799.53 15768.59 12607.15

3.2. Acyclic combined pathways Table 3 lists all twenty-seven APi’s, including the six IPi’s, also identified via our graph-theoretic method [4, 5, 12]. None of the APi’s in Table 3 has been reported previously. It is worth noting that multiple reaction pathways, i.e., cyclic routes and APi’s, coexist under the catalytic environment [5, 27, 31]. Naturally, the crucial role that they might play in the reaction should not be totally neglected. Figure 1 also depicts one of the APi’s, i.e., AP10, comprising the two feasible independent pathways, IP2 and IP3. Note that any arcs of IP2 and IP3 linked in series overlap, which diverge and subsequently converge at two sets of common nodes for active species, thereby constituting two parallel paths, i.e., routes.

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Figure 1. Superimposed P-graph representation of feasible independent pathways IP2 and IP3 and acyclic combined pathway AP10, comprising the two independent pathways: The arcs of IP2 appear as solid lines, and those of IP3 appear as dashed lines.

The overall resistances of all the APi’s, also listed in Table 3, have been computed again by resorting to KLC and KLP (Appendix C). Note that among twenty one APi’s, the resistances of AP10 (12.93 ȍ), AP13 (13.70 ȍ), AP14 (12.92 ȍ), AP17 (12.62 ȍ), AP20 (13.69 ȍ), AP21 (12.91 ȍ), AP24 (12.93 ȍ), AP26 (13.69 ȍ), and AP27 (12.91 ȍ) are less than that of IP 3 (13.71 ȍ), which has been reported earlier as the dominant pathway [24]. Naturally, it is essential that all the APi’s be explored in identifying the dominant pathway; or pathways. Apparently, this can only be accomplished with the current graph-theoretic method based on P-graphs.

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Table 3. Feasible Acyclic Combined Pathways (APi’s) for Decomposition of Methanol. Pathway Estimated R. (ȍ) APi AP1 s1 + s2 + s3+ s4 + s5 + s12 + 2s13 8126.03 AP2 s1 + s2 + s3 + s7 + s8 + s9 - s11 + s12 + 2s13 15799.53 AP3 s1 + s2 + s3 + s7 + s10 - s11 + s12 + 2s13 15768.59 AP4 2s1 + 2s2 + 2s3 + 2s7 + s8 + s9 + s10 – 2s11 + 2s12 + 4s13 15767.81 AP5 2s1 + 2s2 + 2s3 + s4 + s5 + s7 + s8 + s9 - s11 + 2s12 + 4s13 18283.49 AP6 2s1 + 2s2 + 2s3 + s4 + s5 + s7 + s10 – s11 + 2s12 + 4s13 18250.09 AP7 3s1 + 3s2 + 3s3 + s4 + s5 + 2s7 + s8 + s9 + s10 – 2s11 + 3s12 + 6s13 18249.30 AP8 s1 + s6 + s7 + s8 + s9 + s12 + 2s13 44.61 AP9 s1 + s6 + s7 + s10 + s12 + 2s13 13.71 AP10 2s1 + 2s6 + 2s7 + s8 + s9 + s10 + 2s12 + 4s13 12.93 AP11 s1 + s4 + s5 + s6 + s11 + s12 + 2s13 12607.15 AP12 2s1 + s4 + s5 + 2s6 + s7 + s8 + s9 + s11 + 2s12 + 4s13 44.54 AP13 2s1 + s4 + s5 + 2s6 + s7 + s10 + s11 + 2s12 + 4s13 13.70 AP14 3s1 + s4 + s5 + 3s6 + 2s7 + s8 + s9 + s10 + s11+ 3s12 + 6s13 12.92 AP15 2s1 + s2 + s3 + s4 + s5 + s6 + s7 + s8 + s9+ 2s12 + 4s13 44.51 AP16 2s1 + s2 + s3 + s4 + s5 + s6 + s7 + s10+ 2s12 + 4s13 13.70 AP17 3s1 + s2 + s3 + s4 + s5 + 2s6 + 2s7 + s8 + s9 + s10 + 3s12 + 6s13 12.62 AP18 2s1 + s2 + s3 + 2s4 + 2s5 + s6 + s11 + 2s12 + 4s13 2489.15 AP19 3s1 + s2 + s3 + 2s4 + 2s5 + 2s6 + s7 + s8 + s9 + s11 + 3s12 + 6s13 44.26 AP20 3s1 + s2 + s3 + 2s4 + 2s5 + 2s6 + s7 + s10 + s11 + 3s12 + 6s13 13.69 AP21 4s1 + s2 + s3 + 2s4 + 2s5 + 3s6 + 2s7 + s8 + s9 + s10 + s11 + 4s12 + 8s13 12.91 AP22 2s1 + s2 + s3 + s6 + 2s7 + 2s8 + 2s9 - s11 + 2s12 + 4s13 44.65 AP23 2s1 + s2 + s3 + s6 + 2s7 + 2s10 - s11 + 2s12 + 4s13 13.71 AP24 3s1 + s2 + s3 + 2s6 + 3s7 + 2s8 + 2s9 + s10 - s11 + 3s12 + 6s13 12.93 AP25 3s1 + 2s2 + 2s3 + s4 + s5 + s6 + 2s7 + 2s8 + 2s9 - s11 + 3s12 + 6s13 44.26 AP26 3s1 + 2s2 + 2s3 + s4 + s5 + s6 + 2s7 + 2s10 - s11 + 3s12 + 6s13 13.69 AP27 3s1 + 2s2 + 2s3 + s4 + s5 + s6 + 2s7 + s8 + s9 + s10 - s11 + 3s12 + 6s13 12.91 Note: AP1, AP2, AP3, AP8, AP9, and AP11 correspond to IP1, IP4, IP5, IP2, IP3, and IP6.

3.3. Computational efficiency All the IPi’s and APi’s listed in Tables 2 and 3, respectively, have been generated in less than two seconds on a PC (Intel Pentium 4, CPU 3.06 GHz, and 1 GB RAM), thereby demonstrating that the current method is exceedingly efficient computationally. This has also been demonstrated with catalytic or metabolic reactions substantially more complex than MD [4-7, 12, 13].

4. Concluding remarks The stoichiometrically feasible independent pathways (IPi’s) and acyclic combined pathways (APi’s) of methanol decomposition (MD) have been exhaustively identified with the graph-theoretic method based on P-graphs. The potentially dominant pathways of MD have also been identified by resorting to the KLC and KLP as done in a previous work [24]. It has been found that among all the pathways identified, eleven of the twenty one APi’s can be more dominant than the single IPi previous reported [24]. These results, therefore, unequivocally imply the importance of identifying APi’s in addition to IPi’s.

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References [1] D. Murzin, S. Smeds, T. Salmi, React. Kinet. Catal. Lett. 60 (1997) 57. [2] G. Djega-Mariadassou, M. Boudart, J. Catal. 216 (2003) 89. [3] D. Murzin, React. Kinet. Catal. Lett. 90 (2007) 225. [4] L.T. Fan, B. Bertók, F. Friedler, S. Shafie, Hung. J. Ind. Chem. 29 (2001) 71. [5] L.T. Fan, B. Bertók, F. Friedler, Comput. Chem. 26 (2002) 265. [6] D.-Y. Lee, L.T. Fan, S. Park, S.Y. Lee, S. Shafie, B. Bertók, F. Friedler, Metab. Eng. 7 (2005) 182. [7] Y.C. Lin, L.T. Fan, S. Shafie, K.L. Hohn, B. Bertók, F. Friedler, Ind. Eng. Chem. Res. 47 (2008) 2523. [8] F. Friedler, K. Tarjan, Y.W. Huang, L.T. Fan, Chem. Eng. Sci. 47 (1992) 1973. [9] F. Friedler, K. Tarjan, Y.W. Huang, L.T. Fan, Comput. Chem. Eng. 17 (1993) 929. [10] F. Friedler, J.B. Varga, L.T. Fan, Chem. Eng. Sci. 50 (1995) 1755. [11] M.H. Brendel, F. Friedler, L.T. Fan, Comput. Chem. Eng. 24 (2000) 1859. [12] L.T. Fan, S. Shafie, B. Bertók, F. Friedler, D.-Y. Lee, H. Seo, S. Park, S.-Y. Lee, J. Chi. Inst. Eng. 28 (2005) 1021. [13] H. Seo, D.Y. Lee, S. Park, L.T. Fan, S. Shafie, B. Bertók, F. Friedler, Biotechnol. Lett. 23 (2001) 1551. [14] I. Halim, R. Srinivasan, Ind. Eng. Chem. Res. 41 (2002) 208. [15] W. Xu, U.M. Diwekar, Ind. Eng. Chem. Res. 44 (2005) 4061. [16] J. Liu, L.T. Fan, P. Seib, F. Friedler, B. Bertók, Ind. Eng. Chem. Res. 45 (2006) 4200. [17] I. Fishtik, R. Datta, Ind. Eng. Chem. Res. 40 (2001) 2416. [18] I. Fishtik, C.A. Callaghan, R. Datta, J. Phys. Chem. B. 108 (2004) 5671. [19] I. Fishtik, C.A. Callaghan, R. Datta, J. Phys. Chem. B. 108 (2004) 5683. [20] I. Fishtik, C.A. Callaghan, R. Datta, J. Phys. Chem. B. 109 (2005) 2710. [21] I. Fishtik, C.A. Callaghan, R. Datta, Ind. Eng. Chem. Res. 45 (2006) 6468. [22] I. Fishtik, R. Datta, Surf. Sci. 512 (2002) 229. [23] C. Callaghan, I. Fishtik, R. Datta, M. Carpenter, M. Chmielewski, A. Lugo, Surf. Sci.. 541 (2003) 21. [24] S.A. Vilekar, I. Fishtik, R. Datta, J. Catal. 252 (2007) 258. [25] L.T. Fan, Y.-C. Lin, S. Shafie, K.L. Hohn, B. Bertók, F. Friedler, Surf. Sci. 601 (2007) 2401. [26] W.J. Moore, Physical Chemistry, Prentice-Hall, Englewood Cliffs, NJ, 1972, p. 341. [27] J. Happel, P.H. Sellers, Adv. Catal. 32 (1983) 273. [28] P.H. Sellers, SIAM J. Appl. Math. 44 (1984) 784. [29] J. Happel, P.H. Sellers, M. Otarod, Ind. Eng. Chem. Res. 29 (1990) 1057. [30] A.A. Gokhale, S. Kandoi, J.P. Greeley, M. Mavrikakis, J.A. Dumesic, Chem. Eng. Sci. 59 (2004) 4679. [31] J. Happel, P.H. Sellers, Ind. Eng. Chem. Fund. 21 (1982) 67.

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Mathematical Modelling of Feed Pretreatment for Bioethanol Production Melanie T. Ramireza,b, Eric S. Fragaa a

Centre for Process Systems Engineering, Department of Chemical Engineering, University College London (UCL), Torrington Place, London WC1E 7JE, UK, [email protected] b Department of Agro-industrial Engineering, University of Tolima, B. Santa Helena A.A. 546, Ibague, Colombia

Abstract Lignocellulosic biomass provides potentially inexpensive, easily obtainable and a renewable source of feedstock for the production of liquid fuels such as ethanol. Unfortunately, the structure of lignocellulose requires pretreatment before the sugars can be converted to ethanol. There are a number of possible pretreatment steps and this paper considers the use of dilute acid. A mathematical modelling approach, based on the fitting of experimental data and an understanding of the chemical steps involved, is presented. The models are suitable for process design and have been incorporated in the Jacaranda system for process design and optimisation. Results comparing the impact of the choice of acid for the pretreatment of sugar bagasse, a widely available lignocellulosic feedstock, are presented. Keywords: Lignocellulose, Biomass, Ethanol, Model, Optimisation, Design.

1. Introduction There is an increasing interest in the utilisation of lignocellulosic materials to produce transportation fuels such as ethanol. Lignocellulose, consisting primarily of plant cell wall materials, is a complex composite of bio-polymers: cellulose, hemicellulose and lignin. Lignocellulosic materials are composed of cellulose fibres with crystalline structure embedded in a matrix composed of hemicelluloses and lignin. The structures and compositions vary greatly, depending on, for instance, the plant species, the plant parts and the growth conditions [1]. Low cost, widely available and renewable sources of lignocellulosic materials for fuel ethanol production can be divided into six main groups: crop residues, hardwood, softwood, cellulose wastes, herbaceous biomass, and municipal solid wastes [2]. Sugarcane bagasse, the residue after the juice is extracted from sugar cane, is an attractive lignocellulosic feedstock for ethanol production, being cheap, readily available, and having a high carbohydrate content [3]. The fermentable sugars in lignocellulose are derived from cellulose (composed of glucose) and hemicellulose (mainly xylan) but these are not readily accessible to enzymatic hydrolysis. The chemical resistance and the lack of accessibility to the substrate in lignocellulosic materials limit the yields and the kinetics of saccharification prior to fermentation. Pretreatment is necessary, the goal being to increase the accessible surface area of cellulose and enhance conversion of the cellulose to glucose and the hemicellulose to xylose. Pretreatment may remove the lignin seal, solubilise hemicellulose, disrupt cellulose crystallinity, and/or increase pore volume [4].

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The pre-treatment and hydrolysis of lignocellulosic materials can be carry out physically (e.g., steam explosion or pyrolysis), physico-chemically, chemically (by acid or alkaline hydrolysis) and biologically (using cellulases, hemicellulases and ligninases from various fungi), or using a combination of these methods [5, 6]. Pretreatment of the material is therefore necessary, before hydrolysis, to convert the cellulose into glucose and the hemicellulose into xylose. However, pretreatment is the single most expensive element of the bioethanol process, representing about one-third of the overall processing cost [7]. The optimal design of the pretreatment step is therefore critical to the overall process. Among the various treatments possible, dilute acid hydrolysis is economically attractive and currently the most widely used: in a single step, several alterations in raw materials are achieved, including cellulose decrystallinisation, dissolution of acidsoluble lignin, increase in pore volume and available surface area, and hemicellulose removal. This paper presents mathematical models, suitable for optimisation within a design framework, which allow us to compare the effect of different acids in the pretreatment step.

2. The mathematical models for acid pretreatment The modelling of the hydrolysis of a polysaccharide is complex and involves many factors related to the lignocellulosic material (size, particle shape, structure, etc.) and to the reaction medium (type of acid, concentration, temperature, time, etc.) [8]. Based on the simplified model developed by Saeman [9] on the hydrolysis of wood using sulphuric acid, we can describe the hydrolysis of cellulose and hemicellulose by firstorder, irreversible reactions as follows: k1 k2 Cellulose Glucose Decomposition products (1) Hemicellulose

k1

Xylose

k2

Decomposition products

(2)

Where, k1 and k2, different for each reaction, are the kinetic coefficients of the reactions of monomer release and decomposition, respectively, and the decomposition products will differ in each case. In general, this Saeman model can be applied to other polysaccharides; therefore the model can be generalized for any polymer: k1 k2 Polymer Monomer Decomposition products (3) The generalised polymer could be glucan, xylan, araban, etc. Decomposition products can be furfural (from xylose), hydroxymethylfurfural (from glucose) and other compounds such as acetic acid. Solving the differential equations for an isothermal reaction, the following model predicts the concentration of monomers:

M (t ) = M 0 ⋅ e − k 2 t + P0

k1 ( e − k1 t − e − k 2 t ) k 2 − k1

(4)

where, M and P are the concentrations (g»l) of monomer and polymer at time t and the subscript 0 indicate initial conditions. It has been observed that only a fraction of the polymer reacts in the operational conditions [7], leading to a two-fraction model which considers a susceptible or fast fraction and a less susceptible or slow fraction. The ratio between the two fractions is Į (mass fraction of the susceptible polymer in the raw material). The resulting model given that M0≈0, is

Mathematical Modelling of Feed Pretreatment for Bioethanol Production

M (t ) = α P0

1301

k1 (e − k1 t − e − k 2 t ) k 2 − k1

(5)

The value of P0 assumes a total conversion of polymer to monomer without degradation and is determined by:

P0 = f

CPn0 ρ WSR

(6)

where f is the stoichiometric factor for hydration of molecules in hydrolysis (150/132 for pentoses and 180/162 for hexoses), CPn0 is the fraction of the polymer Pn in the raw material, on a dry basis (g»g), WSR is the water/solid ratio used and ȡ is the density of hydrolysates (in g/l). The reaction rate constants (k1and k2) are assumed to have an Arrhenius-type temperature dependence [10] where the pre-exponential factor is assumed to be dependent upon acid concentration (Ca):

k = A Can e − E / RT

(7)

Using non-linear regression, with experimental data from the literature, we have applied these models to the different fractions affected by the hydrolysis using different acids [11, 12, 13, 14]. The results of the parameter estimation procedure are summarised in Table 1. Table 1. Kinetic parameters for acid hydrolysis of sugar cane bagasse for different acids with reference to source of experimental data noted Acid

HCL [13]

HNO3 [14] H2SO4 [12]

Component Xylose Glucose Arabinose Xylose Glucose Arabinose Xylose Glucose

k1 n 1.2 0.8 0.5 3.8 1.1 0.8 0.7 1.9

lnA 28.9 26.2 27.0 39.4 27.8 40.0 31.6 32.3

Parameters k2 n lnA 1.2 23.6 4.3 18.3 13.1 16.2 7.6 4.2 20.0 4.3 9.5 26.4 0.7 25.7 3.3 19.1

Į 0.90 0.12 0.40 0.78 0.09 0.32 0.80 0.13

Ea/R 12 299

12 509 13 080

The values of the parameters for k1, for all acids, are consistent with those reported for dilute-acid hydrolysis in the literature [11, 12, 13, 14]. For xylose, it can be observed that the values for the parameters, for both, k1 and k2 are similar, so that decomposition products and xylose are generated at similar rates. In the case of glucose and arabinose, however, the decomposition reaction proceeds at a lower rate than the main product reaction. We can also observe that the values for Į for xylose agree with the expected behaviour stated in the literature [12]. For the others, however, the values are lower than expected, indicating that dilute-acid hydrolysis is unable to induce the release of the less susceptible fraction. The values of lnA and n for k2 usually are not shown in the literature, the argument being that the values for k2 are too small so that the degradation reactions are not important [12], but we consider these values in this study as they do impact on mass balances.

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3. Optimisation of the pretreatment step The models described above have been implemented in the Jacaranda system for process design and optimisation [15] and have been applied to the pretreatment of sugar cane bagasse. The composition of bagasse used here is, on a dry weight percent basis, glucan 38.9%, xylan 20.6%, araban 5.56%, klason lignin 23.9% and 11.0% other species. This is a composition in line with previous experimental studies [12, 13, 14, 8]. Three different acids have been considered and, for each, the Jacaranda problem formulation identifies four design variables: the water to solid ratio, WSR ȯ[8,10] g water/g solid, for the amount of water to add to the bagasse, the concentration of the acid, Ca ȯ[2,6]%, the residence time in the pretreatment step, t ȯ[0,300] min., and the operating temperature for this step, T ȯ[100,128]°C. The mass balance models incorporate the models described in the previous section to quantify the consumption and generation terms for each species. The objective is to maximise the generation of xylose. Eventually, there will be multiple objectives, including economics and various measures of the sustainability of the process. For an initial investigation, the aim of this work was to demonstrate that the models developed could differentiate between alternative designs and this work provides the base for future developments. A genetic algorithm (GA) procedure, in Jacaranda, was used for the optimisation. As a GA is stochastic, each solution attempt may potentially identify a different solution. For this reason, we attempted each problem 100 times and the results described include a statistical analysis. For each acid, the same objective function value was obtained (to within less than 0.1%) each time. The design variables, however, did vary. These results are summarised in Table 2 where, for each design variable, we present the average value obtained as well as the standard deviation in parentheses. The results obtained demonstrate that the choice of acid has a direct impact not only on how much xylose we can produce but also on the values of the design variables, most notably in the concentration of acid required to achieve the greatest quantity of xylose. From the table, we can conclude that HCl leads to best performance for the objective used. When cost considerations are included, of course, this conclusion could change because, for instance, the residence time is significantly larger than for the other acids and, hence, the size of the pretreatment unit may be larger as well. Table 2. Design variables and objective function mean values and standard deviation for different acids obtained solving each case 100 times in Jacaranda Acid

WSR

Ca

t (m)

T (K)

z (g/L)

HCL HNO3 H2SO4

9.2 (0.55) 9.0 (0.58) 9.1 (0.54)

5.5 (0.45) 4.8 (0.81) 2.7 (0.82)

83 (38) 18 (73) 23 (11)

108 (6) 118 (7) 107 (7)

17.7 13.1 13.6

The behaviour of the design variables is presented in Fig. 1 The graphs use a parallel co-ordinate system representation to show the values, normalised based on their upper and lower bounds, of the design variables and the objective function. Each solution obtained by Jacaranda is represented by a poly-line connecting each variable to an objective function value. The initial point for the search, the same in every case, is shown graphically using a dashed line. The graphs show that, in all cases, the water to solid ratio design variable appears to have no impact and that a lower value of temperature is desirable. The best concentration of the acid used varies from acid to acid, however. For the residence time, for HCl a low to medium value is needed; for

Mathematical Modelling of Feed Pretreatment for Bioethanol Production

1303

HNO3 most of the domain allowed is possible; and for H2SO4 only small residence times are suitable. Previous studies have stated that the type of acid should not affect the kinetics [14] yet we find they do. From the graphs, we are also able to see an inverse linear relationship between residence time and operating temperature for all three cases.

Figure 1. A parallel co-ordinate presentation of the solutions obtained from 100 runs of Jacaranda for each acid considered. The thicker line represents the initial guess for the optimisation.

M.T. Ramirez and E.S. Fraga

1304

4. Conclusions Liquid fuels produced from biomass sources may be a potentially valuable and necessary source of energy in the future. The use of so-called second generation feedstocks, to avoid using crops destined for food production, is appealing but poses challenges. Many readily available second generation feedstocks are lignocellulosic. Such feedstocks are difficult to process directly for the production of, for instance, ethanol. Pretreatment steps are required. This paper has presented a mathematical model of an acid based pretreatment step and has demonstrated that the choice of acid has an impact on the effectiveness of the pretreatment step. The results also provide some insight into the trade-offs between the different design variables. Although this initial investigation has used a simple objective function, the aim is to incorporate the models developed into a larger framework which will not only include more objective functions, such as economics and sustainability, but will consider the impact of pretreatment on the subsequent steps in the production of ethanol. This will be achieved by combining this effort with the models developed in previous work [16].

5. Acknowledgements Financial support from Universidad del Tolima, Colombia, is gratefully acknowledged.

References [1] Y.H.P. Zhang, et al. Biotechnology and Bioengineering 97(2), 214-223 (2007). [2] O.J. Sánchez and C.A. Cardona. Bioresource Technology 99(13), 5270-5295 (2008). [3] C. Martin, et al. Applied Biochemistry and Biotechnology 98-100(1-9), 699-716 (2002). [4] J. Weil, et al. Enzyme and Microbial Technology 16(11), 1002-1004 (1994). [5] B. Antizar-Ladislao and J.L. Turrion-Gomez. Biofuels, Bioproducts and Biorefining 2, 455-469 (2008). [6] Y. Sun and J. Cheng. Bioresource Technology 83(1), 1-11 (2002). [7] S.E. Jacobsen and C.E. Wyman. Applied Biochemistry and Biotechnology 84-86(1-9), 81-96 (2000). [8] S. Gamez, et al. Journal of Food Engineering 74(1), 78-88 (2006). [9] J.F. Saeman. Industrial and Engineering Chemistry 37(1), 43-52 (1945). [10] A. Esteghlalian, et al. Bioresource Technology 59(2-3), 129-136 (1997). [11] G. Garrote, H. Domínguez and J.C. Parajó. Process Biochemistry 36(6), 571-578 (2001). [12] R. Aguilar, J.A. Ramirez, G. Garrote and M. Vazquez. Journal of Food Engineering 55(4), 309-318 (2002). [13] G. Bustos, J.A. Ramirez, G. Garrote and M. Vazquez. Applied Biochemistry and Biotechnology 104(1), 51-68 (2003). [14] A. Rodriguez-Chong, J.A. Ramirez, G. Garrote and M. Vazquez. Journal of Food Engineering 61(2), 143–152 (2004). [15] E.S. Fraga, M.A. Steffens, I.D.L. Bogle, and A.K. Hind. In Foundations of ComputerAided Process Design, M.F. Malone, J.A. Trainham and B. Carnahan, editors, volume 96 of AIChE Symposium Series, 446-449, (2000). [16] O.J. Sanchez, L.F. Gutirrez, C.A. Cardona and E.S. Fraga. In Computer Aided Methods for Optimal Design and Operations, J. Zilinskas and I.D.L. Bogle, editors, 207216. World Scientific Publishing Co. (2006).

1305

Author index Adhitya, Arief, 979 Adonyi, Robert, 1445 Agachi, Serban, 465, 677, 731, 1033, 1183, 1239, 1275 Aguirre, Pio, 573 Ahmadi Afshar, Seyed Hossein, 689 Akkisetty, Pavan Kumar, 159 Aksoy, Burak, 1135 Akyurek, Evrim, 1197 Al-Rashed, Mohsen, 695 Aldaco, Ruben, 1105 Alloula, Karim, 889 Almeida-Rivera, Cristhian, 111, 231 Altimari, Pietro, 285 Alvarez, Carlos Rodrigo, 725 Amaro, Ana, 973 Ani, Elisabeta-Cristina, 731 Araújo, Paulo, 75 Arellano-Garcia, Harvey, 123, 333, 901 Argoti, A., 791 Atala, Daniel I. P., 827, 1387 Atasoy, Ilknur, 623, 1197 Attarakih, Menwer, 1333, 1339, 1345 Avramenko, Yury, 165 Azzaro-Pantel, Catherine, 1263 Bagajewicz, Miguel, 1, 315 Bakker, Bas, 225, 375 Balagurunathan, Balaji, 1051 Barbosa-Povoa, Ana, 399, 973, 1177 Baroodi, Payam, 737 Barral Quirino, Filipe, 1381 Bart, Hans-Jörg, 1333, 1339, 1345 Barton, Paul I., 597, 937 Basualdo, Marta, 1451 Batistella, Benedito, 195 Batres, Rafael, 1171

Batselev, Philipp, 1021 Behdani, Behzad, 979 Belaud, Jean-Pierre, 889 Belfort, Frederico, 629 Bengoa, Christophe, 701 Benítez, Raúl, 267 Berber, Rdvan, 623, 1197 Bertok, Botond, 1293, 1445 Besler, Anna, 243 Bettens, Ben, 779 Biegler, Lorenz T., 609 Bildea, Costin Sorin, 99, 171, 285 Bizon, Katarzyna, 931, 1039 Boer, Dieter, 1099 Bojarski, Aarón, 725 Bollas, George M., 597 Bommareddy, Susilpa, 1135 Bongers, Peter, 111, 171, 225, 231, 375 Bonilla-Petriciolet, Adrian, 189, 635 Bonis, Ioannis, 653 Borchert, Christian, 141 Botar-Jid, Claudiu Cristian, 677 Botelle, Gonzalo, 1451 Bouaswaig, Ala Eldin, 907 Bozga, Grigore, 99 Bozorgmehry Boozarjomehry, Ramin, 1417 Brambilla, Sara, 1147 Brandani, Stefano, 603 Bratfalean, Dorina, 1033 Brauner, Neima, 69, 1233 Bravo Sanchez, Ulises Ivan, 87 Briesen, Heiko, 895 Briones-Ramírez, Abel, 543, 549, 555 Brown, Michael, 1147 Brunchi, Cristian, 99 Bruno Argilaguet, Joan Carles, 1369

1306

Buzzi-Ferraris, Guido, 913 Cafaro, Diego, 429 Calçada, Luis Americo, 147 Canavesio, Mercedes, 985 Carmen Medina, Lilian, 195, 1381, 1435 Castillo-Borja, Florianne, 87 Castro, Pedro, 405 Ccopa Rivera, Elmer, 309 Cecelja, Franjo, 865 Cerdá, Jaime, 429, 1009 Chemmangattuvalappil, Nishanth, 153, 237 Chiu, Y. Y., 791 Chmiel-Kurowska, Klaudia, 949, 955, 967 Cho, Sungwoo, 1429 Cholakov, Georgi St., 69 Chou, S. T., 791 Chung, Hyunseok, 1429 Chung, Paul, 435 Cisar, Petr, 1457 Cisternas, Luis, 213, 417 Clichici, Simona, 677 Coletti, Francesco, 1245 Colombo, Mauro, 435 Conte, Elisa, 249 Continillo, Gaetano, 931, 1039 Corbett, Jason, 351 Cormos, Ana-Maria, 1033, 1239, 1275 Cormos, Calin-Cristian, 1239, 1275 Coronas Salcedo, Alberto, 1369 Cosme Melo, Delba, 537, 1399, 1469 Costa, Caliane B. B., 537, 743, 1387, 1399, 1469 Crescitelli, Silvestro, 285 Cristea, Mircea, 1033, 1183 Cuadros Bohórquez, José Fernando, 195 Cui, Jian, 423

Author Index

Cullinan, Harry, 1135 Cuoci, Alberto, 707, 749 Cárdenas Concha, Viktor Oswaldo, 1381 Dalby, Paul, 1057 De Blasio, Cataldo, 821 de Franceschi de Angelis, Dejanira, 1387 de la Mata, Jose Luis, 1117 De Paula, Mariano, 261 De Ridder, Emmanuel, 779 de Vaal, Philip, 859 Degrève, Jan, 779 Di Maggio, Jimena, 1075 Diaz Ricci, Juan Carlos, 1075 Diaz, Soledad, 1075, 1153 Diaz-Ovalle, Christian, 93 Domenech, Serge, 1263 Dominguez-Ramos, Antonio, 1105 Dondo, Rodolfo, 1009 Dones, Ivan, 477, 767 Dorneanu, Bogdan, 171 Drumm, Christian, 1333, 1339 Duarte, Belmiro, 75 Duarte, Laura, 1357 Dumaz, Patrick, 1263 Dumont, Marie-Noëlle, 303 Duque, Joaquim, 1177 Dzhygyrey, Iryna, 853, 1111, 1227 Dziak, Janusz, 207, 671 Dzido, Grzegorz, 955 Eden, Mario, 153, 237, 1135 Edreder, Elmahboub, 411 Eduardo Vaz Rossell, Carlos, 519, 827 El-Akrami, Hadi, 1313 El-Garny, Mohamed, 1313 El-Halwagi, Mahmoud, 1189 Embiruçu, Marcelo, 1435

Author Index

Emtir, Mansour, 411 Emun Temeliso, Fiethamelekot, 561 Enestam, Sonja, 1423 Engell, Sebastian, 43, 363, 423, 907 Escudero, Gerard, 255, 267 Espuña, Antonio, 883 Estrada, Vanina, 1153 Fabregat, Azael, 701 Faisca, Nuno, 297, 919 Fan, L. T., 641, 791, 1293 Faravelli, Tiziano, 707, 749 Faria, Debora, 1 Farid, Suzanne, 1063, 1069 Ferrari, Juan, 1451 Fiandaca, Giovanna, 603 Fidkowski, Zbigniew, 591 Fieg, Georg, 219, 659, 1081 Filipe, Rui, 471 Floudas, Christodoulos, 381 Fonseca, Jose, 647 Font, Josep, 701 Foo, Dominic, 1189 Fortuny, Agusti, 701 Fraga, Eric, 603, 1299 Frankenhaeuser, Oskar, 525 Fraser, Duncan, 877 Frassoldati, Alessio, 707, 749 Friedler, Ferenc, 641, 1293, 1445 Fry, Jeff, 435 Gadalla, Mamdouh, 561 Gani, Rafiqul, 105, 201, 249, 321, 495, 839 Gao, Yan-Ming, 219 García-Martínez, Antonio, 279 Garea, Aurora, 63 Gassner, Martin, 1405 Gebreslassie, Berhane, 1099 George, Edmund, 1063 Georgiadis, Michael, 183

1307

Gerber, Leda, 1405 Gerkens, Carine, 357 Gernaey, Krist, 321, 925 Ghadrdan, Maryam, 1417 Gierczycki, Andrzej, 955 Gintaras, Reklaitis, 159, 1027 Godini, Hamid Reza, 123 Gomez, Adrien, 1263 González Quiroga, Arturo, 683 Gordienko, Mariya, 501 Gouws, Jacques, 1221 Gozlinska, Malgorzata, 459 Graells, Moisès, 255, 267 Grana, Roberto, 665 Grievink, Johan, 171 Grof, Zdenek, 129, 961 Grossmann, Ignacio, 713, 991 Guillén-Gosálbez, Gonzalo, 997, 1045, 1099 Gurikov, Pavel, 943 Gutierrez-Guerra, Roberto, 189 Gutiérrez-Antonio, Claudia, 543, 549, 555 Gutsche, Bernhard, 1081 Gálvez, Edelmira, 213 Gómez Garrido, Àlex, 1033 Hai, Ri, 1087 Han, Chonghun, 1429 Harwardt, Andreas, 243 Hasebe, Shinji, 447, 1015 Hassim, Mimi, 1141 Haubensack, David, 1263 Heckl, Istvan, 641 Heidebrecht, Peter, 609 Hernandez, Salvador, 189, 279, 543, 549, 713 Hernández Sánchez, Miguel, 1033 Hernández, Hector, 189, 279, 543 Herrera, Gonzalo, 213 Hetreux, Gilles, 345

1308

Heyen, Georges, 303, 357 Hirao, Masahiko, 1123 Hong, Jeong Jin, 327 Hostalkova, Eva, 1457 Hou, Xi-Ru, 659 Hua, Ben, 1375 Huang, Dexian, 273 Huang, Yinlun, 81 Hui, C.W, 1351, 1375 Hungerbuehler, Konrad, 1093 Hurme, Markku, 1141 Huusom, Jakob Kjbsted, 441 Irabien, Angel, 63, 1105 Isafiade, Adeniyi, 877 Jang, Namjin, 1411 Jaradat, Moutasem, 1333, 1339, 1345 Jardini Munhoz, André, 683 Jarzbski, Andrzej, 955 Jensen, Niels, 1129 Jerez, Johnny, 1357 Jezowski, Jacek, 853, 1209 Jimenez, Johnny, 1363 Jimenez, Laureano, 1451 Jimenez-Gutierrez, Arturo, 1257 Jiménez, Laureano, 561, 997, 1045, 1099 Jonnalagadda, Sudhakar, 1051 Jonsson, Gunnar, 773 Jorgensen, Sten Bay, 441, 773, 1129 Juan Carlos, Tapia Picazo, 1463 Jung, Seungho, 93 Kamaruddin, Abd. Hamid Mohd., 839 Kaminski, Wladyslaw, 1203 Kano, Manabu, 447, 1015 Kapon, Jacek, 207 Karimi, Iftikhar A., 453 Kasimova, Alia, 501 Kazemeini, Mohammad, 737

Author Index

Khalfalla, Hamza, 1313 Kikkinides, Eustathios, 183 Kikuchi, Yasunori, 1123 Kiss, Tony, 847, 1287 Klar, Axel, 1333, 1339, 1345 Klemes, Jiri, 1003, 1251 Koci, Petr, 615, 803 Kokossis, Antonis, 865 Kolnootchenko, Andrey, 943 Koltsova, Eleonora, 785, 1021, 1475 Komarysta, Bogdana, 1111 Kopanos, Georgios, 369, 883 Koroishi Tomie, Erika, 1381 Kosek, Juraj, 129, 507, 961 Koukkari, Pertti, 1423 Kouramas, Konstantinos, 183, 297, 919 Kozlov, Anton, 291 Kraslawski, Andrzej, 165, 731 Krause, Przemyslaw, 1081 Kravanja, Zdravko, 25, 585 Kreis, Peter, 815 Krolikowski, Lechoslaw, 207, 761 Kubicek, Milan, 615, 803 Kucharz, Eugene, 21 Kuhnert, Jörg, 1333, 1339, 1345 Kunina, Olga, 1475 Kurowski, Lukasz, 949, 967 Kvitka, Olexandr, 853, 1227 Labrador-Darder, Claudia, 865 Lai, Sau Man, 1375 Lakatos, Béla G., 719 Lam, Hon Loong, 1003 Landín-Sandoval, Verónica, 87 Lastusilta, Toni, 525 Latge, Christian, 1263 Laínez, Jose Miguel, 1027 Le Lann, Jean-Marc, 345, 889 Ledvinkova, Blanka, 129 Lee, Dong-Yup, 1051

Author Index

Legentilhomme, Patrick, 701 Legrand, Jack, 701 Leistner, Kirsten Chantal, 1039 Lek-utaiwan, Pimporn, 201 Lewak, Michal, 1159 Li, Ruifa, 351 Lin, Yu-Chuan, 1293 Lind, Morten, 1129 Linke, David, 489 Linke, Patrick, 489, 865 Litzmann, Oliver, 117 Liu, Lande, 351 Liu, Qiyue, 273 Liu, Songsong, 393 Liu, Zhi-Yong, 1319 Lone, Saulat, 453 Lopes Junqueira, Tassia, 519, 827 Ludwig, Wojciech, 207, 671 Luis, Patricia, 63 Lukszo, Zofia, 979, 1165 Lundell, Andreas, 579 Luo, Xing, 219, 659 Ma, Caiyun, 483 Ma, Chaoyang, 1393 Ma, Hu.Gen, 659 Macchietto, Sandro, 1245 Machado, Dina, 75 Macias, Roberto, 1081 Maciel Filho, Rubens, 195, 309, 519, 537, 683, 743, 827, 1381, 1387, 1399, 1435, 1469 Majozi, Thokozani, 561, 1221, 1281 Makovskaya, Julia, 501 Makridis, Sofoklis, 183 Maliepaard, Rick, 1165 Manca, Davide, 665, 1147 Mancini, Mauricio, 147, 629 Mancusi, Erasmo, 285 Manenti, Flavio, 665, 913 Mannan, Sam, 93

1309

Marcovecchio, Marian G., 573 Marechal, Francois, 1405 Marek, Milos, 615, 803 Marquardt, Wolfgang, 243, 531, 1087 Martinez, Edgar, 683 Martinez, Ernesto, 261, 985 Martinez, Ramiro, 1357, 1363 Matos, Henrique, 399, 471 Matynia, Andrzej, 459 Maugeri Filho, Francisco, 1387 McNeil-Watson, Fraser, 351 Mele, Fernando, 997 Mendes, Fernando, 75 Mendez, Carlos, 1009 Menshutina, Natalia, 291, 501, 943 Merola, Simona Silvia, 1039 Meyer, João Frederico A. C., 1469 Mihálykó, Csaba, 719 Miranda-Galindo, Erick Yair, 549 Mitsos, Alexander, 597 Molga, Eugeniusz, 809, 1159 Mongkolsiri, Nakarin, 201 Monroy, Isaac, 255, 267 Montolio-Rodriguez, Daniel, 489 Morais, Edvaldo R., 1399, 1469 Morales-Rodríguez, Ricardo, 249, 495 Morar, Mihaela, 465 Morris, Julian, 327, 387 Muhammad, Faheem, 1327 Mujtaba, Iqbal, 411, 1313 Mukai, Yosuke, 1015 Muresan, Crina, 1033 Mussati, Sergio F., 573 Muñoz, Edrisi, 883 Mäkilä, Ermei, 821 Nagy, Zoltan K., 1093 Nascimento Lima, Nádson, 1435 Negny, Stéphane, 345 Neves, Filipe, 75 Ng, Denny, 1189

Author Index

1310

Nguyan, Jerome, 387 Nguyen, DuyQuang, 315 Novais, Augusto, 405, 471, 1177 Novak-Pintaric, Zorka, 1215 Nowak, Urszula, 1203 Ochoa, Silvia, 513 Oliveira de Souza Dias, Marina, 519, 827 Oliveira, Luiz Henrique, 629 Oliveira, Nuno, 75 Olivier-Maget, Nelly, 345 Ordonez, Ivan, 1357, 1363 Ortiga Guillén, Jordi, 1369 Ossandon, Karla, 417 Pajarre, Risto, 1423 Papadopoulos, Athanasios, 177 Papageorgiou, Lazaros, 393, 1057 Park, Chansaem, 1429 Parodi, Elisa R., 1153 Pettersson, Frank, 525, 567 Pibouleau, Luc, 1263 Pierucci, Sauro, 797 Pinto Mariano, Adriano, 537, 1387, 1399, 1469 Pinto, Jose, 393 Pinto, Patricio, 417 Piotrowski, Krzysztof, 459 Pistikopoulos, Efstratios, 183, 297, 919 Plewik, Roch, 695 Pokorny, Richard, 961 Polykarpou, Eleftheria, 1057 Ponce-Ortega, Jose M, 1257 Pop, Cristian, 1183 Poplewski, Grzegorz, 1209 Poulsen, Niels Kjlstad, 441 Prado Rubio, Oscar Andrés, 773 Pramparo, Laura, 701 Preisig, Heinz A, 477, 767

Price, Tim, 1281 Primrose, Ken, 351 Pruvost, Jeremy, 701 Puigjaner, Luis, 369, 725, 883, 1027 Qian, Yu, 37 Radermecker, Eric, 303 Ramirez, Melanie, 1299 Ramkrishna, Doraiswami, 141 Ramzan, Naveed, 453, 1327 Ranzi, Eliseo, 707, 749, 797 Rashed, Jamal, 105 Relvas, Susana, 399 Repke, Jens-Uwe, 117, 513 Rico-Ramirez, Vicente, 713 Rodriguez, Manuel, 871, 1117 Rojas-Hernandez, Jaime, 1269 Rolón, María de los Milagros, 985 Romijn, Reinout, 531 Ropotar, Marcel, 585 Rossing, Netta Liin, 1129 Roth, Tim, 815 Rovaglio, Maurizio, 435 Rudniak, Leszek, 809 Russo, Lucia, 285 Saleemi, Anwar Rashid, 453 Samavedham, Lakshminarayanan, 833 Sammons Jr., Norman, 1135 Sandrock, Carl, 859 Sanz, Ricardo, 871 Sarkar, Debasis, 833 Saxén, Henrik, 567 Scenna, Nicolas, 573 Schejbal, Matyas, 803 Schlup, J. R., 791 Schoeneberger, Jan, 901 Schubert, Udo, 333 Scott, Joseph, 937 Seda, Libor, 507, 961 Seferlis, Panos, 177

Author Index

Segovia-Hernández, Juan-Gabriel, 189, 279, 543, 549, 635, 713 Serna-Gonzalez, Medardo, 1257 Shacham, Mordechai, 69, 1233 Shafie, Shahram, 1293 Shakhnovsky, Arcady, 1227 Shang, Xiaolei, 435 Sharma, Vikash, 1333, 1339, 1345 Shaymardanov, Anton, 785 Shen, B. C., 791 Sikos, László, 1251 Silva, Ferney, 1363 Simon, Levente, 1093 Sin, Gurkan, 839, 925 Singh, Ravendra, 321 Skorzinski, Elena, 1233 Smith, Martin, 1069 So, Won, 1411 Solvason, Charles, 153, 237 Sorribas, Albert, 1045 Srinivasan, Rajagopalan, 755, 833, 979, 1051 Stateva, Roumiana, 69 Statyukha, Gennadiy, 853, 1111, 1227 Stepanek, Jan, 615 Stluka, Petr, 1457 Stoffels Mallmann, Evandro, 743 Stonier, Adam, 1069 Stubbs, Shallon, 339 Stüber, Frank, 701 Stünkel, Steffen, 117 Suharoschi, Ramona, 1033 Sundmacher, Kai, 141, 609 Suphanit, Bunyaphat, 201 Synowiec, Piotr, 695 Söderman, Jarmo, 567 Süle, Zoltán, 719 Tan, Raymond, 1189 Tarhan, Bora, 713 Theissen, Manfred, 1087

1311

Theodoropoulos, Constantinos, 653 Thullie, Jan, 949, 967 Tiwari, Sudarshan, 1333, 1339, 1345 Tokos, Hella, 1215 Tomczak, Elwira, 1203 Tometzki, Thomas, 363 Tran, Huu Que, 1021 Troyankin, Alexander, 291 Tweedie, Richard, 351 Ullrich, Christophe, 357 Vafajoo, Leila, 689, 737 Vaglieco, Bianca Maria, 1039 Van der Bruggen, Bart, 779 Varbanov, Petar, 1003 Vasco de Toledo, Eduardo Coselli, 537, 1399, 1469 Vazquez-Roman, Richart, 87, 93 Vega, Marcia, 147, 629 Venegas-Sanchez, Josue Addiel, 543 Venkatasubramanian, Venkat, 159 Verderame, Peter, 381 Verhoef, Adrian, 779 Vezzadini, Luca, 435 Villà i Freixa, Jordi, 1033 Voinovskiy, Alexei, 501 Voynovskiy, Alexander, 291 Vázquez-Castillo, José Antonio, 543 Wallis, Steve, 731 Wan, Jian, 483 Wang, David, 755 Wang, Lin, 447 Wang, Xue, 135, 351, 483, 1393 Westerlund, Tapio, 525, 579, 821 Williams, Michael, 1147 Wisnivesky Rocca Rivarola, Florência, 1381 Witt, Werner, 1327 Wolf Maciel, Maria Regina, 195, 519, 743, 827, 1381, 1387, 1435

1312

Wong, King Hei, 1351 Wozny, Guenter, 117, 123, 333, 513, 901 Wu, Hao, 1375 Wójcik, Janusz, 695 Xiao, Jie, 81 Yang, Yang, 135 Yang, Yu-Zhen, 1319 Yoon, En Sup, 1411 You, Fengqi, 991 Ytsma, Renske, 1165 Yuan, Wei, 1135 Yuceer, Mehmet, 1197 Zhang, Gaobo, 1375 Zhang, Jie, 273, 387 Zhang, Jie, 327 Zhelev, Toshko, 1269 Zhensa, Andrey, 785 Zhou, Chang, 273 Zhou, Ying, 833 Zubov, Alexandr, 507 Zumoffen, David, 1451 Zuñiga Liñan, Lamia, 1435

Author Index