European Symposium on Computer-aided Process Engineering-15: 38th European Symposium of the Working Party on Computer Aided Process Engineering: Escape-15, 29 May - 1 June 2005, Barcelona, Spain

EUROPEAN SYMPOSIUM ON COMPUTER-AIDED P R O C E S S E N G I N E E R I N G - 15 COMPUTER-AIDED CHEMICAL ENGINEERING Adv...

Author: L. Puigjaner | A. Espuna

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EUROPEAN SYMPOSIUM ON COMPUTER-AIDED P R O C E S S E N G I N E E R I N G - 15

COMPUTER-AIDED CHEMICAL ENGINEERING Advisory Editor: R. Gani Volume 1: Volume 2: Volume 3: Volume 4: Volume 5: Volume 6: Volume 7: Volume 8: Volume 9: Volume 10: Volume 11: Volume 12: Volume 13: Volume 14: Volume 15: Volume 16: Volume 17: Volume 18: Volume 19: Volume 20:

Distillation Design in Practice (L.M. Rose) The Art of Chemical Process Design (G.L. Wells and L.M. Rose) Computer Programming Examples for Chemical Engineers (G. Ross) Analysis and Synthesis of Chemical Process Systems (K. Hartmann and K. Kaplick) Studies in Computer-Aided Modelling. Design and Operation Part A: Unite Operations (1. Pallai and Z. Fony6, Editors) Part B: Systems (1. Pallai and G.E. Veress, Editors) Neural Networks for Chemical Engineers (A.B. Bulsari, Editor) Material and Energy Balancing in the Process Industries - From Microscopic Balances to Large Plants (V.V. Veverka and F. Madron) EuropeanSymposium on Computer Aided Process Engineering-10 (S. Pierucci, Editor) EuropeanSymposium on Computer Aided Process Engineering-11 (R. Gani and S.B. Jorgensen, Editors) European Symposium on Computer Aided Process Engineering-12 (J. Grievink and J. van Schijndel, Editors) Software Architectures and Tools for Computer Aided Process Engineering (B. Braunschweig and R. Gani, Editors) Computer Aided Molecular Design: Theory and Practice (L.E.K. Achenie, R. Gani and V. Venkatasubramanian, Editors) Integrated Design and Simulation of Chemical Processes (A.C. Dimian) European Symposium on Computer Aided Process Engineering-13 (A. Kraslawski and I. Turunen, Editors) Process Systems Engineering 2003 (Bingzhen Chen and A.W. Westerberg, Editors) Dynamic Model Development: Methods, Theory and Applications (S.P. Asprey and S. Macchietto, Editors) The Integration of Process Design and Control (P. Seferlis and M.C. Georgiadis, Editors) European Symposium on Computer-Aided Process Engineering-14 (A. Barbosa-P6voa and H. Matos, Editors) Computer Aided Property Estimation for Process and Product Design (M. Kontogeorgis and R. Gani, Editors) European Symposium on Computer-Aided Process Engineering-15 (L. Puigjaner and A. Espufia, Editors)

COMPUTER-AIDED CHEMICAL ENGINEERING, 20B

EUROPEAN SYMPOSIUM ON COMPUTER-AIDED P R O C E S S E N G I N E E R I N G - 15 38th European Symposium of the Working Party on Computer Aided Process Engineering ESCAPE-15, 29 May- 1 June 2005, Barcelona, Spain

Edited by

Luis Puigjaner UPC-ETSEIB Barcelona, Spain

Antonio Espufia UPC-ETSEIB Barcelona, Spain

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The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands.

C o n t e n t s - Part B Process Operation and Control A Framework for the Mixed Integer Dynamic Optimisation of Waste Water Treatment Plants using Scenario-Dependent Optimal Control J. Busch, M. Santos', J. Oldenburg, A. Cruse a n d W. M a r q u a r d t ............................. 955 On-line Fault Diagnosis Support for Real Time Evolution applied to MultiComponent Distillation S. Ferrer-Nadal, I. Ydlamos-Ruiz, M. Graells and L. Puigjaner .............................. 961

Real-Time Feasibility of Nonlinear Predictive Control for Semi-batch Reactors H. Arellano-Garcia, T. Bar,,, M. Wendt a n d G. Wozny ............................................ 967

Control of Integrated Process Networks - A Multi-Time Scale Perspective 973

M. Baldea and P. Daoutidis . .....................................................................................

Minimum-Cost Operation in Heat-Exchanger Networks 979

A. H. Gonzdlez and J. L. Marchetti ...........................................................................

An Online Decision Support Framework for Managing Abnormal Supply Chain Events M. Bansal, A. A dhitya, R. Srinivasan and i. A. Karimi ............................................. 985 Novel Scheduling of a Mixed Batch/Continuous Sugar Milling Plant using Petri nets M. Ghaeli, P. A. Bahri and P. L. Lee ........................................................................

991

Improving Short-Term Planning by incorporating Scheduling Consequences P. Hei./nen, I. B o u w m a n s and Z. Verwater-Lukszo ...................................................

997

Multi-scale Planning and Scheduling in the Pharmaceutical Industry H. Stefansson and N. Shah ......................................................................................

1003

Initiation and Inhibiting Mechanisms for Multi-tasking Control in Discrete Event Systems S. Macchietto, N. J. Alsop, R. J. B a i r d Z. P. Feng a n d B. H. Chen ....................... 1009 Model Based Parametric Control in Anaesthesia P. Dua, V. Dua and E. N. Pistikopoulos .................................................................

1015

Anti-Slug Control Experiments on a Small-Scale Two-Phase Loop H. Sivertsen a n d S. S k o g e s t a d .................................................................................

1021

Using CLP and MILP for Scheduling Commodities in a Pipeline L. Magat6o, L. V R. Arruda and F. Neves Jr .........................................................

1027

Scheduling of a Pipeless Multi-Product Batch Plant using Mixed-Integer Programming Combined with Heuristics S. Panek, S. Engell a n d C. Lessner ......................................................................... 1033 On the State-Task Network Formulation: Time Representations C. T. Maravelias ...................................................................................................... Optimization of Biopharmaceutical Experiences from the Real World

Manufacturing

with

1039

Scheduling Tools -

C. A. Siletti, D. Petrides and A. Koulouris ..............................................................

1045

vi Advances in Robust Optimization Approaches for Scheduling under Uncertainty S. L. Janak and C. A. Floudas ................................................................................. 1051 Proactive Approach to address Robust Batch Process Scheduling under Short-Term Uncertainties A. Bonfill, A. Espu~a and L. Puigjaner ................................................................... 1057 A Rigorous MINLP for the Simultaneous Scheduling and Operation of Multiproduct Pipeline Systems R. Rejowski Jr. and J. M. Pinto ............................................................................... 1063 Multicommodity Transportation and Supply Problem with Stepwise Constant Cost Function Z. Lelkes, E. Rev, T. Farkas, Z. Fonyo, T. Kovacs and I. Jones .............................. 1069 Design and Planning of Supply Chains with Reverse Flows M. I. Gomes Salema, A. P. Barbosa-P6voa and A. Q. Novais ................................ 1075 Heterogeneous Batch Distillation Processes: Real System Optimization S. Pommier, S. Massebeuf V. Gerbaud, O. Baudouin, P. Baudet andX. Joulia .... 1081 Modelling and Optimisation of Distributed-Parameter Batch and Semi-batch Reactor Systems X. Zheng, Robin Smith and C. Theodoropoulos ...................................................... 1087 Optimal Start-up of Micro Power Generation Processes P. I. Barton, A. Mitsos and B. Chachuat ................................................................. 1093 Performance Monitoring of Industrial Controllers Based on the Predictability of Controller Behavior R. A. Ghraizi, E. Martinez, C. de Prada, F. Cifuentes and J. L. Martinez ............. 1099 A Systematic Approach to Plant-Wide Control Based on Thermodynamics L. T. Antelo, I. Otero-Muras, J. R. Banga and A. A. Alonso ................................... 1105 A Multiple Model, State Feedback Strategy for Robust Control of Nonlinear Processes F. E Wang, P. A. Bahri, P. L. Lee and I. T. Cameron ............................................ 1111 A Robust Discriminate Analysis Method for Process Fault Diagnosis D. Wang and J. A. Romagnoli ................................................................................. 1117 Learning in Intelligent Systems for Process Safety Analysis C. Zhao and V. Venkatasubramanian ..................................................................... 1123 Multivariate Decision Trees for the Interrogation of Bioprocess Data K. Kipling, G. Montague, E. B. Martin and A. J. Morris ........................................ 1129 On a New Definition of a Stochastic-Based Accuracy Concept of Data Reconciliation-Based Estimators M. Bagajewicz ......................................................................................................... 1135 The Integration of Process and Spectroscopic Data for Enhanced Knowledge Extraction in Batch Processes C. W. L. Wong, R. E. A. Escott, A. J. Morris and E. B. Martin ............................... 1141 A Systematic Approach for Soft Sensor Development B. Lin, B. Recke, P. Renaudat, J. Knudsen and S. B. Jorgensen ............................. 1147

vii Application of Multi-Objective Optimisation to Process Measurement System Design D. Brown, F. MarOchal, G. Heyen a n d J. Paris ...................................................... 1153 Utilities Systems On-Line Optimization and Monitoring: Experiences from the Real World D. Ruiz, J. Mamprin, C. Ruiz, D. Nelson and G. R o s e m e ....................................... 1159 A Continuous-Time Formulation for Scheduling Multi-Stage Multi-product Batch Plants with Non-identical Parallel Units L. Fu and L A. Karimi .............................................................................................. 1165 Optimal Scheduling of Supply Chains: A New Continuous-Time Formulation A. C. S. A m a r o a n d A . P. B a r b o s a - P 6 v o a ...............................................................

1171

Effect of Pricing, Advertisement and Competition in Multisite Capacity Planning M. Bagq/ewicz ......................................................................................................... 1177 Multi-objective Optimization of Curds Manufacture N. G. Vaklieva, A. Espu~a, E. G. Shopova, B. B. Ivanov and L. Puigianer ............ 1183

Global Supply Chain Network Optimization for Pharmaceuticals R. T. Sousa, N. Shah a n d L. G. Papageorgiou ........................................................

1189

Linear Quadratic Control Problem in Biomedical Engineering L E Sanchez Chdvez, R. Morales-Mendndez a n d S. O. Martinez Chapa ............... 1195

Using Structured and Unstructured Estimators for Distillation Units: A Critical Comparison F. Bezzo, R. Muradore a n d M. Barolo .................................................................... 1201 Modeling of Complex Dynamics in Reaction-Diffusion-Convection Model of CrossFlow Reactor with Thermokinetic Autocatalysis T. TrdvniOkovd, L Schreiber and M. KubiOek ......................................................... 1207 A Design and Scheduling RTN Continuous-time Formulation P. M. Castro, A. P. B a r b o s a - P 6 v o a a n d A. Q. Novais ............................................

1213

Use of Perfect Indirect Control to Minimize the State Deviations E. S. Hori, S. S k o g e s l a d and W. H. K w o n g .............................................................

1219

Constraints Propagation Techniques in Batch Plants Planning and Scheduling M. T. M. Rodrigues a n d L. Gimeno .........................................................................

1225

Information Logistics for Supply Chain Management within Process Industry Environments M. Vegelti, S. Gonnet, G. H e n n i n g a n d H. Leone ................................................... 1231 Plant Structure Based Equipment Assignment in Control Recipe Generation Considering Conflicts with Other Batches T. Fuchino and H. Watanabe .................................................................................. 1237 IMC Design of Cascade Control M. R. Cesca and J. L. Marchetti ..............................................................................

1243

Robust Model-Based Predictive Controller for Hybrid System via Parametric Programming A. M. Manthanwar, V. Sakizlis, V. Dua and E. N. Pistikopoulos ............................ 1249

viii Model Based Operation of Emulsion Polymerization Reactors with Evaporative Cooling: Application to Vinyl Acetate Homopolymerization S. Arora, R. Gesthuisen and S. Engell ..................................................................... 1255 Event-Based Approach for Supply Chain Fault Analysis R. Sarrate, F. Nejjari, F. D. Mele, J. Quevedo and L. Puigjaner ........................... 1261

Back-off Application for Dynamic Optimisation and Control of Nonlinear Processes S. 1. Biagiola, A. Bandoni and J. L. Figueroa ......................................................... 1267

Operational Planning of Crude Oil Processing Terminals A. M. Blanco, A. B. Morales Diaz, A. Rodriguez Angeles and A. Sdnchez ............. 1273

A Hierarchical Approach to Optimize LNG Fractionation Units H. E. Alfadala, B. M. A h m a d andA. F. Warsame ................................................... 1279

First Principles Model Based Control M. Rodriguez and D. Pdrez ..................................................................................... 1285

On-line Oxygen Uptake Rate as a New Tool for Monitoring and Controlling the SBR Process S. Puig, Ll. Corominas, J. Colomer, M. D. Balaguer and J. Colprim .................... 1291 On-Line Dynamic Monitoring of the SHARON Process for Sustainable Nitrogen Removal from Wastewater K. Villez, C. Rosen, S. Van Hulle, C. Yoo and P. A. Vanrolleghem ........................ 1297 Robust Controller Design for a Chemical Reactor M. Bako~ovd, D. Puna and A. Mdsz~ros .................................................................

1303

A M1NLP/RCPSP Decomposition Approach for the Short-Term Planning of Batch Production N. Trautmann and C. Schwindt ............................................................................... 1309 A Framework for On-line Full Optimising Control of Chemical Processes P. A. Rolandi and J. A. Romagnoli .......................................................................... 1315

Wavelet-Based Nonlinear Multivariate Statistical Process Control A. H. S. Maulud, D. Wang and J. A. Romagnoli ..................................................... 1321

Anaerobic Digestion Process Parameter Identification and Marginal Confidence Intervals by Multivariate Steady State Analysis and Bootstrap G. Ruiz, M. Castellano, W. Gonzdlez, E. Roca and J. M. Lema .............................. 1327 An Efficient Real-Time Dynamic Optimisation Architecture for the Control of NonIsothermal Tubular Reactors M. R. Garcia, E. Balsa-Canto, C. Vilas, J. R. Banga andA. A. Alonso ................. 1333 Model Based Control of Solidification B. Furenes and B. Lie .............................................................................................. 1339

h-Techsight: A Knowledge Management Platform for Technology Intensive Industries A. Kokossis, R. Ba~ares-Alc(mtara, L. Jimdnez Esteller and P. Linke ................... 1345 Modelling for Control of Industrial Fermentation J. K. Rasmussen, H. Madsen and S. B. Jorgensen .................................................. 1351

ix

System-Dynamics Modelling to Improve Complex Inventory Management in a Batch-Wise Plant Z. I,'erwater-Lukszo and 7". S. Christina .................................................................. 1357 Dynamic Modeling and Nonlinear Model Predictive Control of a Fluid Catalytic Cracking Unit R. Roman, Z. K. Nag3,, F. AllgOwer and S. Agachi ................................................. 1363 Improving of Wavelets Filtering Approaches R. I.~. Tona, .4. Espu~a ~lncl L. Pui~/aner . ................................................................

1369

Supply Chain Monitoring: A Statistical Approach F. D. Me/e, E. Musulin and L. P u i ~ / a n e r . ...............................................................

1375

Closing the Intbrmation Loop in Recipe-Based Batch Production E. Mztsulin, M. d. Arbiza, A. Bon/il[ and L. Puigffaner ............................................

1381

Agent-Based Intelligent System Development for Decision Support in Chemical Process Industry ): Oao and A. Kokossis ........................................................................................... 1387 Enhanced Modelling of an [industrial Fermentation Process through Data Fusion Techniques S. Triadaphillou, E. B. Martin, G. Montague, P. Je~jkins, S. Stimpson and A. Nordon ..................................................................................................................... 1393

Implementation of Multi-Kalman Filter to Detect Runaway Situations and Recover Control R. Nomen, d. Sem/gere, E. Serra and d. Cano .......................................................... 1399 Supply Chain Management through a Combined Simulation-Optimisation Approach F. D. Mele, A. Espu~a and L. Pui~janer .................................................................

1405

Data-Based Internal Model Controller Design for a Class of Nonlinear Systems A. G. Kalnlukale and M.-S. Chiu .............................................................................

1411

Measurement-Based Run-to-run Optimization of a Batch Reaction-Distillation System A. Marchetti, B. Srinivasan, D. Bonvin, S. Elgue, L. Prat and M. C a b a s s u d ......... 1417 Nonlinear Behaviour of a Low-Density Polyethylene Tubular Reactor-SeparatorRecycle System M. H~/ele, I. Disli-Uslu, A. Kienle, I': M. Krishna, S. P u s h p a v a n a m and C.-U. Schmidt .................................................................................................................... ! 423 Control and Optimal Operation of Simple Heat Pump Cycles J. B. Jensen and S. Skogestad ..................................................................................

1429

Advanced Process Control of Pantolactone Synthesis using Nonlinear Model Predictive Control (NMPC) ('. Cormos and S. A,~zachi ........................................................................................ 1435 Design and Analysis of a Classical Controller to the Residual Oil in a Small Scale Semibatch Extractor A. F. Cust6dio, D. F. Rezende, M. R. Wolj:Maciel and R. M. Filho ....................... 1441 Optimal Sensor Network Design and Upgrade using Tabu Search M. C. Carnero, ,1. L. Hern(mdez and M. C. Sdmchez ...............................................

1447

Multiperiod Planning of Multiproduct Pipelines D. C. Cafaro andJ. Cerdd ...................................................................................... 1453

Statistical Performance Monitoring Using State Space Modelling and Wavelet Analysis A. Alawi, A. J. Morris and E. B. Martin .......................................... , ....................... 1459 Predictve Functional Control Applied to Multicomponent Batch Distillation Column D. Zumoffen, L. Garyulo, M. Basualdo and L. Jimdnez Esteller ............................ 1465 Fault Tolerant Control with Respect to Actuator Failures. Application to Steam Generator Process A. A ~touche and B. Ould Bouamama ....................................................................... ! 471

Open/Closed Loop Bifurcation Analysis and Dynamic Simulation for Identification and Model Based Control of Polymerization Reactors M. P. Vega and M. R. C. Fortunato ........................................................................ 1477 Effect of Recycle Streams on Energy Performance and Closed Loop Dynamics of Distillation Sequences S. Herndndez, J. G. Segovia-Herndndez, J. C. Cdrdenas and V. Rico-Ramirez ..... 1483 Expert System for the Control of Emergencies of a Process Plant M. L. Espasa and F. B. Gibert .................................................... , ............................ 1489 An Expert System for a Semi-Batch Pilot Scale Emulsion Copolymerisation Facility R. Chew, B. Alhamad, V. G. Gomes and J. A. Romagnoli ...................................... 1495

Integrating Data Uncertainty in Multiresolution Analysis M. S. Reis and P. M. Saraiva ................................................................................... 1501

Integrated Approaches in CAPE Integrated Process and Product Design Optimization: A Cosmetic Emulsion Application F. P. Bernardo and P. M. Saraiva ........................................................................... 1507 Design Synthesis for Simultaneous Waste Source Reduction and Recycling Analysis in Batch Processes I. Halim and R. Srinivasan ...................................................................................... 1513

Design and Control Structure Integration from a Model-Based Methodology for Reaction-Separation with Recycle Systems E. Ramirez and R. Gani ........................................................................................... ! 519

Modelling and Optimisation Collaborative Research Project

of Industrial

Absorption

Processes:

An

EC

P. Seferlis, N. Dalaouti, E. Y. Kenig, B. Huepen, P. Patil, M. Jobson, J. Kleme~, P. Proios, M. C. Georgiadis, E. N. Pistikopoulos, S. Singare, C. S. Bildea, J. Grievink, P. J. T. Verheijen, M. Hostrup, P. Harper, G. Vlachopoulos, C. Kerasidis, J. Katsanevakis, D. Constantinidis, P. Stehlik and G. Fernholz ................................. 1525

An Integrated Approach to Modelling of Chemical Transformations in Chemical Reactors T. Salmi, D. Yu. Murzin, J. Wdrngt, M. Kangas, E. Toukoniitty and V. Nieminen .. 1531

xi

An MILP Model for the Optimal Design of Purification Tags and Synthesis of Downstream Processing E. Simeonidis, J. M. Pinto and L. G. Papageorgiou ............................................... 1537 An Upper Ontology based on ISO 15926 R. Batres, M. West, D. Leal, D. Price and }I. Naka ................................................. 1543

Multi-agent Systems for Ontology-Based Information Retrieval R. Ba~ares-Alc~ntara, L. Jim~nez Esteller and A. Aldea ....................................... 1549

An Agent-Based Approach for Supply Chain Retrofitting under Uncertainty G. GuillOn, F. D. Mele, F. Urbano, A. Espu~a and L. Puigjaner ........................... 1555

Pharmaceutical Informatics: A Novel Development and Manufacture

Paradigm for Pharmaceutical

Product

C. Zhao, G. Joglekar, A. Jain, V. Venkatasubramanian and G. V. Reklaitis .......... 1561

A Web Service Based Framework for Information Integration of the Process Industry Systems Xiangyu Li, Xiuxi Li and E Qian ............................................................................ 1567 A Library for Equation System Processing based on the CAPE-OPEN ESO Interface G. Schopfer, J. Wyes, W. Marquardt and L. von Wedel .......................................... 1573 On the Optimal Synthesis of Micro Polymerase Chain Reactor Systems for DNA Analysis T. Zhelev .................................................................................................................. 1579 An Agent-oriented Approach to Integrated Process Operations in Chemical Plants M. Nikraz and P. A. Bahri ....................................................................................... 1585

Entire Supply Chain Optimization in Terms of Hybrid in Approach T. Wada, E Shimizu and J. Yoo ............................................................................... 1591 A Computer Architecture to Support the Operation of Virtual Organisations for the Chemical Development Lifecycle A. Conlin, P. English, H. Hiden, A. J. Morris, Rob Smith and A. Wright ............... 1597 An Approach for Integrating Process and Control Simulation into the Plant Engineering Process M. Hoyer, R. Schumann and G. C. Premier ............................................................ 1603 Process Integration and Optimization of Logistical Fuels Processing for Hydrogen Production F. T. Eljack, R. M. Cummings, A. F. A bdelhady, M. R. Eden and B. J. Tatarchuk 1609 A Systematic Approach for Synthesis of Optimal Polymer Films for Radioactive Decontamination and Waste Reduction T. L. Mole, M. R. Eden, 7". E. Burch, A. R. Tarrer and J. Johnston ........................ 1615 Integration of Planning and Scheduling in Multi-site Plants- Application to Paper Manufacturing S. A. Munawar, M. D. Kapadi, S. C. Patwardhan, K. P. Madhavan, S. Pragathieswaran, P. Lingathurai and R. D. Gudi .................................................. 1621

Review of Optimization Models in the Pollution Prevention and Control E. Kondili .................................................................................................................

1627

Models for Integrated Resource and Operation Scheduling A. Ha~t, M. TrOpanier and P. Baptiste ..................................................................... 1633

xii Automated Process Design Using Web-Service based Parameterised Constructors T. Seuranen, T. Karhela and M. Hurme .................................................................. 1639

Integrated Design of Optimal Processes and Molecules: A Framework for SolventBased Separation and Reactive-Separation Systems A. L Papadopoulos and P. Linke ............................................................................. 1645 A Computer-Aided Methodology for Optimal Solvent Design for Reactions with Experimental Verification M. Foli~, C. S. Adjiman and E. N. Pistikopoulos .................................................... 1651 Development of Information System for Extrusion Forming Process of Catalyst Pastes A. V. Jensa, A. A. Polunin, V. V. Kostutchenko, l. A. Petropavlovskiy and E. M. Koltsova ................................................................................................................... 1657

Integrating Short-Term Budgeting into Multi-site Scheduling G. Guill~n, M. Badell, A. Espu~a and L. Puig/aner ................................................ 1663

An Integrated Modelling Framework for Asset-Wide Lifecycle Modelling S. Sundaram and K. Loudermilk ............................................................................. 1669

AUTHOR INDEX ................................................................................................. 1675

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 ElsevierB.V. All rights reserved.

955

A Framework for the Mixed Integer Dynamic Optimisation of Waste Water Treatment Plants using Scenario-Dependent Optimal Control Jan Busch a, Marcella Santos b, Jan Oldenburg c, Andreas Cruse d and Wolfgang Marquardt a* aLehrstuhl ffir Prozesstechnik, RWTH Aachen, D-52056 Aachen, Germany bSchool of Chemical Engineering, UNICAMP, Campinas- S P - Brazil CBASF Aktiengesellschaft, D-67056 Ludwigshafen dUhde GmbH, Friedrich-Uhde-Str. 15, D-44141 Dortmund

Abstract in many real life processes, operational objectives, constraints and the process itself may change over time. This is due to changing product requirements, market demands and other external or internal influences, which constitute a certain scenario. Modelbased techniques can provide optimal solutions to the corresponding scheduling and process control problems. This paper focuses on those situations, where the objectives and constraints of plant operation depend on the scenario and therefore change over time. A framework is developed, which enables the modelling and scheduling of different operational strategies on the optimisation horizon. A case study involving a waste water treatment plant is used to demonstrate the approach. Existing expert knowledge is used to relate certain operational objectives and constraints to corresponding scenarios. It is shown that easily interpretable optimisation results are obtained. Also, the results are significantly improved as compared to a weighted average approach only approximating sequential strategies.

Keywords: online optimisation, plant scheduling, scenario-dependent optimal control, waste water treatment, mixed integer dynamic optimisation 1. Introduction With recent advances in the fields of process modelling, optimisation algorithms, computing power and practical experience, model-based techniques like online optimisation and plant scheduling have moved from being a purely academic challenge towards industrial relevance. Model-based control and scheduling require process models and models for the operational constraints and objectives. In the following, the operational constraints and objectives are defined as the operational strategy. Two typical operational strategies are to produce a certain product grade at minimum cost or at maximum throughput. Secondly, the scenario is defined to be the whole of those internal and ex-

Author to whom correspondence should be addressed: [email protected]

956 ternal factors, which determine a suitable operational strategy, e.g. stock hold-ups, predicted market demand etc. This paper focuses on those situations, where the operational strategy depends on the present scenario, which may change over time. If such a change occurs on the time horizon which is considered in the optimisation, two or more periods (stages) with different operational strategies have to be scheduled in a way to yield optimal overall plant performance. Therefore, a framework will be proposed, which allows for the accurate modelling and scheduling of such problems, introducing the notion of scenario-dependent optimal control. a)

.

I I ]

stage

0

stage

stage

b)

stage 3

I [ 1 i st. 2 i

I

I

stage 3

I stage 1 i st. 2 i stage 3 ]

I time

time

Figure l a,b. Moving Horizon Control and Plant Scheduling

2. State of the art The types of processes considered in this work are continuous processes, for which optimal base controller set point trajectories are to be determined using dynamic real time optimisation. Disturbances on a fast time scale are not accounted for on this control level, but long-term, predictable disturbances are considered. The optimisation is iteratively performed on a moving horizon, as depicted in Fig. l a. In the following, two approaches will be introduced, which have been extensively treated in literature and which are valid for certain problem specifications. Based on this, the idea of scenariodependent optimal control will be developed. If the operational objectives and constraints are assumed to be time invariant, the horizon can be interpreted as one stage, on which the continuous optimisation problem is solved (single stage formulation). A plant scheduling problem evolves, when different products or product grades are to be produced sequentially, as e.g. in modem multipurpose plants (Papageorgiou et al., 1996). Here not only the individual production campaigns have to be optimised, but also their number, sequence and lengths. The optimisation horizon is split into stages, which correspond to the campaigns. On each stage, the process model and the operational constraints may be different. However, the operational objective is the same on all stages. Although usually performed offiine, an iterative moving horizon implementation is shown in Fig. lb.

3. Scenario-dependent optimal control 3.1 Motivation

In contrast to these approaches, this paper considers situations where the operational constraints and the objectives change over time. Abel and Marquardt (2000) have treated the case that at every point in time a critical event could take place, e.g. the burst of a rupture disc, after which it must still be possible to meet certain safety constraints

957 using a suitable operational strategy. Since the moment of failure is expected at every point in time, this leads to a high problem complexity. Here the case is considered that the sequence of operational strategies depends on predictable scenarios. The motivation to do so originates from research on the optimisation-based control of the waste water treatment plant discussed in the case study. When trying to formulate a suitable model-based operational strategy, it was found that plant operators employ two different strategies. At certain times the objective is to maximise the throughput in order to increase flexibility, at other times it is to minimise the energy consumption. The choice of a strategy mainly depends on the predicted inflow and therefore changes over time. There are several possibilities to approximate the use of scenario-dependent operational strategies, e.g. by considering a weighted average of the individual objectives. This weighted average can be expressed in a single objective function, which is valid at all times and which can be optimised using a single stage formulation. The main difficulty is assigning suitable values to the weights, which means e.g. to assign a monetary value to flexibility that is valid in all possible scenarios. However, to the authors' knowledge, no exact modelling and scheduling methodology for scenario-dependent operational strategies has been reported so far. This paper proposes such a rigorous approach, which can be interpreted as a variation of regular plant scheduling on a moving horizon. The campaigns are substituted by time periods, during which a certain operational strategy is employed. The main difference is that not only the constraints, but also the operational objectives may change from stage to stage, while the process model is always the same. The expected benefits of the are: 1. Expert knowledge concerning the strategies and the heuristics, when to employ which strategy, can be exactly represented. This might enhance the overall optimisation results as compared to approaches only approximating sequential strategies. 2. Since the optimisation results correspond to well known strategies, which are separated in time, they are more easily interpretable by plant operators. This is a key factor in enhancing the acceptance of model-based techniques in industrial settings.

3.2 Formulation of the optimisation problem K

rain Y', w/<:/< (x(t f ,k ),z(t./.,/,. ),u(t /.,/< ),d(t f ,/<), p,t f,l <) u,tf,k /<=1

l(x,x,z,u,a,p,t)=o,

x(to,~)= xo, t e[to,k,t/k],

k {1..... K),

g (x.~.z...u.~,.t)<_ o. s.t.

uk(x.x.z...a.p.t)<_o.

k {1..... K},

,, ), l,,t.:.,. )- o, hk, (.~(t/. ,. ), x(t i. ,. ), z(t j. ,. ),#(tj., ),a(t/., ), l,,t./., )<- o,

(P1)

v,~,, (x(t :. ,. ), x(t:.,. ,, ), ~(t/. ,. ), u(t/. ,~ ),a(t:.

r(,,(t :., ))- ,,(to..,+~ ),

,

{1..... K - 1 1 , {1.....

The proposed problem formulation is given by (P 1). The process model, which is valid on all stages, is determined by f and g*. The disturbances are given by d, u are the controis, x are the differential and z are the algebraic state variables, and p are the parame-

958 ters. The sequence of operational strategies is reflected by a sequence of K stages on the optimisation horizon. Each stage k is assigned one operational strategy, which is modelled in detail by a set of constraints gk and an objective function ~bk.The length of stage k is defined by the interval [t0.k,t~k]. Between the stages, K- 1 switching conditions q~sand hs and stage transition conditions F~ for the differential states have to be defined. The initial conditions x0 have to be determined from measurements or from state estimation. In the overall objective function, the weighted objective functions of the stages are summed up. For two reasons, these weights are much easier to choose than in weighted average approaches. In case there is only one strategy used on the optimisation horizon, no weighting is considered at all. If several strategies are employed, the weighting only has the role of setting priorities among the objectives in a certain scenario, as will be demonstrated in the case study. Since the number, type and order of strategies are not known beforehand, they represent discrete degrees of freedom. There are two possibilities to determine the values for the discrete variables: either they are determined by an appropriate optimisation algorithm together with the continuous optimisation problem, or they are determined beforehand by some decision algorithm or expert knowledge. If they can be determined beforehand, the problem reduces to a so-called multistage problem. Otherwise, a mixed integer dynamic optimisation (MIDO) problem has to be solved. Due to limited space, only the formulation of the multistage problem is presented here. The formulation of the MIDO problem can be derived from Oldenburg et al. (2003). Multistage and especially MIDO problems are computationally more demanding than single stage problems. However, since planning problems are usually solved on longer time horizons, the increase in computation time is not expected to be a limiting factor. The software tool DyOS (DyOS, 2002), which has been developed at the LPT, is an efficient tool for solving problems of type (P 1) as well as MIDO problems and is used in the following case study (Schlegel et al., 2004).

4 Case study: Waste water treatment plant The proposed methodology will be exemplified in a case study involving a simulated municipal waste water treatment plant (WWTP). A simplified flowsheet of the process is shown in Fig. 2. Incoming waste water is stored in a buffer tank. From there, it is transferred to a biological stage, consisting of a denitrification and a nitrification tank, which are connected by a recycle stream. Air can be blown into the nitrification tank and sludge can be withdrawn from it. The biomass and the purified water (product) are separated by membrane filtration. The relevant operational constraints are the upper limits of the buffer tank volume and of the permeate ammonia concentration. The operational cost of the process is mainly caused by the air flow. There is a maximum power consumption level, above which the cost increases dramatically. In the following, this is related to an air flow threshold. From discussions with plant operators, it is understood that there are two operational strategies, whose employment mainly depends on the predicted inflow: 1. Regular inflow: The aim is to bring the buffer tank volume to a certain, usually low target value, while keeping the air flow below the threshold. This is called the flexibility strategy, as it increases flexibility for unforeseen high inflow situations.

959 2.

High inflow: If staying below the air flow threshold and meeting all constraints cannot be achieved due to high inflow, the air flow is allowed to exceed the threshold, but as little as possible. This is called the e c o n o m i c s strategy. These two strategies are modelled with appropriate constraints and objective functions. The stage transition conditions /-" enforce continuity of all x between all stages. No switching conditions h or (p are required. The process m o d e l f g* is given by biological kinetics (Gujer et al., 1999) and mass balances. The membrane is assumed to be an ideal splitter. The resulting model consists of 42 differential and 236 algebraic equations. The size of the problem mainly results from the 13 components considered in each tank. The overall length of the optimisation horizon is 3 days, for which a perfect inflow prediction is assumed to be available. In this case study, a new optimisation mn is performed once per day. The sequence of operational strategies on the horizon is determined manually by inspection of the predicted inflow. The weights wk are chosen such that the minimisation of cost has priority over the increase of flexibility. The degrees of freedom are the controls u and the endpoints of the stages t/:,. waste water

btlffel

tank

denitrification

nitri-

1Fleli1-

fication

brahe

!rec3'cleflow l i t

airflow " sludge withdrawal

Figure 2. Schematic representation o[the waste water treatment 1)/ant

Some results of an extensive optimisation study are depicted in Fig. 3. The inflow history is characterised by a strong rain event on day 7 and a smaller one on day 10, superposed by the regular daily inflow. From day I to day 4, the flexibility strategy is applied. This implies that the air flow does not exceed the threshold of 55 1/day and that the objective of the optimisation is to lower the volume in the buffer tank. On day 5, the strong rain event on day 7 is predicted. As now the flexibility strategy would become infeasible, the economics strategy is employed. The air flow increases as much as necessary. This in turn allows the permeate flow to increase such that the upper limit of the buffer tank volume of 3000 m 3 is met. At the end of day 7, the flexibility strategy is employed again. The interpretation of the results is straightforward, because at every point in time only one operational strategy is employed, the choice of which is deduced from the operational context. This enables simple relations between the operational objective and constraints and the resulting input and state trajectories. Fig. 3 also shows the computed trajectories in the same setting, but approximating the problem with a weighted average single stage formulation. The deviation from the air flow threshold and from the buffer volume target value are weighted and summed up in a single objective function. This implies that both objectives are considered at every point in time. Several weights have been tried and the most successful combination is presented here. While the computed permeate flow and the resulting buffer tank volume are very similar to the results of the multistage optimisation, a different recycle stream and a much higher air flow are computed, leading to an increase of cost by a factor of 170%. This shows that separating the strategies and sequencing them, as suggested by

960 practitioners, leads to substantially better optimisation results. Also, the interpretation of the single stage results is not straightforward (consider e.g. the peak of the air flow on day 7), since at every point in time two competing objectives are considered. Inflow .

~" 6ooo ~4000

.

.

.

.

.

Buffer kink volume

.

.

.

.

.

.

.

.

.

.

3000

.

""'I!2 ''r'''g''

~*""g"

2000

.

- - I~KilKsfage

.

50

.... .

. ]

.

. .

. .

. .

~. . . . . . . . . . . . .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

l'hlme[~.tysl Recycle stream

~_ so .

.

1 2 3 d 5 6 7 8 O 10 1| I2 13 14

Air flow

.

.

I 72°°°'s ~ lo0o

1 2 3 4 5 6 7 8 9 10 |1 112 13 ld Tin~ [daysl

"~ 60

.

.

.

,,, .... .

.

.

.

,, . . . . . .

I :2 3 4 5 6 7 8 9 1011 12 13 t4

Time l~y~l

--

~"

"= s000 =~ 4000 0

......................

1 2 3 4

5 6

7 8 9

t011 12

13 14

Time Iday,q

Figure 3. Optimisation results (multistage a n d single stage f o r m u l a t i o n )

5 Conclusions

Scenario-dependent optimal control allows to model and schedule sequences of different operational strategies, each of which is employed in a certain operational scenario. It leads to easily interpretable and, in the presented case study, to significantly improved optimisation results. Future research should analyse for which processes improved optimisation results can be expected and concentrate on applications. Reliable disturbance forecasting and automatic sequencing are important aspects in this context. References

Abel, O., Marquardt, W., 2000, Scenario-Integrated Modeling and Optimization of Dynamic Systems, AIChE Journal 46, 4. DyOS, 2002, DyOS User Manual, Release 2.1, Lehrstuhl for Prozesstechnik, RWTH Aachen, Aachen. Gujer, W., Henze, M., Mino, T. and van Loosdrecht, M., 1999, Activated Sludge Model No. 3, Water Science and Technology 39, 1. Oldenburg, J., Marquardt, W., Heinz, D., Leineweber, D. B., 2003, Mixed-Logic Dynamic Optimization Applied to Batch Distillation Process Design, AIChE Journal 49, 11. Papageorgiou, L. G., Pantelides, C. C., 1996, Optimal campaign planning scheduling of multipurpose batch semicontinuous plants. 1. Mathematical formulation, Ind. Eng. Chem. Res. 35, 2. Schlegel, M., Stockmann, K., Binder, T., Marquardt, W., 2004, Dynamic optimization using adaptive control vector parameterization, submitted to: Computers & Chemical Engineering. Acknowledgements

The financial support by the DFG (German Research Foundation) in the project "Optimisation-based process control of chemical processes" is gratefully acknowledged.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

961

On-line Fault Diagnosis Support for Real Time Evolution applied to Multi-Component Distillation Sergio Ferrer-Nadal, Ignacio Y61amos-Ruiz, Mois~s Graells and Luis Puigjaner* Chemical Engineering Department, Universitat Politbcnica de Catalunya Av. Diagonal 647, E-08028, Barcelona, Spain

Abstract In this paper, the Real Time Evolution algorithm (Sequeira et al., 2002) is applied to the on-line optimization of a debutanizer distillation column. A fault diagnosis system (FDS) implemented within a supervisory module is responsible for handling incidences (faults and disturbances) happening in the plant by taking the appropriate corrective actions, including the activation of the RTE system. Thus, a more robust on-line performance is achieved. The implementation of the RTE scheme has been performed using Matlab© and the commercial simulation package HYSYS.Plant©, taking advantage of their communication capabilities (COM technology). Different possible plant incidences are addressed, involving different sources and types of disturbances. Results of RTE are compared with those obtained using the standard Real Time Optimization approach, showing better performance in most of the cases.

Keywords: On-line optimization, Real-time evolution, Multi-component distillation, Fault diagnosis.

1° Introduction On-line optimization is a very important issue in chemical and petrochemical plants since it allows immediate response to internal or external disturbances in order to continuously maximize the economic and environmental performance of the whole process. Real Time Evolution (RTE) introduces a new approach to on-line optimization that overcomes the drawbacks reported for the classical RTO approach. According to Friedman (1995), the steady state data required in a common dynamic environment needs heavy filtering and leads to long waiting. Furthermore, detailed process models are demanded whereas a proper trajectory for the implementation of the manipulated variables to reach the optimum is usually not provided. The aim of this work is to show the concept of Real Time Evolution supervised by a fault diagnosis system in a multi-component distillation column. This system operates under a more robust framework, able to distinguish between incidences susceptible to be optimized (disturbances) and incidences that require alternative actions to keep the

Author to whom correspondence should be addressed: [email protected]

962 process stability (faults). This new structure decides continuously whether to operate under RTE or to activate alternative actions depending on the fault diagnosed.

2. Real Time Evolution RTE responds quickly to disturbances (both, external or internal) by a continuous adjustment of the set-point values based on a steady state model. The plant parameters evolve smoothly, but continuously, towards the objectives without performing formal optimization. RTE is able to deal with continuous disturbances because it does not need to reach the steady state to trigger the improvement mechanism, leading to a better overall process performance. Plant model updating is only carried out when the steady state is reached. RTE relies on four main aspects: improvement algorithm, RTE neighbourhood, time between successive executions and steady state model. The improvement algorithm is based on the way that the new points in the surroundings of the current set point values are selected. This neighbourhood is defined as the maximum allowed changes in the process variables to be evaluated. A successful RTE application requires an appropriate parameter tuning and selection of these elements (Sequeira et al, 2002).

3. Supervisory Control The optimization technique described in the previous section runs under a supervisory fault diagnosis system. This supervisory module is the core of the on-line response system against deviations from the normal behaviour of the plant making the overall process more reliable and safe. The supervisory module organizes the global performance of the plant, in such a way that differentiates the incidences that can arise in the plant, classifying them into two main groups. Incidences affecting the profit of the plant are classified as disturbances and are susceptible to operate under on-line optimization by the RTE, while incidences that affect the safety and good performance of the plant are named and classified as faults that may generate different responses of the supervisory module, i.e. activating a set of corrective actions to prevent more critical situations by monitoring different alarms and advising operators in the way they should act against this abnormal events. Incidence detection is carried out through a MSPCA (Multiscale principal component analysis) (Bakshi, 1998), which is based on PCA (principal component analysis), one of the most applied multivariate statistical techniques (Kourti and MacGregor, 1995). Through the structure of MSPCA, the capacity of PCA to extract the relationship between variables is combined with the capacity of wavelets to separate deterministic features from stochastic processes. It approximately decorrelates the auto-correlation among the measurements. Incidence isolation and diagnosis is carried out by a feed forward neural network trained in order to classify the signals received from the plant. Most possible disturbances and faults are tested, to extract enough data for properly training the artificial neural network. Then, it is prepared to classify new data from an abnormal behaviour of the plant.

963

4. System Architecture The supervisory control decides at each moment if data received from plant correspond to normal behaviour or an abnormal situation (figure 1). When an abnormal event arises, it decides if this incidence is critical for the good performing of the plant (fault) or the plant is susceptible to be optimized (disturbance). In this case, RTE is automatically activated by the supervisory control. The time for diagnosing the fault must be minimized to take advantage of the benefits gained by an early reaction of RTE. First, current conditions from the plant are collected and applied to the steady state model. With this model, the improvement algorithm explores the surroundings of the current set-point values evaluating the resulting objective function. The combination improving the objective function value is chosen and immediately applied to the plant through the control system. OUTPUTS

INPUTS

PLANT

E

T Disturbances

I

1

I

I

__

CONTROL

T

i I

~ ....

Faults

I

SUPERVISORY I I I

CONTROL I

FDS

ACTIONS

II _!

L--

Figure 1. R TE supported by fault diagnosis system

When the plant reaches its optimum operation conditions and no disturbances occur, the value of the proposed set-points will not change. Therefore, no action will be done in the plant. in case a fault is diagnosed, the supervisory control shows warnings or advices to the operator. Depending on the nature of the fault, it also can execute a previously designed protocol consisting of corrective actions to be applied to the process. The implementation has been done with a Matlab function. It acts as a data manager establishing the communication between the plant (Hysys in dynamic mode), the model (Hysys in steady state mode), the optimization algorithm (Matlab), and the supervisory module (Matlab). Communication between Matlab and Hysys.Plant® is executed by mean of COM technology.

5. Case Study: D e b u t a n i z e r C o l u m n The debutanizer column provided by Aspentech© at their World Wide Site documentation (http://support.aspentech.com) has been chosen for this paper in order to make the results more reproducible. This multi-component distillation column has fifteen stages and is fed by two streams consisting of a mixture of light hydrocarbons. Firstly, the column has been simulated in Hysys.Plant® in steady state mode. This will

964 be the steady state model for the RTE algorithm. Secondly, the necessary modifications have been made in order to build the dynamic simulation including the control mechanism (Table 1) given by Figure 2. This dynamic simulation will be used as the real plant to be online optimized. Vent

PIC-IO0 Cond Duty Butane Product

Butanes

Feed2

••DReubty

.-.,.

Feed1

LIC-101

C5+

VLM- 101

Liquid Product

Figure 2. Debutanizer Flowsheet Table 1. Parameters for the PI controllers

Controller Kc Ti, min

LIC- 100 1.80 10.00

LIC- 101 2.00 10.00

PIC- 100 2.00 2.00

TIC- 100 5.00 20.00

An objective function IOF (instant objective function) has been proposed in order to evaluate the plant performance at every moment: IOF (t) = (Amount of C4 & lighter in Butane Product) • (Price of Butane Product) + (Amount of C5+ in Liquid Product) • (Price of Liquid Product) - (Flow of Feed l) • (Price of Feed l) - (Flow of Feed2) • (Price of Feed2) - (Condenser Heat Duty) • (Price of Condenser Heat) - (Reboiler Heat Duty) • (Price of Reboiler Heat), m.u./time (1) Table 2. Prices of the feed and product streams

Feed1,

Feed2,

Butane P.,

Liquid P.,

Cond. Heat,

Reb.Heat,

m.u./kg

m.u./kg

m.u./kg

m.u./kg

m.u./kW

m.u./kW

2.00

2.00

3.00

3.00

0.00009

0.0005

As RTO and RTE are not comparable in terms of an instant objective function, a mean objective function is employed taking into account the accumulative produced profit:

MOF

(t) -

I' IOF o

(t)dt

( t - to)

, m.u./time

(2)

965

6. Results A case study is considered for which the decision variables are the set points of one of the controllers (6 th stage temperature) and the reflux rate of the column. RTE requires a parameter tuning depending on the studied scenario, in this case, a maximum allowed change in set points of 0.3% around the old value and 50 seconds between consecutive executions have been considered showing satisfactory results. In a first situation, a step rise (+20%) in the mass flow of Feedl is diagnosed and automatically the RTE optimization is activated. While RTE reacts immediately against this disturbance, RTO has to wait until steady state is reached. This faster RTE response is translated in a better value of the mean objective function compared to those obtained by RTO. Figure 3 shows RTO has reacted later (11000 seconds approx.), losing benefits during the transition to steady state. Feed1

2.9

,",,,,

._

2.8

\

~1

2.7

3.1

~

3

=

Step

Fall to 2.232

kg/s

2.6 .-, 2.5

,,. . . . . . , . - " ' -

iQ~;~

2.3

No Optimiza{ion

................

R T O

0

0.2

0.4

0.6

0.8

Simulation

1

1.2

Ti

me,

1.4

s

1.6

1.8

2 x

10 4

Figure 3. Mean Objective Function for a step disturbance in the Feedl temperature

In case of a continuous disturbance arises in the mass flow of Feedl (-0.0002 kg/s), the optimization by RTO shown in Figure 4 is not possible since the plant never reaches a steady state. This RTO's weak point is where RTE shows better performance, since for these situations RTO may not be applied. Therefore, the obtained results with RTE can be only compared when no optimization is carried out. Figure 4 shows the instant objective function for this case while Figure 5 represents the mean objective function for the simulation time considered. In this distillation column, an example of possible fault is a fall of 20% in the mass flow of Feed2. When the supervisory control diagnoses this fault, a message advises the operator to check the valves involved. In addition, the supervisory control will perform a protocol consisting of a by-pass of the feed flows and an operation change to total reflux until the break-down is mended.

7. Conclusions and Future W o r k A supervisory control based in a fault diagnosis system integrated to the RTE algorithm has been implemented for a debutanizer column. Further work will be orientated to

966

adapt the fault diagnosis system to the new conditions of the plant after an optimization, since current FDS is only prepared to detect disturbances from the base normal operation. It will be also possible to modify critical parameters from the optimization model obtaining for each case diagnosed a more accurate model. Feed1

Ramp

Fall-0.0002

kg/s

3

E 2.5

xx

¢

2

>

1.5

RTE

No

1

'",

Optimization

5000

10000

S i m u l a t i o n

Ti

me,

15000

s

Figure 4. Instant Objective Function for a continuous disturbance in the Feedl temperature Feed1

Ramp

Fall

-0.0002

kg/s

2.8

2.6

S ]~

2.4

2.2

1.8

No

Optimization

"''''"--.

:.

5000

10000

S i m u l a t i o n

Time,

15000

s

Figure 5. Mean Objective Function for a continuous disturbance in the Feedl temperature

References Sequeira, S., M. Graells, and L. Puigjaner, 2002, Real-Time Evolution for On-line Optimization of Continuous Processes, Ind.Eng.Chem.Res., Vol.41, 1815-1825 Friedman, Y., 1995, What's wrong with unit closed loop optimization?, Hydrocarbon Processing, 107

Bakshi, B.R., 1998, Multiscale PCA with Application to Multivariate Statistical Process Monitoring, AIChE J., Vol. 44, No. 7, 1596-1610 Kourti, T. and J.F. MacGregor, 1995, Process analysis, monitoring and diagnosis, using multivariate projection methods, Chemometrics and Intelligent Laboratory Systems 28, 3-21 Acknowledgements Financial support received from "Generalitat de Catalunya" (FI program) and Spanish "Ministerio de Educaci6n y Ciencia" (grant FPI) is fully appreciated.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

967

Real-Time Feasibility of Nonlinear Predictive Control for Semi-batch Reactors Harvey Arellano-Garcia*, Tilman Barz, Moritz Wendt and Gtinter Wozny Department of Process Dynamics and Operation, Technical University of Berlin TU Berlin, Sekr. KWT-9, D-10623 Berlin, Germany

Abstract In this work a nonlinear model predictive control scheme for on-line optimization of semi-batch reactors is presented. Since the true process optimum occasionally lies on a boundary of the feasible region defined by one or more active constraints, the process is forced into an infeasible region due to the uncertainty in the parameters and measurement errors. An alternative new approach is proposed to assure both robustness and feasibility with respect to input and output constraints. This approach is based on the backing off of the constrained output variable bound along the moving horizon. With this strategy, a trajectory of mathematical constraint limits will be formed. The trajectory of these bounds is dependent on the amount of measurement error and parameter variation including uncertainty. The perl%rmance of the proposed approach is assessed via an application to a semi-batch reactor under safety constraints, where a strongly exothermic series reaction conducted in a non-isothermal batch reactor is considered to show the analytical steps of the approach, and to demonstrate the efficiency of the proposed online framework.

Keywords: NMPC, Output-Constraints, Dynamic Real Time Optimization, Batch Processes, Safety. 1. Introduction Batch processing provides greater flexibility in the production of specialty and pharmaceutical chemicals. The trend in the chemical industry towards high value products has increased interest in the optimal, model-based control of batch processes. These control problems are generally posed as tracking problems for time-varying reference trajectories defined over a finite time interval. However, during the course of a typical batch, process variables swing over wide ranges and process dynamics go through significant changes due to nonlinearity. Furthermore, batch processes are characterized by significant uncertainties, a certain number of noisy measurements and the fact that the controlled properties are usually not measured on-line. Therefore, the potential advantages of a model based control system are likely to lead to significant tracking errors. With the aim of dealing with model uncertainties and process disturbances, the optimal control problem can also be solved on-line. The on-line

Author to whom correspondence should be addressed:

are i

lano-garcia@tu-be rlin. d e

968 optimization problem is generally non-convex for NMPC. Thus, practical implementation of NMPC becomes difficult for any reasonably nontrivial nonlinear system (Mayne D. Q., 2000). However, critical issues are robustness and the feasibility of the optimization problem, i.e. the presence of an input profile that satisfies the constraints. In this contribution an alternative new approach is proposed to assure both robustness and feasibility with respect to input and output constraints.

2. Problem Formulation A strongly exothermic series reaction conducted in a non-isothermal batch reactor is considered to demonstrate the efficiency of the proposed online framework. The reaction kinetics are second-order for the first reaction producing B from A, and an undesirable consecutive first-order reaction converting B to C. The intermediate product B is deemed to be the desired product. Since the heat removal is limited, the temperature is controlled by the feed rate of the reactant A and the flow rate of the cooling liquid in the nominal operation. The reactor is equipped with a jacket cooling system. At the start, the reactor partly contains the total available amount of A. The remainder is then fed and its feed flow rate is optimized to maximize the yield. However, the accumulation of A at the start of the batch time must be prevented, otherwise, as the batch proceeds; exhaustion of the cooling system capacity can not be avoided. Furthermore, whilst the reaction proceeds, the reactor's volume diminishes so that the computation of the corresponding cooling capacity is adapted according to the remaining cooling jacket area. The developed model takes in both the reactor and the cooling jacket energy balance. Thus, the dynamic performance between the cooling medium flow rate as manipulated variable and the controlled reactor temperature is also included in the model equations. Thereby, it can be guaranteed that later the computed temperature trajectory can be implemented by the controller. Moreover, by this means the limitations of the cooling system (pump capacity) can explicitly be taken into account for the optimization. The resulting model comprises 5 differential states, 2 algebraic state variables, and 3 time-varying operational degrees of freedom. The objective is to maximize the production of CB while minimizing the total batch time subject to diverse operational, quality as well as safety related constraints during the batch and at its final time. The objective function then reads: min (-C B (t r ) + ~ . t r ) %oo,,Fe~d,At There are open-loop final time operation,

with

~=

1 70

(1)

path and end point constraints for the reaction process to be fulfilled by the optimal recipes. First, a limited available amount of A to be converted by the is fixed to NAtot(tf)=500mol. Furthermore, so as to consider the shut-down the reactor temperature of at the final batch time must not exceed a limit.

Tr ( t f ) ~ 303 K

(2)

There are path constraints for the reactor temperature and the adiabatic end temperature r r ( t ) < 356 K

(3)

T~ (t) _<500 K

(4)

969 •~. 500

.~. 3 5 5 L

m

L

335

450

e,~

e'~

E 40O

E 315 .=,=,

'1o ¢..

o ,,,,=, o 295 L

®

350

f .Q 3 0 0 1500

500

2500

3500

4500

."o

0

900

time [s]

1800

2700

3600

4500

time [s]

Figure 1. Path constraints: Reactor temperature (left) and adiabatic end temperature (right). Tad is used to determine the temperature after failure (Abel and Marquardt, 2000). Additionally, the cooling flow rate changes from interval to interval are restricted to an upper bound abs[

(k)] o,o

...., (k +

(5)

The decision variables u(t) are the feed flow rate into the reactor, the cooling flow rate V,,,,, and the different time intervals. A multiple time-scale strategy based on the orthogonal collocation method in finite elements is applied for both discretization and implementation of the optimal policies according to the controller's discrete time intervals (6-12s; 600-700 intervals). The resulting trajectories of the reactor temperature and the adiabatic end temperature for which constraints have been formulated are depicted in Fig. 1. It can be observed that during a large part of the batch time both states variables evolve along the upper limit. The adiabatic end temperature, in particular, is an active constraint over a large time period. Although operation at this optimum is desired, it typically cannot be achieved with simultaneous satisfaction of all constraints, because of the influence of external disturbances (Loeblein and Perkins, 1999). Thus, an NMPC based approach is proposed to implement such an optimal strategy despite disturbances.

3. Nonlinear Model Predictive Control NMPC provides a systematic methodology to handle constraints on manipulated and controlled variables not being limited to a certain model structure. However, for the online optimization of the semi-batch process, the momentary criteria on the restricted controller horizon with regard to the entire batch operation are insufficient. Therefore, the original objective (eq. 1) must be substituted by an appropriate alternative which can be evaluated on the local MPC prediction horizon. N~

min ~'oo]

Ntj

J (N,,N~,N~,)-Zd(j).[.~(t+ j It)-w(t+j)~ + ~ ' 2 ( j ) . [ A u ( t + j - 1 ) ~ -

'

j=N I

(6)

,/'=1

The optimization objective is reduced to a tracking problem. The first term stands for the task of keeping as close as possible to the calculated open loop optimal trajectory of the reactor temperature, whereas the second term corresponds to control activity under the consideration of the systems restriction's described above. Both reactor temperature and adiabatic end temperature are defined as hard-constraints. However, it is well known that hard output constraints can cause problems for two reasons: the optimization can become infeasible, and some of the constraints must then be relaxed or

970

m.~

!

:

i

i

hmcl constraints :.; ,

upl:~, r b o u ! n d

:leterval

n:

deviation by measurement (

iii y

- ri~al

:;

i

;

i

i..................;..................!....................hOr, .........izon ...........................;..................i...................i..................i..................

t=%

future

_'-

Figure 2. Back-off strategy within moving horizon. eliminated. In the latter both approaches rely on relaxation which is, in fact, inapplicable for safety restrictions. In this work an alternative new approach is proposed to assure both robustness and feasibility with respect to input and output constraints. This approach is based on the backing-off of the bound of the hard-constrained output variable along the moving horizon (8intervals). Thus, a trajectory of mathematical constraint limits will be formed. For the near future time points within the horizon, these limits (bounds) are more severe than the real physical constraints and will gradually be eased (logarithmic) for further time points (see Figure 2). The trajectory of these bounds is dependent on the amount of measurement error and parameter variation including uncertainty. The back-off strategy is introduced into the optimization to guarantee that the safety restrictions are not violated at all when the calculated trajectory is applied to the batch process. The basic idea is shown in Fig. 3. The true process optimum lies on the boundary of the feasible region defined by the active constraint. Due to the uncertainty in the parameters and the measurement errors, the process optimum and the set-point trajectory would be infeasible. By introducing a back-off from the active constraints in the optimization, the region of the set-point trajectory is moved inside the feasible region of the process to ensure, on the one hand, feasible operation, and to operate the process, on the other hand, still as closely to the true optimum as possible.

rain u .

.....

.

.

Y <_ymaX ~ack-O~

opiimaibacked off~ ; ~

feasibler e g m n •

.

de/ inistic

. .~%~ . . . . ., e .r ~ . . .

J(u)

point

H 1

Figure 3. Back-offfrom active constraints

971 Table 1. Objective function parameter and hard-constraints back-off.

Tp prediction horizon Tc control horizon MV variation weighting factor offset weighting factor T,,,a., maximum allowable Reactor temperature T,......=356K T,a maximum allowable adiabatic end temperature T,,,ox=508.5K

8 intervals 8 intervals 3000 o~{rrP-i) with ~=0, 7 T ..... ( j = 2...8) = T"~..... - ~,,~x.a'(j--~' with 7~.... =4K, T ..... ( ~ - 2 . . . s ) :

will,

~ ..... =3K,

a~=0.5 ~5;" .... - ~, .... .o, ''--~'

a=0.5

For the formulation of the NMPC-based online optimization, the objective function parameters (eq. 6) and the hard-constraints back-off are presented in Table 1, respectively. The decision variable is again the cooling flow rate. In order to compare the performances of the open-loop nominal solution and the nominal NMPC with the proposed on-line framework under uncertainty, different disturbances have been considered, namely: catalyst activity mismatch and fluctuations of the reactor jacket cooling fluid temperature. Additionally, all measurements are corrupted with white noise e.g. component amount 8%, Temperature 2%.

4. Dynamic Real-Time Optimization The size of the dynamic operating region around the optimum (see Figure 3) is affected by fast disturbances. These are, however, efficiently rejected by the proposed regulatory NMPC-based approach. On the other hand, there are, in fact, slowly time-varying nonzero mean disturbances or drifting model parameters which change the plant optimum with time. Thus, a re-optimization i.e. dynamic real-time optimization (D-RTO) may be indispensable lbr an optimal operation. When on-line measurement gives access to the system state, on-line re-optimization promises considerably improvement. Moreover, additional constraints can be formulated. In this work, we assume that the state information is available.

n1parameters_

Feed

Y

reference trajectory

~ ~ V

(Model)

,,

disturbances

reference trajectory

ad [ Constraints /

I

cSonstrainafety

L

Feasibility

re-optimization D-RTO

__q ~,,~a,,o. s,.,e'I" 'Tri.,.r I ~°-°~'

Figure 4. On-line Framework: Integration of NMPC and dynamic re-optimization

972

(9

1

~

',

,

i

350

335 (9

E (9

320

,4,=,1 L_

0

,!==1

305

refei'ence trajectory ~:

to

(9 '- 290

f

900

I

1800

2700

I

3600

I

4500

time [s] Figure 5. On-line re-optimization." reactor temperature

In order to compensate slow disturbances, the on-line re-optimization problem is automatically activated three times along the batch process time according to a trigger defined as the bounded above difference between the reactor temperature and the temperature reference trajectory (see Figure 5). New recipes resulting from this are then updated as input to the on-line framework. Due to the different trigger time-points the current D-RTO problem progressively possesses a reduced number of variables within a shrinking horizon (Nagy and Braatz, 2003). As a result of this, and a catalyst contamination the total batch time increases. But, despite the large plant mismatch and the absence of kinetic knowledge nearly perfect control is accomplished.

5. Conclusions Feasibility and robustness with respect to input and output constraints have been achieved by the backing-off strategy. The resulting NMPC scheme embedded in the online re-optimization framework is viable for the optimization of the semi-batch reactor recipe while simultaneously guaranteeing the constraints compliance, both for nominal operation as well as for cases of large disturbances e.g. failure situation. The proposed scheme yields almost the same profit as the one of the off-line optimization operational profiles. Currently, the approach is extended to a probabilistically constrained nonlinear model predictive controller.

References Abel O. and W. Marquardt, 2000, AIChE J., 46, 4, 803-823. Loeblein C. and J. D. Perkins, 1999, AIChE J., 45, 5, 1018-1029. Mayne D. Q., 2000, Automatica, 36, 789-814. Nagy, Z.K., and R.D. Braatz, 2003, AIChE J., 49, 1776-1786. Acknowledgements The authors gratefully acknowledge the financial support of the German Research Foundation Deutsche Forschungsgemeinschaft (DFG) under the contract WO 565/12-2.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

973

Control of Integrated Process N e t w o r k s - A Multi-Time Scale Perspective M. Baldea a and P. Daoutidis a.* a

Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave. SE, Minneapolis, MN 55455, USA

Abstract In this paper, we analyze the dynamics of integrated process networks featuring large recycle streams and small purge streams. We consider a prototype network comprising of a reactor and a condenser, and, within the framework of singular perturbations, we establish that the dynamics of such a network exhibits three time scales. We describe a model reduction procedure which leads to an explicit nonlinear description of the dynamics in each time scale, and we outline a controller synthesis procedure that rigorously accounts for this time-scale multiplicity.

Keywords: model reduction, singular perturbations, plant-wide control

1. Introduction Process integration, through material and energy recycle streams, represents the rule, rather than an exception, in the process industries. While offering significant economic benefits, tightly integrated process networks pose distinct challenges, as the feedback interactions among the process units, induced by the recycle, give rise to complex, overall network dynamics, in addition to the dynamics of the individual units. Yet, most studies on control of process networks with recycle streams (e.g. Luyben, 1993; Yi and Luyben, 1997) are within a multi-loop linear control framework. The strong coupling between the control loops in such an approach has been recognized as a major issue that must be addressed in a plant-wide control setting (Price and Georgakis, 1993; Luyben et. al., 1997; Ng and Stephanopoulos, 1998, Larsson and Skogestad, 2000; Skogestad 2004). In our previous work (Kumar and Daoutidis, 2002), we considered process networks with large material recycle. Within the framework of singular perturbations, we established that the large recycle induces a time scale separation, with the dynamics of individual processes evolving in a fast time scale, and the dynamics of the overall network evolving in a slow time scale. We proposed a model reduction method for deriving nonlinear low-order models of the slow dynamics and a controller design framework comprising of properly coordinated fast and slow controllers. In (Baldea et.

Author to whom correspondence should be addressed. Email: [email protected]. P. Daoutidis currently at Aristotle University of Thessaloniki, Thessaloniki, Greece

974 al., 2004), we focused on process networks with recycle, in which small quantities of inert components are present and a small purge stream is used for their removal. Adopting again a singular perturbation perspective, we established the presence of a slow, core dynamics associated with the presence of the inert and outlined a framework for rationally addressing the control of inert levels in the network. In the present paper, we analyze the dynamics of integrated process networks featuring large recycle streams and inert components purged through a small stream. Specifically, we consider a prototype network comprising of a gas phase reactor and a separation system with a gas recycle stream. Within the framework of singular perturbations, we establish that such a network exhibits three time scales: the fastest time scale, in the order of magnitude of the time constants of the individual units, a fast one, in which the dynamics of the entire network evolves, and a slow time scale associated with the presence of the inert and the small purge flowrate. Furthermore, we describe a model reduction procedure which leads to an explicit nonlinear description of dynamics in each time scale and we outline a controller synthesis procedure that rigorously accounts for the time-scale multiplicity feature of such networks. Finally, we provide illustrative numerical simulation results.

2. Modeling of Process Networks with Recycle and Purge We consider the network of Figure. 1, consisting of a gas-phase reactor and a condenser.

R

Fo~yAo~ylo ~

P

BKym

L

Figure 1. Process network with large recycle and purge The reactant A is fed at a constant molar flowrate Fo to the reactor, where a first order, irreversible reaction takes place with reaction constant kl. The outlet stream from the reactor is fed to a partial condenser that separates the light unconverted reactant A from the heavy product B. The gas phase is then recycled at a high rate back to the reactor. A very volatile impurity I is also present in the feed stream in small quantities, and a small purge stream P is used to remove this impurity from the recycle loop. The interphase mole transfer rates for the components A, B, I in the condenser are governed by rate expressions of the form NJ = K ja(yj-P~)~v xy)V')~,,, where Kja represents a mass transfer coefficient, yj the mole fraction in the gas phase, the mole fraction in the liquid phase,/~j the saturation vapour pressure of the component j, and P the pressure in the condenser. Assuming isothermal operation, the dynamic model of the network has the form:

975 M e -(+R-F 1

•

YI,R -- ~

[F,(Y,

,o

- v . I,R

-

I

-y,.)]

H

~VI,. - F -

R-

N-

P

1

)[,/ = ~

1 [F(,,',~-, )'/ ) - N , + y , N ]

M~=N-L "~[t - ~-]-L

•

1

N]

(1)

MR, Mv, Mr. d e n o t e the m o l a r h o l d u p s in the r e a c t o r and c o n d e n s e r v a p o u r a n d

where

liquid phase, respectively, and N=N~+N~+Nz. We consider F

to be 0(1), and define

c z=Fo/R,, as the ratio of the steady state values of the feed and recycle flowrates. Note

that, due to the assumption that the recycle flowrate is much higher than the throughput, e'~ << 1. Also, we define c~ - P / F << 1 (under steady-state conditions, the purge flowrate is much smaller than the feed), the scaled (possibly manipulated) inputs uR=R/R,, u c = F / F , and u p = P / p , and the O(1) ratio k = F / R , . We assume that the mole fraction of the inert in the feed is very small, i.e. y j . , - % c , where % = O(1), that the inert is very volatile, i.e. p / / p = a: / x, with a 2 - O(1), and that its mass transfer rate is very small, i.e. K ~ a = a ~ x ~-, c~ =O(1), the latter two assumptions implying that a negligible amount of inert leaves the recycle loop and exits through the liquid stream at the bottom of the condenser. Based on the above assumptions, the model of the process network takes the form: 1 ~,~ = F +-- F, (,~ - k.,. ) g1

:i'.,.z, = ~

'

1

i',,R = - ~

M~.

F(I-azc~ -Y,.e )- knA//z,Y.,.R+--F,.,.ue()[ig,-.Y.,je)

'

1

1

F, ( ~,c~ - v ,,~ ) + --e,&'" ~(y~ - >'''~ )

- N , N B -(a~e~_y~ + a, a2c~x z) Mz PL

1 gl

'fi

j:, =--~. --F,kz,, (y ~.,~- y , ) - N, + y~(N , + N,)+ y.,(a,c~y, +a, os2e=xt) ML ] Pl. I = 1 F kzL (yz.R-yz)-(crv~ vz + rztrz_~2xz)M,. +yz(N~ + NB)+),z(al~:v~ +oflc~2~2xz) ML M~ = N ~+ N B + ( u ~ )'~ + a~m_e'~_.,<~) M~ _ L PL

k t =I[N,MI.

G~x l) M z-] x I(N t + N e) -.r,(ofl~:,'l+oc, ~ .

.

-fz =--~ (a,e;)q +a, u2e=xz)

.

.

.

P~. I

""-xz(N, + Ne)-xz(a,e~y I +a,a:e=xl) Mc PL PL I

976 Evidently, the above model contains terms of O(1), O(1/e) and O(e), which suggest potentially a three time scale behaviour. In what follows, we document this feature within the framework of singular perturbations.

3. Model Reduction and Control We begin by obtaining a description of the fastest dynamics of the network. To this end, we define the fastest, stretched time scale r~=t/el. In the limit ~ ~ 0, corresponding to an infinitely large recycle flowrate, we obtain the following description of the network dynamics in this fastest time scale: MR .- F . (u R. kttF . ) dr I ....

Y..I.R dr 1

M~___L=F.,.(kUF_UR ) dr~

YI___L=F., kUF(Y.,,a _ y.,) dr~ M r

F"' Yl.R - =1 MR UR(YA - Y..~.R) -dr

F °" uR(Yl-YI.R) MR

(3)

y__L_~=F,. kur(y~, _ y,) dr~ M~.,

M~ = 0 x.,~ _ 0 X--L-~= 0 dr I dr I dr~ Note that not all the nontrivial algebraic equations that correspond to the equilibrium of the fastest dynamics are linearly independent. Specifically, the last three nontrivial equations can be expressed as functions of the first three. This implies that the steadystate condition associated to the fastest dynamics does not specify isolated equilibrium points, but rather a six-dimensional manifold in which a slower dynamics evolves Also, note that the control objectives in this time scale must be addressed using the large inputs u 1, as the inputs u' and d' have no effect on the fastest dynamics. Turning now to the dynamics on this equilibrium manifold, multiplying Eq. (1) by e~ and considering the limit e 1 ~ 0, the linearly independent constraints: 0 = u~ - k u r , 0 - t g k ( y A --YA.k)' 0 - u R ( y ~ --Y~,R)are obtained, which must be satisfied in the fast time scale. In this limit,

the terms which involve division of the above functions with the small parameter e~ become indeterminate. Let z l denote these finite, but unknown terms. Then the model of the dynamics after the fastest boundary layer becomes a Differential Algebraic Equation (DAE) system of nontrivial index (owing to the unspecified variables z!). Setting the large flowrates u ~with appropriate feedback laws (in the prototype network considered, we use ue=l-k,,R(Mv.sp-Mv) and ur=l-k,,F(MR..v,-Mn)), the algebraic variables zl can be computed after one differentiation of the algebraic constraints (Kumar and Daoutidis, 2002). Thus, the index of the DAE system is exactly ~wo. Employing a coordinate change which involves the total material holdup of the recycle [oop. and the holdups of the individual components in the recycle loot'., i.e. ~, - MR + M y ' ~2 - MRYA.R + M v Y A ' ~3 -- MRY,.R + M, ," ),~ ' ~=~ - M ~ 46 - x , , r l ,

- u~(x)

+ ku~(x),rh

- u~(x)(y~

- y.~,~),rl~ .... u ~ ( x ) ( ) , ~

"~

:= - x ~'

(4)

- ),,.~ )

the resulting underlying ODE model becomes: ¢, = Yo - U ~ - X .

- e2~,

~2--"-(g2Fo., ,k k,y~2

Up +

- ~Fo...

k, ~2 k,r MR..,.~,- k F Y.4,o ~ k,r + k k,r N A ~1

Jr- ~2 kuR e2 Hp F,s)/(~ 1 (k kuF -.[- kuR))

-

kkl~2

977 ~4 -

NA + Ne + g2NI - L

~5 - N4 - ~ (N.4 + NR + g2~, ) with ~ - ( a ~ g ~ / , ~

(5)

+a~a~_~6)~a/PL" Notice that the above model is still stiff, due to the

presence of the small singular perturbation parameter 6' 2 . Repeating the model decomposition procedure followed above, we can derive separate representations for the fast and slow dynamics. Specifically, considering the limit 6"2-----+0 (corresponding to the absence of the inert component from the feed and a zero purge flowrate) in a slow, compressed, time scale re=tee we obtain the following description of the slow dynamics d ~3 _( _ g ue Fo, + F a, ,~, ) / ~:, dr 2

(6)

The control objectives at the network level (such as product purity, control of total material holdup, etc) can be achieved in the fast time scale using the manipulated inputs u', as neither the large inputs z/, nor the purge stream have any effect in this time scale. Similarly, the control of the inert levels in the network can only be accomplished in the slow time scale using the purge stream d'.

4. Simulation Study We carried out simulation studies on a specific process network of the type presented in Figure 1, with the parameter values and nominal steady state given in Table 1. Table l. Nominal process parameters MR, tool

4007.0

p~, , m o l / m 3

15000.0

KA,mOl/m 2 rain

1140.0

My, mol

2710.33

3' ~.,,

0.98

K s , m o l / m e min

1200.0

Mz ,mol

1069.82

y/.~,

0.020

K ~ , m o l / m 2 min

60-0"10-6

F,,mol/min

100

pi'p a

1.16-10 s

a, m2/m -~

17.5

R, m o l / m i n

1002.73

P~,Pa

1.67"105

kr

0.05

F, m o l / m i n

1102.73

P[,Pa

5.67.107

k, R

0.01

P, mol/rain

2.28

~], m 3

3.0

k,L

0.04

/tl, 1/ rain

0.06

T~,K

373.0

T o,,j,K

273.0

Specifically, we controlled the liquid level in the condenser (and, thereby, the total holdup of the network) using the effluent flowrate and a proportional controller, L=L~(1-kL(M~.v,-ML)). Subsequently, we designed an input-output linearizing feedback controller with integral action (Daoutidis and Kravaris, 1992) for the product purity xB = 1-xA-x~, using the reactor holdup setpoint MR..v, as a manipulated input and requesting the critically damped second order response xe + fl~ ~dxB _ + f12 d2xu dt 2 - x~.~.~with fl1=60 min, fl2=900 min 2. Finally, we employed the derived reduced-order model of the slow dynamics (Eq. 6) to design an input-output linearizing controller with integral action for the total inert holdup, requesting the first order response ~3 + Y d~ 3 / dt - ~'3.v, with

978 7" = 1200rain. Figure 2 shows the closed-loop behaviour of the process network for a step change in the product purity setpoint xB,=p and in the presence of unmeasured disturbances. Clearly, the proposed controller exhibits a very good setpoint tracking and disturbance rejection performance. :~::~ ~.

a:,~[~

..................................................................

:~ 2 ~

.

.

.

.

.

.

.

.

.

.~.~.,)

...................................................................................

.............................................

/ .

.

.

.

.

.

.

.

a

.

b

Figure 2. Closed-loop responses of the reactor-condenser network for (a) a step change in the purity setpoint to 0.33 and (b) for a 20% estimation error of the mass transfer coefficient KB

5. Conclusions In this paper, we analyzed the dynamic behaviour of integrated process networks with large recycle flows and small purge streams. Using a prototype network comprising of a reactor and a separator, we showed that such systems possess a dynamic behaviour featuring three distinct time scales and we outlined a controller design framework that naturally accounts for this time scale separation.

References Baldea, M., P. Daoutidis and A. Kumar, 2004, Dynamics of process networks with recycle and purge: time scale separation and model decomposition, In: Preprints of ADCHEM'03, Hong Kong, pp. 645-650. Daoutidis, P. and C. Kravaris, 1992, Chem. Eng. Sci., 47(4), 837-849. Kumar, A. and P. Daoutidis, 2002, J. Proc. Contr., 12, 475-484. Larsson, T and S. Skogestad, 2000, Mod. Ident. Contr., 21(4), 209-240. Luyben, M.L., B.D. Tyreus and W.L. Luyben, 1997, AIChE J., 43, 3161-3174. Luyben, W.L., 1993, Ind. Eng. Chem. Res., 32, 466-486, 1142-1162. Ng, C. and G. Stephanopoulos, 1998, Plant-wide control structures and strategies, In: Proceedings of DYCOPS-5, Corfu, Greece, pp. 1-16. Price, R.M. and C. Georgakis, 1993, Ind. Eng. Chem. Res., 32, 2693-2705. Skogestad, S. 2004, Comp. Chem. Eng. 28, 219-234. Yi, C.K. and W. L. Luyben, 1997, Comp. Chem. Eng. 21 (1), 25-68.

Acknowledgements Partial financial support for this work by ACS-PRF 38114-AC9 and NSF-CTS 0234440 is gratefully acknowledged.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) (~?)2005 Elsevier B.V. All rights reserved.

979

Minimum-Cost Operation in Heat-Exchanger Networks Alejandro H. Gonzfilez a and Jacinto L. Marchetti a a institute of Technological Development for the Chemical Industry (INTEC) Guemes 3450, 3000 Santa Fe, Argentine

Abstract This report revises the use of the maximum energy recovery criterion as objective function for real-time optimisation of heat-exchanger networks. Though in general this criterion leads to minimum total heat exchanged in the service units, it is not sufficient to achieve the actual minimum operation cost. This analysis discusses the characteristics of the network structure for which the last statement is applicable, and proposes an alternative performance index to address more directly the final economic objective for which these heat-recovery systems are created. An application example demonstrates the significant differences in operating conditions that may result from using one or the other criterion, something of outmost importance when defining online optimisation for these systems.

Keywords" heat-exchanger networks, optimal operation, utility cost, heat integration 1. Introduction Marselle et al. (1982) was one of the firsts articles to discuss the optimal operation problem of heat-exchanger networks (HEN), where simultaneous regulation and optimisation are considered. More closely, important results on these topics were presented in Mathisen thesis (1994), Uzturk and Akman (1997), Aguilera and Marchetti (1998) and Glemmestad et al. (1999). Most of these works provide specific representation models of HENs that can be used for searching the convenient operating point attending to the full network capacity under given inlet stream conditions and temperature targets. When an optimal operation is regarded, it means that at least the following two goals are pursued: i) outlet temperature targets for the process streams, and ii) minimum operating cost. This second goal, however, has been frequently understood as attaining the operation condition that yields the greatest possible heat integration. However, this report objective is to demonstrate and analyse the existence of an additional optimisation space going beyond maximum energy recovery. The presented results show that though maximum heat integration in HENs implies minimum overall heat exchanged in service units, in many cases it is not sufficient for determining minimum operating cost. The following section describes the structural network conditions that are necessary for the existence of an extra degree of freedom associated to the service units. Then, the third section shows how the optimisation problem must be formulated when minimum utility costs are pursued. The numerical results of running an example problem with

980 different objective functions are shown in Section 4, and the final section gives the conclusions of this work.

2. Conditions for Extra Degrees of Freedom of the Service Variables Based on the energy balance of the total network, Aguilera and Marchetti (1998) analysed the degrees of freedom of a HEN as structural possibilities of optimisation once process stream targets and input conditions are fixed. However, once maximum heat integration is achieved in a flexible HEN, there may be additional degrees of freedom for the service variables depending not only on the network structure but also on conditions of temporary operating points. To determine when these characteristics are present, let us analyse first the relationships describing the tasks to be accomplished on each process stream with a temperature target. To reach the temperature target a hot process stream i has to release the energy Qi and a cold process stream j has to receive the energy Q;. These energies are released and received through different process-to-process exchanges q~ and service tasks qci and qhj along each stream path, namely

Q~=-~-'~qk-qc,,

ieH,

Q/-

kcK i

~~qk +qhj,

j~C

(1)

kEKj

where H stands for all the hot streams, C represents all the cold streams, and Ki and Kj are the subset of heat-exchangers on streams i and j respectively. Because the sum of all the process-to-process heat-exchanger duties represents the same integrated energy in both equations, a simple relationship between cold and hot service units can be obtained

Zqh,-Zqc, j~C

=ZQ/+ZQ,

i~H

j~C

•

(2)

icH

Furthermore, notice that for fixed temperature targets and defined inlet conditions, the right side of (2) is constant. Calling global network duty D to this constant, the following expression is reached:

~-~qh~ -~-~qo, +D" jcC

(3)

ieH

Let us consider now a performance index typically used when maximum heat integration is required, or equivalently, an index expressing the total heat flow handled by the service units

J-~-'q~ j~C

+~-'qc,

(4)

icH

Combining (3) and (4) gives the following relationship:

J - Z~-" qo + D icH

- 2~-" qh - D

(5)

jeC

According to (5), for any HEN having nh active heaters and no active coolers, under optimal heat integrating condition, an extra degree of freedom may appear when nh > 2+no, or no > 2+nh. For instance, if all the qo, = 0 (or qh, = 0), the index function J is constant despite of how many qhj (or qc, ) are in the network, how is the connecting

981 structure, or how is the total service duty distributed among the q~,, (or q~, ). However, performing the same heat duty in different exchanger units (with different UA) implies different utility flow rates. Thus, once the maximum heat integration is attained, different combinations of q/, (or q~: ) are still possible, which implies different use of utility streams and consequently different utility costs. This extra degree of freedom, which goes beyond heat integration, appears also when a HEN having any number of cooling and heating services goes to temporary operating points where the number of active service units complies with any of the above relationships.

3. The Optimal HEN Operation Problem Let us assume that the HEN structure and the heat exchanger areas are completely defined for a given case problem, where there are enough degrees of freedom as to perform steady-state optimisation. Assume also that all process stream targets are known, and that the convenient control structure for temperature regulation has been already defined. When the desired condition actually focus on minimum operating cost, the optimal solution can be obtained by solving the following minimization problem:

subject to - ~--'~qk - q~.(w ) - Q,

i E H,

(7)

j~C,

(8)

k E 1,he+s},

(9)

k~K i

qx +q,, (% ) - Q~ k~K~

-q, < 0

k e {1,ne + s} ,

q~. (w ) = e (w ) L (w. ) qh, ( % , ) = e,, ( % , ) L~,,

i~H, j ~ C,

(~o) (11) (12)

where ne stands for the total number of process-to-process heat-exchangers, s is the total number of serviced units, w~.i stands for the cold utility flow rate of the service unit on the hot stream i, and wl~/is the hot utility flow-rate of the service unit on the cold stream j. The supra index " in (9) indicates fully open control valve or fully closed bypass; the functions e and L are defined in the Appendix. Note that the utility costs per unit mass (c~i and chi) are included in the performance index, and that (11) and (12) are non-linear equations determining w~; and whj at the optimal operation condition. if the network structure does not include stream splits or multiple bypasses (bypass to more than one unit), excellent initialisations for the above NLP problem are obtained by first solving the associate LP for maximum heat integration; this LP uses heat flows as exclusive optimising variables and excludes the equality constraints (11) and (12).

982

4. Example Problem Figure 1 shows the sketch of a HEN composed by two process-to-process exchangers and three service units connected by one hot and two cold process streams. Table 1 gives the stream conditions, and Table 2 shows the UA values for two network designs A and B. The factor F, is assumed 1.0 in all the units, and the utility cost cci and chj are also set to 1. The first row in Table 3 shows the results obtained by solving the above optimisation problem when the design A is used. Though the problem of maximizing the utility expenses J makes no sense from the operating point of view, when this maximum is subject to the same energy recovery obtained before, an important reference solution is determined. For instance, the result in the second row of Table 3 is obtained by including the constraint q l + q2 = 115, or equivalently q~l + q~2 + q.~3 = 60, in the problem formulation. Thus, the results in rows 1 and 2 become the extremes of a set of infinite solutions maintaining the same energy recovery, but showing different levels of utility expenses. Any of these solutions in the set could be reached by minimizing the total service heat duty depending on the initialisation or the numerical method used to find the minimum. A similar numerical experience is repeated for design B, where the results show a greater cost function difference than in case A (see rows 3 and 4). Analysing the slack variables when there is an extra degree of freedom, it was noted that each extreme operation condition is associated with an active constraint (9) related to different units located in the path connecting $2 and $3. Notice that with the stream conditions in Table 1, the solutions avoid using the cooler S 1, creating the condition for an extra degree of freedom. However, when the output temperature of stream H1 is set to 50 °C, the cooler is activated and the extra degree of freedom is lost; see rows 5 and 6 where both, the min J and the constrained max J problems give the same solution for each design. Nevertheless, even though the designs A and B have the same total exchange area, they show different operation cost.

%

Figure 1: General structure of the HEN example

Csl

983 Table 1. Nominal process and service stream conditions

wc bTlet temp. ('C) Outlet temp. (°C)

H1

C1

C2

Csl

1.0 190 75

1.5 80 160

0.5 20 130

1.0 1.0 1.0 15 200 200 . . . . . .

Hs:

Hss

Table 2. UA values used in the above network

UA (case A) UA (case B)

ql

q:

5.0 5.0

2.0 2.0

q.,.1 3.0 3.0

q.,.2

q.,.s

3.0 1.0

1.0 3.0

Table 3. Effect of the extra degree offi'eedom on the operation cost.

Case A-minJ A - max J B- minJ B - max J A-min/max J B min/maxJ

q~

102.07 67.44 102.07 85.98 102.07 102.07

q:

q.,.1

12.93 47.56 12.93 29.02 31.50 31.50

0.0 0.0 0.0 0.0 6.43 6.43

q,:

17.93 52.56 17.93 34.02 17.93 17.93

q.,.s

x,t

x,.2

x,s

J

42.07 7.44 42.07 25.98 23.50 23.50

0.0 0.0 0.0 0.0 0.155 0.155

0.345 0.757 0.39 1.0 0.345 0.390

0.32 0.088 0.274 0.213 0.208 0.201

0.665 0.845 0.664 1.213 0.533 0.591

5. C o n c l u s i o n s Any HEN having nh active heaters and nc active coolers, which operates under optimal heat integration, may have an extra degree of freedom when nh > nc +2, or when nc > nh +2. The reference to active service units emphasizes that this additional optimisation space may turn on and off depending on the operating condition. The immediate consequence of this finding is that the problem formulation for HEN online optimisation has to be adapted to effectively address the minimum utility cost objective. In other words, the extra degree of freedom means that optimising service costs by directly minimising expenses associated to utility flow rates may yield additional benefits as compared to maximising heat-integration. Besides, minimising expenses associated to utility flow rates implies maximising heat-integration. Furthermore, these results also show that HEN designs based on maximum energy recovery combined with minimum total-exchange-area cost should be revised when operation cost is the main goal.

References Aguilera, N. and J. L. Marchetti, 1998, Optimising and Controlling the Operation of HeatExchanger Networks, AIChE Journal, 44 (5), 1090. Glemmestad, B., S. Skogestad, and T. Gundersen, 1999, Optimal Operation of Heat Exchanger Networks, Comput. Chem. Eng., 23,509. Marselle, D.F., M. Morari, and D.F. Rudd, 1982, Design of Resilient Processing Plants: II. Design and Control of Energy Management System, Chem. Eng. Sci., 37 (2), 259. Mathisen, K.W., 1994, Integrated Design and Control of Heat Exchanger Networks, Doctoral Thesis, University of Trondheim, Norway. UztOrk, D. and Akman, U., 1997, Centralized and Descentralized Control of Retrofit HeatExchanger Networks, Comput. Chem. Eng., 21, $373.

984 Acknowledgements

This work has received the support from Universidad Nacional del Litoral and CONICET. Appendix" M o d e l of a H e a t E x c h a n g e r in a N e t w o r k

A convenient way of writing the main equations modeling the stationary condition of a single heat exchanger is obtained from the steady energy balance and the constitutive equation for the heat transferred, namely q

= wici(Ti 0 -Ti)

- wjcj(Tj.

-T O) -

(A1)

UA(FrATn,,)

In this expression, the supra index 0 stands for inlet conditions, A is the heat-exchanger area, U is the overall heat transfer coefficient, and F r is a factor correcting the logarithmic mean temperature difference ATml to account for deviations from pure counter-current pattern. Algebraic rearranges combining the above equalities show the convenience of defining the following parameters: wjcy .__ (T~°-T~) R ___..__:_ WiC i (Tj - V°) '

Xvu

- - UA WjCj

and

B-exp{UruFv(R-l)}

- -( T_ j __ T.O )

(A2)

These three parameters help the computation of the heat-exchanger efficiency defined by 1- B 1 - RB

( T j - T ° ) for R:/:B:/:I, or ( Ti° - T° )

e

Nru for R l + Ur~:

B

1

(A3)

Combining Eqs. A1 to A3 allows writing the heat flow rate as q = q(wi, wj) = e(wi, w s ) L ( w j ) , with

L(Wj)= W/cs(Ti ° - T° )

(A4)

where L(wj) may be interpreted as the virtual amount of exchangeable energy and the efficiency e(wi,wj) defines the amount of heat transferred when a finite exchange area is available between the two fluids. Thus, the equations representing any heat-exchanger k being part of a network at the stream match (ij) are similar to Eqs. (A4), the main difference is that the heat-exchanger inlet temperatures T~° and T° are the results of previous exchanges, namely Ti° ( k ) = riiin

1 Z qli' Win i Ci

TO

(k)-

[i ~ prei(k),

i~H

(A5)

1i

Ti n 1 ~ + w~"cj ~ qtj,

l~ ~ pre~(k),

j ~ C

(A6)

lj

where the superscript in stands for inlet to the network, and prei(k) and prej(k) represent exchanges previous to k. Notice that w/or wj may be different from the nominal inlet stream flow rate because of the control valve position. Thus, the heat duty upper bound is determined by (A4) for fully open control valve or fully closed bypass, namely q< _ q° =e(wi" ,wji.~) L,twji~) - eOLo .

(A7)

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

985

An Online Decision Support Framework for Managing Abnormal Supply Chain Events Mukta Bansal, Arief Adhitya, Rajagopalan Srinivasan*, and I.A. Karimi Laboratory for Intelligent Applications in Chemical Engineering Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore

Abstract Enterprises today have acknowledged the importance of supply chain management to achieve operational efficiency, and cutting costs while maintaining quality. Uncertainties in supply, demand, transportation, market conditions, and many other factors can interrupt supply chain operations, causing significant adverse effects. These uncertainties motivate the development of simulation models and decision support system for managing disruptions in the supply chain. In this paper, we propose a new agent-based online decision support framework for disruption management. The steps for disruption management are: monitoring the KPIs, detecting the root cause for the deviation of KPIs, identifying rectification strategies, finding the optimal rectification strategy and rescheduling operates as necessary in response to the disruption. The above framework has been implemented as a decision support system and tested on a refinery case study.

Keywords: Risk Management, Optimization, Agent-Based, Uncertainty 1. Introduction In the face of highly competitive global markets, companies are pressurized to reduce costs and increase efficiency. As a consequence, they are employing new strategies which result in complex supply chains. These strategies include outsourcing, single sourcing, and centralised distribution. An efficient supply chain requires transparency among its constituent entities. Complex and lengthy supply chains lack visibility and this leads to disruptions. Unhindered and timely material, information and finance flow between different entities of supply chain is another important element. Blockage in any of these would lead to undesirable events like process shutdown, financial loss, under-supply or over-supply, etc. Hence there is a greater need for risk and disruption management. A disruption management system should be capable of detecting abnormal situations before they occur, diagnose the root cause, and propose corrective actions as required. While a complete rectification is desirable, in cases where the effect of disruption is

Author to whom correspondence should be addressed: [email protected]

986 manifested very late, it may only be feasible to effect a partial recovery. A robust system should be capable of handling both complete and partial rectification. The challenges involved in developing disruption management system are: 1) Supply chain entities are dynamic, disparate and distributed; and 2) they are tightly linked at intra- and inter-enterprise levels and affect the performance of one another. These make the detection of disruption and the root cause difficult. Further, complex rectification strategies are needed to partially or completely overcome the disruption. For example, the implementation of a rectification strategy in some cases will need rescheduling of operations. In this paper, we propose an agent-based framework for disruption management. Intelligent agents measure key performance indicators in each supply chain entities. Disruptions are detected when these KPIs deviates from a pre-specified set points or when unplanned events are detected. Root causes are diagnosed using a causal model. Rectifications are proposed and optimised through a model of supply chain linkage. When necessary, rescheduling is performed to recover from a disruption. In this paper, we present the details of the framework and its implementation and illustrate it using a refinery supply chain. 1.1

Literature Review

There is limited literature in the area of disruption management; no general structured methodology exists to date. Sheffi et al. (2003) describe mechanisms which companies follow to assess terrorism-related risks, protect the supply chain from those risks and attain resilience. They provide classifications of disruptions, security measures and ideas to achieve resilience. They report various case studies and interviews with executives of companies. Wilson (2003) focuses only on transportation disruptions. Julka et al (2002; a, b) proposed an agent-based framework for modelling a supply chain. In their framework, the behaviour of every entity in the supply chain is emulated using an agent that imitates the behaviour of various departments in refinery. Mishra et al. (2003) reported an agent-based decision support system to manage disruptions in a refinery supply chain. In the event of a disruption, agents collaborate to identify a holistic rectification strategy using heuristic rules. In this paper, we generalize their approach and develop a model-based framework for managing supply chain.

2. Framework and Methodology for Disruption Management The proposed framework is described in Figure 1 and is capable of handling situations where 1) occurrence of a disruption is manifested only through deviations from set point and the root cause is not observable, as well as 2) cases when disruptions can be detected at source i.e., the root cause is observable. From control theory, the former needs feedback control while the latter requires a feedforward mechanism. In the general case, the steps for disruption management are carried out by the following components: KPI Monitors: To manage disruptions in supply chain, it is essential to measure key performance indicators (KPIs) and to identify their effect on the supply chain. We use stock inventory, throughput, and other similar indicators to monitor the state of each constituent of the supply chain. These can be measured at regular intervals and

987 monitored by comparing their day-to-day values against pre-specified limits. Alarms are generated when a sustained deviation in any KPI is detected. {

•

I*2PIs

,-

...... :

hffOHnatiOll of Deviation

Alarms

m

e

I) lsluptioll ( ( - ' O1 l"e c t i v e

Action 2,~e<essalT)

i

Possible Causes

I

Y os sible Re ctifi c atiOllS m

Ne~v N:hedule and ('oHecW~e Actkms k-PIs fOl each '~ • •

I ecHfi(

~ (-)primal RectifF. ation

atlOll

i

y

S Cell211 i 0

........S c ~ e d u ! e r

..........................~

"

A

[NNNN ...........

New Sdledule

Figure l. Frameworkjbr disruption management system 2.

Root Cause Identifier: Causal models are used to identify the possible causes for the alarms. Hypotheses are proposed to identify the root cause and confirmed if all expected consequences are manifested online. 3. Rectifications Proposer: The list of corrective actions to rectify the root cause is generated using a causal model, which accounts for the linkages among the supply chain entities. Each rectification strategy is simulated using a supply chain simulator and feasibility and KPIs for each scenario is evaluated. 4. Optimizer: One rectification strategy is selected based on feasibility and KPIs. 5. Scheduler: In a general case, disruption may make the existing operation schedule infeasible or sub-optimal. Optimal rectification strategy may require rescheduling of operations. Our rescheduling scheme is described in more detail in Section 2.1. 6. Coordinator: Numerous activities may be necessary to partially or completely rectify the disruption. The implementation of these rectification strategies can be coordinated by this agent. All the above steps are necessary for disruptions whose root cause is not observable. In cases where the root cause is observable, the occurrence of abnormal event triggers a comparison with KP|s. If corrective actions are found necessary steps 3 to 6 described above are implemented.

988

2.1 Methodology for rescheduling Our rescheduling approach is described in Figure 2. Implementation of the optimal rectification strategy may require changes which affect the original schedule, i.e. some operations may be cancelled or rescheduled and new operations may be necessary. These changes are reconciled with the original schedule by the scheduler agent. New schedules are generated based on heuristics taking into account relevant data from the plant hardware model. The evaluator calculates the profit of each new schedule so that the best one can be implemented.

Scheduler A~ent

n

Optimal Rectification

; ~

Strategy

1

blew schedules

:

i

'--

EvalUator

:]*-- [: :Heuristic: ~ : ] ............. ::::::::::: . . . . . . [: R e s c h e d u l e r : "~-

(.~riginal.~_~_~ ........ Schedul~~ ~ " Sales(Productiont a r g e t s ) / |

[

• Procurement (Crude

j/~/Plant [

procurementdata)

/

[.. • LogistiCs (Ships arrival)

J

"

i ,.,,o

Hardware ''" ..... , Model ""~:,

.........,. - ~ p p e ~ ~

~ p ~ °

i

".. transter rates etc,)

Figure 2. Scheduler agent of the disruption system

The rescheduler uses a heuristic multi-step block preservation strategy. An operation spanning one or more periods is considered a block if it involves no intervening change in configuration. As a corollary, adjacent blocks are separated by a change in configuration. Our approach seeks to minimize changes to blocks. First, feasibility of the disrupted schedule is checked. Second, a heuristic rescheduling strategy is employed to improve optimality of the disrupted schedule for each type of disruption. Five types of disruption have been considered: ship arrival delay, SBM/jetty unavailability, tank unavailability, equipment unavailability, and demand change. To deal with ship arrival delays, relative positions of the blocks of operation as mapped by the original schedule are maintained while adjusting the lengths of the blocks and the volumes involved in the blocks. In response to unavailability of equipment (e.g. pumps, tanks, CDUs, etc.), alternate processing strategies that can retain the blocks of operation from the original schedule are sought. To handle changes in demands, the relative positions of the blocks are kept while adjusting the volume involved in the blocks. The key here is to preserve the characteristic of the original schedule, which is the map of the blocks of operations scheduled. Finally, the objective value of the new schedule is evaluated.

3. Case Study We have implemented the above framework as a decision support system in Gensym's G2 expert system shell. In this section, we illustrate it using a case study derived from the supply chain of a Singapore refinery. Consider the scenario where there is a sudden increase in demand starting from the 41 st day. Operation therefore increases throughput

989 immediately. As a consequence, the KPI monitor finds that the crude oil inventory for the 42 ~d day has gone low and generates an alarm. The root cause identifier finds out the possible causes of the deviation: raw material delay, high demand of products, or the efficiency of process decreases such that more crude oil is required. Comparison of the actual and planned ship arrival indicates that there is no arrival delay. Similarly, a check with the operation department reveals that there is no problem with the efficiency of process. Further check with the sales department indicates that the demand is higher than previously projected by 330 kbbl. The diagnosis agent thus confirms the root cause for the low inventory alarm to be a new order on the 41 ~t day. The rectification proposer agent finds two possible rectifications: 1) postponement of other orders, and 2) emergency crude procurement. The optimizer agent evaluates the two options and flags emergency crude procurement of 330 kbbl to arrive on the 44 th day as the optimal rectification strategy. The flow of events in this case study is shown in Figure 3. The optimal rectification strategy is then passed to the scheduler agent who reschedules the operation as shown in Figure 4 and 5. The new schedule (Figure 5) includes the emergency crude and deals with the increase in demand by rescheduling operations. ...-.

['~1 " M°nit°ring~ I ow Inventory Deteot-~ L 1

~..

l 4" EmergencY ardval Crude

..."-.. ... /

"--.. \ \

", I

.. \

Day I~:--...,. __ I 41 "q.i:ii_-- ......... - - - ~ 4 _ e ,............ 2 Diagnosis .....: . . . . . '[,... High demand ,' .............

, I 44 /~.~Optimal Rectification"?'--.. 43 _----~-------------__

[ \

Emergency Crude

,]

,%. Procurement-Passed

.,M/

"--._._

to Scheduler _ _ _ j ~ -

Figure 3. Eventjlow./br the case study I

I

,i
c:~......... + :::; > ~

n

4

i

An-~ount ~

......."I ........ l

'i

. . . . . . . . . .

t

]

.........................................

A~"~ount

t::!~

L-£-;i;!:~;:~:!t 'i :::~,,i 3 i,.-; charging :':::~i.::~kbbl to C.i:::::;i..i2 on day ~::[i

Amou~'~t I

. ".

........ "

-----~J ,~_/v

. . .[ . :i~-~i:s is r.,:.i,,.i.~ :.;:i::ii::ikb~, f~o~ v~!!~:i~=!~:~,:i!:~.ion ,W 4S I <~;" Figure 4. Original operation schedule

990

[,,,,Resche,d,ul,ed operations ] Ta~,k: .

41 .Amo~n,.

42 Am'~'[],,,

Z, ~gVL~ ~~~~ 4~.

~,~:=0

4~

4S

L~S

Amoor, l

4~

A.t',~r,t

:f .... [>

~~%~i .%

Arno,Jn,

4:8

4g

Amour, t Amo,jnl

#~.............................. .,4

2

3

-so ul :-7o u~ J d " ~ 3 ~ : E ~ I d 6 % ] * - 7 o

:~:

iU:2::~::::O2:

u~ ,7:o u1-7o u~

2 ~ :P4:'

I Emergency Crude (EC) - prevents stock-out Figure 5. New operation schedule including emergency crude

4. Conclusions Disruptions are common in supply chains. In this paper, we proposed a systematic framework for disruption management. One key advantage of the proposed approach is that it can handle a wide variety of disruptions, whether due to supplier, transport, operation, or customer problems. The success of this method is predicated on the accuracy of the supply chain model. Our current work is directed towards improving robustness of the approach.

References Julka, N., R. Srinivasan and I. Karimi, 2002, Agent-based Supply Chain Management-l: Framework, Comput. Chem. Eng. 26(12), 1755-1769. Julka, N., R. Srinivasan and I. Karimi, 2002, Agent-based Supply Chain Management-2: A Refinery Application, Cornput. Chem. Eng. 26(12), 1771-1781. Mishra, M., R. Srinivasan, and I. A. Karimi, 2003, Managing disruptions in refinery supply chain using an agent-based decision support system, Presented in the AIChE annual meeting, San Francisco, Nov 16-21. Sheffi, Y., J.B. Rice, Jr., J.M. Fleck, and F. Caniato, 2003, Supply Chain Response to Global Terrorism: A Situation Scan, Eur OMA-POMS Conference. Wilson, M.C., 2002, Transportation Disruptions in the Supply Chain: Simulator as a Decision Support Tool, Proceedings of the 31 st Annual Logistics Educators Conference.

Acknowledgements This research work is funded by NUS and TLIAP.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) ,<32005 Elsevier B.V. All rights reserved.

991

Novel Scheduling of A Mixed Batch/Continuous Sugar Milling Plant Using Petri nets M. Ghaeli a, P.A. Bahri b*, P. Lee a aDivision of Engineering, Science and Computing, Curtin University Bentley, WA 6845, Australia bSchool of Engineering and Science, Murdoch University Murdoch, WA 6150, Australia

Abstract Scheduling of processes in mixed batch/continuous plants, due to their hybrid nature can become very complex. This paper presents the Timed Hybrid Petri net (THPN) as a suitable tool for modelling and scheduling of hybrid systems. One of the major benefits over traditional methods is a significant reduction in complexity during problem formulation. A sugar milling plant containing both batch and continuous processing units is considered as a case study by which the application of the proposed scheduling algorithm is illustrated.

Keywords: scheduling, mixed batch/continuous, Petri net 1. Introduction A scheduling method should formulate a problem by considering all the associated constraints to find the best sequence of operations that optimises a specific objective function. Although much research has been done on the development of different methods for scheduling of either continuous or batch chemical plants, there is a distinct absence of research in the scheduling of mixed batch/continuous systems (hybrid systems). In the past, scheduling of these plants has been accomplished by either discretising time or considering a continuous time model (Nott, 1998). Simulation models have often been used to schedule these plants. Djavdan relied on such a model with an emphasis on the importance of the size of intermediate storage (Djavdan, 1993). Many researchers have acknowledged that the scheduling of mixed-batch/continuous plants is a very important issue (Neville et al., 1982; Sicignanoet al., 1984) but still, a concrete method for solving these types of scheduling problems with less computational complexity remains. The Timed Petri net based formulation has proven to be a promising technique to solve many scheduling problems (Ghaeli et al., 2004). This paper considers a timed Hybrid Petri net (THPN), which is a class of Petri net, as a suitable tool for modelling and scheduling of mixed batch/continuous plants. A substantial reduction in the complexity of the problem formulations has also been achieved. This is because the THPN tool Author to whom correspondence should be addressed: [email protected]

992 allows for effective illustration of the batch and continuous operations and storage between continuous units with the associated capacities and all other constraints. Initially, an introduction to THPN is presented. Then, in section 3 the model of a sugar milling case study, which is an example of a mixed batch/continuous plant is developed and the proposed approach applied. Finally, a brief conclusion is presented.

2. Timed Hybrid Petri net A Petri net is a particular kind of bipartite directed graph populated by three types of objects: places, transitions and directed arcs. The dynamics of the model are represented by the movement of tokens, which are located in places and illustrated by either small dots or a real number. The firing rules of transitions in a Petri net model make the consideration of the resource use, storage policy and product sequence decisions. The graphical and Mathematical properties of Petri net are also useful when it is used to model hybrid plants. Hybrid Petri net (HPN) is a class of Petri net made up of a "continuous part" (continuous places and transitions) and a "discrete part" (discrete places and transitions). Figure 1 shows the graphical notations for places and transitions in HPN as used in this paper.

Discrete Place

Discrete transition

O

II

Continuous Place

I" I

Continuous Transition

Figure 1. The representation o f places and transitions in H P N

Formally, HPN is a six-tuple H P N - { P , T ,

p r e , p o s t , m o , h } (David and Alla, 2001)

where P = {P1,P2 ,.-., f',, } and T = {T~,T2,..., Tn} are finite but not empty set of places and transitions respectively; p r e : P

× T - - ~ R + is the input incidence matrix while

p o s t : P x T - ~ R ÷ is the output incidence matrix. Note that P ~ T = ~b; m ° : P - ~ R +is

the initial marking. An incidence matrix is a matrix, which includes the weights of the arcs connecting places to transitions or transitions to places. A node is defined to be either discrete (D) or continuous (C) by the hybrid function: h ' P c~ T ~ {D, C} ; °P~( ° T ) and ~° (T; °) depict the set of input transitions (places) and the set of output transitions (places) respectively. The state equation is the same in a hybrid Petri net m = m o + U . V and the difference is that in HPN an integer value in vector V is related to the number of firings of a discrete transition while a nonnegative real number corresponds to a firing quantity of a continuous transition. To consider quantitative properties in a THPN, time is added to HPN. Based on how the places and transitions are defined in a THPN, time can be introduced to either places or transitions.

993 3. C a s e S t u d y

To show the details of the proposed method, a sugar milling case study (Nott, 1998) is considered. Sugar Milling is a hybrid system, which can be divided into two parts: the high-grade and the low-grade systems. The flowsheet for the sugar mill is given in Figure 2. Boxes with a solid outline represent batch operations, whereas continuous operations are represented with a broken outline. Triangular shapes represent storage facilities. The input and output of each pan are shown in the flowsheet. As the use and production of water does not have any effect on the scheduling, it is not considered in the flowsheet. The processing time of each pan is depicted in the parenthesis next to each pan in the flowsheet. The main assumption is that processing of fugal A and fugal B can not be done simultaneously. The maximum flowrate of super, csystems and dryer are 16.5, 32.5, 22 tonnes per half hour, respectively. The syrup flow into the system is 106 tonnes per hour. The maximum capacity as well as the initial amount for each storage are given in Table 1.

Hi(5)

]25 i

12~1 3

j ~ 8o

~

0

Pan H2 (6) I I Pan H4 (5)

I

"•

?,

3O >-] P~' H3 (6) I 200;

pan H5 (6) I -

~

IPanL3 (8)

44.221

80160

I

200¢

34.84 671

v

fu,,al ~(0 ~)

.

67

fugalB (0.~)

36.t3° I ° " -i

~

I ;

\

, Csystems ', , _ ~__.~. . . .

r .......

1

,

[ ~"J'Sr__i

//

......... ,

Figure 2. The flowsheet of the sugar milling case study Table 1. Storage Specoqcations (tonnes) Syrup

Magma

AMolasses

BMolasses

Ree3

Rec5

LRee

Wetsugar

Max

410

50

310

200

330

330

230

250

Initial value

1O0

20

140

110

200

200

70

25

'

994 In order to solve the scheduling problem of this case study, the model should first be created using THPN.

3.1 Model of the case Study The THPN model of the sugar mill system is depicted in Figure 3. In this model, it is assumed that there is a possible change of flowrates for the continuous processing units every half hour. While discrete transitions are used to show the batch operations, continuous units are represented by continuous transitions. In addition, discrete places between the batch operations show the availability of the materials in the previous batch processing unit and the continuous places illustrate the storages. The major benefit of the proposed model is the formulation part of the problem, which is much less complicated than traditional methods. Applying THPN for modelling and scheduling of hybrid systems, the formulation of the important constraints such as assignment constraints, material balance constraints and resource constraints will become much simpler as discussed below: • Assignment constraints: consideration of places having one token as an input to a discrete transition enforces the constraint that there should not be more than one task processed in a processing unit at any time. • Material balances constraints: the amount of inputs and outputs of a processing unit are considered as weights located on arcs connecting a transition (place) to a place (transition). • Resource constraints: for the storages with a limited capacity, a place is connected as an input to a transition (operation unit) producing the products to be stored in the associated storage. The arc connecting this place to the transition has a weight equal to the amount of the resulting products. The same amount is released as soon as the materials leave the associated processing unit. It should be noted that all the above constraints have been considered in the firing rules of transitions and there is no need to set any time consuming formulations or variables. The objective function of the system is to find a schedule with the maximum product (profit) or equivalently minimum idle time (A period during which a processing unit is not in use, but is available), within a horizon time of 16 hours. There is also a penalty of 0.1 for changes in the flowrates of continuous units. 3.2 Proposed algorithm In the proposed approach, there are two steps. First, based on some initial values for the flowrates of continuous units, the scheduling algorithm will find the optimal schedule with respect to the objective function. Second, the optimal schedule obtained is passed to the CFSQP optimisation algorithm (Lawrence et al., 1997). CFSQP will find the best flowrates for each continuous unit, which maximises the products (sugar and Cmolasses) within the obtained optimal schedule. It should be noted that before applying the proposed algorithm, the horizon time is divided into half hourly periods. This will allow the change in the flowrate of each continuous unit every half hour. The following shows the steps of the scheduling algorithm" SI" Begin with the initial marking and a large value for the lower_idle_time; set the flowrates of the continuous units to some initial values. $2" With the initial marking, check if the current transition is not enabled due to the lack of materials or space in the storage, then consider the associated idle time.

995 $3" With the initial marking, check if the current transition is enabled; determine the new marking and the usage time of each processing unit including its idle time and put them all with the old markings into one result matrix. $4: If there are more enabled transitions with the current initial marking, go to $2. $5: Check the last two rows of the result matrix and perform merging if the related transitions are not in conflict; in case of conflict check if the shared input place has enough markings (weights) to fire these two transitions simultaneously. If so perform the merging and repeat $5 for the next two rows. $6: Check the time of all the batch processing units and if there is at least one with the time of less than the horizon time go to $2. $7: If the latest total idle time of the batch processing units is less than the lower_idle_time update loweridle_time to this time. $8: If all the rows of the result matrix have been assessed, the search is complete. Output the lower_idle_time and the feasible schedule to this lower_idle_time. $9: Start checking from the last row of the result matrix upward and find the row in which the associated transition is enabled and has not been fired yet" set the marking of this row as the initial marking and go to $2. The scheduling algorithm was implemented in the C programming language and the optimal solution yields the Gantt chart shown in Figure 4. As was mentioned previously, based on the optimal schedule, CFSQP gives the best flowrate per half hour for each continuous processing unit (Table 2).

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996 Applying the proposed method to solve the sugar mill case study reduces the computational time from 140 seconds in the previous method (Nott, 1998), which used a sets implementation technique, to 1 second in the current study. This confirms the power of THPN for modelling and scheduling of hybrid systems. Units

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Time 0-2 hours 2-14 hours 14-16 hours

fl (super) 2.04375 2.06875 2.04375

f2 (dryer) 7.0125 7.0375 7.0125

f3 (Csystem) 2.16875 2.19375 2.16875

4. Conclusions The THPN has been introduced as a suitable tool for systems with both discrete and continuous behaviour in which many of the constraints can be shown graphically. The great potential of this model for handling complicated operations in the mixed batch/continuous processes has been illustrated through a sugar milling case study, which is an example of a hybrid system. An algorithm, which is a mixture of scheduling and optimisation, is proposed to solve the scheduling problem of the case study. A substantial reduction in the computation time is achieved thereof. Division of the horizon time into a smaller period is currently being researched.

References David, R and H. Alla, 2001, On Hybrid Petri net, Discrete Event Dynamic Systems: Theory and Application, vol. 11, pp.9-40. Djavdan, P., 1993, Design an on-line scheduling strategy for a combined batch/continuous plant using simulation, Computers and Chemical Engineering, vol. 17, pp.561-567. Ghaeli, M., P.A. Bahri, P. Lee and T. Gu, 2004, Petri-Net Based Formulation and Algorithm for Short Term Scheduling of Batch Plants, Computers and Chemical Engineering, Accepted. Lawrence, C., J.L. Zhou and A.L. Tits, 1997, User's Guide for CFSQP Version 2.5: A C Code for Sloving (Large Scale) Constrained Nonlinear Satisfying All Inequality Constraints. Neville, J.M., R.Ventker and T.E. Baker, 1982, An interactive process scheduling system, the American Institute of Chemical Engineers. Nott, H.P., 1998, Modelling alternatives for scheduling mixed batch/continuous process plants with variable cycle time, Doctor of Philosophy Thesis, Murdoch University. Sicignano, A., J.D. McKeand, S.F. LeMasters, 1984, IBM Pc Schedules batch processes, cuts inventories at Houston refinery, Oil and Gas Journal, pp.63-67.

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

997

Improving short-term planning by incorporating scheduling consequences Petra Heijnen*, Ivo Bouwmans, Zofia Verwater-Lukszo Faculty of Technology, Policy and Management Delft University of Technology Delft, The Netherlands

Abstract Decisions in short-term planning and scheduling in multi-product multi-purpose plants are often taken in isolation from each other and may be based on conflicting objectives. This may result in decisions that are sub-optimal for the plant as a whole. A more integral perspective on the decision-making could lead to a better overall performance. This paper describes a mathematical reformulation of the short-term planning and scheduling decisions in a bi-level top-down program. It is based on a recursive formula and a smart definition of the cutting rules, which greatly reduces the complexity of the optimization. A practical case shows that the reliability of the planning results increases significantly.

Keywords: Bi-level programming, short-term planning, scheduling, optimisation, decision support

1. Introduction In a multi-product multi-purpose plant, decisions are usually taken at different locations and on different hierarchical levels, too often in isolation from each other (Shobrys et al. 2002). Together, however, these decisions influence the overall performance of the plant to a high extent. Ryu, Dua and Pistikopoulos (2003) address plant-wide planning and network decisions. This paper aims at the planning and scheduling level. Planners as well as schedulers can only decide about their own decision factors and have no control over the others, but the decisions can mutually interfere, causing far from optimal results. This happens in particular when the respective decisions are based on conflicting objectives. Therefore, a more integral perspective on short-term planning and scheduling decisionmaking in the plant is desirable to guarantee a better overall performance. Multi-level programming is a specific way of mathematically formulating such multi-level decision problems in a complex system, by incorporating the consequences of one decision on the other, aiming at a better performance of the system as a whole (e.g. Bialas et al. 1982).

Author to whom correspondence should be addressed: [email protected]

998 In this paper, the short-term planning and scheduling decisions in a multi-product plant, aiming at different, conflicting objectives, are mathematically reformulated in a bi-level top-down program. The method is based on a recursive formula by which the scheduling objective function can be calculated. The use of this recursive formula and a smart definition of the cutting rules significantly reduce the complexity of the search for an optimal planning.

2. Short-term planning and scheduling in a multi-product plant In the short-term planning, customer orders are accepted or rejected based on a chosen criterion, which in our example is profitability. At the start of each week, the planners receive the set of customer orders from the sales department. Every customer order indicates the amount of product, the date the order should be delivered and the type of product. Since capacity is limited, only the most profitable set of orders from the order list is selected and passed on to the schedulers. In the scheduling, the orders accepted in the planning stage are sequenced minimizing the total tardiness, i.e. the total time of delivery after due date. To reduce complexity, the assumption is made here that all orders are to be produced in one reactor. The scheduling performance highly depends on the planning decision, since the schedulers have to schedule all the orders selected by the planners, whereas another selection of orders might have led to a better schedule with less tardiness. Moreover, if in the final schedule two consecutive orders are of different types of product, extra changeover costs are made, reducing the profit. The planners, however, only estimate the profit by correcting every order with a fixed sum of changeover costs, disregarding the real consequences of the scheduling process. The schedulers, in turn, have no influence on the order selection procedure. The problem situation described here might seem a little artificial, since planners and schedulers, working for the same company, should aim at a better overall performance and not only at their own objectives. Nevertheless, isolated decision making is not uncommon in practice for various reasons, such as habits, the complexity of integrated decision making, or the impossibility of unambiguously defining the influence of lowerlevel activities on strategic objectives.

2.1 Mathematical formulation of the planning and scheduling decisions Each week, the planners solve the following decision problem:

From the total set of customer orders, find the subset of orders that maximize the profit and for which the total available capacity is not exceeded. Let

C=[[cl,,di,Pi ] i E{1,2 ..... m}]

(1)

be the total set of customer orders received from the sales department, where ag is the ordered amount of product (in tons), di the due date (in working hours from the start of the week), and pi the type of product ordered. The planners should then find the binary vector x - [xl, x2, ..., Xm] for which the total profit

999 tn

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(2)

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is maximized. Here, J(pi) is the profit that can be achieved with one ton of product of type p;. The decision vector x_is bounded by the constraint

~ a , t ( p i )x, <_T,

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i 1

in which t(pi) is the time (in hours) needed to produce one ton of product of type p;. Also weekly, the schedulers solve the following optimization problem:

For the selected orders received fi'om the planners, find the production sequence that minimizes total tardiness. Let S(x) be the set of n selected orders received from the planners,

.... ,m}]

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The schedulers should find the permutation.~ = HS(x) for which the total tardiness

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(5)

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3. Solving the planning and scheduling problem The planning and the scheduling decision can be solved separately by a branch-andbound algorithm, first proposed by Land and Doig (1960). However, better results can be achieved when the consequences of the planning results on the scheduling level are incorporated in the planning process. Therefore, the planning and scheduling decisions are reformulated into a bi-level top-down decision-making problem here, assuming that the decision makers on the planning level have complete knowledge about the optimization problem solved on the scheduling level.

3.1 Bi-level programming In a bi-level program, two levels are distinguished where closely related decisions are taken, and where the decision makers at one level can only decide about a limited set of decision variables and have no power on the decision variables of the other level. A top-down program is a specific form of a bi-level program in which • the decisions on the upper level determine the parameter values on the lower level, constraining the feasible region of the lower-level solution space; ° the decision on the lower level influences the degree to which the objective on the upper level is achieved; • the decision on the upper level is taken before the decision on the lower level.

1000 The objectives on both levels are generally conflicting in that the optimal values of the decision variables of either level influence the solution of the other level negatively. As a consequence, to determine the best performance of the overall system the different optimisation problems of both levels should be integrated and solved jointly. However, in general this is unfeasible. The usual strategy to solve bi-level optimisation problems is to incorporate the resulting decisions of the lower level into the upper level decision and solve the optimisation problems of the lower level iteratively. This is done under the assumption that the decision makers on the upper level have complete knowledge about the objective functions and constraints of the lower level.

3.2 Planning and scheduling bi-level program For the decisions on the planning level, a better performance of the system as a whole can be achieved when the consequences of the planning on the scheduling level are incorporated in advance. On the scheduling level, the orders selected on the planning level are sequenced to minimize total tardiness (Pinedo, 1995). However, every changeover between different types of products in the chosen schedule will reduce the profit. Although the planners cannot decide about the final production schedule, they can expect that within the limited solution space caused by the planners' selection of orders, the schedulers will choose the optimal schedule with respect to their own objective of minimal tardiness. The planning decision problem is therefore reformulated to incorporate scheduling results: II Find the binary vector X=[Xl,X2,...,Xm]for which the total profit m

P(x__)-Z aif (Pi)xi-qC(L)

(7)

i=1

is maximized, in which C(X*) is the number of changeovers in the optimal schedule y*, belonging to the planned orders, and q is the fixed costs for one changeover. As before, the decision vector x_ is bounded by the constraint (1.3). The formulation of the scheduling problem remains the same.

3.3 Top-down solving of the planning and scheduling problems The new top-down formulation of the planning and scheduling decisions makes solving of the planning problem much more complex, since for the evaluation of the profit expected from a planning, the scheduling problem must be solved as well. The planning problem is solved by a branch-and-bound algorithm. The complexity of a branch-and-bound search strongly depends on the efficiency of cutting branches from the solution tree. For the planning problem, the tree starts with an empty planning, [ ]. Every node in the tree, corresponding with a binary vector xl of length smaller than or equal to m, is split into two branches, indicating that the next order is added to the planning, resulting in node [xl, 1], or that it is not, resulting in node [xl,0]. A branch of the planning tree can be excluded from further analysis if either • the total completion time of the orders selected so far is larger than the available capacity T, or

1001 •

the potential profit, i.e. the profit obtained with the selected orders plus the total profit of all orders not considered so far, is smaller than a certain lower bound. However, for the second cutting rule the maximum potential profit of an incomplete planning in a certain node can only be determined by solving the scheduling problem for every complete planning branching from that node. This procedure will be far from efficient. Under the assumption that the profit achieved from a customer order will always be more than the costs for one extra changeover, q, the maximum profit achievable in a planning that branches from a certain node corresponding with x~ is at most

N([xl,l,1,...,1])-l) is the number of different product types in the planned orders corresponding with xl and in the remaining orders. Since N([xl,l,1,...,1])-l) is a lower bound for the total number of changeovers in a schedule belonging to the planning [x~,l,1 .... ,1], Equation (1.8) will yield a lower bound for the potential profit of an incomplete planning x~. By using this lower bound for the profit, the scheduling problem only needs to be solved when a complete planning is achieved in one of the leaves of the planning tree. The actual profit can then be computed taking into account the real changeover costs that result from the optimal schedule for that planning. Still the complexity of the planning algorithm is high and the reuse of previous scheduling results is not that simple. Let schedule I and schedule II be the optimal schedules belonging to planning I and planning II, respectively. Even if planning I consists of the orders of planning II plus just one order extra, the orders in schedule I and schedule II may have a totally different sequence. The complexity of calculating the tardiness of a schedule, however, can be reduced significantly by using the following recursive formula. Let S(x) be the set of selected orders in a certain planning, represented by the binary vector x. Let S~ be an ordered subset of S(x) and let S_~ be the complement of S~, $2 = S(x_)\S~. Let T(S2,S~) be the tardiness of the orders in S~, when the orders in $2 are completed before the orders in S~ can start. Then

T(S2 \{kI,[k,S,l)-T(S2,Xl)+max(O,C(S2)-dk)

(9)

in which C($2) is the total completion time of all orders in set S 2. With this recursive formula, the planners can efficiently optimize the set of orders, which results in a better solution for the plant as a whole. The example in the next section illustrates this.

4. An illustrative example Assume that for the coming week a company has received the fourteen customer orders given in table 1. In this example the extra costs for one changeover amount to (~ 3000. The total available production time equals 90 h. The due date indicates the hour within this available time at which the order should be finished.

1002

Table 1. Customer orders for the following week. Order number Amount(t) Due date(h) Product type

1 85 52 5

2 55 26 5

3 58 58 2

4 50 25 2

5 44 83 4

6 36 56 2

7 31 70 4

8 29 61 4

9 28 75 4

10 26 41 2

11 21 27 5

12 19 32 5

13 16 48 3

14 15 40 4

If the planning and scheduling activities are executed independently, the following results are obtained. The optimal planning without incorporating the scheduling results is S = {3,4,6,7,10,13,14}, with an estimated total profit off~ 318,048. The optimal scheduling of the planned orders, minimizing total tardiness, is .2" = [4,14,10,13,6,7,3] (total tardiness 32 h). This schedule requires six changeovers and the actual profit is f~ 321,048. Incorporating the scheduling results in advance results in a higher profit, with S = {3,4,6,7,9,10}. The optimal scheduling for this planning, with a tardiness of only 19.2 h, is j = [4,10,6,3,7,9]. Implementation of this planning and schedule algorithm, including the required changeover, results in a total profit off~ 332,188. 5. C o n c l u s i o n s

The use of a bi-level top-down optimization algorithm significantly enhances the reliability of the planning results, in that the predicted profit is closer to the actual one that is obtained after the scheduling process. In addition, the set of orders handed over to the schedulers by the planners has the potential to yield a result that is better for the plant as a whole, in contrast with the sub-optimal result that can be expected when the planning and the scheduling are optimized separately. The mathematical reformulation that is presented in this paper effectively reduces the computational complexity. Using this process, that can be completed within reasonable time, the planners are able to anticipate the decision of the schedulers. References Bialas Wayne F., Mark H. Karwan, 1982, On two-level optimization, IEEE transactions on automatic control, Vol. AC-27, No. 1. Land A. H., A. G. Doig, 1960, An Automatic Method for Solving Discrete Programming Problems, Econometrica, Vol.28, pp. 497-520. Pinedo M., 1995, Scheduling: Theory, Algorithms and Systems, Prentice Hall. Ryu, Jun-Hyung, Vivek Dua, Efstratios N. Pistikopoulos, 2003, A bilevel programming framework for enterprise-wide process networks under uncertainty, Computers & Chemical Engineering. Shobrys, Donald E., Douglas C. White, 2002, Planning, scheduling and control systems: why cannot they work together. Computers & Chemical Engineering 26, 149-160. Acknowledgements The research is part of the program Next Generation Infrastructures. For more information: www.nginfra.nl

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1003

Multi-scale Planning and Scheduling in The Pharmaceutical Industry Hlynur Stefansson a and Nilay Shah a* aCentre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, London SW7 2AZ. United Kingdom.

Abstract Most sophisticated planning and scheduling approaches for the process industry consider a fixed time horizon and assume that all data is given at the time of application. In this contribution we propose a planning and scheduling approach for a continuous and dynamic decision process where decisions have to be made before all data are available. As an inspiration we have a real world problem originating from a complex pharmaceutical production plant. The approach we propose is based on a hierarchically structured moving horizon framework. At each level we propose optimisation models to provide support for the relevant decisions. The levels are diverse regarding time scope, aggregation, update rate and availability of data at the time applied. The framework receives input data piece by piece and has to make decisions with only a partial knowledge of the required input. Solution procedures have been developed and the optimisation models have been tested with data from the real world problem. The solution procedures were able to obtain solutions of good quality within acceptable computational times.

Keywords: Production planning, Scheduling, Integrated multi-scale approach, Realtime optimisation, MIP

1. Introduction The pharmaceutical industry has become a very competitive and unpredictable industry where customers constantly demand low prices as well as high service levels and flexibility. Flexible multi-product production processes have become commonly used as they help companies to respond to changing customer demand and increase plant utilisation, but the greater complexity of these processes together with the altered market conditions have rendered the simple planning and scheduling techniques previously used insufficient. It is thus very important to improve production plans and schedules in order to strive for superior utilisation of resources, flexibility and response time at the same time as cutting down cost of production. There is an extensive body of literature dealing with planning and scheduling problems in the process industry. Recent reviews of planning and scheduling problems can e.g. be found in (Shah, 1999, Pinto and Grossmann, 1998, Shah, 2004, Kallrath, 2002).

Author to whom correspondence should be addressed: [email protected]

1004 However most planning and scheduling approaches that can be found in the literature for the process industry consider a fixed time horizon and assume that all data is given or subjected to given stochastic uncertainties at the time of application. In this paper we propose a planning and scheduling approach for a continuous and dynamic decision process where decisions have to be made before all data are available. This has been motivated by a real world problem originating from a complex pharmaceutical enterprise.

2. Problem Description We focus on the single plant production planning and scheduling for a secondary pharmaceutical production facility with order-driven multistage, multi-product flowshop production. The plant consists of a large number of multi-purpose production equipment items on each production stage, operated in batch mode. When switching between batches containing products from different product families large sequence dependent set-up and cleaning times are required. These times are much lower when switching between batches containing different products within the same product family. The plant therefore uses campaign production where a campaign is an ordered set of batches containing products from the same product family produced consecutively by the same machine. Each product has a number of different feasible production routes through the plant. The overall goal of the problem is to determine campaign plan and to schedule customer orders within the campaigns. The customers request certain delivery dates for their orders and the production attempts to meet those requests.

3. Modelling Approach 3.1 Online and Dynamic Characteristics of The Problem

In order to develop optimization models and an overall approach that is realistic and can be applied in actual circumstances it is necessary to acknowledge and cope with the continuous dynamic decision process and the online characteristics of the problem we are considering. Most planning and scheduling approaches that can be found in the literature for the process industry can be classified as "offiine" approaches where the ideal case is assumed with all data given or subjected to a given stochastic uncertainties and a fixed time horizon is considered (Kallrath, 2002). A review of heuristics for theoretically oriented online scheduling problems can be found in (Sgall, 1998). Some practical online scheduling approaches are also described in the literature and for an example (Sand et al., 2000, Sand and Engell, 2004) describe online scheduling algorithms from a real world multi-product batch plant producing expandable polystyrene where demand as well as the production process is subjected to stochastic changes. An interesting telescopic decomposition approach with a number of layered sub-models of different degrees of temporal aggregation is suggested for solving online scheduling problems in multi-product batch plants by Engell et al. (2001). Order driven production planning and scheduling in the pharmaceutical industry is a critical example of a continuous and dynamic online optimisation problem. The production is an ongoing process that is affected by several uncertain inputs where the

1005 most important one is the demand from customers. The first task of the planning process is to create a campaign plan for long term planning purposes such as raw material procurement as the lead time is often very long. The campaign structure has to be decided quite a lot earlier than the orders become available and demand predictions are used instead of the actual orders. Then later the plant receives new customer orders each week with a requested delivery date and the orders need to be scheduled and feedback given to customers with a confirmed delivery date. When the orders are scheduled within the campaigns the information about other orders that will later be added to the same campaigns are not available. The decision maker does not have access to the whole input instance at the time decisions need to be made and instead he or she sees the input piece by piece and has to make new decisions with only a partial knowledge of the input. Once decisions have been made it can be difficult to change them later on. As more information become available the uncertainty of the decision problem decreases and the planning horizon is continuously moving as production of older orders is finished and the plan is built further ahead, step by step. 3.2 Hierarchically Structured Framework To cope with the continuous dynamic decision process we propose a multi-scale hierarchically structured framework. On each level of the hierarchically structured framework we propose optimisation models to provide support for the relevant accisions. The different levels are diverse regarding the scope and the availability of information at the time when they are applied. Aggregation / Available information ~ n Lev

Uncertainty /

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Figure 1. The.figure shows the hierarchical ~'amework drawn together with the representation of uncertainty and availahiliO: ((information with regard to time This is a continuously moving framework updated daily as the nature of the actual decision problem and the models are used with a different frequency depending on their level of aggregation and the update ;ate of their input factors. The most detailed decisions are made as late as possible when more information is available and the uncertainty has decreased.

3.3 Levels in The Framework 3.3.1 Campaign Planning at Level 1 At the top level in the hierarchical framework we propose an aggregated optimisation model to optimise the long-term campaign plan with the objective to fulfil demand and minimize cost of production. The input for this model is mainly based on a combination

1006 of sales forecasts and long-term customer orders as well as information regarding products, production process, performance and current status of production. The output from the model is a campaign plan that considers all machines on all production stages. The time horizon of this model is 12 months and it is used every 3 months or more often if new sales forecasts or other aggregated information becomes available. We use mathematical programming techniques to formulate the model and propose a novel and efficient mixed integer linear program with a discrete representation of time.

3.3.2 Simultaneous Campaign Planning and Order Scheduling at Level 2 At the middle level we propose an optimisation model to optimise campaign plan simultaneously with optimising allocation of orders and other production tasks, within the campaigns. The campaign plan is now based on more accurate input information compared to the earlier level as the customer orders are more or less available here. As output from this model we receive a revised campaign plan and a production schedule that specifies in which campaign each order is produced on every production stage and it also specifies the delivery date of the order. After the delivery dates have been confirmed it is very desirable to respect them although the production schedule can be changed in many other ways. The time horizon for this level is 3 months and the optimisation model is used once every week. For this level we also propose a novel and efficient mixed integer linear program with a discrete representation of time. 3.3.3 Detailed Scheduling at Level 3 At the lowest level in the hierarchical framework we propose an optimisation model for the detailed scheduling of production tasks. The optimisation is based on the confirmed customer orders together with the newest possible information each time it is used and the resulting production schedule specifies in which campaign each order is produced on each production stage, the production sequence of the orders, its precise starting time and duration and the setup tasks required between orders. The model accounts for sequence dependent setup times between the campaigns as well as between the orders within the campaigns. The time horizon is one month and the model should be used every day if some new information has become available that affects the feasibility or optimality of the last production schedule. For this level we propose a model unlike the two preceding ones regarding the representation of time as the model is based on a continuous time representation similar to that of Mendez et al. (2001) and the starting times of events are not restricted to the resolution of a time grid and can therefore be very detailed.

3.4 Integration of Levels The different levels interact with a directed flow of information between them. Results from the higher level models are transferred and used as input for the lower level models. From the first level the campaign plan is transferred and used as input for the second level. The second level is however not required to strictly respect the campaign plan and is allowed to revise it if it results in an improved schedule. The campaign plan and confirmed delivery times are transferred to the third level together with allocation of orders in the campaigns which the third level model can change to improve the schedule and react to more current and detailed information. When the flow of information between hierarchically structured levels is directed it is very important to ensure that the results transferred from higher levels provide feasible

1007

input for lower levels, if that is ensured, a mono directional integration should be sufficient. However if not, we may need to transfer information from the lower levels and develop bi directional integration of levels through feedback loops.

4. Solution A p p r o a c h e s Planning and scheduling problems, in particular scheduling problems, are known to be very difficult to model and solve in an efficient manner (Kallrath, 2002). Our objective is to provide realistic and accurate models solvable within acceptable computational time but that is very difficult for complex and comprehensive real-world problems such as the one we are working with.

4. 1 Decomposition Algorithm After standard solution methods failed to provide solution to the problems at the middle and top level we developed and implemented decomposition heuristic. The decomposition heuristic is inspired from the production performance problems found in the case we are working with. When we started analysing production data and schedules from the plant, it was obvious that there were two bottlenecks in the overall production process, at the first production stage and at the last production stage. Because of the limited capacity at the first and the last production stage we decomposed the problem into two main components: first to solve the problem for the first and last stage and then to solve the problem for the intermediate stages. The two components are integrated with a minimum expected flow time for the intermediate stages and the flow time is adjusted and the models resolved iteratively if feasible solutions are not obtained at first attempt.

4.2 Lower bounds improved with Valid Inequalities Resource constrained scheduling models often suffer from poor LP relaxations and in some cases this has made them very difficult or even impossible to solve with MILP methods. Resource constraints can easily be fulfilled with fractional values of the binary variables used in the discrete time formulations and as a result the lower bounds become very weak (Kallrath, 2002). To improve the lower bounds for our models we added two kinds of valid inequalities, valid inequalities for the minimum number of campaigns required and for the minimum unavoidable delays, that is the delay of the requested or confirmed delivery dates of customer orders. We used two methods to estimate the minimum number of campaigns, one was a simple data analysis routine and the other was a more complicated heuristic method. To obtain the value for the minimum unavoidable delays we used a two step algorithm based on first solving a relaxed model and then using its solution to provide a valid lower bound for the delays and solved the complete model with the valid inequalities for the delays.

5. Results The models that we have developed and briefly described in this paper have been implemented and tested with real world data from the problem under consideration. By

1008 using data collected in the pharmaceutical plant we created several full scale test cases that reflect the decisions problems at each level in the hierarchical framework. Table 1. Results from solving real world test cases with the proposed models for each level. Performed on Unix based machines with 2GB RAM, 1.8 GHz processor and CPLEX 9.0 solver. Level 3 3 3 2 2 2 1

Number of Orders 25 50 75 100 150 200 225

LP Objective S o l u t i o n Value 17.11 17.11 17.11 17.11 17.11 17.1I 13.15 14.05 20.17 20.39 28.91 29.51 29.87 32.84

SolutionTime [CPU seconds] 10 68 318 693 7234 32458 49621

Gap [%] 0 0 0 6.4 1.1 2.0 9.0

The results obtained so far indicate that the models and solution procedures proposed for the hierarchical framework are capable of obtaining solutions of good quality within acceptable computational time for very difficult real world problems.

6. Conclusions and Future W o r k Much research has been undertaken in planning and scheduling for the process industry however research considers a fixed time horizon with data being given. We believe that multi scale dynamic online procedures are more suitable for many specific types of planning and scheduling problems found in the process industry and should be further explored. A lot of work remains on improving the integration and flow of information between the levels in the hierarchical framework and different strategies need to be evaluated with the objective to capture the imperatives and the dynamics of the decisions problem. It is also of interest to introduce uncertainty in the models as there are several sources of uncertainty apart from the demand that affect the problem.

References Engell, S., Markert, A., Sand, G., Schultz, R. and Schutz, C. (2001) In Online Optimization of Large Scale Systems, SPRINGER-VERLAG BERLIN, Berlin, pp. 649-676. Kallrath, J. (2002) Or Spectrum, 24, 219-250 Mendez, C. A., Henning, G. P. and Cerda, J. (2001) Computers" & Chemical Engineering, 25, 701-711. Pinto, J. M. and Grossmann, I. E. (1998)Annals of Operations Research, 81,433-466. Sand, G. and Engell, S. (2004) Computers & Chemical Engineering, 28, 1087-1103. Sand, G., Engell, S., Markert, A., Schultz, R. and Schulz, C. (2000) Computers & Chemical Engineering, 24, 361-367. Sgall, J. (1998) In Online Algorithms, Vol. 1442, pp. 196-231. Shah, N. (1999) AIChE Symposium Series, 320, 75-90. Shah, N. (2004) Proc ESCAPE-14, Portugal.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1009

Initiation and inhibiting mechanisms for multi-tasking control in discrete event systems S. Macchietto ~, Nicholas J. Alsop, Ross J. Baird, Zhang P. Feng and Bing H. Chen Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK

Abstract A theoretical analysis is presented of sequential controller initiation (pre-check) and inhibition for concurrent operations within a formal Procedural Control Theory (PCT) framework. These aspects are essential to the safety and performance of multitasking sequential controllers at the design and operation stages. The pre-check mechanism ensures the correct initial state of the process when controller is synthesized. The inhibit function prevents nominated controllers potentially using shared devices from starting while another controller is already active. The ideas are explained via a small illustrative example.

Keywords: formal

methods, procedural control theory, discrete event systems, safety.

1. Introduction Formal techniques to support the design of automation software for discontinuous processes are grounded in logic and discrete systems theory. Their primary goal is the improvement in process safety and operation by eliminating errors in sequential control software that often occur during the design of control logic and its implementation in automation systems. Unlike the verification approach (Nimmo 1994, Moon et al 1992), which checks controlled process against specifications, the idea in sequential control synthesis methods is to develop "provably correct systems" that can be shown a-priori to meet all specifications and generate no undesired behaviours. The Procedural Control Theory (PCT) (Sanchez and Macchietto, 1995, Sanchez et al., 1999) is one of them. Industrial sequential controllers are programmed in control languages typically organized into sets of "operations" (in the ISA $88 standard sense, ISA 1995). Each operation is started by an operator or a supervisory control system. Control architectures are multitasking, i.e. support concurrent control by multiple operations. Operations use process related hardware resources (e.g. pumps) that are usually shared with other operations. Without adequate safeguards, an operation could be started when its resources are in an inappropriate state or already in use by other operations. In either case conflicts may arise and at the very least the proper execution of the operation cannot be guaranteed. At worst, unsafe states of the process could be reached. Therefore, suitable initiation and inhibit logic is required in such circumstances, but

Corresponding author, Tel: +44 20 5945575, Fax: +44 20 75945604, email: [email protected]

1010 these issues have been ignored in the literature. This work deals with them by formally introducing controller initiation (pre-check) and inhibition within the PCT framework.

2. Process Modelling within PCT In PCT, a Discrete Event Systems (DESs) model of a process is described as a Finite State Machine (FSM) comprising of a finite set of states and transitions, by 7 tuples:

M -{Q,V'Z",E,~,y, qo,Qm}

(l)

where Q is the set of states and Z, = Z,c u Z, the set of transitions (other symbols are defined in the nomenclature). Controllable transitions Ec, e.g. turning on/off a pump, are forced by a controller while uncontrollable Zu transitions, such as the increase/decrease of a level sensor signal in a tank, occur indirectly and may only be observed. In PCT, an elementary device (e.g. pump or sensor) is represented by a unique "state variable" which may take a number of discrete realizations (states) and by the set of "transitions" that take the device from one state to another. Two operations on FSMs generate the model of a composite system: the "Asynchronous Product" to interleave states from each FSM and the "Synchronous Product" to intersect two FSMs to generate strings common to both original FSMs. The FSM model M of a system represents every possible combination of feasible states and process trajectories in the open loop process. Desirable behaviour of the process is defined by imposing the existence or otherwise of states and transitions, or allowable strings of process events, via formal specifications.

3. The Closed Loop Controller Initiation with Pre-checks The closed loop behaviour obtained by a controller c X that implements given specifications on model M is denoted by (L(Cx/M) In general, controller performance .

is sensitive to any departure in the initial state of process M from its nominal initial state q0 '. Thus, additional functionality is required to handle possible variability in the initial state of the process. The simplest mechanism is a pre-check that ensures that an operator request for starting controller c x from a process state q is granted only if q is the nominal initial state q0' of the process. A sufficient condition for

q=qo' is

that

every elementary component of M is in its nominal initial state. We define a new transition ax to represent the actual start of controller c x . Strictly, this is not an elementary process event (i.e. o-X~ Y_,) and therefore does not alter the process state. Then the pre-check mechanism is to ensure that the process is in state q0 for event ax to occur (i.e. for the controller cx to start). Therefore, o-~ is included in the model of the process as a self-looped transition at each potential starting state q e Qx. The closed loop behaviour of a system M under control of cx with pre-checks is then formulated as:

L(Cx/M ) = E* "err'L(. sXwcr)nL(Sffi'M)z,, .

(2)

This can be read as: the closed loop language generated by c x on M with pre-checks is the set of physically possible strings made up from the concatenation of an open loop

1011 trajectory and the starting event o-, plus the closed loop behaviour. M is not under control from ~' until the event o-, at a potential starting state q e Qx- Similarly, the marked closed loop response is given by: . L,,,(C,/M)

-

(3)

. s X~,, " c , . ) A L m ( S ~ - ' M ) ,Y_,*-a,.L,,,{

4. C o n t r o l l e r I n h i b i t i n g A controller inhibit mechanism is defined to disable a controller from starting if the system does not satisfy a given set of conditions. In particular, this mechanism checks the state of nominated controllers in a multitasking control system. Checks are performed before a controller is started so that abortive action can be taken to avoid the concurrent operation of controllers that compete R)r the same resource. The approach is based on the concept of non-cooperation (Alsop, 1996) and requires the closed loop language generated by the process under parallel control by controllers c~ and c, each with pre-checks. The cooperative and non-cooperative properties are used as follows: if c, is non-cooperative with c,., then c, must inhibit c , , and if d, cooperates with c, then no inhibition mechanism is necessary.

4.1 Closed loop language with pre-checks for two controllers in parallel Using the closed loop language generated by a single controller (equation 2), the closed loop language generated by two controllers c, and c, on process M augmented with the self-loop or, at each possible initial state ~/e (2, and dr,, at each possible initial state qe (2,. with a pre-check mechanism is given by:

L(C v "~C,,/M)-7O,71{Z:'I.o,.L(S~",C,)IA~,:'{Z:I,.o,,.L(S~"IC,,)JAL(SQ'SQ'M)} •

"

"

"

"

"

.

.

.

.

u."

-

v

(4)

O'v

where Z = E , uZ,, and Z, hE,, _cZ,,. The first term of equation 4 is equivalent to the first term of equation 2 with the addition of the proiection operation /~,71 . This operation permits any event from (E-Z,)vodr,, , and thereby restricts no events generated b y e , . Similarly, the second term represents the set of strings generated by controller c',,, which permits any event generated by C," The third term is the set of physically possible strings (i.e. the process model), augmented with self-loops or, at each state re(J, and or, at each state qe(2,

The augmented self-looped transitions

allow both controllers to start when the process is appropriately initialised.

4.2 Inhibit design for controllers with shared controllable items In the lormulation of the combined closed loop language (equation 4), it is necessary for the two controller languages to not share controllable transitions (i.e. E, hE,, _c E,, ). At first this may appear to reject from the inhibit analysis the case in which c, and c, share elementary components generating controllable events (e.g. driving the same valve). Typically, inhibits are necessary between pairs of controllers which drive the same equipment item. However situations may arise in which two controllers cooperatively employ the same equipment item. A special modelling technique is

1012 employed to handle this case to ensure that controllable transitions will not be generated concurrently by both controllers. In other words, it is not possible for the controllers to synchronise on a common controllable event. Therefore two common controllable transitions generated by the two controllers are unique, and must be labelled accordingly. The labels identify an event with the controller from which it is generated, i.e. transitions in cx and cy need be relabelled to respect the condition that Y--x and :~y share only uncontrollable events. In this work, we use a 'convert' technique (Wonham, 1996) for re-labelling transitions. For convenience, the set ~:v,, is defined as all those controllable events in E,, which have an equivalent gx : Z.~:v = { G E E o , / V q E Q,d(cr, q ) ! , 3 c r ' e Ecx s.t. 6(o-',q)!Aa(o-',q)=6(cr,q)}

(5)

Events in E~, can occur in the open loop process or when generated by Cy, but not when controller cx is the only active controller. Similar occurrences apply to events in Ey X. A regulator R is therefore introduced to meet this requirement by interlocking shared controllable items. Its language is given by:

L(R) = 7__,*.o-~.[7__,-gxy . ]* .Oy .Z* w 7__,*. O y . [ g - g y x ]* .o-~. . Y_,*

(6)

The first term prohibits events not in [E-Exy] after starting c~ and before starting cy with the reverse for the second term. The closed loop language generated by process M under parallel control from c~ and cy with pre-checks where c X and Cy share elementary components generating controllable events is given by:

x x. /~,71 }m L(S~'S~"M)mL(R) , y L(C x "~Cv/M)=T)xl{gx.Crx.L(Sz,,'xCx)In . {g~,. . a y •L(Sz,~.~,C:,)

(7)

Two controllers are cooperative (can be concurrent without inhibits) if the condition L(Cx ~ Cy/m) is a subset of U.ax.~-~L(Sx) holds true (Alsop, 1966) and vice versa.

5. An Example A liquid ingredient is dosed in a tank (Figure 1) using Feed Valve (FV), Drain Valve (DV) and level sensors LV1 and LV2. These devices are modelled as two state FSMs (Figure 2). Nodes on the graph represent states and edges transitions. Controllable transitions of FV and DV are duplicated for the use of inhibitions. Uncontrollable transitions are shown as dashed arcs, while controllable ones as solid arcs. Level Sensor LVI

Level Sensor LV2

Feed Valve

20 ......

i'~

~:::~.::

,......

Figure 1. Dosing tank

1 ~

/ 2

3 ~

l6

Drain Valve

2

~ 4

8

~

208

Figure 2. Elementary components modelled as F S M s

We wish to design a procedure is to fill the tank to level 2, ready for the next stage of the process. The initial and goal (marked) states are: • Initial state: FV is closed, DV is closed, LV 1 is low and LV2 is low. • Goal state: FV is closed, DV is closed, LV 1 is low and LV2 is high.

1013 The overall process model (Figure 3), obtained by the asynchronous operator of the components of Figure 2, includes all possible combinations of state variables {FV,DV,LV1,LV2} and transitions. A standard controller (i.e. befl)re pre-checks and inhibits) for filling the tank up to level sensor 2 is obtained (Figure 4 (a)) using the lollowing specifications" Static constraints: 1. The process should never reach a state where LV1 is high 2. When LV2 is low, LV1 cannot be high Dynamic constraints: 3. If DV is closed it is impossible for LVI or LV2 to fall If FV is closed it is impossible for LV1 or LV2 to rise . 5. If FV is open, do not allow DV to open 6. If LV2 is low, do not allow FV to close 7. If FV and DV are closed and LV 1 and LV2 are low, then open FV 8. If FV and DV are closed, LV 1 is low and LV2 is high, do not open DV 9. If FV and DV are closed, LV 1 is low and LV2 is high, do not open FV 10. If LV2 is low, do not allow DV to open 1 1. If valve DV is closed, do not open it

~:i:~'::~:; :>::71:.~i::~ "*-:i~!! ~!-,:~ i~21:~::~,;*i ,:..............~.:.,,

..... ~...,,~

...........* . . ~ .

.:,..........~:.,.,....

~,.:...~.........

Figure 3. Asynchronous product for the Dosing tank, where C for 'closed', O for 'open', L for 'low', H for 'high'respectively

(a) (b) Figure 4. Controllers for filling tank up to level 2 (a) and level 1 (b) without pre-check

Adding pre-checks to ensure that the initial state is consistent with the nominal initial state gives the close loop language of Figure 5(a), where or. =111 is defined as the starting event of this controller, which we call c,.. A similar procedure to fill up to level 1 can be obtained (Figure 4 (b)) which uses the same valve and sensor devices. The closed loop language of two parallel controllers with pre-check is shown in Figure 5(a) and (b). The regulator language for the concurrent use of the two parallel controllers is shown in Figure 6. It can now be formally established that the two controllers are noncooperative and hence c,_ must inhibit c,, and vice versa. 1,2,3,4 1.2

i, 2 3,4

5,6,7,8 2{)5,206 207,208

)4

Cx O F F Cy O F F

5 . 6 , 7, 8 ,2

207, 2()8

C~ON CyOFF

1,2

\

117 ~ ~ ~ / I

/I IIII Cx~FV CyON"

1,2,3,4 ~ 205,206

Cy O N

207, 2O8

(a)

(b)

Figure 5. FSM with pre-checks for two controllers in parallel

Figure 6. Regulator language for controllers with shared controllable items

1014

6. Conclusion The novel theoretical d e v e l o p m e n t presented allows incorporating controller initiation and controller inhibiting features within a PCT framework. These two mechanisms guarantee essential safety properties of a multitasking sequential control system, prohibiting the start of control actions in inappropriate situations. The p r e - c h e c k m e c h a n i s m ensures that control is initiated only when the state of the process is compatible with predefined nominal initial state(s). Similarly, the inhibit function prevents nominated controllers from starting while a given controller is already active. The formal closed loop language generated by a controller with a p r e - c h e c k m e c h a n i s m on a process was derived. This formulation, combined with that for the closed loop language generated by two parallel controllers, yields a general formal definition of the closed loop behavior generated by two parallel controllers each with p r e - c h e c k s . A further extension in the form of a regulator language handles the special case of shared controllable items. Further extension to multiple parallel controllers is immediate. The example used here is illustrative only. Larger applications will be published elsewhere.

Nomenclature C~and C,, - Controllers - Closed loop language generated by controller Cx and process M Lm(C~/M) - Closed loop language generated by controller Cx and marked process

L(C:/M)

L ( C x "~ C y / M )

-Closed loop language

q'0 - Nominal initial state S x - The specification for controller C, S X,,, - The self-loop operation at wait state with Y'u

uncontrollable transition E,,

generated by parallel controllers C, and C,. M - Process model FSM Q - Set of states Qm - Set of marked states qo - Initial state

transition from o-x . V..... The set of states each represented by n state

Greek Symbols 7 - State variable transition partial function - State transition partial function - Controller state transition partial function E - Set of transitions or alphabet of process events

E* - The set of all process trajectories composed of transitions in E ~ - Process event

s.~,- The self-loop operation at state Q, with

variables

Reference Alsop, N. J. 1996, Formal Techniques for the Procedural Control of Industrial Processes, PhD thesis, University of London ISA, 1995, Batch Control Part 1: Models and Terminology. Moon, I., G.J. Powers, J.R. Butch and E.M. Clarke, 1992, Automatic verification of sequential control systems using temporal logic. AIChE, 38(1), 67. Nimmo, I., 1993, Start up plant safely, C h e m i c a l E n g i n e e r i n g p r o g r e s s 89(12), 66. Sanchez A and S. Macchietto, 1995. Design of procedural controllers for chemical process, Computers and Chemical Engineering, 19S, 381. Sanchez, A., G. Rotstein, N. Alsop and S. Macchietto, 1999, Synthesis and implementation of procedural controllers for event-driven operations, AIChE J, 45 (8), 1753. Wonham, W.M., 1996, N o t e s on C o n t r o l o f D i s c r e t e - E v e n t Systems, Systems Control Group, Dept. of Electrical & Computer Engineering, University of Toronto. ECE 1636F/1637S.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. gspufia(Editors) (O2005 Elsevier B.V. All rights reserved.

1015

Model Based Parametric Control in Anesthesia Pinky Dua ~, Vivek Dua b and Efstratios N. Pistikopoulos a°* aCentre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK bCentre for Process Systems Engineering, Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, UK

Abstract This work presents a compartmental model for delivery of three drugs (isoflurane, dopamine and sodium nitroprusside) for regulation of anesthesia. The key feature of this model is that mean arterial pressure, cardiac output and unconsciousness of the patient can be simultaneously regulated. This model is 'validated' by carrying out a number of dynamic state simulations and then used for designing model based parametric controllers.

Keywords: Anesthesia, Mean Arterial Pressure, Model Based Control, Parametric Controller

1. Introduction Safe and adequate anesthesia is characterized by muscle relaxation, hypnosis and analgesia while maintaining vital functions such as mean arterial pressure (MAP), heart rate and cardiac output (CO) within certain desired ranges. A tight control of these vital functions is very important; otherwise it may lead to fatal situations. The anesthesiologist maintains these vital functions by regularly infusing various anesthetic drugs and/or intravenous fluids. Automatic control of the vital functions can reduce undesirable situations and improve the safety of the patient, by monitoring conditions that can not be measured easily, allowing the anesthesiologist to focus on critical issues, and also reduce the cost of the drugs and the time spent in the post-operative care unit. The automatic control techniques rely on a model of the patient that can incorporate the dynamic response of the patient to drug infusions and disturbances (Yasuda et al., 1991; Rao et al., 2001; Mahfouf et al., 2003). Gentilini et al. (2001) observed that controlling MAP and hypnosis simultaneously with isoflurane was difficult. Yu et al. (1990) proposed a model for regulating MAP and CO using dopamine (DP) and sodium nitroprusside (SNP), but the control of hypnosis was not considered. In the next section, a compartmental model is presented, which allows the simultaneous regulation of the MAP, CO and the unconsciousness of the patients. The model is characterized by: (i) pharmacokinetics for the uptake and distribution of the drugs, (ii)

Author to whom correspondence should be addressed: [email protected]

1016 pharmacodynamics which describes the effect of the drugs on the vital functions and (iii) baroreflex for the reaction of the central nervous system to changes in the blood pressure. The model involves choice of three drugs, isoflurane, DP and SNP. In Section 3 model based controllers for the regulation of anesthesia are designed by using Model Predictive Control (MPC) Toolbox (1998). Note that MPC solves a quadratic program at regular time intervals. Pistikopoulos et al. (2002), have presented model based parametric controllers that partition the space of state variables into a number of regions and each region is characterized by a control law, which is an explicit function of the state variables. This parametric control technology is used to design an explicit controller for the infusion of isoflurane for regulation of MAP and BIS. This reduces implementation of model based controllers to simple function evaluations. Concluding remarks are presented in Section 4.

2. Modelling Anesthesia The model is based on the distribution of isoflurane in the human body (Yasuda et al., 1991). It consists of five compartments organized as shown in Figure 1. Respiratory System J" soflurane

Tl

U

Uptake

Injection of DP and

SNP

Figure 1. Compartmental Model

The compartments 1-5 represent Lungs, Vessel rich organs (e.g. liver), Muscles, Other organs and tissues and Fat tissues respectively. The distribution of the drugs occurs from the central compartment to the peripheral compartments by the arteries and from the peripheral to the central by the veins. The first compartment in Figure 1 is the central compartment and heart can be considered to be belonging to the central compartment, whereas compartments 2-5 are the peripheral compartments.

2.1 Pharmacokinetic Modelling The pharmacokinetic model is developed based on the works of Yasuda et al. (1991), Yu et al. (1990) and Gentilini et al. (2001). The uptake of isoflurane in central compartment via the respiratory system is modelled as: V dCinsp

dt

- Q i n C i n - (Qin - A Q ) C i n s p - f R (VT - A ) ( C i n s p - C o u t )

(1)

1017 where C~n.v,is the concentration of isoflurane inspired by the patient (g/mL), C;,, is the concentration of isoflurane in the inlet stream (g/mL), Co,,, is the concentration of isoflurane in the outlet stream (g/mL), Q;, is the inlet flow rate (mL/min), AQ is the losses (mL/min), V is the volume of the respiratory system (mL), j)~ is the respiratory frequency (1/min), Vr is the tidal volume (mL) and A is the physiological dead space (mL). For the central compartment, the concentration of isoflurane is given by:

VI - &

i=2

~

- Cl

11

+ fR (VT - A)(Ci,,.w - Ci )

(2)

where Ci is the concentration of the drug in compartment i (g/mL), R~ is the partition coefficient between blood and tissues in compartment i, Q~ is the blood flow in compartment i (mL/min). The concentration of DP and SNP in the central compartment is modelled as follows:

v, ~

--£-c,

+c,~,-~-c,v,

7=2

(3)

rl/~2

where C w is the flowrate of the drug infused (g/min), Vi is the volume of compartment i (mL) and "c~/2 is the half-life of the drug (min). The distribution of isoflurane in compartments 2 to 5 is given by Vi - ~

- Qi CI -

- kiC i, i = 2 .... ,5

(4)

The natural decay of DP and SNP in the body, for compartment 2 to 5, is given by: d C i ( C i )

v,7--e,

c,---£, -

1

(5)

c i v i , i= 2,..,5

2.2 Pharmacodynamic Modelling DP and SNP affect MAP indirectly. These drugs influence two of the heart's characteristic parameters: maximum elastance (E,,,,,) and systemic resistance (R,,,), which is given by: d E f f = k 1C N (E f f m ax - E l f ) - k 2 E f f dt

(6)

where JEff is the measure of the effect of drug on the parameters of interest,

'~max - '~max,O 0 + ~S.r,~-,~ ...... ),

'~<

- ~s~s,O O-'~SS,~,~-R,.,..,.-

~SS~<,~-R,.,..,.)' ~" k~

are the rate constants and N is the non-linearity constant. MAP can be expressed as a function of E,,,~,x and R,,,, as:

1

MAP 2 ---7+ 2K2 MAP - 2K2VLvEmax R~,~

- 0

(7)

The relationship between MAP and CO is given by: MAP = R>~x CO where MAP is the mean arterial pressure (mmHg) and CO is cardiac output (L/min).

(8)

1018 Isoflurane affects MAP as follows:

MAP =

Q1 ~-'~(gi,o (1 +biCi) ) i=2

(9)

where, gi, o is the baseline conductivities (mL/(min.mmHg)) and bi is the variation coefficient of conductivity (mL/g). There is experimental evidence that a transportation delay exists between the lungs and the site of effect of isoflurane on the unconsciousness of the patient. In order to model this, an effect compartment is linked to the central compartment. The concentration of isoflurane within this compartment is related to the central compartment, which is given by: dCe ~=keo(C

dt

(10)

1 -C~)

where Ce is the concentration of isoflurane in the effect compartment (g/mL), and ke0 is the kinetics in the effect compartment (min-1). The action of isoflurane can be then expressed as follows"

Cey

A B I S - SaNIS MA X

(11)

c; + ECho where A B I S - B I S - B I S 0 , A B I S M A X - B I S M A x - B I S o , BISo is the baseline value of BIS (assumed to be 100), BISMAx is the maximum value of BIS (assumed to be 0), ECso is the patient's sensitivity to the drug and 7 is the measure of the degree of non-linearity.

2.3 Baroreflex Baroreflex is obtained from a set of transfer functions relating the mean arterial pressure to the maximum elastance and the systemic resistance and is given by:

ec(MAP-MAPO) bfc = 1 + ec(MAP-MAP0)

(12)

where c is the empirical constant (mmHg). For further details on the model and the parameters used see Dua et al., 2005.

3. Control of Anesthesia The model presented in the previous section was validated by carrying out a number of dynamic simulations for different amounts of drug dosages and disturbances using gPROMS (2003). This model was then used for designing model based and parametric controllers. For designing model based controllers, the model was linearized at the nominal values of inputs: 0.6% vol. of isoflurane, 2 ~tg/kg/min of DP and 4 gg/kg/min of SNP and outputs: 57.38 mmHg of MAP, 61.1 BIS and 1.21 L/min of CO to obtain a state-space model consisting of 23 states, 3 outputs and 3 inputs. This state-space form of the model is then adapted for designing model predictive controller by using the MATLAB Model Predictive Control Toolbox (1998). For designing the MPC controller, the following input: 0 < D P < 7 ¢tg/kg.min, 0 < S N P < 10 ¢tg/kg.min, 0 <

1019 lsq#urane < 5% vol., and output constraints: 40 <_ MAP< 150 mmHg, 40

<

BIS < 65, 1 <

CO < 6.5 L/min are used. A prediction horizon of 5, control horizon of 3 and sampling

time of 0.5 minutes are considered. A set point of [20 -10 1]' deviation from the nominal point of the output variables is given and the performance of the controller is shown in Figure 2 where the control variables are also deviations from the nominal values. It is observed that the MPC tracks the set point quite well. Ou-l:~>uts

20-

' •

~':)

....

P.s

co

:

0

.. 10 .

.

0

2

.

4

.

6

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Figure 2. MPC Performance for Anesthesia

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Figure 3. Parametric Controller: State Profiles

1020 For the design of parametric controller (Pistikopoulos et al., 2002) a reduced form of the model, presented in section 2, corresponding to the infusion of isoflurane regulating MAP and BIS is considered. The model has 7 states, xl to xT, representing the concentration of isoflurane in the 5 compartments and its effect on Emax and Rs,,s and the input variable is given by the inlet concentration of isoflurane. Prediction and control horizons of 3 and equal weightings on state and control variables are used resulting in 48 regions in the space of the state variables. The performance of the parametric controller was tested for a given input and the profile of the state variables is shown in Figure 3. It was observed that the profiles match closely with those obtained from the simulation of the nonlinear model by using gPROMS.

4. Concluding Remarks Automatic regulation of anesthesia can provide tighter control allowing anesthesiologist to focus on more critical issues which will result in less time spent by the patients in the post-operative care unit, reduction in the amount of drugs used and side-effects and above all a much safer platform for surgery under anesthesia. A compartmental model for anesthesia based upon the infusion of three drugs for the simultaneous regulation of mean arterial pressure and unconsciousness of the patient has been presented. This model was validated and then used for designing model based and parametric controllers. The performance of the controllers was tested and observed to be very good. From the results obtained it can be inferred that the model based and parametric control are promising technologies for automatic control of MAP, CO and unconsciousness of the patients being operated under anesthesia.

References Dua, P., V. Dua and E.N. Pistikopoulos, 2005, accepted for publication in the l6 th IFAC World Congress, Prague. Gentilini, A., C.W. Frei, A.H. Glattfelder, M. Morari, T.J. Sieber, R. Wymann, T.W. Schnider and A.M. Zbinden, 2001, IEEE Engineering in Medicine and Biology, 20(1), 39-53. gPROMS, Introductory User' s Guide, 2003, Process Systems Enterprise Ltd., London UK. Mahfouf, M., A.J. Asbury and D.A. Linkens, 2003, Control Engg. Practice, 11(12), 1501-1515. Morari, M. and N.L. Ricker, Model Predictive Control Toolbox User's Guide, 1998. Pistikopoulos, E.N., V. Dua, N.A. Bozinis, A. Bemporad and M. Morari, 2002, Comput. Chem. Engg., 26, 175-185. Rao, R.R., C.C. Palerm, B. Aufderheide and B.W. Bequette, 2001, IEEE Engineering in Medicine and Biology, 20(1), 24-38. Yasuda, N., S.H. Lockhart, E.I. Eger, R.B. Weiskopf, J. Liu, M. Laster, S. Taheri and N.A. Peterson, 1991, Anesthesia and Analgesia, 72, 316-324. Yu, C., R.J. Roy and H. Kaufman, 1990, Med. Prog. Technol., 16, 77-88.

Acknowledgements PD would like to acknowledge financial support from the Overseas Research Student Award Scheme (ORS) and the Industrial Consortium of the Centre for Process Systems Engineering. A. P. Muller and S. Chrysafi's contribution to this work is also acknowledged.

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1021

Anti-slug control experiments on a small-scale two-phase loop Heidi Sivertsen and Sigurd Skogestad* Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway

Abstract Anti-slug control applied to two-phase flow provides a very challenging and important application for feedback control. It is important because it allows for operation that would otherwise be impossible, and challenging because of the presence of both RHP-poles and RHP-zeros. To conduct experiments on pipeline-riser anti-slug control, a small-scale slug-loop has been build. The loop has been modeled and analyzed using a simplified model by Storkaas. The results from this analysis and experimental results using a PI-controller is presented in this paper.

Keywords: feedback control, riser slugging, controllability analysis 1. Introduction Some of the problems in the offshore oil industry that have received increasingly interest in the last years are related to multiphase flow. In multiphase flow different flow regimes can develop, depending on parameters such as flow rates, fluid properties and pipeline geometry. Slug flow is a flow regime which can cause a lot of problems for the production facilities. The slug flow is characterized by alternating bulks of gas and oil, and can be further divided into hydrodynamic and terrain induced slugging. Hydrodynamic slugs are caused by velocity differences between the phases and occur in near horizontal pipelines. These slugs are usually short and appear frequently. Terrain induced flow however, can contain a lot of liquid and therefore induce large pressure variations in the system. This flow is induced by low points in the pipeline geometry. When the low-point is realized by a downsloping pipe terminating in a riser, we get what is known as riser slugging. Because of the large and abrupt fluctuations in pipe pressure and gas and liquid flow rates at the outlet, these slugs cause huge problems for the processing equipment. Unwanted variations in the separator level give rise to poor separation and possible overfilling. The pressure fluctuations wear and tear on the equipment and can sometimes result in unplanned process shutdowns. *e-mail: [email protected]:phone: +47-7359-4154; fax: +47-7359-4080

1022

T 4

4----

3

Figure 1. Illustration of the cyclic behavior (slug flow) in pipeline-riser systems The behavior of pipeline-riser slug flow is illustrated in Figure 1. Liquid accumulates in the lowpoint of the riser, blocking the gas (1). As more gas and liquid enters the system, the pressure will increase and the riser will be filled with liquid (2). After a while the amount of gas that is blocked will be large enough to blow the liquid out of the riser (3). After the blow-out, a new liquid slug will start to form in the lowpoint (4). Several solutions for eliminating or reducing these problems have been proposed (Sarica and Tengesdal, 2000), but they usually come at a price. Choking the valve at the top of the riser is one example of this. The slugging will disappear, but the increased pressure drop over the valve will lead to a lower production rate. Stabilizing the flow using active control has been proposed earlier and also tested out both on experimental rigs (Hedne and Linga, 1990) and on offshore installations (Havre et al., 2000) and (Courbot, 1996). It has been proved that it is possibly to stabilize the flow at a pressure drop that would lead to slug flow if left uncontrolled. However, there is still a lot that can be done on deciding which measurements and control configuration gives the best results. Some measurements, like the inlet pressure, can even be hard to implement and maintain. A small-scale loop (the Miniloop) was build in order to test out and analyze different control strategies in a cheap and easy way. The loop is very simple with a flow consisting of only two phases, air and water. We still get the same slugging phenomenon as expirienced offshore, with pressure fluctuations and varying flow rates. This makes it possible to screen different ideas before testing them on larger and more expensive experimental rigs and a lot of money can be saved.

2. Experimental setup To test different control configurations, a small-scale two-phase flow loop with a pipelineriser arrangement was build. The flow consists of water and air, which are mixed at the inlet of the system. Both the pipeline and the riser was made of a 20mm diameter transparent rubber hose, which makes it easy to change the shape of the system. A schematic diagram of the test facilities is shown in Figure 2. From the mixing point the flow goes trough the low-point at the bottom of the riser and depending on different conditions, slug flow may occur. At the top of the riser there is a separator, which leads the water to a reservoir. From there the water is pumped back into the system through the mixing point. The air is being let out through a small hole at the

1023

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i

J

ii;

i

!:

i ? i:i !

i!: .,2,,,; . . . . . .

Figure 2. Exlwrimental settq~ top of the separator. For slugging to appear there must be enough air in the system to blow the water out of the 1,5 meter long riser. This requires a certain amount of volume, which is accounted for by a buffer tank (BT) between the air supply and the inlet. The volume of the gas can be changed by partially filling this tank with water. The flow rates of gas (Qair) and water (Qw) determines whether we will have slug flow in open loop operation or not. These flow rates are being measured upstream the inlet. Typically flow rates during an experiment are 1 l/rain for the gas and 3 l/rain for the water. So far there are three pressure sensors located at different places in the loop. One is located at the inlet (P1) while the two others are topside measurements, located at the top of the riser (P2) and at top of the separator (P3). The latter is used for measuring the flow of air out of the separator. Fiber optic sensors (S1, $2) give a signal depending on the amount of water in the hose where they are located. They can easily be mowed around to measure the holdup at different locations in the loop. A control valve is placed at the top of the riser. A signal from the control panel sets the opening percentage of the valve. The control panel converts the analog signals from the sensors into digital signals. These signals are then sent to a computer. The signals are continuously displayed and treated using Labview software. Depending on the control configuration, some of the measurements are used by the controller to determine the opening percentage for the control valve.

3. Controllability Analysis Storkaas et al. (2003) have developed a simplified macro-scale model to describe the behavior of pipeline-riser slugging. The model has three states; the holdup of gas in the feed section (;~;,c;1), the holdup of gas in the riser (';~J¢72), and the holdup of liquid (~I~,L). Using this model we are able to predict the variation of system properties such as pressure, densities and phase fractions. In order for the model to fit the MiniLoop, it needs to be tuned. To do this we compare the bifurcation diagrams for the model and the Miniloop, plotted in Figure 3. The upper lines shows the maximum pressure at a particular valve opening and the lower line shows the

1024 minimum pressure. The two lines meet at around 20% valve opening. This is the point with the highest valve opening which gives stable operation when no control is applied. When Storkaas' model is properly tuned, the bifurcation point from the model will match the one from the experimental data. The dashed line in the middle shows the unstable steady-state solution, which is the desired operating line with closed-loop operation. 1.25

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L 20

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Figure 3. Bifurcation diagrams from experimental data (dotted line) and Storkaas' model (solid line) When the model is tuned it can be used to perform a controllability analysis on the system. This way we can predict which measurements are suitable for control, thus avoiding slug flow. The analysis shows that the system consists of the poles given in Table 1. Table 1. Poles of the system for valve openings z=O.12 and z=0.25 z

0.12 -20.3411 -0.0197 ± 0.1301i

0.25 -35.2145 0.0071 + 0.1732i

Since all poles of the system are in the LHP when using a valve opening of 12%, this valve opening results in stable flow in the pipeline. However, when the valve opening is set to 25% we get a pair of RHP poles leading to riser slugging. This could also be predicted from the bifurcation diagram in Figure 3. To stabilize the flow we have available several measurements. Four of these are topside measurements; pressure P2, density p, volume flow Fq and mass flow Fw. The fifth measurement is the inlet pressure, P1. The zeros of the system using different measurements are given in Table 2.

Table 2. Zeros of the system using different measurements at valve opening z=0.25

~'~

P2

p

Fq

p~

- 1.285

46.984 0.212

0.092 -0.0547

-3.958 -0.369 ± 0.192i

-65.587 -0.007 ± 0.076i

It is well known that stabilization (shifting of poles from RHP to LHP) is fundamentally difficult if the plant has a RHP-zero close to the RHP-poles. From this, we expect no

1025 particular problems using P1 as the measurement. Also, Fq and Fw could be used for stabilization, but we note that the steady-state gain is close to zero (due to zeros close to the origin), so good control performance can not be expected. On the other hand, it seems difficult to use O or Pg_ for stabilization because of presence of RHP-zeros. From the controllability analysis we therefore can draw the conclusion that when using only one measurement for control, the inlet pressure/:'1 is the only suitable choice.

4. Experimental results The analysis showed that using the inlet pressure P 1 w a s the only possibility when using only one measurement for control. Based on this, a PI-controller was used to control the system using this measurement. The MiniLoop was first run open loop for two minutes, with a valve opening of 30%. This is well inside the unstable area, as the bifurcation diagram shows. The result is the pressure oscillations plotted in Figure 4, which illustrates how the pressure and valve opening varies with time. Both experimental and simulated values using the simplified model are plotted. When the controller is activated after two minutes, the control valve starts working. The flow is almost immediately stabilized, even though the average valve opening is still within the unstable area. It remains that way until the controller is turned of again after 8 min. When the controller is turned off, the pressure starts oscillating again. Pl

z

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A ~.18

g~

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Figure 4. Experin~ental and simulated results using a Pl-controller

From Figure 4 we see that the controller efficiently stabilizes the flow, confirming the results from the analysis. However, this measurement can be difficult to use in offshore installations because of its location.

1026 Using other control configurations or measurements other than the ones analyzed in this paper might be the solution if there are only topside measurements available. The plan is to test out different ways to do this in the near future. The first possibility that will be explored, is using a cascade configuration involving the topside pressure/92 and one of the flow measurements F~ or Fq. Storkaas and Skogestad (2003) have proved theoretically that this works for another case of riser slugging.

5. C o n c l u s i o n From the controllability analysis it was found that using the bottom hole pressure was the only measurement of the five measurements analyzed, that could be used for controlling the system. The experiments confirmed that the model used for the analysis was good, and that using this measurement we where able to control the flow without problems. We are, however, looking for other ways to control the flow because of the problems related to down hole measurements. When using some of the other measurements analyzed, we must use combinations of measurements in order to avoid the problems related to the zeros introduced.

References Courbot, A. (1996). Prevention of Severe Slugging in the Dunbar 16" Multiphase Pipeline. Offshore Technology Conference, May 6-9, Houston, Texas. Havre, K., Stornes, K. and Stray, H. (2000). Taming Slug Flow in Pipelines. ABB review, 4:pp. 55-63. Hedne, E and Linga, H. (1990). Supression of Terrein Slugging with Automatic and Manual Riser Choking. Advances in Gas-Liquid Flows, pp. 453-469. Sarica, C. and Tengesdal, J. (2000). A new teqnique to eliminating severe slugging in pipeline/riser systems. SPE Annual Technical Conference and Exibition, Dallas, Texas. SPE 63185. Storkaas, E. and Skogestad, S. (2003). Cascade control of Unstable Systems with Application to Stabilization of Slug Flow. Storkaas, E., Skogestad, S. and Godhavn, J. (2003). A low-dimentional model of severe slugging for controller design and analysis. In Proc. of MultiPhase '03, San Remo, Ita(v, 11-13 June

2003.

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1027

Using CLP and MILP for Scheduling Commodities in a Pipeline Leandro Magatfio*, L.V.R. Arruda, Flfivio Neves-Jr. The Federal Center of Technological Education of Paranfi (CEFET-PR) Graduate School in Electrical Engineering and Industrial Computer Science (CPGEI) Av. Sete de Setembro, 3165, 80230-901, Curitiba, PR, Brazil Tel: +55 41 310-4707 - Fax: +55 41 310-4683 [email protected] arruda@cpgei, cefetpr.br [email protected]

Abstract This paper addresses the problem of developing an optimization structure to aid the operational decision-making in a real-world pipeline scenario. The pipeline connects an inland refinery to a harbor, conveying different types of commodities (gasoline, diesel, kerosene, alcohol, liquefied petroleum gas, etc). The scheduling of activities has to be specified in advance by a specialist, who must provide low cost operational procedures. The specialist has to take into account issues concerning product availability, tankage constraints, pumping sequencing, flow rate determination, and a series of operational requirements. Thus, the decision-making process is hard and error-prone, and the developed optimization structure can aid the specialist to determine the pipeline scheduling with improved efficiency. Such optimization structure has its core in a novel mathematical approach, which uses Constraint Logic Programming (CLP) and Mixed Integer Linear Programming (MILP) in an integrated CLP-MILP model. Moreover, a set of high-level modeling structures was created to straightforward formulate the CLPMILP model. The scheme used for integrating techniques is double modeling (Hooker, 2000), and the CLP-MILP model is implemented and solved by using a commercial tool. Illustrative instances have demonstrated that the optimization structure is able to define new operational points to the pipeline system, providing significant cost saving.

Keywords: Optimization, Scheduling, Constraint Logic Programming (CLP), Mixed Integer Linear Progralmning (MILP), and Pipeline. 1. Introduction The oil industry has a strong influence upon the economic market. Research in this area may provide profitable solutions and also avoid environmental damages. The oil distribution problem is within this context, and pipelines provide an efficient way to convey products (Kennedy, 1993). However, the operational decision-making in pipeline systems is still based on experience, and no general framework has been established for determining the short-term scheduling of operational activities in pipeline systems. The approach to address (short-term) scheduling problems is manifold, but the struggle to Author to whom correspondence should be addressed: [email protected]

1028 model and solve such problems within a reasonable computational amount has challenged the development of new optimization approaches. In the front line of such approaches, Operational Research (OR) and Constraint Programming (CP) optimization techniques are merging. More specifically, Mixed Integer Linear Programming (MILP) and Constraint Logic Programming (CLP) are at the confluence of OR and CP fields. The integration of CLP/MILP has been recognized as an emerging discipline for achieving the best that both fields can contribute to solve scheduling problems (Hooker, 2000). Following this tendency, this paper develops an optimization structure based on CLP and MILP techniques (with their well-known complementary strengths). This structure is used to aid the scheduling of activities in a real-world pipeline scenario.

2. Problem Description The considered problem involves the short-term scheduling of activities in a specific pipeline, which connects a harbor to an inland refinery. The pipeline is 93.5 km in length, and it connects a refinery tank farm to a harbor tank farm, conveying different types of commodities (gasoline, diesel, kerosene, alcohol, liquefied petroleum gas, etc). Products can be pumped either from refinery to harbor or from harbor to refinery. The pipe operates uninterruptedly, and there is no physical separation between successive products as they are pumped. Consequently, there is a contamination area between miscible products: the interface. Some interfaces are operationally not recommended, and a plug (small volume of product) can be used to avoid specific interfaces, but plug inclusions increase the operational cost. The scheduling process must take into account issues concerning product availability, tankage constraints, pumping sequencing, flow rate determination, usage of plugs, and operational requirements. The task is to specify the pipeline operation during a limited scheduling horizon (H), providing low cost operational procedures, and, at the same time, satisfying a set of operational requirements. An in-depth problem description can be found in Magat~o (2003). 3.

Methodology

An optimization structure to address this pipeline-scheduling problem was proposed by Magat~o et al. (2004). This structure, which is illustrated in Figure 1, is based on an MILP main model (Main Model), one auxiliary MILP model (Tank Bound), a time computation procedure (Auxiliary Routine), and a database (Data Base), which gathers the input data and the information provided by the other optimization blocks. The Tank Bound task involves the appropriate selection of some resources (tanks) for a given activity (the pumping of demanded products). Its main inputs are demand requirements, product availability, and tankage constraints. As an output, it specifies the tanks to be used in operational procedures. The Auxiliary Routine takes into account the available scheduling horizon, the product flow rate, and demand requirements. It specifies temporal constraints, which must be respected by the Main Model. The Main Model, which is based on MILP with uniform time discretization, determines the product pumping sequence and it establishes the initial and the final time of each pumping activity. The final scheduling is attained by first solving the Tank Bound and the Auxiliary Routine, and, at last, the Main Model. The Main Model must respect the

1029 parameters previously determined by the Auxiliary Routine. In this paper, we also use this optimization structure, but with one fundamental difference: the Main Model is b a s e d o n a c o m b i n e d CLP-MILP approach. In the former approach, the Main Model was just based on an MILP formulation, and, depending on the problem instance, it can demand a computational effort from minutes to even hours. The Tank Bound and the Auxiliary Routine, which demand few seconds of running, are essentially the same models of Magatfio et al. (2004). For simplicity, these models are not herein discussed, and they are considered to provide input parameters to the new CLP-MILP Main Model. In order to straightforward formulate the CLP-MILP model, a set of high-level modeling structures was created (details are given in Magatfio, 2003). Thus, the model builder just needs to establish a "high-level" CLP-MILP modeling statement, and, afterwards, CLP and MILP equivalent expressions could be automatically derived. In a modeling standpoint, the MILP vocabulary, which is just based on inequalities, is poorer than the CLP vocabulary (Williams and Wilson, 1998), and the high-level structures provided and insight to overcome the modeling difference between MILP and CLP techniques. Figure 2 illustrates a high-level "if and only if' proposition that is expressed according to CLP and MILP approaches +. In this proposition, a binary variable c~. has to be set to one if and only if E/a~/xy < bk, where J is the set of variables (/E J), K is the set of constraints (kEK), akj's are constraints coefficients on continuous variables Xj'S, b~'s are requirements. Moreover, Lk's and U~'s are, respectively, lower and upper bounds, such that Lk <-Eiak~j- bk < U~., and c is a positive small tolerance value. The CLP-MILP model is composed by both CLP and MILP formulations, which are iteratively invoked. Space restrictions preclude that the detailed mathematical formulation be presented (Magatgo, 2003). Basically, MILP is used to establish a continuous time scheduling model that enhances the traditional CLP search mechanisms (constraint propagation and domain reduction;) by providing (linear programming) relaxations to the CLP model during the search procedure ("upper/lower bounds"). Therefore, the scheme used for integrating CLP and MILP approaches is double modeling: each constraint is formulated as part of a constraint programming model and as part of a mixed integer model. The two models are linked and pass information to each other (Hooker, 2000). The double modeling scheme is implemented in the commercial tool ILOG OPL Studio 3.6.1 (ILOG, 2002). MAIN M O D E L L, i

• ank Bound ~

formulation Data ~ Base

Main Model

Auxiliary ~ / / ' Routine V

Figure 1. Optimization structure

I"

I

~- formulation

:"",a~JExample I "" ~., of high-level proposition:L~,..} k;.................................... Ic'Lpformulation" MIEPformulation:

Figure 2. CLP-MILP framework

+The CLP and MILP formulations are done by, respectively, one equivalence (+-~)and two inequalities. *For a detailed cxp|anation about CLP scarch mechanisms and a comparison bctwccn the main characteristics of CLP and MILP techniques see, for instance, Hooker (2000).

1030

4. Results This section initially considers an example involving the pumping of four products from the harbor to the refinery followed by other four pumped from the refinery to the harbor The illustrative example covers since the minimum scheduling horizon (H mi'= 114 hours), which is determined by the Auxiliary Routine, up to 144 hours. The considered case study represents a typical operational scenario of the real-world pipeline modeled. Table 1 provides information about the optimization structure simulation on a Pentium IV, 2.4 GHz, 1 Gbyte RAM. In Table 1, H is the scheduling horizon, MILP, CLP, and CLP-MILP labels refer to, respectively, a pure MILP, a pure CLP, and a combined CLP-MILP approach. Therefore, a numerical comparison amongst three different Main Model versions is presented. For each scheduling horizon (H), the optimization structure is run, and a specific operational cost is attained (see Table 1, column "Cost"). The Auxiliary Routine and the Tank Bound simulation data are neglected. These structures required a computational time lower than one second, for all illustrative instances (114 _
1031 Table 1. Main Model illustrative instances- MILP, CLP, and CLP-MILPjbrmulations H

Number

of Variables

Number

of Constraints

OptimaliU'

proved

in (s)

Nodes

Exploited

Cost

(h)

MILP

('LP

(q.P-MiI~P

MII~P

CLP

('I.P-MII.P

MILP

(?LP

(/I.P-MILP

MII.P

(/LP

('LP-MILP

114

361

273

417

1132

571

16211

15

0.8

5.0

9451_

57 5

575

174

115 116 117

425 425 425 425 425 425

305 305 3115 3O5 3(15 305

48 48 48

1324 1324 1324

631 631 631

IS60 1860 1,',;60

17 19 22

69 35;I 417

7.3 7.4 16~

11573 13492 15708

15 6 10' 62710 ~ 871) 10 ~

614 714 1655

175 176 177

48 48 48

1324 I ~24 1324

631 631 631

1861~ 1860 1860

23 34 42

629 1075 6312

16 16 _~_~

1502~ 23091 28509

1.25 I 0" 1.911 1()" 13.7 1(/'

1642 1783 3596

174 I 71 168

425 425 425

305 305 3O5

1324 1324 1324

631 631 031

1860

1860 1860

41 46 75

37 36 44

32258 491) 79

4073 3976 51146

164 160 156

425 425 425

3O5 115 3O5

1324 1324

631 631

1324

631

! N60 186(I 1860

85 61 64

39 ~8 49

56613 37645 44967

4509 448t)

126

48! 481 481 481 481 4Sl

5911

153 150 147

127 12,~

425 425

3O5 3O5

481

631 63

1860

1860

91 78

46 40

612t)2 48898

5419 4685

144 141

425 425 425

31t5 305 ]()'~

481 48! 481 481

1324 1324

129

!324 I ~24 1324

63 63 63

1860

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25

! 860

411

25

25499 50686

2749 2879

138 139

1860

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26

22185

2988

140

425 425 425

~t15

481

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1324 1324 1324

63 63 63

186() i 860 I S60

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25 26 25

31741) 1651 27005

2888 2900 2783

139 140 141

425 425 425

305 305 3~15

481 481 481

1324 1324 1324

63 63 63

1860 I S60 I N60

41 84 64

26 26 26

47142 48055 348611

2878 2883 2844

142

136 137 138 139 141t

425 489 489

3115 ~7 ~3 V

1724 1516 t5t6

63 69 69

22 25

8N

26

489 489 489 489

33 337 337

1516

69

I5 !6

69

28 28

2547 2835 2873 3067 31)91

144 145 146 147 148

69 64

170 113 73 57

36620 27746 43455 62824 61t221

1516 1516

I N60 1110 !~() 21~10 2 i O0 100 i O0

73 52

141 142 143 144

481 545 545 545 545 545 5-15

29

32219

3116

149

77

29202

8445

150

I I ,~ I 19

1211 121

122 123 124 125

130 131 132

133 134 135

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143

144

The data presented in Table 1 represent a realistic pipeline-scheduling scenario, which demanded running times of seconds to few minutes, at least for MILP and CLP-MILP approaches. In order to further investigate the computational effort trend presented by the Main Model, some hypothetical problem instances were also tested. Such instances do not necessarily represent typical operational scenarios. In fact, the main goal was to test MILP, CLP, and CLP-MILP approaches in theoretically more time-consuming problem instances. In such instances, basically, a fixed volume of each product is demanded; the number of demanded products is progressively increased from 8 to 12; and, the scheduling horizon varied from the minimum scheduling horizon (H '''j'') up to Ig"*"+ 6 hours (see details in Magatfio, 2003). Figure 4 summarizes the results of such experiment: it presents the average computational time of MILP, CLP and CLP-MILP models as a function of the total number of demanded products ("problem instance"). i

r

.

i [

( ' o x / v x . Schedtdin,,,,, H o r i z o n

i

.

.

.

.

.

.

A v e r a g e C o m l m l a l i o n a l Time

4o] 3~)

?'1

211

152 150 ] I~

1(1

144

I

(1 I IJ I It, l IN 1211 1

Figure 3. Cost

I

velwu,s"

4

scheduling horizon

Figure 4. Average computational timejbr MILP, CLP and CLP-MILP models

7

1032 Figure 4 indicates that, in average, the CLP-MILP model tends to solve this specific problem faster than the MILP and the CLP models as the total number of demanded products (instance) was increased. Obviously, one might argue that even the CLP-MILP model has an exponential-time computational behavior, but, for certain, the combined model could "go a step further" than both, the MILP and the CLP models.

5. Conclusions The economically important problem of product distribution through a real-world pipeline is addressed. The task is to predict the pipeline operation during a limited scheduling horizon, providing low cost operational procedures, and attending a series of operational requirements. The scheduling of operational activities has to take into account product availability, tankage constraints, pumping sequencing, flow rate determination, and a variety of operational procedures. The computational expense is concerned and an optimization structure is proposed (Figure 1). The core of such structure (Main Model) is based on a novel mathematical approach that combines Constraint Logic Programming (CLP) and Mixed Integer Linear Programming (MILP) techniques. The scheme used for integrating CLP and MILP is double modeling (Hooker, 2000), and a set of high-level modeling structures is used in order to straightforward formulate the CLP-MILP model. The large-scale model is implemented and solved in a commercial tool. Computational results have indicated that the combined CLP-MILP model performs better than both: the pure MILP model and the pure CLP model (Figure 4). Therefore, the integration of CLP and MILP approaches provided an effective alternative to deal with this pipeline-scheduling problem. Currently pipeline operation is still based on experience, but the developed model can aid the decision-making process. Furthermore, the optimization structure has indicated that economic improvements are feasible (e.g. Figure 3), and it has demonstrated the importance of model formulation to help solve problems with improved efficiency.

References Dantzig, G.B., 1963, Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, USA. Hooker, J.N., 2000, Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction. Wiley-Interscience Series in Discrete Mathematics and Optimization, New York, USA. ILOG, 2002, ILOG OPL Studio 3.6.1 - Language Manual. ILOG Corporation, France. Kennedy, J.L., 1993, Oil and Gas Pipeline Fundamentals. PennWell Publishing Company, Oklahoma, USA. Magat~o, L., 2003, Integrating Mixed Integer Linear Programming and Constraint Logic Programming. Technical Report, CEFET-PR/CPGEI, December 2003, 119 pages. Magat~o, L., Arruda, L.V.R. and F. Neves-Jr., 2004, A mixed integer programming approach for scheduling commodities in a pipeline. Computers & Chemical Engineering, 28 (1-2): 171-185. Williams, H.P. and J.M. Wilson, 1998, Connections between integer linear programming and constraint logic programming. INFORMS Journal on Computing, 10 (3): 261-264.

Acknowledgements The authors acknowledge financial support from ANP and FINEP (PRH-ANP / MCT PRH10 CEFET-PR).

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1033

Scheduling of a pipeless multi-product batch plant using mixed-integer programming combined with heuristics Sebastian Panek ~, Sebastian Engell ~, Cathrin Lessner 2 University of Dortmund Process Control Lab (BCI-AST), University of Dortmund, Dortmund 44221, Germany 2 Axxom Software AG Axxom Software AG, Munich, Germany

Abstract The work presented here deals with short-term scheduling in the chemical industry. It proposes an alternative model to STN and RTN in the form of a MILP formulation which describes the plant at a lower level of detail. The aim is to reduce the complexity of the model and thus to increase the solution efficiency. The main simplification compared to STN/RTN is the that product stocks and mass balance constraints are ignored because discrete fixed-size batches are assumed. The proposed MILP formulation is used for the scheduling of a real-life example provided by a customer of Axxom, a lacquer production in a pipeless plant. Three types of recipes that involve cycles, rigid timing constraints between individual operations, and parallel allocations of stationary and mobile units are considered. Several dozens of production orders of different lacquer types in various colors with hundreds of operations have to be scheduled. A special solution procedure combines the solution of the MILP problem in two separate steps with three different heuristics which further reduce the model complexity. Several problem instances of the lacquer production are solved to demonstrate the successful application.

Keywords: supply chain management, scheduling, planning, multiproduct batch processing, pipeless plant

1. Introduction Research efforts in the past l0 years in the area of batch plant scheduling (batch sizing, resource allocation, sequencing) have led to powerful general modelling frameworks as STN (Kondili et al., 1993; Shah et al., 1993) and RTN (Schilling et al., 1996). They enable the user to express a large variety of constraints that might arise in the processing industry, such as capacity constraints on units and products, timing constraints between operations, sequence-dependent changeover procedures, various storage policies, complex production recipes etc. Within both frameworks, the representation of time turned out to be crucial for the performance of the solvers of the mathematical models. This led to continuous time STN/RTN representations with uniform and non-uniform

1034 grids (e.g. Ierapetritou et. al., 1998). Many recent publications focused on this problem by proposing improved modelling and solution approaches. For solver performance, it is usually beneficial to reduce the complexity of the model in terms of the number of equations and variables. This is of[en done by refining and adapting the constraints to exploit special properties of the plant and the production scheme. A discussion of various representations of time can be found in (Floudas et. al., 2004). We refer to two recent continuous-time modelling approaches here. The first one is slotbased and suitable for network-based production schemes involving mass balances and product flows (Pinto et. al. 1994). The second one is based on order-oriented sequential processes without time slots (Manne, 1960; Cerda et. al. 1997). The work presented here is strongly related to the latter approach. It aims at overcoming the difficulties mentioned above by an order-based modelling scheme. An alternative to STN and RTN in the form of a different MILP formulation which describes the plant at a lower level of detail is proposed. The aim is to simplify the representation of time and thus to increase the solution efficiency. An explicit representation is often avoided by establishing a minimal set of event points without predefined order. Sequencing decisions are encoded using dedicated binary variables which correspond to typical binary disjunctions arising in all sequencing problems. This leads to an efficient model formulation in which the resource assignment and the sequencing are decided in parallel. The main simplification compared to STN/RTN is that no product stocks and mass balance constraints are considered. Discrete fixed-size batches are assumed. This work also suggests a two step solution procedure. It combines the solution of the MILP problem in two separate steps with three different heuristics which further reduce the model complexity. The remainder of this paper is structured as follows: after stating the problem the modelling approach is described in detail. In the following section the solution procedure is discussed and the results of numerical experiments are given.

2. Problem Statement The proposed MILP formulation is used for the scheduling of a real-life example provided by a customer of Axxom, a lacquer production in a pipeless plant. The plant facilities consist of 5 mobile mixing vessels and 9 stationary processing units. The stationary units are: pre-dispersion line, main dispersion line, special pre-dispersion unit, dose distributor, two identical dose spinners, two identical filling stations and a laboratory for quality checks. Two mixing vessels have capacities of 19,000 litres, the other three vessels can hold 20,000 lives. The plant topology with traffic on limited routes, possible collisions and different distances is not considered here. Three basic recipes for lacquers, each with 6-8 operations are given. The recipes involve cycles, rigid timhlg constraints between individual operations, and parallel allocations of stationary and mobile units. Three different types of constraints involve either 1) starting or 2) ending or 3) ending and starting dates of individual operations within the recipes. Each of these constraints establishes a link between two operations and forces them to either start or to end within a time window defined by the constraint. The cycles in the production comprise two steps: dosing and quality checks. The termination of a cycle depends on the result of the last quality check. During the processing steps, no

1035 material flows from and to the vessels are considered such that the amount of product in the batch remains constant. Raw materials and the storage for end products are unlimited and available at any time. The market demand is represented by 29 production orders for different products and with irregular release and due dates spread over several months. The objective is to minimize the overall production cost which consists of penalties for missing the due dates. The recipe for a standard metallic lacquer is depicted in Fig. 1. The main processing steps are: assignment of a mobile mixing vessel, dosing, quality check, correction, second quality check and filling. The other recipes have a similar structure but involve two additional pre-processing steps. The mixing vessel holds the product during all steps and is thus allocated in parallel. Dosing

Quality check

Correction Mixin• v

e

Qualitycheck

Filling

~

Figure 1. The recipe graph of metallic [acqlter

3. Modelling A p p r o a c h 3.1 Simplifications and Assumptions Some simplifications with respect to the original problem are made. As the demanded product amounts and vessel capacities are quite similar and do not vary much, we assume equal mixing vessels with sufficient capacities to hold one batch of each product. Another simplification is related to the cycles. The results of the quality checks in the laboratory are a-priori unknown. Since the following steps depend on them, the overall number of processing steps is also unknown. We avoid stochastic modelling and assume that the first quality check always fails and the second one always succeeds. Thus, the loop in the recipe is always taken twice and we get 29 batches of different lacquer types in various colours with 202 operations in total that have to be scheduled. Since the lab is an unlimited resource quality checks may take place at any time arbitrarily often, but require a fixed amount of time. This allows us to remove all quality checks and the lab from the model. Appropriate timing constraints are established to make sure that the necessary minimal amount of time passes between the dosing, correction and filling operations. This reduces the total number of operations to 144 and the number of stationary units to 8.

3.2 The MILP Formulation The key idea of the formulation discussed here was originally proposed by (Manne, 1960) and developed further in (Cerda et. al. 1997). The main contribution is the consideration of additional constraints, simplifications and more complex recipes. The approach uses continuous event points for the starting and the ending dates of the operations instead of time grids and slots. For each pair of operations o and o' that can be processed on the same unit m, a binary variable is introduced to ensure mutual exclusion in resource utilization. It is set to 1 if o precedes o' and set to 0 otherwise. Since resource assignment is also subject of optimization, we define that this binary

1036 variable is 0 if either o or o' are assigned to an alternative unit (and no collision can occur). The resource assignment is modelled by additional binary variables. Starting and ending dates of operations are expressed by real variables. If an operation can be processed on alternative units, further copies of these variables are introduced for each possible unit. 3.2.1 Sets, P a r a m e t e r s a n d C o n s t a n t s

The following sets are used: jobs J , operations O, operations of job j : Oj c_ O, j E J , units (machines) M , alternative units for operation o: M o c_ M ,

operations to be

executed on unit m: 0 m c_ O , operations of job j that can be processed on unit m: Ojm c_ O , j ~ J , m c m .

Release and due dates of jobs: r e l j , d u e j , recipes of jobs: r e c j , j ~ J . Minimum and maximum operation durations on machine m " durom,duro+m,m ~ M , o c 0 m . Three types of timing constraints between starting and ending dates of operations are defined: ss (starting-starting constraints), es (ending-starting)and ee (ending-ending). Every constraint defines a time window [too,m,t+o,m] which limits the difference of the corresponding event points (e.g. the end of the dispersion and the beginning of the dosing). The time windows for the three types of constraints are denoted by: SS--

~SS +

.CS--

~CS +

CC--

.CC+

t

R;o,o E 0 m . The order of subsequent operations of a job is established using e s - c o n s t r a i n t s . A safe time horizon for Big-M constraints is HeN. too,m,too,m,too,m,too,m,too,m,too,m,C

3.2.2 Variables

Machine allocation variables: aom ~ {0,1},m ~ M , o E 0 m . Variables representing starting and ending dates of operations: Som,eom precedence relations of operations:

Poo'm E

E N,m E M,o E 0 m .

{0,1},mc M , o , o '

Variables

to encode

c 0m .

3.2.3 Equations

Every operation must be processed on one machine and started after the release date of

the job" Vo c O" Z

a°m = 1, V j C J , V o c O j " E

I

s°m >- r e l j ,

I

meMo

meMo

Starting and ending dates of operation o on machine m are set to 0 if another machine is assigned to o: V m ~ M , Vo ~ 0 m :Som <_H . a o m ,%m <- H ' a o m • Minimum and maximum operation durations: V m ~ M , Vo c 0 m "Sore + durom . aom

<_eom,Som + duro+m . aom >_ eom .

Timing constraints between operations: v j ~ J , V o , o' e Oj :

Z mEMo Z

m~Mo

Som + too'm <--

Z

So'm ~

meMo' "es+ > Corn + Ioo'm - Z

m~Mo

Z

Som + loo'm --

m~Mo s°' m

Z

m~Mo

m ~ meMo'

ee-
Z m~Mo

Z

%m

+es Z loo'm --

meMo Co'm,

Z

tee+ -> Z Corn + -oo'm

m~Mo

So'm

meMo' e° 'm •

m~a4o,

If o and o' are processed on m and o precedes o' then o' must not precede o: V m • M , V o , o ' • 0 m : Poo'm + Po'om <- aom,Poo'm + Po'om < ao'm,Poo'm + Po'om >- aom +ao'm - 1 .

Operations on the same machine must not overlap: V m • M , Vo, o' • 0 m :

1037 %m - So'm < H(I - Poo'm) + H(2 - aom eo, m -Som < H . Poo'm + H(2 - aom

-

- ao,tn).eom

-So,

m >_

a o , m ) . e o , m - S o r e >_

- H "Poo'm

-

H(2 - aom

-H(I - Poo'm) - H(2 - aom

-

ao,m)

- ao, m )

3.2.4 The o b j e c t i v e f i m c t i o n

The objective function penalizes the accumulated tardiness of the final operations of all jobs. These are the mixing vessel operations MV/ which finish later than the filling operations because of the cleaning of the vessels" min ~ - Z max { d u e / - eMv/m, 0}

o

.jcJ

4. S o l u t i o n P r o c e d u r e

The commercial package GAMS/Cplex was used. Parameter studies of various Cplex parameters yielded that dpriind = 1 clearly increased the solution performance. This setting was used for the procedure described below, the other parameters were set to their default values. The heuristics used here are similar to those in (Cerda et. al., 1997). • H1 - Non-overtaking of non-overlapping jobs: if d u e / < relj, then Vm e M, Vo e O/m,O' c 0i'm : eom < So'm H2 - Non-overtaking of jobs with equal recipes: if reci = recj,/~ d u e / < due/, then Vme M, Vo e O/m,O' e O7,m : eom <_So, m

•

•

H3 - Earliest due date: if d u e / < due/, then Vm c M, Vo c Olm,O' c 0i,,7 :eom < So, m .

Note that H1-H3 preserve enough degrees of freedom to keep the problem non-trivial. i-rl and H2 do not exclude possibly optimal schedules. The 2-step solution procedure is: 1. Apply heuristics H3 to the problem by fixing the corresponding p-variables. Solve the problem and save the integer solution which represents a valid schedule. 2. Relax the variables fixed in step 1. Apply H1 and H2 by fixing the corresponding p variables. Solve the problem using the solution from step 1 as initial solution. The solution obtained in step 1 is always a valid solution in step 2 and therefore can be used as an initial solution. This is because p-variables fixed to 1 in HI and H2 are also fixed in H3. Being the most restrictive heuristics H3 fixes more p variables to 1 than H1 and H2 together. Both steps were implemented within the same GAMS model. 5. O p t i m i z a t i o n

Results

The model and the solution procedure were implemented in the GAMS 21.3 language and solved with Cplex 9.0 on a 2.4 GHz Athlon machine with 1 GB of memory. Both steps of the solution procedure were limited to 20 min. computation time and a optimality gap of 5%. In order to investigate the scalability, several problem instances ranging from 10 to 29 jobs were solved. The job table was sorted according to due dates and for each instance, the first jobs from the table were taken. The results are shown in Table 1. The first column gives the problem size and the next 5 columns show the number of variables and equations of the problem as already reduced by Cplex. The final two columns show the solution times of both steps in seconds. All problem instances could be solved to optimality (accumulated tardiness and lower bound equal to 0) with reasonable computational effort (less than 700 seconds). While the number of real variables does not change between steps I and 2, the number of discrete variables increases considerably when the heuristics are switched from H3 to H I+H2. The first step of the solution procedure was always sufficient to compute optimal solutions. No

1038 better solutions could be derived within the second step. The time spent in step 2 was needed to determine that the optimal solution had been found in step 1. Hence, the EDD heuristics (H3) led to optimal solutions in all test cases. Table 1. Results of both stepsl and 2 in the scalability experiments. #Jobs

#gqus.l+2

#Vars. 1

#Vars. 2

#disc. Varsl

#disc. Vars2

Time l

Time 2

10 14 16 18 20 22 29

9807 19187 25005 31553 39007 47273 81903

1070 1901 2406 2942 3559 4234 6971

1376 2585 3320 4016 4886 5800 9194

762 1457 1898 2378 2923 3526 6043

1068 2141 2812 3452 4250 5092 8266

5.33 20.12 37.87 57.07 126.99 243.71 693.78

0.33 0.77 1.21 1.64 2.00 2.61 5.32

6. Summary, Conclusions and Remarks This work demonstrates a successful application of a MILP formulation for short and mid-term scheduling problems to a real-life example from the chemical industry. An example problem with more than 80,000 equations and 9,000 variables could be solved to optimality in less than 700 seconds. Although less powerful (in terms of modelling strength) than the widely used STN/RTN approach, our model is sufficiently expressive to model sequencing constraints, resource assignment, various timing constraints and complex recipes with parallel operations. Sequence-dependant changeover procedures and more complex objective functions, involving storage costs and makespan, can also be accommodated in the proposed formulation. Unlike STN/RTN, the batch sizes must be planned in a separate pre-processing step. The solution efficiency was improved by introducing a two-step solution procedure involving heuristics. The authors gratefully acknowledge financial support from the EU AMETIST project (IST-2001-35304). References

Cerda. J., G. Henning and I. Grossmann, 1997, A Mixed-Integer Programming Model fbr ShortTerm Scheduling of Single-Stage Multiproduct Batch Plants with Parallel Lines, Ind. and Eng. Chem. Res. 36 (1997), 1695-1707. Floudas, C. and X. Lin, 2004, Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review, Comp. and Chem. Eng. 28 (2004), 2109-2129. Ierapetritou, M. and C. Floudas, 1998, Effective continuous-time formulation ~br short-term scheduling. 1. multipurpose batch processes, Ind. Eng. Chem. Res. 37 (1998), 4341-4359. Kondili, E., C. Pantelides and R. Sargent, 1993, A general algorithm for short-term scheduling of batch operations - i. milp formulation, Comp. and Chem. Eng. 17 (1993), 211-227. Manne, A. S., 1960, On the job-shop scheduling problem, Op. Res. 8, Issue 2 (1960), 219-223. Pinto, J. M. and I. E. Grossmann, 1994, Optimal cyclic scheduling of multistage continuous multiproduct plants, Comp. and Chem. Eng. 18 (1994)~ 797-816. Schilling, G. and C. Pantelides, 1996, A simple continuous-time process scheduling formulation and a novel solution algorithm, Comp. and Chem. Eng. 20 (1996), 1221-1226. Shah, N., C. C. Pantelides and R. Sargent, 1993, A general algorithm for short-term scheduling of batch operations- ii. computational issues, Comp. and Chem. Eng. 17 (1993), no. 2, 229-244.

European Symposiumon ComputerAided Process Engineering- 15 L. Pui~janerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1039

On the State-Task Network" Time Representations Christos T. Maravelias* Department of Chemical & Biological Engineering, University of Wisconsin-Madison 1415 Engineering Drive, Madison, WI 53706, USA

Abstract To model and solve complex Supply Chain problems we study the relationship between the discrete- and continuous-time State-Task Network (STN) representations. We show that the first is a special case of the second. We also propose a new mixed-time representation where the time grid is fixed but processing times are allowed to be variable and span an unknown number of time periods. The proposed scheme accounts linearly for holding and backlog costs, can be extended to handle continuous processes, accounts for due dates at no additional computational cost, and handles variable processing times; i.e. it combines the modelling advantages of both discrete- and continuous-time STN models. Finally, we present strong cutting planes that are used to enhance the solution of the proposed MIP model.

Keywords: Scheduling, State Task Network, Time Representations 1. Introduction The purpose of the paper is to present a time representation for STN models that can be readily used for Supply Chain (SC) optimization. Issues usually neglected in standalone scheduling models become important when scheduling is considered within SC: • Smooth demand patters at the customer-facing nodes are transformed into high demand peaks at the production facilities, due to the various inventory policies applied at the intermediate nodes (warehouses, distribution centres) to account for demand uncertainty. • Demand cannot always be satisfied and backlog costs are introduced to account for unmet demand and/or late deliveries. • Shipments are usually made at fixed time intervals which means that scheduling models have to handle multiple intermediate due dates at low computational cost. • Features such as seasonality of demand, low volume products with large minimum batch sizes, scheduled maintenance and shut-downs require long planning horizons. Thus, the lot-sizing problem (holding vs. changeover costs) becomes very important. To optimize the SC of process industries, therefore, current planning and scheduling methods should be amended to simultaneously account for lot-sizing, holding, backlog, changeover and shipment costs and multiple due dates, while solution methods should be enhanced to effectively solve problems over long time-horizons. The State-Task Network (STN) formulation (Kondili et al., 1993) and the equivalent Resource Task [email protected]

1040 Network (RTN) formulation (Pantelides, 1994) are two powerful modelling tools that have been refined by several researchers (Schilling and Pantelides, 1996; Ierapetritou and Floudas, 1999; Mockus and Reklaitis, 1999; Castro et al., 2001; Maravelias and Grossamnn, 2003; Sundaramoorthy and Karimi, 2005) and extensively used for planning and scheduling problems. Nevertheless, continuous-time STN models do not account linearly for holding and backlog costs and are computationally expensive for the solution of problems with due dates, while discrete-time STN models are computationally expensive for operations with variable processing times. In this paper, we rigorously study the relationship between the two representations, and explore whether we can circumvent their limitations and combine their advantages.

2. Discrete-time Models: a Special Case of Continuous-time Models A compact form of the continuous-time model (M1) of Maravelias and Grossmann (2003) in Table 1, and the discrete-time model (M2) of Shah et al. (1993) in Table 2 are used as the basis of our analysis. Indices i, j, s, n and r are used to denote a task, unit, state, time point (or period) and shared resource, respectively. Table 1. C o n t i n u o u s - t i m e S T N m o d e l (M1) o f M a r a v e l i a s a n d G r o s s m a n n (2003).

Time Grid TO=0, Tu = H

T.+~_>T. Vn

(1) (2)

Assignment Constraints Z ( ~ W s ~ . , - Z W f . , ) <_1 Vj, Vn

(3)

icl(j) n'<_n

R,.o : R

Wf,,

Vi, gn

BSin_1 + Bpm_, = Bp,,, + Bf,,

B,

Wf,, < B f .
gi, Vn

S~. = S....., + Z p , s B f . + Zp,sBs,. < C. i~O(s)

Vi, Vn

Tf. >7",, + D i , , - H ( 1 - W s i . ) Vi, Vn Activation of binary variable WJj,, * Tf,,,_,
(5) (6) (7)

Vs.Vn

(9) (10) Vr, Vn (11)

i

Tf. < T,, + D~I, + H(1-Ws,,,)

Batch-size and Mass Balance Constraints BiMIN rr r vvsm < B&,, < B~MAXWsm Vi, Vn MAX

, - ~ R f , , . , +~_Rs,,.,
n

MIN

Vi, Vr, Vn

Calculation of duration Di, and finish time T f , D m =aiW&,, + fl~Bs,,, Vi, Vn (12)

(4)

Vi

Vi, Vr, Vn

RZ,.,1 = 7",,.WZ, + 6,,.sBf, ,

n'
ZWsi. = ZWf. n

Utility Constraints Rsi,.,, =Z~,.Ws~,,-6ir.Bsi.

Tf,,,_, > T._, - H(1-Wf,,)

(8)

Vi, Vn

(13) (14) (15) (16)

• Different constraints hold for zero-wait storage

i~l(s)

Table 2. D i s c r e t e - t i m e S T N m o d e l (M2) o f S h a h et al. (1993). T,, = n ( % ) =

nAt

(17)

Vn

n'<_n

2

2ve~,,,,<-1 W,v,

(18)

i d ( j ) n'>n-r+l

Bi~tlN Wsi,, <<-Bsi,, <- B i~ 4X~ si,' Ssn = S ..... 1 +

Vi, Vn

(19)

2 P',Bsi .... , - 2 pi,,.Bs~,, < C~ leO(s)

Vs, gn

(20)

id(s)

n'<_n arn = Z

Z(YirWSin,-[-(~iraSin,)~ i n'>_n-r

a f VIAX

VF, Vpl

(21)

In model (M1), binary Wsin (Wfn) is equal to one if task i starts at (finishes at or before) time point n E{O, 1, ..N}. The batch size of task i that starts at, is being processed at, and finishes at or before time point n is denoted by Bsi,, Bpi, and Bf~, respectively. The amount of state s at time point n is denoted by Ss, and the amount of resource r

1041 consumed by various tasks at time point n is denoted by R,.,,. The processing time of task i is denoted by Di,,. The start time of task i is always equal to time point T,, and thus time matching constraints are used only for the finish time, Tf~, of task i. The same variables Wsm, Bs~,,, S,n and R,.,, are used in model (M2) for uniformity. Model (M2) is obtained from model (M1) if A) the time grid is fixed, and B) the processing times of all tasks are constant multiples of the interval At=H/N of the fixed time grid. The implications of restrictions A and B are shown in Table 3.

Table 3. Restrictions applied to (M1). Restriction Implication Fixed time points Constant processing times Binary Wf,, function of Wsi,, Variable B/5,,function of Bsi,,

Constraint

7",, = nat Vn

(17)

Oi, , = riWsi, ,

(22)

Vi, Vn

Wf,, = Wsi...... Vi, Vn > r, (23) B~,, = Bs,..... Vi, Vn > r; (24) ~,'_
Variable B/in function of Bsi,,

Bp,, = ~.Bs,,,. Vi, Vn (25) n'2 tl- r i + 1

An outline of the reductions that can be applied to model (M1) follows: 1. If the time grid is fixed, equations (1)-(2) are replaced by eq. (17). 2. If we replace Wf,, from eq. (23) into eq. (3), we obtain eq. (18) of(M2). If no tasks that finish after H are allowed to start, eq. (4) is trivially satisfied due to eq. (23). 3. Eq. (5) is the same as eq. (19). If we replace Wf,, from eq. (23) into eq. (6), we obtain eq. (5) for n_>r,; i.e. eq. (6) is removed, if we plug eq. (24) and (25) into eq. (7) we obtain a constraint that is trivially satisfied, and hence dropped. By replacing Bfn from eq. (24) into eq. (8) we obtain eq. (20) of model (M2). Constraints (5)-(8) of (M1), therefore, are equivalent to constraints (19)-(20) of (M2). 4. If we replace Rsi,.,, from eq. (9) and Rf,.n from eq. (10) (which is a function of Wsin and Bsi,, due to equations (23) and (24)) into eq. (11) we obtain eq. (21) of (M2). 5. Constant processing times imply that eq. (12) is replaced by eq. (22). Constraints (13) and (14) are used to enforce the condition t h a t / f Wsi,,=l then Tf,,=T&,,+D~n, otherwise unconstrained, and cannot be simplified further. 6. Constraints (15) and (16) are used to enforce the following condition: if a task that started before point n finishes between T,,_l and T~, then Wf~=l. Variable Wf~, however, is uniquely defined by eq. (23), and constraints (15) and (16) are trivially satisfied, and therefore removed. The reduced model (MI*) consists of equations (17)-(21) of model (M2) and equations (13)-(14) and (22)-(25). Note that variables Wf~, D~, Bfn, Bp~ and Tf~ do not appear in equations (17)-(21), and that for any feasible solution of model (M2) (i.e. equations (17)-(21)), we can find values of variables Wf,,, Di,,, Bf~, Bpi,, and Tf,, that satisfy constraints (13)-(14) and (22)-(25). Moreover, a solution of (MI*) corresponds to a unique solution of (M2). In other words, the feasible regions of model (M2) and the reduced model (M1 *) in the space of variables Wsi~, B&,,, &,, and R,.n (i.e. when variables Wf,,, Din, Bf,,, Bp~,, and Tf,, are projected out) are exactly the same. The discrete-time model (M2), therefore, is equivalent to the reduced model (MI*), which means that model (M2) is a special case of the continuous-time model (M1) when restrictions A and B are applied.

1042

3. A New Time Representation In the previous paragraph, we showed that the assumption of the fixed-time grid is not necessarily coupled with the assumption of constant processing times. This allows us to develop a new time representation, where the time grid is fixed but processing times can be variable. Tasks are forced to start exactly at a time point but are allowed to span an unknown number of time intervals and finish anywhere within a time interval. The proposed MIP model (M3) consists of equations (3)-(17) and has a number of modelling advantages: • Compared to (M 1), it accounts linearly for holding and backlog costs. • Compared to (M 1), it accounts for due dates at no additional computational cost. • Compared to discrete-time models, it does not require the introduction of additional binary variables for the modelling of tasks with variable processing times. • It can be readily extended to account for continuous processes, with very good computational results (not presented in this paper due to space limitations). The only modelling drawback of model (M3) is that it cannot handle zero-wait storage policy between two batch processes. Zero-wait policy, however, is usually applied between two continuous processes, and this case is effectively handled.

4. Computational Improvements Model (M3) appears to "carry the computational curses" of both discrete- and continuous-time representations (i.e. large number of time intervals and poor LPrelaxation gaps). Nevertheless, the fact that the time points are fixed allows us to apply several computational improvements that greatly enhance the solution of model (M3). Note that similar improvements cannot always be applied to general continuous-time models. The most important enhancements are: 1. Tightening of big-M parameters: The inequality Tfn>T~ is always valid, which means that eq. (16) can be removed. We can also use H=O in eq. (14). Moreover, we can use H = D ~ X - A t in eq. (13) and in eq. (15), where D f tax (=~i+fliBiMAX) is the maximum processing time of task i. 2. The minimum Ni MIx and maximum N Y x number of time intervals a task i can span is determined by N/~N=/-Di~N/At ]and NyAX=[-D y X / A t ~, where DiMIN (=a4+fl~B~aylN) is the minimum duration of task i. This allows us to generate the valid inequalities of Table 4 that tighten the formulation. Additional valid inequalities can be developed and used in a branch-and-cut algorithm.

Table 4. Valid inequalities added to model (M3). O< N j~t~

O<_Nf f ~v

Wsi,, < ~ Wf,,+o Vi, Vn

(26)

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0>_Ni ~°'~

(27)

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n '<_n

~-'Ws,,. < 1 Vj, Vn --

(28)

ZWf"' < ZWsi"" Vi, Vn n'<_n

(29)

n"<_n - N ~ ~ *

i e I ( j ) n ' > n - Ni ~aN

Finally, the balance constraints of Sundaramoorthy and Karimi (2005) can be used for the calculation of the remaining processing time on an equipment unit, instead of big-M constraints ( 13)-(16).

1043

5. E x a m p l e and C o m p u t a t i o n a l Results Model (M3) is used for the scheduling of the STN in Figure 1 (modified from Kondili et al., 1993; data given in Table 5). The scheduling horizon is 10 hours and there are three orders for 20 kg of P 1 each (with intermediate due dates at t = 4, 6 and 8 hr). The objective is to meet the orders on time and maximize the revenues from additional sales. ) P1 ($10/kg) 40% ,I

-D

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1 B

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'

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Table 5. Processing data (BAn"V/B~4vin kg, a in hr, fl in hr/kg).

Unit HT RI RII DC

Task ~ B 'vnx B~4.v 50 100 25 50 40 80 100 200

H

a 1 .

fi 0 .

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a . .5 .5 .

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.

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a . .25 .25 .

fl .02 .0125 .5

.01

To model intermediate due dates using a continuous-time model we have to introduce additional binary variables. In model (M3), however, we only introduce a (demand) parameter in eq. (8). The example is solved using both the continuous-time model (M1) with N=8, 9 and 10, and model (M3) with At=0.5, 0.33 and 0.25 hr (solution statistics given in Table 6). Model (M1) cannot be solved to optimality within 600 CPU sec, and the best solution has an objective value of $1,797.3 (found with N=8). However, a solution with an objective value of $1,805.4 is obtained using model (M3) with At= 0.25hr (N = 40) in 542.9 CPU sec. Model (M2), in other words, yields a better solution in less time than an "accurate" continuous-time model. Moreover, good solutions are also obtained with At = 0.5 ($1,720) and At = 0.33 ($1,763.3) in less than two minutes. The Gantt chart of the optimal solution of (M3) with At = 0.25 hr is shown in Figure 2. Table 6. Computational results of models (M1) and (M3) (At in hours).

(M1)

(M3)

N=8 N=9 N=IO At=0.5 At=0.33 At=0.25 LP-rel. 2,498.9 2,539.0 2,561.4 2,081.4 2,054.7 2,095.9 Objective 1,797.3 ~ 1,783.61 1,788.4 ~ 1,720.0 1,763.3 1,805.3 CPU-sec 2 600 600 600 43.1 76.3 542.9 Nodes 114,651 71,106 65,620 2,368 1,534 5,106 Optimality gap (%) 2.03 8.71 12.3 0.5 0.5 0.5 1 Best solution found after 600 CPU sec. 2 Using GAMS 21.3/CPLEX 9.0 on a Pentium M at 1.7 GHz; solved to 0.5% optimality gap.

1044 H RI RII

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Figure 2. Gantt chart of optimal solution of (M3) with At=0.25 hr.

The scheduling of batch process remains a very hard problem and better methods are needed, especially for the solution of problems over long scheduling horizons. Nevertheless, model (M3) can be used for the solution of batch scheduling problems with intermediate release and due times, for which continuous-time models cannot be solved to optimality within reasonable time. Furthermore, it can be used for the solution of problems where holding and backlog costs are important. Finally, the proposed representation can be extended to account for continuous processes, with very good computational results. More details can be found in Maravelias (2005).

6. Conclusions In this paper we formally show that discrete-time STN models are a special case of continuous-time models. A new mixed time representation (fixed grid, variable processing times) is proposed. Computational enhancements for the solution of the proposed representation are also presented.

References Castro, P.; Barbosa-Povoa, A. P. F. D.; Matos, H. An Improved RTN Continuous-Time Formulation for the Short-term Scheduling of Multipurpose Batch Plants. Ind. Eng. Chem. Res. 2001, 40, 2059-2068. Ierapetritou, M. G.; Floudas, C. A. Effective Continuous-Time Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes. Ind. Eng. Chem. Res. 1998, 37, 4341-4359. Kondili, E.; Pantelides, C. C.; Sargent, R. A General Algorithm for Short-Term Scheduling of Batch Operations - I. MILP Formulation. Comput. Chem. Eng. 1993, 17, 211-227. Maravelias, C. T.; Grossmann, I. E. A New General Continuous-Time State Task Network Formulation for the Short-Term Scheduling of Multipurpose Batch Plants. Ind. Eng. Chem. Res., 2003, 42(13), 3056-3074. Maravelias, C. T. A Mixed Time Representation for State Task Network Models. Submitted for Publication (2005). Mockus, L.; Reklaitis, G.V. Continuous Time Representation Approach to Batch and Continuous Process Scheduling. 1. MINLP Formulation. Ind. Eng. Chem. Res. 1999, 38, 197-203. Pantelides, C. C. Unified Frameworks for the Optimal Process Planning and Scheduling. Proceedings on the Second Conference on Foundations of Computer Aided Operations. 1994, 253-274. Shah, N.; E.; Pantelides, C. C.; Sargent, R. A General Algorithm for Short-Term Scheduling of Batch Operations- II. Computational Issues. Comput. Chem. Eng. 1993, 17, 229-244. Schilling, G.; Pantelides, C. C. A Simple Continuous-Time Process Scheduling Formulation and a Novel Solution Algorithm. Comput. Chem. Eng. 1996, 20, S1221-1226. Sundaramoorthy, A.; Karimi, I.A. A Simpler Better Slot-based Continuous-time Formulation for Short-term Scheduling in Multipurpose Batch Plants. Chem. Eng. Sci., In Press, 2005.

Acknowledgements The author would like to thank Professor Ignacio Grossmann for stimulating discussions on the time representation of STN models.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1045

Optimization of Biopharmaceutical Manufacturing with Scheduling Tools - Experiences from the Real World Charles A. Siletti a*, Demetri Petrides a and Alexandros Koulourisb aIntelligen, Inc. New Jersey, USA bIntelligen Europe Thermi-Thessaloniki, Greece

Abstract This paper presents industrial experience with a resource-constrained batch process scheduling program. The batch process representation is loosely based on the ISA $88 batch process standard. This representation allows the import of batch process information from other software, e.g. batch process simulators. The scheduling algorithm is a non-optimization approach that proceeds in two steps. First a bottleneck analysis is done to determine a lower bound on the process cycle time, and all the batches are scheduled accordingly. Second, if conflicts remain, they are resolved by applying progressively aggressive modifications to the schedule. This approach to scheduling was tested on several biotech processes. These processes consist of a sequence of batch steps performed with dedicated equipment. The scheduling challenges in biotech processes lie in the ancillary operations: media and buffer preparation, vessel and line cleaning, and chromatography column preparation. Such operations may use shared resources and may serve to couple process suites with otherwise dedicated equipment. These considerations are further complicated by variability in process durations. Three case studies, which are based on a process for the manufacture of monoclonal antibodies (MABs), illustrate the value of a constrained-resource scheduling tool for biotech processes. In the first case study, the scheduling tool shows that auxiliary cleaning equipment can limit batch production. A second case study shows how scheduling tools can calculate the size of a purified water system. A third case study illustrates how to use scheduling tools to mitigate the effects of process variability.

Keywords: scheduling,

process modelling, biotech, pharmaceutical manufacture

1. Introduction Biotechnology manufacturing capacity is currently in very high demand. In recent years the estimated capacity utilization has been 90% for both microbial and mammalian cell culture production (S. Fox et al., 2001). Some biotech firms have estimated potential revenue losses of well over $100 million due to lack of Author to whom correspondence should be addressed: [email protected]

1046 manufacturing capacity (R. Rouhi, 2002). Thus there is substantial motivation to improve process efficiency in biotechnology manufacturing.

1.1 Bioprocessing Overview A typical biopharmaceutical process consists of two parts: an upstream process in which a living organism produces the product in a raw form and a downstream process in which the product is purified. Most biotech upstream processes employ either microbial fermentation or mammalian cell culture. From a scheduling viewpoint, biotechnology processes generally have the following features: • They are batch processes • Primary processing equipment is dedicated to a particular processing step • Wait-time between process steps is either zero or limited • From 20 to 30 buffers may be made for each batch and each has a limited life • There is some variability in processing times especially in the upstream processes • Equipment cleaning is common after most process steps and often requires auxiliary clean-in-place (CIP) skids, which are not dedicated Biopharmaceutical manufacture is regulated, and manufacturers need to prove, through studies or clinical trials, that a process change will not adversely affect the product. Manufacturers therefore tend to avoid any direct changes in the process itself.

1.2 Scheduling Challenges For most bioprocesses, scheduling the main process does not pose a significant challenge. Because the steps usually proceed with no wait, the timing is fixed when the batch start is fixed. Scheduling challenges arise in the support operations such as cleaning and buffer preparation. Such support operations may impose unexpected limits on the process. Common utilities, such as purified water, may impose scheduling limits because they impose limits on both peak and average resource consumption. Finally, planning for process variability and failures presents a significant challenge.

2. A Scheduling Tool for Bioprocessing Most bioprocess manufacturers employ spreadsheets for process scheduling because spreadsheets are inexpensive, readily available, easy to learn and highly flexible. For more complicated situations, however, spreadsheets have very clear drawbacks including poor visualization tools and poor maintainability. Furthermore, spreadsheet solutions are usually "owned" by an individual and may be difficult to transfer to another individual or to another site. The scheduling tool and approach described in this section maintains many of the advantages of the spreadsheet approach while minimizing the disadvantages. Pekny and Reklaitis (1998) describe a generic scheduling tool consisting of graphical user interface, a representation layer, and problem formulation and solution layers.

2.1 The Interface The interface should provide both an easy means of entering and maintaining scheduling information and appropriate displays of the scheduling outputs. The equipment occupancy chart is the most popular way to display scheduling information

1047 for bioprocesses. Equipment occupancy charts, as shown in Figure 5, display Ganttstyle time-bars for equipment.

2.2 The Representation Layer The representation consists of a model for the process and its associated resources and constraints. The instructions for making a single batch of a product constitute a recipe. The recipe structure, which is loosely based on the ISA SP88 standard, consists of unit procedures and operations. A unit procedure is a primary process step and is assigned a single unit of primary equipment. Operations are individual tasks within a unit procedure. All resources other than primary equipment, i.e. auxiliary equipment, labor, materials and utilities, are associated with operations. Operation durations may be fixed or rate and/or equipment dependent. Rate dependent durations are linearly dependent on the batch size. Scheduling precedence relationships exist among operations. Specifically, an operation may have any of the following timing dependencies: (1) the operation starts at the beginning of the batch, (2) the operation starts simultaneously with a reference operation, (3) the operation starts at the end of a reference operation or (4) operation finishes at the start of a reference operation. In addition to the relationships above, an operation may have a fixed or flexible shift time. A fixed shift indicates the time after (or before) which the dependency condition is fulfilled that the operation actually starts. A flexible shift indicates the maximum time that an operation may be delayed.

2.3 The Formulation and Solution Layers There is an abundance of proposed problem formulations and solution algorithms for scheduling problems. The goal of the scheduling methodology described below is to allow a user to generate and evaluate a schedule interactively. The user enters a plan with one or more campaigns each of which consists of a number of batches of a particular recipe and either the due date or start date. The system lays out a preliminary schedule using the cycle-time analysis and conflict resolution methodology. The user may edit the resulting schedule. The system schedules a campaign by scheduling batch starts according to the estimated cycle time. The cycle time for a recipe is the average time between consecutive batch starts. The minimum cycle time, Tcycle, is estimated by the following relation from Biegler et al. (1997). Tcycle = Max(Ti/Ni) j o t i = (1, M)

(1)

77 is the duration of unit procedure i, Ni is the number of alternative primary equipment units, and M is the number of unit procedures. This estimate does not account for shared primary equipment, auxiliary equipment, or down-time, so a conflict resolution scheme is employed to ensure that the resulting schedule is feasible. Conflicts are resolved by (1) selecting other equipment, (2) adding a flexible delay, or (3) delaying the start of a batch.

3. B i o p r o c e s s i n g Case Studies The case studies draw on a process for producing a monoclonal antibody product. The process, shown in Figure 1, consists of multiple upstream suites and a single

1048 downstream suite, which is detailed in Figure 2. The upstream process is limited by the production bioreactor, which has a processing time of 12 days. Multiple upstream suites allow for a batch every 48 hours, while the downstream suite has a minimum cycle time of 33 hours. The limiting equipment in the downstream process is the buffer hold vessel, DCS- 103. Upstream(multiplesuites) Tcycle= 48 h

Downstream(singlesuite) T c y c l e = 33 h

I I..... lum H Bio- ~ Prep. reactor

PrimaryR ...... y H naietPor H I..... hange H Hydrophobic k l Final I Viralinactivation Chromatography Chromatography Chromatography Filtration Figure 1. Monoclonal Antibody Process

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3.1 Case Study 1 CIP Skids The objective is to schedule the downstream process to accommodate upstream improvements that would reduce the upstream cycle time to 36 hours. When the system is given a target cycle time of 36 hours, it reports that the process may not be scheduled. In fact target cycle times of 46, 36 and 35 hours aren't met. Target cycle times of 48, 45, and 34 hours, however, are achieved. The equipment occupancy chart in Figure 3 reveals the problem. CIP-SKID-1 is conflicting from batch to batch. The cleaning skid is used to clean the bioreactor harvest tank, V-101 and is required at the same time to clean the IEX elution buffer tank in the second batch, so the second batch is delayed at the expense of the cycle-time target.

1049 +~

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The key to resolving the problem lies in understanding where to add flexibility. While a delay in a step that affects the product would probably not be allowable in a biopharmaceutical process, a short delay in cleaning a vessel would be acceptable. In this example, a delay of up to 2 hours before cleaning the buffer tanks allows any cycletime target greater 33 hours.

3.2 Case Study 2 Estimating Water for Injection Requirements Purified water known as water for injection (WFI) is used extensively in bioprocesses both for the process and for cleaning vessels. A WFI system consists of a still, surge tank and circulation system. The still capacity surge vessel requirements are dependent on the production schedule. A plot of WFI consumption, shown in Figure 4, gives the basic design parameters. Under peak conditions a four-hour WFI turnover is chosen. The plot shows the instantaneous consumption (light red), the 4-hour average consumption rate (dark blue) and the 4-hour cumulative consumption (brown). The approximate still capacity can be set to peak average rate (9,000 L/h) and the vessel size to the peak 4-hour consumption (35,000 L).

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3.3 Case Study 3, Scheduling for Uncertainty An important source of uncertainty in bioprocesses arises from variability in bioreactor durations combined with the long processing times. In the MAB process above, the completion time of an upstream batch may easily vary by a day.

1050 An analysis of the cycle time shows that a 24-hour delay in the upstream process will cause a conflict in the downstream schedule. The upstream cycle time is 48 hours, and the downstream cycle time is 33 hours. A 24 hour delay in the upstream process reduces the time between consecutive branches as follows: ( 4 8 h - 24h) < 33 h. As noted earlier, the cycle-time limiting procedure is a buffer hold step. Buffers are normally made up about a day in advance and held. See the DCS equipment in the first batch in Figure 5. In an emergency, buffer preparation could reasonably be delayed as long as the buffers are ready in time for the chromatography. The user interactively resets the start times for the buffer preparation steps in batch 3 and shifts the start of batch 2 by 24 hours as shown in Figure 5. "(:i!f::!~:~:£1 : i q "

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4. Conclusion For most bioprocesses, tight constraints dictate much of the scheduling. Under such conditions interactive scheduling tools can deliver a considerable benefit even if they do not generate mathematically optimized schedules. References Biegler, L. T., I. E. Grossmann and A. W. Westerberg, 1997, Systematic Methods of Chemical Process Design, Prentice Hall, Upper Saddle River, New Jersey, 721. Fox, S., L. Sopchak and R. Khoury, 2001, A Time to Build Capacity, Contract Pharma, September. Pekny, J. and G. Reklaitis, 1998, Towards the Convergence of Theory and Practice: A Technology Guide for Scheduling~Planning Methodology, In Proceedings of Foundations of Computer-Aided Process Operations, J. Pekny and G. Blau, Eds., AIChE, 91. Rouhi, R., 2002, No Vacancy, Chemical and Engineering News, 80, 7, 84-85.

European Symposiumon ComputerAided Process Engineering- 15 L. Pui~ianerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1051

Advances in Robust Optimization Approaches for Scheduling under Uncertainty Stacy L Janak a and Christodoulos A. Floudas a* aDepartment of Chemical Engineering Princeton University Princeton, NJ 08544-5263

Abstract The problem of scheduling under uncertainty is addressed. We propose a novel robust optimization methodology, which when applied to Mixed-Integer Linear Programming (MILP) problems produces "robust" solutions that are, in a sense, immune against uncertainty. The robust optimization approach is applied to the scheduling under uncertainty problem. Based on a novel and effective continuous-time short-term scheduling model proposed by Floudas and coworkers (Ierapetritou and Floudas 1998a, 1998b; lerapetritou et al. 1999; Janak et al. 2004; Lin and Floudas 2001; Lin et al. 2002, 2003), three of the most common sources of uncertainty in scheduling problems can be addressed, namely processing times of tasks, market demands for products, and prices of products and raw materials. Computational results on a small example with uncertainty in the processing times of tasks are presented to demonstrate the effectiveness of the proposed approach.

Keywords: Process scheduling, uncertainty, robust optimization, MILP 1. I n t r o d u c t i o n The issue of robustness in scheduling under uncertainty has received relatively little attention, in spite of its importance and the fact that there has been a substantial amount of work to address the problem of design and operation of batch plants under uncertainty. Most of the existing work has followed the scenario-based framework, in which the uncertainty is modeled through the use of a number of scenarios, using either discrete probability distributions or the discretization of continuous probability distribution functions, and the expectation of a certain performance criterion, such as the expected profit, which is optimized with respect to the scheduling decision variables. Scenario-based approaches provide a straightforward way to implicitly incorporate uncertainty. However, they inevitably enlarge the size of the problem significantly as the number of scenarios increases exponentially with the number of uncertain parameters. This main drawback limits the application of these approaches to solve practical problems with a large number of uncertain parameters. A recent review of scheduling approaches, including uncertainty, can be found in Floudas and Lin (2004). Author to whom correspondence should be addressed: [email protected]

1052 In this work, we propose a novel robust optimization approach to address the problem of scheduling under uncertainty. The underlying framework is based on a robust optimization methodology first introduced for Linear Programming (LP) problems by Ben-Tal and Nemirovski (2000) and extended in this work for Mixed-Integer Linear Programming (MILP) problems.

2. Problem Statement The scheduling problem of chemical processes is defined as follows. Given (i) production recipes (i.e., the processing times for each task at the suitable units, and the amount of the materials required for the production of each product), (ii) available equipment and the ranges of their capacities, (iii) material storage policy, (iv) production requirement, and (v) time horizon under consideration, determine (i) the optimal sequence of tasks taking place in each unit, (ii) the amount of material being processed at each time in each unit, (iii) the processing time of each task in each unit, so as to optimize a performance criterion, for example, to minimize the makespan or to maximize the overall profit. The most common sources of uncertainty in the aforementioned scheduling problem are (i) the processing times of tasks, (ii) the market demands for products, and (iii) the prices of products and/or raw materials. An uncertain parameter can be described using discrete or continuous distributions. In some cases, only limited knowledge about the distribution is available, for example, the uncertainty is bounded, or the uncertainty is symmetrically distributed in a certain range. In the best situation, the distribution function for the uncertain parameter is given, for instance, as a normal distribution with known mean and standard deviation. In this paper, we will discuss bounded uncertainty as well as uncertainty with a known distribution.

3. Robust Optimization for MILP Problems Consider the following generic mixed-integer linear programming (MILP) problem:

Min / Max crx + d r y x,y

s.t.

Ex + Fy = e Ax+By<_ p x L <x<x

y =

(1)

U

0,1}

Assume that the uncertainty arises from both the coefficients and the right-hand-side parameters of the inequality constraints, namely, aim, blk and Pl. We are concerned about the feasibility of the following inequality.

Zat~xm +Zbt~yk < p, m

(2)

k

Our objective here is to develop a robust optimization methodology to generate "reliable" solutions to the MILP program, which are immune against uncertainty. Two types of uncertainty are addressed, (i) bounded uncertainty and (ii) uncertainty with a known distribution.

1053 3.1. Bounded Uncertainty Suppose that the uncertain data range in the following intervals:

[a,m-a,,~ I<-Ela,,~ I, Ib,~.-b,~. I<_cIb,~. I, I~,-P, <-cIp, [

(3)

a~,,,, blk and Pl are the "true" values, al,,,, b/a and Pi are the nominal values, and e > 0 is a given (relative) uncertainty level. We call a solution (x,y) robust if: (i) (x,y) is feasible for the nominal problem, and (ii) whatever are the true values of the coefficients and parameters within the corresponding intervals, (x,y) must satisfy the /-th inequality constraint with an error of at most 6 max]l, p~], where 8 is a given infeasibility tolerance. Given an infeasibility tolerance 8, to generate robust solutions, the following so-called (~,8)-interval Robust Counterpart (IRC[~,8]) of the original uncertain MILP problem can be derived.

Min / Max

cTx + dry

X, y , It

s.t.

Ex + Fy - e Ax+By<_ p m

m ~M I

_< p~

x

L

k

kcK t

(4)

- c[p~ [+,5" max]l, ]p~ [], Vl

<x m
Vm

y~ - {0,1}, V k

where Ml and /£1 are the set of indices of the x and y variables, respectively, with uncertain coefficients in the /-th inequality constraint. The derivation of this formulation can be found in the full-length manuscript of Lin et al. (2004). Note the mathematical model given in (4) remains an MILP model and compared to the original deterministic MILP problem, the robust counterpart has a set of auxiliary variables Um and a set of additional constraints relating the variables Xm and u,,,. 3.2. Uncertainty with a Known Distribution Assume that in inequality constraint l, the true values of the uncertain parameters are obtained from their nominal values by random perturbations"

a~m - (1 + g~:l,, )aim,

blk - (1 + g~:,k )b,k,

Pl - (1 + ~ 4 z ) P l

(5)

where ~'/,,, ~'/a and ~:1are independent random variables and e > 0 is a given (relative) uncertainty level. In this situation, we call a solution (x,y) robust if: (i) (x,y) is feasible for the nominal problem, and (ii) for every l, the probability of the event

Z ~ImXm -+-Z b/kYk > Pl -3t-(~max]l,] P t ] m

is at most K, where 8 > 0 is a given

k

feasibility tolerance and K > 0 is a given reliability level. If the distributions of the random variables ~l,,,, ~lk and ~:t in the uncertain parameters are known, it is possible

1054 to obtain a more accurate estimation of the probability measures involved. Denote a new random variable ~ as the following:

-- Z

~'m l alm I Xm + ~ ~Zk I b/k l Y k - ~z I P, I

mcM l

(6)

k~K l

Assume that the distribution function of ~ is"

F;(A) - Pr{~ _ 2} - 1 - P r { ~ > 2} - 1-~c

(7)

where • is a given reliability level and the inverse function (quantile) can be represented as follows:

f~ -1 ( 1 - K:) - f(,Z,I aim

I Xm,I bzk I y~-,I p,

1)

(8)

Then, given an infeasibility tolerance, 6, and a reliability level, K, to generate robust solutions, the following so-called (e,6,~:)-Robust Counterpart (RC[~,8,K]) of the original uncertain MILP problem can be derived. The additional constraints in the RC problem:

~-'~atmXm + ~ btkyk +~f(A,I alm I xm,I btk l Yk,I p, I) ,,

k

(9)

__ p, + 6 max[1,l Pt I], v/ Several different distribution functions can be modeled this way including the uniform distribution, normal distribution, difference of normal distributions, and several discrete distributions such as Poisson or binomial (Janak et al., 2005). This robust optimization methodology can be applied to address the problem of scheduling under uncertainty, including three classes of problems: (i) uncertainty in processing times/rates of tasks, (ii) uncertainty in market demands for products, and (iii) uncertainty in market prices of products and raw materials. In this work, we will only consider uncertainty in the processing times/rates of tasks.

4. E x a m p l e P r o b l e m Consider the following example process that was first presented by Kondili et al. (1993) and has been widely studied in the literature. Two products can be produced from three feeds according to the state-task network as shown in Figure 1. The objective is to maximize the profit from sales of products manufactured in a time horizon of 12 h. The continuous-time formulation proposed by Floudas and coworkers (Ierapetritou and Floudas 1998a, 1998b; Ierapetritou et al. 1999; Janak et al. 2004; Lin and Floudas 2001; Lin et al. 2002, 2003) is used to solve this simple scheduling problem. The example is implemented with GAMS (Brooke et al., 1988) and solved using CPLEX 8.1 on a Linux 3.0 GHz workstation. The "nominal" solution is shown in Figure 2, which features intensive utilization of units U2 and U3 and an objective value (profit) of 3639. However, this solution can become completely infeasible when there is uncertainty in the processing times of the tasks. Consider the case where the uncertainty of the processing times is bounded and the (relative) uncertainty level, ~, is 15% and the infeasibility tolerance level, 8, is 10%. Then, by solving the IRC[~,8] problem, a "robust" schedule is obtained, as shown in Figure 3, which takes into account

1055 .Product 1

Heating ~

l

I

IntAB

4 o.4

( ~

Io.~ r , ,

Reaction 2 [ . . . . ~ ) ~,

Feed A

0.6

re E

I Feed B

0"8lReacti°n31

I

T0.5

0.1

_I

0

0.2

Product 2

Feed C

Figure 1. State-task networkjbr the example problem.

uncertainty in the processing times. Compared to the nominal solution, the robust solution exhibits very different scheduling strategies, such as task-unit assignments and task timings. The robust solution ensures that the robust schedule obtained is feasible with the specified uncertainty level and infeasibility tolerance. However, the resulting profit is reduced, from 3639 to 2887, which reflects the effect of uncertainty on overall production. A comparison of the model and solution statistics for the nominal and robust solutions can be found in Table 1. [30.00

U4 89_00 T2 50_00 T2

It? U2

52_00 T[ I

U1

80_00 T3 50_C~0 W3

I I 20_(210 T[ t

1

52_0 0 T1

."

I

80.00 T4

8C~_00 T2

I 5":u:u') T3

I

[

80_00 T3 50_0C~ T3

50_00 T4

[ I

4

5

6

8

7

T5

I 68.75 I T4 50_00 T4 I [ 6_00 T1 I

I

[

3

[ [8.75

T5

I

9

40:30 T3

10

11

12

Figure 2. Optimal solution with nominal processing times.

97_ 50

L[,4

I 80.0 (-i T2 50.00 T2

U3 U2

l_0 0_0 0

U1

T[

II II 3 6_0 0

II-- T[ t

0

8,0_(J(-i T3 50.130 T3

1

80.00 T3

il I I

50.00 T4

I~-

i 47.5 (-I T4 I I

72_ 1_9

T5

I

I 2219 T4

]

74.00 T2

I

T5

50.00 T4

I

I

80_ 00 T3 50.00 T3

II II

I I

i i

,c. "~

t

i

t

i

L

i

I

3

4

5

6

7

8

•~.

I

10

i

11

Figure 3. Robust solution with uncertainty level (~)of 15%, infeasibilit)' tolerance (0")of 10%.

5. Conclusions In this work, we propose a new approach to address the scheduling under uncertainty problem based on a robust optimization methodology, which when applied to MixedInteger (MILP) problems produces "robust" solutions which are in a sense immune

1056 Table 1. Model and solution statistics for the example problem.

Profit CPU Time (s) Binary Variables Continuous Variables Constraints

Nominal Solution 3638.75 0.40 64 346 489

Robust Solution 2887.19 10.10 64 346 713

against uncertainties in both the coefficients in the objective function, the left-hand-side parameters and the right-hand-side parameters of the inequality constraints. A unique feature of the proposed approach is that it can address many uncertain parameters. The approach can be applied to address the problem of production scheduling with uncertain processing times, market demands, and/or prices of products and raw materials. Our computational results show that this approach provides an effective way to address scheduling problems under uncertainty, producing reliable schedules and generating helpful insights on the tradeoffs between conflicting objectives. Furthermore, due to its efficient transformation, the approach is capable of solving real-world problems with a large number of uncertain parameters (Lin et al., 2004). References Ben-Tel, A. and A. Nemirovski, 2000, Robust solutions of Linear Programming problems contaminated with uncertain data, Math. Program. 88, 411. Brooke A., D. Kendrick and A. Meeraus, 1988, GAMS: A User's Guide, San Francisco, CA. Floudas, C.A. and X. Lin, 2004, Continuous-Time versus Discrete-Time Approaches for Scheduling of Chemical Processes: A Review, Comp. Chem. Engng. 28, 2109. Ierapetritou, M.G. and C.A. Floudas, 1998a, Effective Continuous-Time Formulation for ShortTerm Scheduling: 1. Multipurpose Batch Processes, Ind. Eng. Chem. 37, 4341. Ierapetritou, M.G. and C.A. Floudas, 1998b, Effective Continuous-Time Formulation for ShortTerm Scheduling: 2. Continuous and Semi-continuous Processes, Ind. Eng. Chem. 37, 4360. Ierapetritou, M.G., T.S. Hene and C.A. Floudas, 1999, Effective Continuous-Time Formulation for Short-Term Scheduling: 2. Multiple Intermediate Due Dates, Ind. Eng. Chem. 38, 3446. Janak, S.L., X. Lin and C.A. Floudas, 2004, Enhanced Continuous-Time Unit-Specific EventBased Formulation for Short-Term Scheduling of Multipurpose Batch Processes: Resource Constraints and Mixed Storage Policies, Ind. Eng. Chem. Res. 43, 2516. Janak, S.L., X. Lin and C.A. Floudas, 2005, A New Robust Optimization Approach for Scheduling under Uncertainty: II. Uncertainty with Known Distribution, submitted for publication. Kondili, E., C.C. Pantelides and R.W.H. Sargent, 1993, A General Algorithm for Short-Term Scheduling of Batch Operations - I. MILP Formulation, Comp. Chem. Engng. 17, 211. Lin, X., E.D. Chajakis and C.A. Floudas, 2003, Scheduling of Tanker Lightering via a Novel Continuous-Time Optimization Framework, Ind. Eng. Chem. Res. 28, 2109. Lin, X. and C.A. Floudas, 2001, Design, Synthesis and Scheduling of Multipurpose Batch Plants via an Effective Continuous-Time Formulation, Comp. Chem. Engng. 25,665. Lin, X., C.A. Floudas, S. Modi and N.M. Juhasz, 2002, Continuous-Time Optimization Approach for Medium-Range Production Scheduling of a Multiproduct Batch Plant, Ind. Eng. Chem. Res. 41, 3884. Lin, X, S.L. Janak and C.A. Floudas, 2004, A New Robust Optimization Approach for Scheduling under Uncertainty: I. Bounded Uncertainty, Comp. Chem. Engng. 28, 1069.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1057

Proactive approach to address robust batch process scheduling under short-term uncertainties A. Bonfill, A. Espufia and L. Puigjaner Universitat Polit6cnica de Catalunya, Chemical Engineering Department, ETSEIB, Diagonal 647, E - 08028 Barcelona, Spain e-mails: [anna.bonfill, antonio.espuna, luis.puigjaner]@upc.edu

Abstract A contribution is made in the area of proactive scheduling with the aim to properly define the scheduling problem explicitly incorporating the effects of short-term uncertainties. The idea is to identify a robust initial schedule with the flexibility to react to unexpected events with minimum effects. The problem is modelled using a stochastic optimization approach where not only a set of anticipated scenarios can be considered, but also the capability to react to events once they occur. A stochastic genetic algorithm is developed to efficiently identify robust schedules with minimum expectance for the wait times and idle times that commonly arise in the operation of batch processes with variable operation times and machine breakdowns. The application of the proposed modelling framework to different batch processes shows the flexibility of the identified initial schedule and highlights the importance of exploiting the information of the uncertainty at the decision stage.

Keywords: Proactive schedule, rescheduling, robustness, uncertainty. 1. Introduction Process variations and incomplete information are inherent characteristics of any process system, and flexibility to respond quickly and effectively to the dynamic and uncertain environment has become an essential feature for effective scheduling. Research in scheduling under uncertainty has mostly been focused either on reactive scheduling algorithms, implemented according to the actual situation of the plant once the uncertainty is realized or unexpected events occur, or on proactive scheduling approaches, which tend to generate schedules that are in some sense robust or insensitive to a priori anticipated uncertainties. The execution of optimal schedules based on nominal parameter values and the implementation of rescheduling strategies to face disruptions could result cumbersome and might lead to inefficient or costly reconfigurations as well as to plant nervousness. On the other hand, a robust schedule exhibits an optimum expected performance, but it is not likely to be the optimum one for the actual scenario that will finally occur. Both methodologies have usually been implemented independently, and relatively little attention has been given to the consideration of short-term uncertainties proactively (O'donovan et al., 1999; Kim and Diwekar, 2002; Jensen, 2003).

1058 The incorporation of rescheduling aspects at the time of scheduling is proposed in this work. The identification of a robust initial schedule with the flexibility to react to unexpected events with minimum effects is pursued by explicitly addressing the major effects of variable processing times and equipment breakdowns in short-term scheduling of batch processes. These effects can be characterized by their main consequences in terms of task scheduling. On one hand, if a breakdown occurs and/or the actual processing time of a task is longer than the scheduled one, the time spent by batches waiting for the availability of the next unit increases. This might lead to unexpected delays, and eventually result in quality problems for sensitive or unstable materials that force the rejection of batches with the consequent increase of operational costs. On the other hand, if processing times are shorter than the scheduled ones, idle times appear and subsequent equipment under-utilization occurs (Figure 1). The approaches proposed so far that recognize the importance of considering the uncertainty into the decision level do not explicitly address not even analyze these critical situations that can arise during the execution of the schedule. However, the knowledge of this uncertainty can be usefully incorporated at the time of scheduling to reduce the gap between theory and practice, thus reducing reschedule requirements and improving the overall plant performance avoiding the occurrence of the full force of a perturbation. It is highly desirable to balance the trade offs between robustness, rescheduling and performance, and develop an initial schedule able to absorb anticipated disruptions, thus minimizing their effect on planned activities while maintaining acceptable plant performance. Predicted schedule

°, {ii!iii{i{

o~

jii{gi~iiiig~iigii

u2

~:~ii~ii"ii~i~ii~~

................... ..............the scheduled ones "";...................... WAIT TIME (wt) []

--, wt .................. u l i:~i~ii~i~'~i~ii~{~ iiiii~i~ ...........

I

wt

o'it/ca/for unstab/e materia& ...........Shorter times than ....................... the scheduled ones

U2

~,<~,~D~.--it

......

~::~J~J~i::i<~!~J} ...........

poor p/ant uti/izat/on

Figure 1. Effects of processing times variability.

2. Problem statement The scheduling problem addressed comprises a multistage batch plant with a set of orders to be fulfilled, the set of processing stages required by each order, a set of units where they can be processed, the operations required by each stage, and the processing times of each operation, represented by probability distributions. This information has been modelled using the Process-Stage-Operation hierarchical approach defined by the standard ISA-$88 (ANSI/ISA, 1995), which provides a standard terminology and hierarchical structured models for batch processes.

1059

Due to the uncertainty in the operation times a detailed schedule is not pursued, but only the minimum information to be released to the batch process control is established. This information is related to the production sequence, the assignment of units to stages and the initial (expected) processing time of each process. The effects that may arise due to the uncertainty are explicitly managed by minimizing a weighted combination of the expected makespan and the expected wait times resulting from the execution of the schedule under a set of anticipated scenarios. The following assumptions are made: • From the schedule, the control level (ISA $88) requires only information related to the sequence, the assignment of units to stages and the processes start times. Then production proceeds according to the control recipe. • The Non-Intermediate Storage policy (NIS) between stages is assumed. • Within each stage, all the operations must be executed without interruption. When at the end of a stage (or before a transfer operation) the next unit is not available, a wait time has to be introduced. On the other hand, if a unit is available before the time it is required by the next stage, an idle time appears. Uncertainty associated with operation times can be represented indistinctly by discrete or continuous probability distributions. The scenario-based representation of the uncertainty is then adopted by sampling over all the probability space to approximate the expectation of the objective function. Other sources of short-term uncertainties can be easily incorporated within the proposed framework at the expense of a larger number of scenarios required to represent significantly all the uncertain space. 3. M o d e l l i n g The integrated framework for planning and scheduling of batch chemical plants developed by Cant6n (2003) is used in this work for the modelling of the system. A set of tools, integrating both heuristic rules and optimization algorithms, are available to establish the number of batches to be performed, the sequence, and the assignment of production stages to specific units. Based on the characteristics of the problem and the specified objective function, different strategies combining these tools can be used. I

[ Genetic

Algorithm

OPTIMIZER ~ . ~

MODELER

Makespans

Wait times S

/ /

/

New

L

!

I Generation ["

Individuals OF/Fitness

TOPs

MODEL ~

•

I I

~

Mks/Wts I

"' ~

Y

' evaluation l

................. ~ .................... Uncertain ~ - -

Figure 2. Stochastic optimization framework.

Selection Crossover

Term~nabon

_ ~ e crlterlon r ~ F

~

........C.!~°ve.r....P.r.°!~ a.b.i.!!t~...............................................................................................................

EEMk+ Wt]

:i:~: ,~

S a m p l i n g loop

Mutation probability Crossover method Mutationmethod

1% overlapping

Schedule min

Initial batch start times Production sequence Assignment

E[Makespan + Wait time] \

Populationsize I Numberof generations

~ .

be£

Parameters

~ • ~-Sampling I / I ........ -

~ Schedulewith , I rain E[Mk+Wt] k

Parameters (scenario)

Figure 3. stochGA solution procedure.

1060 A stochastic genetic algorithm (stochGA) has been designed and implemented within this scheduling framework. The GAlib C++ library (Wall, 1996) has been used with customised genome classes. Each individual of the population identifies an initial schedule, and is encoded using a mixed representation involving a real-valued string for the initial batch times, a permutation representation for the sequencing decisions, and a string of integer values for the assignment. For the reproduction process, suitable operators have been implemented in each part of the solution vector. The developed stochGA involves two recursive loops (Figure 2), and the algorithm proceeds as represented in Figure 3. There is an outer optimization loop controlled by the genetic algorithm, which directs the search to the identification of the initial times of each batch, the sequence and the assignment decisions that minimize a weighted combination of expected makespan and wait times, thus introducing robustness features as pointed out before. This outer procedure incorporates an inner sampling loop within which a set of probable scenarios are anticipated by sampling over the probability space to evaluate the probabilistic fitness for each individual. Specifically, the expected performance of each individual (schedule) is evaluated by computing for each scenario the wait time and makespan values that would occur when implementing its sequence, assignment and initial times under the assumed rescheduling policy; that is, the capability to react to events once they occur is considered when evaluating the individuals. The number of scenarios required to obtain a given accuracy for the actual mean and standard deviation of the performance measure is assessed.

4. Results The proposed methodology has been applied to a case study based on a process plant involving 3 production stages and 8 operations. A scheme of the process is shown in Figure 4. Uncertainty in the operations of loading, heating and discharging has been introduced and characterized with a uniform distribution function. Two different products can be produced and five orders have been considered for scheduling.

IPr°~andkUrel

3f-~~ ~

~FprOcedure3~ Reactor k 1// Pr°cedure "l Reactor2/

....

Transfer

k

J

i/ ii iiiiit heating dischargeI clean

Procedure1 load I hold Transfer ) time

Figure 4. Case study.

The scheduling problem was solved using the proposed stochastic modelling and assuming a right-shifting rescheduling strategy. For comparison purposes, the deterministic problem considering only one scenario with nominal operation times was next solved. The production sequence, the assignment and the processes start times thus obtained were fixed, and the makespan and wait time values that would arise after the occurrence of each particular scenario were computed. The results obtained are summarized in Table 1. Figures 5 and 6 depict the schedules that would be executed in the plant for the nominal scenario and for one of the randomly-generated scenarios, respectively.

1061 Table 1. Production sequence, initial batch times, expected makespan and wait time, and makespan and wait times in the nominal scenario (Mk ........ Wt......,), .for the deterministic and stochastic optimized schedules.

Batch

Deterministic Product

Tin

Stochastic Product

Tin

1

A

0.0

A

0.0

2 3 4 5

B B A A

5.6 l l.2 19.4 25.3

B A B A

5.8 13.8 19.8 25.6

Mk .....i~al Wt .....inal

39.0

39.7

0.0

0.0

From these results it can be observed that the deterministic modelling overestimates the system performance. Although the makespan and wait time values of the deterministic schedule are optimal in the nominal scenario, when the schedule is used to face the uncertainty the expected makespan and wait time value raises about 4%. The schedule identified with the stochastic approach shows a better expected performance over the anticipated scenarios of processing times. Despite the simplicity of the analyzed case study, and the relatively small variability associated with the uncertain operations, it is important to notice the consequences of neglecting the known uncertainty and the quick loose of optimality when implementing a deterministic schedule. Concerning the rescheduling features, different policies can be followed when the uncertainty is revealed or unexpected events occur besides avoiding changes once the execution of a schedule has already started: • resolution of the new scheduling problem from scratch, • right-shifting, generating the new schedule from the initial one just delaying the operations affected by the event, more sophisticated rescheduling methods.

Reactor1

'

.

.....

JI'

]

.

.

.

.

i

.

.

'J °

Reactor2 . . . . .

Tankl:]::]tliti

. . . . . . . . . . . .

, !] lt:i

(a) Makespan" 39; wait time: 0

(b) Makespan: 39.7; wait time" 0

Figure 5. Schedules that would be executed ![the nominal scenario.finally occurred according to (a) the deterministic and (b) the stochastic optimization approaches.

Particularly, it can be considered that once a breakdown or an unreasonable wait time is detected, tasks can be just right-shifted or reassigned to alternative units, batches can be

1062 immediately rejected and new ones ordered, thus avoiding unnecessary wait times. In such a case, this knowledge related to the rescheduling policy should be incorporated proactively at the time of scheduling to improve flexibility and plant performance. Reactor1

+ JBmi~ I~1__~+,+++o+,+++ ++°+++++~+,+l~++ .........+++~ t +~ +li

Pu+ ................... _j ...........+ ...............++ ...................... + +..............+ +................................ ~+ .

(a) Makespan: 39.7; wait time: 1

.

.

.

.

.

..

(b) Makespan: 39.7; wait time: 0

Figure 6. Schedules that would be executed in a particular scenario according to (a) the deterministic and (b) the stochastic optimization approaches.

5. C o n c l u s i o n s A stochastic modelling and optimization approach is proposed in this work to address the processing times uncertainty arising in scheduling of batch processes. A robust initial schedule is identified which shows reduced expected wait times and acceptable line occupation, thus reducing eventual quality problems or unexpected delays. The applicability of the proposed framework highlights the importance of exploiting the information of the uncertainty at the decision stage by incorporating not only anticipated scenarios but also suitable reactions to improve the flexibility and the final quality of the schedule's overall performance.

References Cant6n J., 2003, Integrated support system for planning and scheduling of batch chemical plants, PhD Thesis, Universitat Polit6cnica de Catalunya, Espafia. (http://www.tdx.cesca.es/TDX0707103-125200/index_cs.html) International soc. for measurement and control, ANSI/ISA-S88.01-1995, Batch Control, Part I: Models and Terminology. Jensen, M.T., 2003. Generating Robust and Flexible Job Shop Schedules using Genetic Algorithms. IEEE Transactions on Evolutionary Computation, 7, 275 - 288. Kim. K., Diwekar, U.M., 2002 Efficient Combinatorial Optimization under Uncertainty. 1. Algorithmic Development. Ind. Eng. Chem. Res., 41, 1276- 1284. ) O'donovan, R., Uzsoy, R., McKay, K.N., 1999. Predictable scheduling of a single machine with breakdowns and sensitive jobs. Int. J. Prod. Res., 37, 4217 - 4233. Wall, M., 1996. Galib: A C++ library of genetic algorithm components. (http://lancet.mit.edu/ga) Acknowledgements Financial support received from the spanish Ministerio de Educaci6n, Cultura y Deporte (FPU research grant to A. B.) and Ministerio de Ciencia y Tecnologia (project DPI2002-00856); from the Generalitat de Catalunya (project I0353); and from the European Community (contracts GIRD-CT-2000-00318 and MRTN-CT-2004-512233) is fully appreciated.

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) ,9 2005 Elsevier B.V. All rights reserved.

1063

A Rigorous MINLP for the Simultaneous Scheduling and Operation of Multiproduct Pipeline Systems R. Rejowski Jr. a, J. M. Pinto a'b* ~Department of Chemical Engineering, University of Sio Paulo Av. Prof. Luciano Gualberto, t.3,380 - Silo Paulo, SP, Brazil .05508-900 bChemical and Biological Sciences and Engineering, Polytechnic University 6 Metrotech C e n t e r - Brooklyn, NY, USA 11201

Abstract The problem addressed in this work is based on a system that is composed by a refinery that transfers multiple products through a single pipeline connected to several depots. The depots must supply local consumer markets with large amounts of oil derivatives. The objective of this work is to develop a rigorous formulation for pipeline scheduling. This novel formulation for pipeline scheduling uses a continuous time representation and also considers a rigorous hydraulic approach for pipeline operations. The MINLP formulation is compared to a hydraulic linear formulation that parameterizes flow and yield rates. The results show that the MINLP presents better solutions and computational performance.

Keywords: pipeline, scheduling, hydraulic, continuous time representation.

1. Introduction Pipelines transfer large amounts of different petroleum types and their products at a lower cost than any other transportation mode. Pipeline scheduling is a challenging operation due to their multiproduct nature and to the large amounts of energy required. Westerlund et al. (1994) solve the optimal pump configuration that consists of a set of series and parallel pumps. Van den Heever and Grossmann (2003)show a hydrogen supply chain network where optimal flow rates are obtained from a detailed hydraulic representation. Neiro and Pinto (2004) and Rejowski Jr. and Pinto (2004) present mixed-integer models for planning and scheduling of pipeline operations, respectively. The objective of this work is to develop a hydraulic formulation for pipeline scheduling. The formulation is based on a continuous time representation that handles variable flow rates in the pipeline.

2. Problem Description A refinery must transfer P petroleum products to D depots connected to a single pipeline. The depots have to satisfy product demands determined by local consumer

Author to whom correspondence should be addressed: [email protected], [email protected]

1064 markets. Furthermore, several booster station configurations may be utilized for pumping the products along the time horizon (Figure 1).

[--]0=1

~ p=p Him]

1;:;::::;::::::i::: : i: : ::::i :: ::::1

~-~¢~..¢~.

.~/"

.......

-~'kt.. 7"..: k = 1 !::_:.. I k=0 I

..:.

.;.:..............................................,.Q~,. "-.,

'~..,,]c=2

............... 577515 T;77TC777/T7;5TT77;7>>!.CUUT,,,,75;.7/#7..~=,~"

I I

:.-~')--~

....................................................................... ~< .................. i...;...;..,.;..~.,.i..A':R'~'/~--~', .................. ,/ .........i ! ~ , ~ " i ~ A . ; "

/

! 5-/

i

Rermery

I~{"~~ ~L'JF~ '(beginning /~k=0

....................................................................................................................................................................................................... Q# [ m 3 / h ]

of the' operation)

Figure 1 - Distribution pipeline system The refinery stores its products in dedicated tanks and these load their derivatives at predetermined amounts and initial and end time instants along the time horizon. Whenever the pipeline receives any product from the refinery, the same amount leaves it and feeds the depots at the same time in order to satisfy volume and flow rate constraints. The depots have to control their inventory levels and fulfill product demands. Due to demand variations, the pipeline operation is in most cases intermittent. Figure 1 also shows the system and the pump operating curves. The hydraulic behavior depends on the sequencing of products and their allocation inside the pipeline, the flow rate variations, the topographical profile of the pipeline and diameter variations. The pump curves operating depend on the pump types, adjustable speeds, and represent the energy that is provided by the booster stations to transfer the products. Moreover, the pipeline operating point is given by the intersection of these two curves.

3. Optimization Model The MINLP formulation is based on the previously MILP developed by Rejowski Jr. and Pinto (2004), which was however based on a discrete time formulation. The objective function is shown by equation (1).

CERp.VRp,k +

Min C = ~ k=l P

p=l D

C E D p , d . V D p , j , k .A k p=l d=l

K

P

P

D

K

+2 Z Z CP~.OPWd.k.Ak +Z 2 Z Z CONTACTp,p,.TYpa,p,,k p = l d = l k=l

p = l p'= d = l k=l

(1)

1065 The terms in brackets represent the inventory costs at the refinery and at the depots that take into account the variable time interval duration (A~). The next term accounts for the pumping costs, that are composed by the overall power consumption by the booster stations (OPWa.~.) and the time interval that the pipeline remains in operation (&). The last term corresponds to costs associated to product interface formation (Rejowski Jr. and Pinto, 2004).

3.1 Temporal and refinery constraints The refinery sends the products to its tanks in lots (i) with predefined amounts and initial and end instants, as shown in Figure 2. The temporal constraints must satisfy the operational time horizon (/-/), according to equation (2) and their initial (Ti~) and end instants (Tf ) along the transfer operation, as in equations (3) and (4), respectively. The mass balances at the refinery are given by (5) and their volumes are bounded in (6). ~:i T'- 1

R e r m e ~ w P r odu c t i o n L o t s

[

i = 1 R P I , I,~

:

7)

T~/Tf~: slta11.,,'end t h n e foi~ loading operation for product lot i composed by p r o d u c t p at t h n e / e l K ~ : Set of t i m e h l t e r v a l s that receive a product lot f r o m t h e

1

f

2

rermel.w p r o d u c t i o n

.#eL,

/~O: 1 ~ t t i m e h l t e r v a l b~fore production lot )'~ , : 1~1[ t i m e h l t e r v a l olr production lot i

I#1

--

i

I

" Tim e ~

Figure 2 - Production lots and continuous time representation K

~-'A k - H

(2)

k:l

77i

Vi

(3)

/"k - T~

Vi

(4)

Vp, d:l,k

(5)

Vp, k

(6)

~" A k

-

k _
i

VR,~-VRZERO,+~_, ~_, (RP,.:.~,xA~-XR ~,xUj) i I k'~k

VRMIN ~r < VR ~. < VRMAX k

3.2 Pipeline scheduling and depot constraints The idea of this approach is to assign logical variables XVp.l,k ~: to each (product, depot, pack, time). The pipeline operation can be expressed by disjunction (7) (Rejowski Jr. and Pinto, 2004) that is composed by two additional terms that relate the flow rate variations and the time interval durations. This linear disjunction can be transformed into mixed-integer constraints. Boolean variable Yd,k controls the pipeline segment operation and is expressed as logical 0-1 variable XSa.~ in mixed-integer form.

1066 Y

t

,

k

d

,

k

d = XTp,d,k X Vp,l,k

gp,l = 1

XVj,,. k = X V p,l-l,k-1 J

gp, l = 2 ..... L,

XVt;~,,,k = XV~'/,,,k_,

V p , l = 2 ..... L d

XDp,d.k + XTp,,,+,,k= XVj.,~, ,k-1

~7fP

XDv.j. k + XTp.j+,. k = 0

Vp

Vp,~-

A STOP LO < A k < n cp -STOP

A, = U d / ( v k . A ) L O < Vk < _V k -_

xv;',,, = xv;',,,,

UP

_v k = 0

vk

Vd> 1, k=2,...,K

(7)

If YJ,k is true, the first pack of the segment takes the feed variable values (XTp.d,k or d = 1). The products in the pipeline are displaced from pack 1-1 to pack 1. The product stored at pack Ld can be sent to depot d (XDp,d,k) o r to the next segment (XTp.J+l.a). The velocity limits (vk) must be respected when the pipeline operates and its time interval (&) is equal to the ratio between the pack size (Uj) and the flow rate used at time k. If the segment remains idle, Yj,a is false and all packs keep their contents. Interfaces are detected when the first two packs from the segments store different products. Moreover, any pipeline segment can only be stopped if it does not contain any interfaces. The depot constraints are similar to the ones of the refinery and demands must be met at the end of the operation. Finally, Rejowski Jr. and Pinto (2004) propose integer cuts that relate demands and the initial inventory at the depots and in the segments. The temporal variables are disaggregated into two parcels. The first one (Ale) regards

XRp,k for

the pipeline operation, whereas the second ( A ,2) considers the time that the pipeline remains idle. Equations (9) and (10) state that the time that the pipeline operates at interval k must be equal to the ratio between the pipeline volume pack (Ud) and its operational flow rate

(v,.A).

Equation (11) imposes zero values to A~k whenever the

pipeline remains idle. The product velocities must take positive values when the pipeline is operative, according to (12). A~ = A~1 + A~2

vk

(8)

iX'k" (v,.A) = U~.X'S~

Vd, k

(9)

Vd, k

(10)

Vd, k

(11)

Vd, k

(12)

AL°sToP'~I - X S a

uP k] < - A 2h -< A s r o p ' I 1 -

vkL°.XSd, ~ -< vk -< vUe'xsjk

,k

X S a ,k

3.3 Flow rate and hydraulic constraints The hydraulic model is described by disjunction (13). If Yj,~ is true, the friction factor

(fd,/,k) follows equation (13a), where logical 0-1 variable XVpdt,k is multiplied by an exponential that depends on the product physical properties. The friction losses for each pack I take into account the friction factor, the pipeline internal diameter ( D i n ) , the pack extension ( L E X T I ) and the pipeline flow rate, according to (13b). The yield rates (r/k) used by the booster stations are represented by an mt-h order polynomial that depends on

1067

the velocity. The booster stations have several stages (N) that can be activated during the operation from binary variable ( NS,;~k ) and their power consumption ( PW,~/~ ) must satisfy lower and upper bounds, according to (13d). Finally, the energy balance over the pipeline is given by (13e) and the overall power consumption from (1) is given in (13f). If the pipeline remains idle, the friction factor and losses, the power consumed by the booster stations and the yield rates equal to zero, as shown by (13g) to (13k).

J]LZ.k = ,~__,XV:/.Lk.(a,,'vk ' ~' )

VI < Lj

(13a)

_

Y/,k

P

lw/;,.,., = LEX7],.,.f,.z , .,,~ /2.Di,,

,,,--cm.(.,)'"

+c,,,, (.,)

.... '+...+c .... .(,,) ..... +...+co ,,3c)

PW]°.NSj,k <_PWII~, < P L,I

(13b)

V! <_ L,

'"~

VI < L, (13g)

/w/]L,./< = 0

VI_< Lj (13h)

11/` = 0

(13d)

~.,g.p,,.(zj~-zj~ ,)+ ~,h.t'/]L,.~, vkA = l-1

PWJ~,,,

(13e)

Vd, k

(13i)

W,.~ = 0

L,/

[ 0

./],.,.~ = 0

Vn

OP Wj,k = 0

(13j)

( 13k)

_

t~1

OPW~/'k = £PWJ/' ~

(13f)

"'~

4. Examples This section addresses two examples that are composed by a depot. In both examples the proposed MINLP (M1) is compared with an MILP proposed by Rejowski Jr. and Pinto (2003) (M2). In M2, the pipeline operates with fixed flow and yield rates and uses a discrete time representation. Data for this example are given in table 1. GAMS/CPLEX/DICOPT++ (Brooke et al., 2000) was used to implement and solve the models. Examples E1 and E2 consider a 100 and 150 hours time horizon, respectively. Table 1 - Data for Example Folwmlation

Number (?['Time Intervals (K) E1 (H=I00 hours)

MINLP (MI) MILP (Rejowski Jr. and Pinto, 2003) (M2)

Production Profile Product Gasoline (1) Diesel Oil (2) LPG (3) Jet fuel (4)

14 20 (5 hours each) 50 first hours 50 last hours

(p= 1, p=2) (1)=3,p=4) CERp[$/m3.h] CED ¢,.j[$/m'.h] RPp,i,z [xl0-= m3/h] 0.010 0.009 0.005 0.007

0.0240 0.0250 0.0240 0.0250

Product

VRZERO~,[xl0 -2 m 3]

2.5 2.5 1.5 1.5 VDZERO¢,.j[xlO-=m ~]

Gasoline (1) Diesel Oil (2) LPG (3) Jet fuel (4)

1,000 1,050 400 700

150 200 200 200

E2 (H=150 hours) 15 30 (5 hours each) 100 first hours 50 last hours

(p= 1, p=2) (p=3, p=4) CONTACTp4,,[xl0 -2 $]

(1,2)/(1,3)/(1,4) 100/150/120 (2,1)/(2,3)/(2,4) 100/150/120 (3,1)/(3,2)/(3,4) 150/X/X (4,1)/(4,2)/(4,3) 120/X/X XVZEROt,.~u DEMp,d [xl0-= m 3] El/E2 0 /=1,2,3,4,5,6,7,8 0 0

170/150 100/100 10/110 50/50

Table 2 shows the objective function values as well as the computational performance for both examples and models.

1068 Table 2 - Results for the proposed example Example - Model E 1.M 1 E 1M2 Relaxed Solution (C) 26,042.2 8,372.3 Solution Found (C) 26,060.2 38,247.5 Gap (%) 0.000 CPU Time [s] 197.6 3,544.7 Number of Equations 2,286 5,296 Number of Variables 1,537 3,217

E2.M 1 34,927.2 45,865.1 532.9 2,448 1,647

E2.M2 10,326.01 103,756.8 0.8100 54,900.0 7,936 4,827

The MILP presented by Rejowski Jr. and Pinto (2003) (M2) has several limitations. Firstly, it requires a large number of time intervals to synchronise the loading and unloading tasks. Consequently, a much larger model is created that increases CPU times. Furthermore, model M1 demands fewer time intervals for the operation and allows variations in the flow and yield rates within the time horizon. Another important aspect of formulation MDH besides its fixed time interval duration is that it can also provide flow rates that result in low yield rates for the booster stations during the horizon due to the tasks synchronisation at the refinery, as shown in Figure 2. Model E 1.M 1 found a solution that is 46.8% higher than model El.M2, whereas model E2.M1 found a solution with total costs 126% higher than model E2.M2. These factors result in formulations with fewer time intervals and with better objective function values for this challenging problem. Figure 3 shows the yield and flow rates for examples E2.M1 and E2.M1. Note that in E2.M1 the pipeline remains idle in the first 50 hours, whereas in E2.M2 it does not operate at the end of the operation. ~-MI •,I,- y l , l[I ~ l e

E2-M? ~, 11o4o r:.,le ~-6

6.'r

6.T

i66

,.';4.

"r66

,,66 •

6

J66

~';

. . . . . .

-- ,k,~

J66

6

Figure 3 - Yield and flow rates for E2.M 1 and E2.M2

5. Conclusions This work addresses the simultaneous multiproduct pipeline scheduling and hydraulic operation. The resulting MINLP showed better results than a previous MILP.

References Brooke, A., Kendrick, D., Meeraus, A. A., 2000, The Scientific Press. Redwood City, USA. Neiro, S., Pinto, J. M., 2004, Comp. & Chem. Eng., 28, 871. Rejowski Jr.,R., Pinto, J.M., 2003, AIChE Annual National Meeting [446y], San Francisco, USA. Rejowski Jr., R. & Pinto, J.M., 2004, Comp. & Chem. Eng., 28, 1511. Van den Heever, S.A.; Grossmann, I.E., 2003, Comp. & Chem. Eng., 27, 1813. Westerlund, T., Petterson, F., Grossmann, I.E., 1994, Comp. & Chem. Eng., 18, 845.

Acknowledgements The authors would like to thank FAPESP (01-10944/9) and CAPES (BEX1312/03-0).

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) ~i 2005 Elsevier B.V. All rights reserved.

1069

Multicommodity transportation and supply problem with stepwise constant cost function Zoltan Lelkes a*, Endre Rev a, Tivadar Farkas a, Zsolt Fonyo a, Tibor Kovacs b and Ian Jones b aBudapest Univ. of Technology and Economics, Department of Chemical Engineering H- 1521, Budapest, Hungary bSABMiller Europe P.O. Box 53, H-1553, Budapest, Hungary

Abstract A new model has been developed for multicommodity transportation and supply chain problems including stepwise constant costs. The model is expressed as an MILP problem. The modelling equations are presented here. The new model has been tested on multicommodity problem of SABMiller Europe, and compared to other methods from the literature. A feasibility checking method has been developed for large scale MILP problems having binary variables in the objetive function only. This feasibility checking is made by solving a special relaxed LP problem; and the most probable physical reason is pointed out by the feasibility check results in case of infeasibility.

Keywords: supply chain, transportation, multicommodity, MILP 1. Introduction The transportation problem of a commodity deals with a set of source sites, and a set of destinations. The task is to satisfy all the demands of the destinations and utilize all the supply of source sites with minimum transportation cost. This is the basis of much more complicated problem classes, like supply chain allocation and distribution. There is no standardized model for supply chain allocation problems accepted in the literature. According to Vidal and Goetschalckx (1997) the problem involves the determination of the number, location, capacity, and type of manufacturing plants and warehouses to use; the set of suppliers to select; the transportation channels to use; the amount of raw materials and products to produce and ship among suppliers, plants, warehouses, and customers; and the amount of raw materials, intermediate products, and finished goods to hold at various locations in inventory. Here we consider a much simpler problem class where several commodities are produced in several plant sites with capacity constraints, and distributed to several destination sites according to demands and transportation constraints. We deal with the special case where fix cost contribution to the objective can be expressed as a stepwise

*Author to whom correspondence should be addressed: [email protected]

1070 constant function. The stepwise cost function is a consequence of working with shifts. In case of the usual constraints, the task can be expressed as a mixed-integer linear programming (MILP) problem, where integer variables are applied for deciding on opening the plants, and on operating the manufacturing lines inside the plants, and on the number of necessary shifts in each plant. The logic or binary decisions are usually dealt with some special techniques, like Big-M or Convex Hull. The models found in the literature usually do not consider stepwise constant functions, although Ttirkay and Grossmann (1996) deal with stepwise nonlinear (i.e. discontinuous) cost functions. Neither do they utilize the tendency of costs to monotonously increase (more shifts are more expensive). Initialization is also difficult with the literature models. We have developed a new model that utilizes the main characteristics of the presented problem class, but not too specialized that would prevent it from being useful in similar cases.

2. Problem description Given a set of plant sites (simply called plants), customer sites (customers), and products. Customers have specified demand for products, which has to be supplied. Products are produced in plants, and packed in the finite number of packaging lines of the plants. Plants have the capabilities to produce certain types of products only. The processing and packaging capacity of the products in the plants are given. Figure 1 illustrates the problem for three plants, three packaging lines in each plant, and for ten customers. Processing plants

Packaging lines

Customer sites

Figure 1. Problem description The target is to minimize the sum of distribution costs, production costs, and packaging costs. The distribution costs are proportional to the amount of transported products. Production and packaging costs consist of variable cost, which is proportional to the amount of the products, and of fix costs. Fix costs are given by stepwise constant functions, as is shown in Figure 2. Intervals for defining the production fix costs can be given e.g. according to the utilization of the processing plant, and in each interval a constant fix cost can be specified. Similar cost functions can be given for packaging

1071 lines, according e.g. to the working shifts. The steps in the production fix costs are normally monotonously increasing with exception of a single point at zero capacity that may be higher that zero and express the cost of closing a plant.

Q

bc3

bc2

o

bco

x

I

p

I

)

1

o ~

bc~

I I I I I

i I I !

bao

bal

I I I I I I I I

I I I I I I I I I

I ! ! I I I I I ! ! I I

I ! I I I ! I ! ! I ! I

ba2

ba3

Amount of product

Figure 2. Shape of thefix cost.fimction The main difficulty is solving a large scale problem with discontinuous objective function. Discontinuity is handled with logic or binary variables; and the computational labour and time increase exponentially with the number of such variables.

3. Model formulation Our intention was possibly applying the best relaxation to the discontinuous equations and variables. Because the problem is of a large scale one, assignment of good initial values are also important. Since we deal with a large set of constraints, finding feasible initial values is not a trivial task. Finally, we have to assign as tight bounds to the variables as possible. We work as follows. The logical decisions on operating plants and shifts are transformed to algebraic equations, in MILP form. The fix cost (C) of the plant depends on the amount of product (A). The range of variable A is divided into a number of intervals i ( i ~ I ) . The borders of these intervals are given by the upper bound of interval i, bai. The constant fix cost of the plant in interval i is given by parameter bci. Binary variables )'i are assigned to the intervals. If the value of the independent variable is in or above interval i then yi=l, else y~=0. Thus, if the value of the independent variable is in the kth interval ( k ~ I ) then y;~= 1, and yi>z.=0. This can be expressed by Equation 1, where variable Da~ is the length of interval i. Equation 2 expresses monotinicity, i.e. the cost cannot be smaller than the cost of the kth interval. Equation 3 specifies that the intervals have to be considered one after the other.

icI

1072 (2)

C>-Z(yi'Dci) ici

i~{ili~I,i>O} i~{ili~I,i-O}

Yi <- Yiq

Yi --0

(3) (4)

where Dai and Dci are parameters specified by Equations 5-9.

Da i -ba i -bai_ 1

i ~ {i l i ~ I, i > 1}

(5)

D a i - ba i

i ~ {i [ i ~ I , i - 1}

(6)

Oa i -

0

i ~ {i l i ~ I , i -

0}

(7)

DC i -

bc i -bc,_

i ~ {i l i ~ I , i > 0}

(8)

i ~ {i l i ~ I , i - 0}

(9)

Oc i

1

-- b c i

Tight bounds to all the non-decision variables are computed, based on the problem formulation, from bounds given to the decision variables, see Chapter 5. Note also that Equations 1-2 need not be given as equality constraints because of the monotonity of the cost function, and because the cost is minimized during the optimization.

4. Example problems Results of test runs on a middle scale and a large scale problems, given by SABMiller Europe, with charactesistics summarized in Table 1, are presented here.

Table 1. Characteristicsof the exampleproblems Problem Small Large

Processing plants 3 25

Packaging lines Products in a plant 3 13 5 100

Customer sites 67 250

Steps of cost function of plants lines 6 4 5 6

Table 2. Comparison of models Problem

Small Large

Model Multi-M Ttirkay Convex Hull New model New model

Number of equations 4,035 3,927 3,981 3,852 671,626

Number of Number of variables binary v. 5,632 66 5,632 66 5,764 66 5,632 66 1,281,201 875

Number of Solution time iterations (CPU sec) 3,384 1,046 2,350 750 1,121 453 543 312 437,364 19,357

The middle scale problem is used to compare the efficiency of some usual model formulations applied to the given problem type. The problem was solved by GAMS (Brooke et al., 1998) using CPLEX as MILP solver on a PC Pentium 4 CPU 2.4 GHz.

1073 The results are collected in Table 2. The same optimum was found in all the cases. The number of iterations and the solution time in CPU sec are shown in the last two columns. The Ttirkay model is a forward development of the Big-M technique. The Convex Hull technique applies tighter bound / better relaxation than either Big-M or Ttirkay, that is why the solution properties improve according to this sequence. Our new methodology utilizes the monotonicity property; that must be the main reason of the improvement. The lower row in Table 2 demonstrates that large scale problems become solvable with our suggested model formulation. The problem was solved using the same solver on the same machine as above. The solution was found with 1,33% relative gap between the best integer and the best relaxed solution.

5. Feasibility check and solution methodology Checking feasibility may involve examining all the binary combinations in general case. Our special formulation, however, applies binary variables in the terms of the cost function only; and a relaxed LP problem (RLP) can be generated by excluding those terms from the cost function. Any (LP) problem, see below, can be extended (and called LPV) by introducing vn (negative perturbation) and vp (positive perturbation) variable arrays: m

min min

w-

z - cx Ax

- b = 0

x > O,b > O, x e R "

,-:1

(LP)

vp-

m

~-'vp,. + ~ v n , . vn + Ax

,.:1 - b = 0

(LPV)

x > O,b > O, vp > O, v n > _ O xeR",vpeRm,vneR

m

where m is the number of equations. LPV always has a solution; LP has a solution if, and only if the optimum of LPV is w:0; if the optimum of LPV is w=0, vp*=O, vn*=O, and x*, then x* is a feasible solution of LP. If w:/:O, vp*:/:O, and/or vn*:/:O then RPV is infeasible. Which element(s) of the array v=[vn, vp] is(are) nonzero tells us which constraint(s) is(are) voilated. If there were not minimum capacity utilizations specified in the original problem then the solution of RLP would be always a feasible solution of the original problem, as well. But such minimum utilizations are specified, and binary variables related to the existence of plants cannot be excluded, involving a rather difficult problem. Instead, we check the feasibility of the most probable binary combination only; this is the case that all the plants included in the model work with some capacity. The final program is illustarted in Figure 3. The problem data are collected in MS Acces, and transformed into GAMS readable format using mdb2gms.exe (Kalvelagen, 2004). The GAMS model has three main parts. (1) First the feasibility of the problem is checked using LPV. If w:/:0 solution is found then the program stops, and reports the value of the nonzero perturbation variables. (2) RLP is solved in the other case, and provides with proper initial values for the variables. (3) Finally, the original MILP, formulated according to the new modelling equations, is solved. The results of the GAMS run is transformed into MS Access format using GDXViewer (Kalvelagen,

1074 2004). The result data can be read in MS Access, or it is transformed into graphical form by MS MapPoint. This latter form is illustrated in Figure 4. with a theoretical example including 4 processing plants and 24 customers. Circles are assigned to the customers; their size visualise the total demand of the customer, whereas circle sectors represent what parts of the demand are satisfied from different sources.

i• .........

. . . . . . . . .

Data in mdb2gms.I MS Access I ~

-"

I

J'] Solve LPV~

I

es

i •

2[Initialization

I. . . .

___

l[

Solvethe

I

I .

i

i

i

• GDX Viewe~

i

i .

i

,

~

.

i

.

i

.

i

.

i

.

i

=

~

.

i

,

i

w

~

MS Access

+

q

MS MapPoint Figure 3. Algorithm of the final program

.!!!:¸~: :i:i ..e.

::::::::::::::::::::::::::: ::::::::::P:::::::::::[

Figure 3. Graph visualization of the results of a theoretical example

6. Conclusions and recommendations The new model works well for the studied problem with objective function including terms with stepwise constant cost functions. Test on middle case problems resulted in better computation properties than Big-M or Convex Hull, and large scale problems can also be solved with it. The relaxed formulation (RLP) in its transformed form LPV, together with the elaborated GAMS program, can be successfully applied to check the feasibility of the problem prior to trying MILP solution. When RLP is infeasible, the results of LPV provides useful information on the possible reasons of the infeasibility. References

Brook, A., D. D. Kendrick and A. Meeraus, 1992, GAMS. A User's Guide. boyd & fraser, USA Kalvelagen, E., 2004, http://www.gams.com/-erwin/interface/wtools.zip Tt~rkay, M. and I.E. Grossmann, 1996, Ind. Eng. Chem. Res. 35, 2611-2623. Vidal, C.J., and M. Goetschalckx, 1997, Eur. J. Op. Res. 98, 1-18. Acknowledgements

This study was partially supported by OTKA T037191 and OTKA F046282.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1075

Design and Planning of Supply Chains with Reverse Flows Maria Isabel Gomes Salema a, Ana Paula Barbosa Pdvoa bY, Augusto Q. Novais c aCMA, FCT, UNL, Monte de Caparica, 2825-114 Caparica, Portugal bCEG-IST, Av. Rovisco Pais, 1049-101 Lisboa, Portugal CDMS, INETI, Est. do Pago do Lumiar, 1649-038 Lisboa, Portugal

Abstract A multi-product model for the design of global supply chains with reverse flows is proposed. Two levels of decisions are considered, one strategic and one tactical. The first is modelled through a macro perspective of time where the determination of the network structure and flows is accomplished. At tactical level, a micro perspective of time is considered, where production planning and inventory management are addressed in detail. A mixed integer linear programming formulation is developed which is solved with standard Branch and Bound techniques. The model accuracy and suitability are studied using a case study.

Keywords: Supply Chain design, Optimization, Reverse Logistics, Planning.

1. Introduction In modern society, used products constitute a major challenge. Governments are facing overflowed landfills, while creating legislation to shift product management responsibility towards the producers. Used/disposed products are now placed in a different perspective, as company managers perceive new business opportunities whereby these products should be returned to factories for remanufacturing/recycling. Consequently, the supply chain must be extended and no longer terminate at the end customers, but account also for the products return. Only recently the scientific community started looking into this problem. Thus the reverse logistics problem appears as an emerging field where only a limited number of models have been, so far, presented in the literature. These are essentially case study dependent and mostly consider the reverse flow on its own and not as an integral part of the supply chain. As the most generalized published models, one should refer to: Fleischmann et al. (2001), where forward and reverse flows of a given product are integrated, with no limiting capacities in the involved facilities and flows; Jayaraman et al. (2003), who proposed a MILP model for the reverse distribution problem, without taking into account the forward flow; Fandel and Stammen (2004), that proposed a MILP general model for extended strategic supply chain management, based on a twostep time structure, but where no testing of adequacy to any example/case was explored; and finally Salema et al. (2004) who developed a capacitated multi-product design

Author to whom correspondence should be addressed, [email protected]

1076 network model where forward and reverse flows were considered, the flows differ not only in terms of structure but also in the number of products involved. Within these few works, one important area of research not yet explored, is the simultaneous design and planning of such structures (Goetschalckx et al., 2002). In the present paper, we look into this issue and propose an optimal multi-product supply chain design model where both forward and return flows are integrated considering simultaneously the design and planning of such structures. A Mixed Integer Linear Programming formulation is developed where two different perspectives are employed for the treatment of time: a macro perspective (strategic), for the determination of the network structure and flows, and a micro, more detailed perspective (tactical), for the production planning and inventory management. An illustrative case-study is solved showing the model applicability.

2. Problem Definition Figure 1 shows a schematic representation of ~ l~~ a supply chain network with reverse flows. A ~ ~ ~ two echelons forward distribution network is considered where factories are linked to ~l"llili"iiFactory iiliii:;i~i'"i"i"ii;'"i:i~' i"~ customers through warehouses. No direct

connection, factory-costumer, is allowed. The

~

Customer

~ - - ' [ : i ~ DisassemblyCentre

same applies for the reverse flow where a two Figure 1: Distribution network with echelons structure is also present, customers reverse flows. being linked to factories through disassembly centres. Again, customers cannot send their products directly to factories, since products must pass through disassembly centres. Forward and returned products might be treated as independent since we consider that original products may loose their identity after use (e.g. paper recycling paper products after use are simply classified as paper). However, if required, it is also possible to track the same product in both flows. Furthermore, a disposal option is considered within the structure in study. At the disassembly centres if collected products are found to be unsuitable for remanufacturing, a disposal option is made available. Using these structural options the model considers two levels of decisions at different time scales. A "macro time" scale, where the supply network is designed, and a "micro time" scale, where planning activities are set (e.g. macro production and/or storage planning). These time scales can be years/months, years/trimester, month/days or whichever combination suits the problem. The chosen facilities will remain unchanged throughout the time horizon while the throughput will undergo changes. Flows are not necessarily instantaneous (customers will not have their demand satisfied in the same time period when products are manufactured) and thus travelling times might be considered. A travelling time is modelled as the number of micro time periods that a product takes to flow from its origin to its destination. If all travelling times were to be set to zero, a multi-period location/allocation model would be obtained. Finally, a profit function is assumed for the objective function where revenues and transfer plus selling prices are considered. The former are defined whenever there are products flowing between facilities (from factories to warehouses or from disassembly

1077 centres to factories) and the latter whenever products are sent to customers by warehouses or collected by disassembly centres. In terms of costs different terms are identified: investment costs (whenever a facility is chosen), transportation costs, production costs, storage costs and penalty costs (for non-satisfied demand or return). In short, the proposed model can be stated as follows.

Given" • the investment costs • the amount of returned product that will be added to the new products • travelling time between each pair of network agents • the minimum disposal fraction and for each macro period and product: • customers' demand and return values, • the unit penalty costs for non satisfied demand and return, and in addition, for each micro period: • the unit transportation cost between each pair of network agents, • the maximum and minimum flow capacities, • the factory production unit costs, • the facilities unit storage costs, • the maximum and minimum production capacities, • the maximum storage capacities, • the initial stock levels, • the transfer prices between facilities, • customers' purchase and selling prices. Determine, the network structure, the production levels and storage levels, the flow amounts, and the non-satisfied demand and return volumes. So as to, maximize the global supply chain profit. 3. I b e r i a n

Case

3.1 Case description This example was created based on a company that operates in the Iberian Peninsula. This company needs to determine the network design for a supply chain that will involve two forward products (F1 and F2) and one single returned product (R1). At the strategic level customers are grouped into 16 clusters, where each cluster is named after the city it represents. Customers' clusters, from now on designated simply as customers, are respectively located in Barcelona, Bilbao, Braga, Coimbra, la Corufia, Granada, Lisbon, Madrid, Malaga, Oviedo, Porto, Santander, Saragossa, Seville, Valencia and Valladolid. Six of these cities are possible sites to locate warehouses and/or disassembly centres (Barcelona, Bilbao, Lisboa, Madrid, Porto and Sevilla). For the factories there are only two possible locations: Lisbon and Madrid. In terms of time, a macro period is defined over ten years and a micro period over twelve months per year: macro period - "year" and micro period = "month". Since the model considers a horizon of ten years, some data have to be estimated. These include the demand and return volumes as well as variations in costs over the years. These

1078 estimates were based on some assumptions: transportations costs are proportional to the distance between each city and after the first year an inflation rate of 3% (or some other convenient value) is applied to these and all other costs; if flows link cities in different countries, a tax is applied to the corresponding transportation cost namely, 6% from Portugal to Spain and 3% from Spain to Portugal; in the first year, customers' demand is made equal to a fraction of the city inhabitants (a value between 0.8 and 0.9) while in the remaining years a variation factor (ranging from 0.98 to 1.08) is considered, allowing for an increase or decrease in the demand value; in each year, customers' returns is set as a 0.8 fraction of the corresponding demand. The problem also assumes zero initial stock levels; for product recycling F1 incorporates 0.6 of product R1 and product F2 incorporates the remaining 0.4 of product R1; the disposal fraction is set to zero; minimum and maximum capacities are defined for production (0.8"106 and 1.0"106 , respectively); no limit is imposed on flows; travelling time is set to nil, which seems a reasonable assumption given the chosen time scale (years/month) and the particular geographical area under study. 3.2 Results

The resulting MILP model was solved by GMAS/CPLEX (built 21.1), in a Pentium 4, 3,40 GHz. The model is characterised by 46 337 variables (14 binary) and 5 703 constraints and took about 392 CPU seconds to solve (0% optimality gap). The optimal value found for the objective function is 96xl 09 currency units and the optimal network is characterised by a single factory location (Madrid). /

//

.o................

i--

Figure 2a: Forward networks

Figure 2b: Reverse networks

In the forward flow, the Madrid factory serves four warehouses (Bilbao, Lisboa, Madrid and Porto). The associated connections are depicted in Figure 2a: solid lines link the factory to warehouses and dotted lines connect warehouses to customers. One can see that Lisboa and Bilbao have just one customer and that Madrid acts has a geographical centre. Every warehouse supplies the customer located in the same city, while there is one single customer which is served by a warehouse outside the country (Coruna is served by Porto). The number of connections between the two countries is therefore small, which is a result of the taxation imposed for flows between countries. Finally, all customers had their demand fully supplied. In terms of the reverse network (Figure 2b), all six different locations were chosen for the disassembly centres (Barcelona, Bilbao, Lisboa, Madrid, Porto and Seville). As in

1079 the forward network, every disassembly centre serves the customer located in the same city. Concerning the tactical level of decision three different analyses can be made, respectively for production, storage and distribution. As the model produces a large wealth of information, only some examples will be presented.

Figure 3. Facto~ production plan.

In terms of production, Madrid factory operates continually at the minimum level. To meet demand fluctuations, this factory has the products returned by the disassembly centres. To illustrate the optimal production plan, the first, fourth and tenth years are depicted in Figure 3. In terms of storage, the optimal solution leads to a zero stock policy. This is a result of the negative impact that storage has on the objective function (i.e. inventory is costly). Finally in terms of distribution, four examples are given. Each one refers to a different network level. il ir :

• 11 !i!

i:i

i

i:i

.... Iliiill i!l il Figure 4. Distribution.17ows between Madrid and Lisboa.

Figure 5. Demand served to Braga's customer.

Figure 4 shows in detail the flows between the factory and the warehouse located in Lisboa. The relaxation of the capacity constraints resulted in very dissimilar flow patterns. In Figure 5, Braga's customer supplying plan is depicted. The difference between amounts supplied has to do with the simultaneity of supplies received by this customer, as noted in the third and sixth years. On the contrary, in the ninth year there are three separate visits. In the remaining years, every product is supplied in one single separate delivery. With regard to return volumes, Figure 6 shows the total return of product R1 between customers and disassembly centres. The dissimilarity among values is a consequence of

1080 the customers return volumes. Lastly, the return of Lisboa disassembly centre is depicted in figure 7. One can see that each year returns are sent to remanufacture (Madrid factory, labelled Mad) as well as to the disposal option (f0). However, the number of times these activities are performed, varies between once and twice a year. ~:~.~

i

-

.......................

o:o ~ : ~ -i...................................................... I

:~ ° ° ° ' ~

~

::~.~;~E~

.)~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~°~ ~ ' ~

...............................

..................

I

. . . . . . . . . . . . .

......... '........ I I .... . . . . . . . . .

:~

Figure 6." Total return for the first year.

...... II i .?..l...... ...I...!..........

....... i...... iI!

¢~~ , ~

...................................................... m .......................................................

Figure 7." Lisboa disassembly centre return

flOWS.

4. Conclusions In this paper, a multi-period, multi-product design model for a supply chain network with reverse flows is proposed. Two time levels are modelled allowing the establishment of two different levels of decisions: a strategic level defining the network design of the supply chain and a tactical level defining the production, storage, distribution and returning planning. The obtained MILP formulation is fairly flexible since several products can be considered in both networks; different time units can be correlated (years/semesters, years/months, months/days...); limits can be imposed on flows, production and storage capacities; and different travelling times are allowed. The mathematical formulation which supports this model, while it is likely to increase significantly in complexity with the problem dimension, still appears as an important tool to help the decision making process at the strategic and tactical levels of the supply chain management decisions. In order to overcome the computational burden of such a formulation, different solution techniques are now being explored to speed up resolution. Further research is also being undertaken with a view to both strengthen the model formulation and to treat production planning with greater detail, with the introduction of bills of materials.

References Fandel G. and M. Stammen, 2004, Int.J.P.E. 89: 293-308. Fleischmann M., P. Beullens, J.M. Bloemhof-Ruwaard and L.N. Van Wassenhove, 2001. POM 10: 156-173. Goetschalckx M., C.J. Vidal and K. Dogan, 2002. EJOR 143: 1-18. Jayaraman V., R.A. Patterson and E. Rolland, 2003. EJOR 150: 128-149. Salema MI, AP Barb6sa-P6voa and AQ Novais, 2004. POM (submitted).

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1081

Heterogeneous Batch Distillation Processes: Real System Optimisation Pommier S6bastien a, Massebeuf Silvbre a, Gerbaud Vincent a, Baudouin Olivier b , Baudet Philippe b and Joulia Xavier a* aLaboratoire de G6nie Chimique, 118 route de Narbonne, F-31077 Toulouse Cedex 04, France bproSim SA, Stratbge OffShore, Bfitiment A - BP 2738 F-31312 Lab6ge Cedex, France

Abstract in this paper, optimisation of batch distillation processes is considered. It deals with real systems with rigorous simulation of the processes through the resolution full MESH differential algebraic equations. A specific software architecture is developed, lying on the ProSim BatchColumn simulator and on both SQP and GA numerical algorithms. The efficiency of the proposed optimisation tool is illustrated by a case study of heterogeneous batch solvent recovery by distillation. Significant economical gains are optained along with improved process conditions. For such a multiobjective complex problems, GA is preferred to SQP that is able to improve specific GA solutions.

Keywords: Optimisation, Batch Distillation, Heterogeneous Azeotrope

1. Introduction Solvent recovery is a major issue in the pharmaceutical and specialty chemical industries. In that purpose, batch distillation is a separation process of choice. For azeotropic or close-boiling mixtures, the addition of an entrainer, partially or totally miscible with one of the initial binary mixture components, is viable and its choice is the first key issue of azeotropic batch distillation. A whole set of entrainer selection rules has been published for both homogeneous and heterogeneous azeotropic distillation for the separation of azeotropic binary mixtures or close boiling components (Rodriguez Donis, 2001a and 2001b). These rules also hint at a feasible sequence of batch needed to perform the separation together with the initial feed stream location in the ternary diagram. But the optimisation of the batch sequences is a second key issue and this contribution validates a framework for the optimisation of complex distillation.

2. Problem definition The goal of batch sequences optimisation is to minimise an overall economical criterion while respecting constraints such as purity, .... It can be considered as a nonlinear constraint optimisation problem. The classical formulation involves an objective function ~ , equality constraints and inequality constraints (gi and hj respectively):

Author/s to whom correspondence should be addressed : [email protected]

1082 Min

f (x)

gi(x) = 0

i = 1,..., ng

hj(x) < 0

j = 1,...,n h

(1)

2.1. Objective function The objective f u n c t i o n f i s the summation of six cost functions ci: Table 1. Economical cost functions taken into account in the objective function 6

cost f = Z ci object function 1 cl c: c3 c4 c5

expression

immobilisation energy load entrainer column treatment

c~ = c: = c3 = c4 =

used variable

al.t + bl a:. Q a3.L a4.E

c5 = as.R + b5

t = total separation duration Q = total required energy L = global column load E = entrainer amount added initially R = residual column load

lit

C6

tanks treatments c6 = Z a~'Tk + b6k Tk = final load of each of the nrtanks (including still) k=l

2.2. Constraints The constraints of the NLP problem are defined with respect to target purity and/or quantity specifications at the end of the distillation process. Each constraint hj is expressed as follows: (2)

h j : x k - xik obj

where x/k and X~obj are the effective and target fraction of component i in tank k.

2.3. Action variables Action variables are chosen among all the available running specifications of the batch process, that is a collection of successive tasks and the initial load of entrainer (Table 2). Table 2. Available action variables

Available action variable (* for each task i) Entrainer load Boiling duty * Subcooling temperature *

Task duration * Reflux ratio of light phase * Reflux ratio of heavy phase *

3. Problem resolution 3.1. Overall resolution software architecture The proposed optimisation methodology lies on a rigorous simulation of the considered batch processes. Most of the variables values required to evaluate the objective function and the constraints are calculated through this process simulation. From a defined column configuration and defined initial settings, a full MESH (Material balance,

1083 Equilibrium, Summation of molar fraction, Heat Balance) set of differential algebraic equation is solved using the ProSim BatchColumn software (ProSim SA, France). Main results from the batch simulations are mass and composition in each distillate tank and in the boiler, as well as the total heating and cooling duties. The economical optimisation criterion and the constraints values is evaluated from these results. These evaluations stand for the heart of the resolution software architecture, as shown in

Figure 1. Optimisation algorithms offer strategies to change the values of the action variables in order to solve the constraint minimisation problem. Simulation

Batch Column simu1ator ~~,,,,~~.~

Lsettings [

Action

i

Manager ~,q variables J criteria ~ evaluation ~ Action variab1es • Simulation '7 ~ ~ j ~ Objectivefunction value

results

simulation

1 Optimisation pack

Constraints value

objective function and constraints evaluation

optimisation

Figure 1. Optimisationsoftware architecture 3.2. Optimisation methods Two optimisation techniques are used: a SQP-based deterministic method, and a home made Genetic Algorithm as a stochastic one. The SQP algorithm is the donlp2 tool, available at www.netlib.org (Spellucci, 1998). It incorporates the exact ll-merit function and a special BFGS quasi-Newton approximation to the Hessian. The optimisation problem is strictly equation (1). The genetic algorithm is real-coded. In order to use such an unconstrained optimisation technique, the constraints are introduced into the objective function by penalty terms. The optimisation problem aims then at finding the minimum of the following it; function:

{O with

P, (x) -

80

if gi (x) -- O tf g; (x) ~ 0

{O and

Qi(x)-

oo

if hi (x) <-O (fh~(x)>O

and Pi ° and Qi ° are weighting factors proportional the inverse of the squared tolerances on the constraints.

4. Separation of pyridine from water using toluene as entrainer 4.1 Problem settings We study the separation of the minimum temperature homoazeotropic binary mixture w a t e r - pyridine. According the Rodriguez-Donis et al. (2002) and Skouras (2004), the separation is possible using a heterogeneous entrainer. Toluene is added to the mixture, forming a minimum temperature homoazeotrope with pyridine and a minimum

1084 temperature heteroazeotrope with water. Three distillation regions exist with the w a t e r toluene heteroazeotrope being the unstable node in each region and the stable node being the pure vertexes. The distillation boundaries are strongly curved and tangent to the vapour line at the heteroazeotrope, like any residue curve in the VLLE region. During the heterogeneous batch rectification process, removal of the aqueous phase in the decanter is expected and reflux of either the non-aqueous phase or a combination of both decanter phases is possible. In this work, the whole non-aqueous decanter phase is refluxed. This operating mode is called Mode B by Skouras (2004) who described elegantly the heterogeneous batch distillation process issue and feasibility in complement to Rodriguez-Donis et al. (2002). According to Skouras (2004), the initial charge composition must be above the line p y r i d i n e - aqueous phase to make the process feasible. The batch distillation boundary has no impact on mode B process feasibility (but does on mode A, see Skouras (2004)). The residue curve/distillation boundaries have no impact on feasibility despite their curvature. Table 3. VLL and LL Thermodynamic parameters (liquid." NRTL," gas." ideal gas)

Parameter value (cal/mol)

Aijo

Ajio

otijo

Water- Toluene Water- Pyridine Toluene - Pyridine

3809.1 1779.18 264.64

2776.3 416.162 -60.34

Aijv

0.2 0.6932 0.2992

AjiT

21.182 0 0

GtijT

-7.3179 0 0

0 0 0

F o r N R T L : gij-gjj=Aijo+AijT.(T-273.15); gji-gi~=Aj~o+AjiT.(T-273.15); ~ij=Gtij0+GtijT.(T-273.15)

.....

298K LLE enveloppe

toluene [sn] (383.8K)

VLLEResidueenVeloppecurves

/#, ,W~I!,.,, \

.................................. Residue curve boundary . . . . .

......

_ j~, ~ Still path

Batch distillation boundary Vapour line Az tol-pyr [sa] (383.3K)

' / ',

o o o o Distillate path

',

/ \ '\ .~" ....................... 7\............................ ~!~ A

#

'~

/

'~z~/~,:j

/;:\,,

/%

'\\

/",X /\,,

/./,<,,/\/ ',,X/., /',, /',, , / ,, ° ........................... )...,

/ ",, \

... XD,R~

..............-/~

Az tol-wat [un] (357K)

i

pyridine [sn] 1388.3K)

/

Az wat-pyr [sa] (368K)

Figure 2. Water/Pyridine/Toluene ternary diagram

\

water [sn] (373.1K)

1085 The column has 16 plates (incl. decanter), initial charge of 100 moles with molar fractions [water: 0.4; toluene: 0.1; pyridine: 0.5] is placed in the still. Decanter and plate holdup equals 5 and 1 moles respectively. All plate efficiency are set to unity. Decanter is subcooled to 25°C. Column pressure is 1 atm. and pressure drop is 0.05 atm. The process consists of three tasks: filling, infinite reflux and distillation (water phase removal). Thermodynamic model parameters are given in table 3. These parameters are used to compute VLLE in the column and 25°C LLE in the decanter. The optimisation problem aims at minimising overall costs and satisfying two molar composition inequality constraints: • hl(Xwater)> 0.992 in the distillate tank at the process end. • h2(xpyridine)> 0.95 in the still at the process end. Costs c~, c2, c4, and c5 (table 1) are used with arbitrary cost factors not detailed here. Five action variables are defined: entrainer load (FE); heat duty (Qb/ROc) and task duration (t/Roe) for the infinite reflux task; heat duty (Qb/Dist) and task duration (t/Dist) for the distillate removal task. Tolerances in the constraints are set to 0.001. For the GA, initial population equals 100 to ensure efficient sampling of the five dimensional space; stop criteria equals 0.1. For the SQP, centered gradients are used. Influence of costs factors and optimiser parameters are not considered in this presentation. 4.2 Results and discussion Results of the optimisation are given in table 4. The initial point does satisfy the constraints on purpose (with respect to tolerances for hl(Xwater)). If not, results not shown here indicate that the initial criteria is very high because constraint h2(xpyr~d~ne) is not satisfied and its Qi ° factor is proportional to 1/(0.0012). Only the GA finds a solution while the SQP does not. Table 4. Optimisation results

initial

SQP

GA

SQP after GA 0.806

FE (kg)

2

1.954

0.866

Q j R oc (kcal/hr)

3000

2998

1212

1209

t/R oc (hr)

0.2

0.154

0.043

0.026

QJDist (kcal/hr) t/Dist (hr)

3000 0.6

3000 0.533

1437 0.647

1433 0.617

Criteria f

155.468

13 7.182

82.090

77. 882

Criteria ft~

183.453

NA

82.090

NA

-4.24E-04

- 7.10E-05

8.9E-04

1.4E-03

h2(Xpyridine)

5.38E-03

9. 70E-03

9.1E-03

-5. OE-04

Water purity

0.992

0.992

0.993

0.993

Pyridine purity

0.955

0.960

0.959

0.949

Water recovery

100%

100%

95%

93%

Pyridine recovoy

82%

82%

85%

87%

Gain

0%

12%

47%

50%

For results in table 4, the SQP improvement of initial conditions is slight. GA ends after 10 population generations but the after the first generation, the criteria has already

1086 improved to f=fp=90.03 with a mean criteria f=128.3 and fp= 1.0 106 indicating a wide sampling of the solution space. An important reduction of the heat duty is observer along with a reduction of the entrainer load. SQP improvement of the GA solution is acceptable. Of course, results are dependant of the cost factors and problem setting. Indeed, for the separation considered, the entrainer load can be much lower to ensure a feasible separation (see skouras, 2004). When done with a cost of entrainer c4 25 times greater than other costs, the optimiser logically finds a best entrainer load equal to 0.294 kg, but heating required is greater. Besides, for a given purity, Qb/Dist and t/Dist are linked: heating more implies less time to obtain as much water. On this particular problem and on all problems of batch distillation process optimisation we have performed, the SQP does not perform well when the initial point is infeasible, whereas the GA is always able to find a suitable solution to the problem. In fact, SQP should be used on a feasible solution like the final result of a GA run. This indicates that the GA should always be ran first, unless a specific tuning on a feasible solution is sought. Simulation of the optimal solution of the SQP optimisation done after the GA (last column) leads to the composition profiles reported in figure 2 for the still and the distillate composition. As can be seen, the distillate at the end of the infinite reflux period lies on the vapour line and rapidly shifts to the LLE envelope at 298K. The still path moves towards the pyridine vertex. Those paths are in agreement with the path already published (Rodriguez-Donis et al., 2002; Skouras, 2004)

5. Conclusion An optimisation framework coupling stochastic GA and deterministic SQP approaches has been devised and suited for batch distillation processes, homogeneous or heterogeneous, single batch or batch sequence. In the present contribution, validation is done on a double task single rectifier heterogeneous batch process for the separation of water- pyridine with toluene. The five action variable problem is solved. The use of GA followed by an SQP is the recommended choice. As careful weighting of the action variables shows, such a powerful optimisation tool should be used by users well acquainted with the process expected behaviour.

References Rodriguez Donis I., Gerbaud V. and X. Joulia, 2001a, Ind. Eng. Chem. Res., 40, 2729-2741. Rodriguez Donis I., Gerbaud V. and X. Joulia, 2001b, Ind. Eng. Chem. Res., 40, 4935-4950. Rodriguez-Donis I., Gerbaud V. and X. Joulia, 2002, AIChE Journal, 48 (6), 1168-1178. Skouras S., 2004, PhD Thesis available at http://www.nt.ntnu.no/users/skoge/publications/. Spellucci P., 1998, Math. Prog., 82, 413-448.

Acknowledgements This work was performed in collaboration with ProSim SA (Toulouse, France), and supported by the french environment and energy agency (ADEME).

European Symposiumon ComputerAided Process Engineering- 15 L. Pui~ianerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1087

Modelling and Optimisation of Distributed-Parameter Batch and Semi-batch Reactor Systems Xiaoping Zheng, Robin Smith, and Constantinos Theodoropoulos* School of Chemical Engineering and Analytical Science University of Manchester, Manchester, M60 1QD, UK

Abstract Macro-mixing effects in batch and semi-batch reactors are investigated by constructing 3-dimensional models using a network of zones (NoZ) discretisation. System dynamics including volume changes due to continuous feeding are successfully predicted. Detailed flow fields are calculated from phenomenological correlations which include parameters such as reactor size and configuration, impeller type and speed and fluid physical properties. The Proper Orthogonal Decomposition method is subsequently applied to extract reduced models from the large-scale NoZ-based ones that can be used for computationally efficient design, optimisation and optimal control studies.

Keywords: network of zones, non-ideal mixing, proper orthogonal decomposition

1. Introduction Batch and semi-batch reactors are increasingly employed in the industrial production of fine and specialty chemicals, pharmaceuticals, polymers and crystals due to their economic efficiency, including low capital investment and typically high yields, and their versatility to operate with a range of reactants and products. Nevertheless, due to the complex system dynamics involving turbulent flows and mixing phenomena, optimal and safe reactor scale-up and operation are challenging tasks, increasing considerably the uncertainties in reactor design and set-up (Zaldivar et al, 1996, Brucato et al. 2000). Modelling approaches that have been proposed to predict and optimise batch reactor performance range form simple compartment-based models (David et al., 1992, Cui et al., 1996) which use only a few parameters and can yield good agreement with experimental results, but can not give detailed insight for detailed design, to more complex models involving detailed CFD-based flow field simulations (e.g. Brucato et al., 2000, Bakker et al., 2001). Turbulent CFD models can give detailed flow information, but they are computationally intensive, commonly used k-~ models introduce inaccuracies by assuming isotropic turbulence and more advanced models (e.g. LES) require parameter tuning through experimental validation (Vrabel et al., 2000). In this work we have adopted the network-of-zones (NoZ) approach (Nienow et al. 1992, Rahimi and Mann, 2001, Hristov and Mann, 2002), where the reactor is finely discretised in a number of cells. The NoZ model can successfully predict the effects of

Author to whom correspondence should be addressed: [email protected]

1088 macro-mixing, reactor design and operating conditions. It can be integrated with CFDbased flow calculations (Brucato et al 2000) as well as with models describing micromixing and drop or bubble dispersion and movement phenomena. Here, we calculate detailed flow fields in a computationally efficient way by using complex correlations involving a large range of design parameters (Platzer and Noll, 1988) and we have developed a new network structure to deal with reaction volume change effects.

2. N e t w o r k of zones m o d e l Existing NoZ models assume that the reaction volume in every zone does not change during a batch cycle. However, in reality there are changes due to reaction, feeding or mass transport. In this work an improved model is proposed where the network of zones is constructed based on the volume of the reactor. Fig. 1 depicts the structure of this new model, which involves 3 types of zones: a. Empty zones above the fluid surface; b. halfempty zones containing the fluid surface and c. Fluid-occupied zones below the surface level. If the reaction volume changes during the batch process, the surface of the fluid will move up into the empty zones or down towards the fluid-covered zones leaving more empty zones at the top. Accordingly, the mathematical description of this model includes equations describing reaction volume changes. Consider the mass transfer between one zone (i, j, k) and its adjacent zones. Equations (1), (2) and (3) are three ordinary differential equations (ODEs) describing the rate of change of volume VO,j,~) , molar amounts, N~0,j,~),and concentrations C oJ,~) of each component l, in this zone.

~lf-empty zones Fluid-covered zones !ili~

...........

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2- Dimensional View

3- Dimensional View

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C i/.,-1,j,k)

- Vol _ f l o w _ in (. 1 , j , k ) X -

dt

+Vol _flow

_in(i+l,j,k ) x C i l i + l , j , k ) - t -

(1) Vol

Vol

_ o~ow

_ i" ( i , j - l , k )

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1

f l o w _ in(i,j.,,_l)x C(i,j,k_l) + Vol _ f l o w _ in(;,j,,+l)x C ( i _ l , j , k + l ) t~r

Vol _ f l o w _ out ( i , j , k ) X C (i,j,k) l ~- Vol ( i , j , k ) x -p =1

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)

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V o l f l o w _ i n and Vol__/qow_out are the volumetric convective flow rates through the surfaces of the zone, calculated by integrating the flow field across each surface. Rct_rate and F d rate and M o l a r _ v o l : are the reaction rate, feed rate and component l molar volume, respectively. Each zone is assumed to be well-mixed, its volume is determined by the level of discretisation and remains fixed during the simulation. For the fluid-covered zones, reaction volume is the same as the zone volume, so the volume changes from equation (2) are used to compute the new level of the fluid surface. Beyond a volume change threshold the flow field is re-computed. Note that only equations (2) and (3) need to be solved being both expressed in terms of equation (1).

2.1 Flow field computation In several works employing NoZ models, the flow rate through surfaces of zones was calculated only based on impeller overall circulation convective capacity (Nienow et al., 1992; Rahimi and Mann, 2001; Hristov and Mann, 2002). This flow rate was then equally distributed through all the zones. There are several drawbacks in this method. It can not capture velocity variations at different regions inside the reactor vessel and does not fully exploit the benefits of the NoZ model. Also, it uses too few reactor configuration parameters, thus it cannot be used for reactor design and optimisation. Usually other parameters like tank size, impeller type, baffle number and size are of great interest in reactor engineering. Here, a sophisticated correlation system (Desouza and Pike, 1972; Platzer and Noll, 1988) is used which divides the flow field into three characteristic model parts: (1) rotational flow due to impeller rotation; (2) Circulating flow in the "bulk" cells; (3) distinct jet flow (near the impeller). Different correlations have been developed for these 3 parts. The correlations can give detailed 3-D flow field information, i.e. velocity vectors at every cell in the vessel. The parameters involved include reactor configuration (tank size, impeller type, size and position and baffle number and size), operating conditions (impeller speed, fluid depth and feed position) and fluid properties (density and viscosity). This model has been tested against CFDbased calculations giving results of comparable accuracy for a wide range of parameters (Zheng et al 2004). Furthermore it is much more computationally efficient.

3. Case study A system proposed by Nienow et al. (1992) in order to characterise imperfect macromixing and partial segregation in a stirred semi-batch reactor is considered. The predictions of our model were compared with experimental results and simulation results reported in the literature. The chemistry is based on a pair of parallel reactions

A

kl >S

A+B

~~ >R

where A (a diazonium salt) is initially charged in the reactor and B (a pyrazolone) is added continuously at a constant rate. R, a dyestuff is the product and S the unwanted

1090 by-product. The reaction kinetics, operating conditions and kinetic parameters are reported in (Nienow et al., 1992). The height and diameter D of the vessel are both 0.3m. Four 0.1D strip baffles were used with a Rushton turbine with diameter DI=D/3 and clearance C=D/3. A 3-D NoZ model was constructed using 20 zones in each direction (axial, radial and circumferential -8000 zones in total) resulting in a system of 48000 ODEs which were integrated in time using DASPK (Maly and Petzold, 1996). Fig.2 shows a comparison between results from the 3-D network (diamonds) experimental results (squares) and simulation results from the literature (triangles- Nienow et al 1992) for a range of impeller rotation speeds. Simulations assuming ideal mixing (circles) over-predict the yield. Our 3-D simulations agree very well with the experiments and are in better agreement than the literature results, which are, however, close since the volume change effects are small in this case. Further parametric studies have shown that better yield can be achieved by supplying both feeds continuously from the same feed position near the tip of the impeller. These results along with results from a second case study where volume change effects were more pronounced (Paul and Treybal 1972) are presented in a forthcoming publication (Zheng et al, 2004). 0.97

0

0

0

0

0

0.96 0.95 0.94 0.93 0.92

.....~i~.....!i

~

~dtea~Mi~ng

0.91 0

50

1O0

150

200

250

300

350

Rotation Speed(RPM)

Figure 2. Comparison between yield predictionsfrom our 3-D model, and experimental and simulation results from the literature.

i~i~:!~:~~!i:~:i:!i? i~i,i:~,i~:~'~~i~:i

3 seconds

18 seconds

Figure 3. Concentration snapshots o f the product R on a vertical plane in the reactor vessel at t=3 and t = 18 s. The blue (red) colour denotes low (high) concentration.

1091 Fig. 3 shows concentration distribution profiles of species R at a vertical plane inside the reactor at t-3 and 18 s. The right side is the reactor centreline. The impeller rotation speed was 78 RPM. Blue (red) colour denotes low (high) concentration. The concentration at the top empty zones is zero. As it can be seen, areas of lower mixing intensity are the comers of the reactor, the impeller shaft and the circulating zones. As time progresses reactants in these parts eventually participate in the reactions and are converted to products or by-products.

3. Reduced model The NoZ model coupled with flow correlations typically results to systems containing (hundreds of) thousands of ODEs. The simulation of large-scale ODE-based systems is nowadays achievable in realistic CPU times with large yet reasonable memory requirements. Nevertheless, optimisation studies and optimal control design and implementation cannot be based on such large-scale systems since a huge number of function evaluations is required. In this work we have employed the Proper Orthogonal Decomposition method (POD) (Holmes et al., 1996) to extract accurate low-order models from the full-scale ones. In POD a small number of semi-empirical eigenfunctions are computed from a database of detailed full-scale simulations (or even experiments) that can capture the energy of the system i.e. can accurately describe the system in the parametric range of interest. The dynamic low-order model can then be obtained by a Galerkin projection of the governing equations onto these few basis functions. POD has been used successfully in a number of works (e.g. Rowley et al, 2004; Cizmas et al, 2003; Shvartsman et al 2000). Here the s c a l a r - v a l u e d method is employed (Rowley et al. 2004) computing POD modes for each variable (concentrations and reaction volume). We have constructed a simulation database for the case study presented above, by performing simulations using the NoZ model at 3 different rotation speeds: 39 RPM, 197 RPM and 302 RPM recording snapshots every 0.5s. It was found that 20 basis functions for each species (100 in total) and only 1 basis function for the volume were sufficient to capture 99.9 % of the energy of the system. A Galerkin projection of equations (1)-(3) onto these eigenfunctions produced a reduced model of only 101 ODEs that can accurately predict the system behaviour.

~:~:'i!!!ii!i!ii!ili!

i 3 seconds

.........

l

i 18 seconds

Figure 4.Concentration snapshots of the product R at t=3 & 18 s on a vertical plane in the reactor obtained from the reduced model. The blue (red) colour denotes low (high) concentration.

1092 In Fig. 4 concentration profiles obtained from the reduced model at the same conditions as the profiles showed in Fig. 3 are depicted. As it can be seen the agreement between the full-scale and the reduced model results is excellent both for the short term (3s) and for the longer term (18s) dynamics. It is worthwhile to note that the case simulated here (impeller speed 78 RPM) is not included in the simulation database. Results of this reduced model at other conditions also show the same agreement with results from the full model. It can be concluded that the reduced model can predict the system behaviour very well requiring much less computer memory and CPU time.

4. Conclusions We have constructed 3-D models of batch and semi-batch reactors using a network of zones discretisation. The computational domain is discretised in an appropriately large number of cells and local velocity distributions are computed by detailed flow correlations. Mass balances coupled with volumetric changes are then superimposed onto the computed flow resulting in large-scale ODE-based systems. The model can successfully predict the effects of non-ideal macro-mixing and includes a large number of important design and operating parameters than can be used for system scale-up, optimisation and control. The POD method was subsequently used to extract reduced computationally-amenable models from the full-scale ones that can be efficiently employed in parametric studies, model-based optimisation and optimal control.

References Bakker, A., A.H. Haidari and L.M. Oshinowo 2001, Chem. Eng. Prog., 97, 45. Brucato A., M. Ciofalo, F. Grisafi, R. Tocco 2000, Chem. Eng. Sci. 55,291. Cizmas, P.G., A. Palacios, T. O'Brien and M. Syamlal 2003, Chem. Engi. Sci. 58, 4417. Cui, Y.Q., R.G.J.M. van del Lans, H.J. Noorman and K. Luyben 1996, Chem. Eng. Res. Des. 74, 261. David, R., H. Muhr and J. Villermaux 1992, Chem. Eng. Sci. 47,2841. Desouza, A. and R.W. Pike 1972. Can. J. Chem. Eng. 50, 15. Holmes P., J.L. Lumley and G. Berkooz 1996, Turbulence, coherent structures, dynamical systems and symmetry, Cambridge University Press. Hristov, H.V. and R. Mann 2002, IChemE, 80, 872. Maly, T. and L.R. Petzold 1996, Appl. Numer. Math. 20, 57. Nienow, A.W., S.M. Drain, A.P. Boyes, R. Mann, A.M. E1-Hamouz, and K.J. Carpenter 1992. Chem. Eng. Sci. 47, 2825. Paul, E. L. and R.E. Treybal 1971 AIChE J. 17, 718. Platzer, B. and G. Noll 1988. Chem. Eng. Proc. 23, 13. Rahimi, M. and R. Mann 2001 Chem. Eng. Sci. 56, 763. Rowley, C.W., T. Colonius and R.M. Murray 2004 Physica D: Nonlin Phen. 189, 119. Shvartsman, S. Y., C. Theodoropoulos, R. Rico-Martinez, I.G. Kevrekidis, E.S. Titi and T.J. Mountziaris 2000 J. Proc. Control, 10, 177. Vrabel P, R.G.J.M van der Lans, K.Ch.A.M. Luyben, L. Boon and A.W. Nienow 2000, Chem. Eng. Sci. 55, 5881. Zaldivar, J. M., H. Hernfindez and C. Barcons 1996 Thermochimica Acta, 289, 267. Zheng X., R. Smith and C. Theodoropoulos, Manuscript in preparation.

European Symposium on Computer Aided Process Engineering - 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1093

Optimal Start-up of Micro Power Generation Processes Paul I. Barton a*, Alexander Mitsos a, and Benoit Chachuat a a

Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue (room 66-464), Cambridge, MA 02139-4307, USA

Abstract Fuel cell based systems are a promising alternative to batteries in man-portable power generation applications. These micro power generation processes must operate fully autonomously and automatically without the intervention of operators. Operational considerations are indeed so important that they influence the optimal design, following the paradigm of interaction of design and operation. This paper presents a methodology for the simultaneous optimization of design and operation of such systems. We illustrate the methodology with two case studies, focusing on the start-up procedure. A small rechargeable battery is necessary to satisfy the power demand during the start-up while the device temperature is too low for power generation. The optimization problem is formulated as minimization of the mass of fuel and battery required to heat the device up to operating temperature.

Keywords: man-portable power; micro power generation; micro fuel-cell system; optimal start-up operation; dynamic optimization

1. Introduction The widespread use of portable electric and electronic devices increases the need for efficient man-portable power supplies (up to 50 W). Currently, batteries are the predominant technology in most applications, even though they have a large environmental impact, high cost and relatively low gravimetric and volumetric energy densities; furthermore, the upper limit on performance is now being reached. Out of the alternatives that are possible, we are focusing on micro scale power generation devices based on the electrochemical conversion of common fuels and chemicals, such as hydrocarbons or alcohols, in fuel cells. These process-product hybrids have the potential to yield much higher energy densities than state-of-the-art batteries, because the above mentioned fuels have very high energy contents and fuel cells can in principle achieve very high efficiencies. Since most power consuming devices are operated periodically and have rapidly changing power demands, the dynamics and automated operation of portable power production are very important and must be considered thoroughly. In this paper, the focus is on the optimal start-up of micro power generation processes. It is most likely that the devices will be coupled with a relatively small, rechargeable battery; its role is to ensure that the power demand is met when the fuel cell is unavailable or can only Author/s to whom correspondence should be addressed: pib@mi t. edu

1094 satisfy part of the demand, to provide the energy needed to heat the stack up to a temperature at which chemical and electrochemical reactions are fast enough, or to provide an electric spark for the initiation of a combustion reaction.

2. Methodology Our methodology relies on the assumption that intermediate fidelity models can approximate the performance of the devices and can be used for optimization purposes. Our models do not require the specification of a detailed geometry and rely mainly on first-principles, containing only a minimal number of modeling parameters. This is possible because the relative importance of physical phenomena at the micro scale makes one-dimensional spatial discretization sufficient. We assume that the molar flux in the gas channels of the fuel processing reactor, fuel cell and burners is convective in the flow direction (PFR), and axial diffusion can be neglected; on the other hand we assume that diffusion in the radial direction is fast enough to ensure a uniform profile in the cross-section. These assumptions have the consequence that micro-fabricated units such as reactors or fuel cells can be approximated by an idealized model using 1-D species balances, without the inclusion of the diffusion term. We neglect the pressure drop along the gas channel and assume an ideal gas. Back-of-the-envelope calculations based on the expected device dimensions using Hagen-Poiseuille's equation provide an estimated pressure drop in the order of a few kPa, i.e., a relative pressure drop of a few percent only. We note that this value is in good agreement with the measurements for a micro-fabricated reactor made by Arana (2003). As a consequence, no solution of momentum equations is necessary. We further assume that heat transfer is fast enough, so that the temperature throughout the device, or regions of the device, is near uniform. This is typically the case at the micro-scale for silicon based reactors. Finite element simulations were also performed, which confirm this assumption. It is important to note that considering a uniform temperature allows one to not specify a particular geometry for the unit operations and their arrangement in the stack. Otherwise, not only the generality of our study would be inherently affected, but problems would also be encountered as several micro devices and components of the proposed processes are not fully developed thus far. Due to material constraints and technological limitations the start-up time will be in the order of at least one minute, much longer than the residence time of gases in the process, which is in the order of ms. We therefore assume pseudo-steady-state concentration profiles along the various units at each time instant. This assumption allows us to solve the concentration profile at each time step using an integration along the spatial axis, similar to the the steadystate case (Chachuat et al., 2004) without requiring method of lines semi-discretization of the state variables; in some cases this assumption even allows the calculation of analytical solutions for the concentration profile. It should be noted that if one wanted to explicitly calculate the material stresses developed, a fully transient model would be necessary. The objective of the start-up problem is to bring the fuel cell to its nominal temperature while minimizing the total mass (battery and fuel) required for this heat-up and meeting the nominal power demand at all times. In the case studies we assume that the battery

1095 can also be used for heat-up of the device. Additional constraints can also be specified, such as a maximum rate of change for the temperature based on structural stability considerations, or requirements concerning the emission of toxic gases. Since different operating modes are described by different sets of equations (e.g., discharging and recharging of the battery), the start-up problem is formulated as a hybrid discrete/continuous dynamic optimization problem (Lee and Barton, 2002). This optimization problem is solved by using recent developments in numerical methods for dynamic optimization with hybrid systems embedded.

3. Case Studies 3.1. Case Study 1: Butane Based Process A very promising process for micro power generation is the partial oxidation of butane, with subsequent electro-chemical conversion of the generated syngas in a Solid Oxide Fuel Cell (SOFC) (Mitsos et al., 2004a); one of the main advantages of this process is that butane has a very high energy content, and partial oxidation is an exothermic reaction. Therefore, oxidation of the fuel cell effluents is sufficient to overcome the heat losses at steady-state operation. A conceptual flowsheet for the process is shown in Figure 1; the reactor, fuel cell and catalytic burner are assumed to be thermally coupled and operate at a common uniform temperature. The drawbacks of this process are that butane partial oxidation has not yet been demonstrated at the micro-scale and limited kinetic data are available; therefore the model presented should be considered preliminary and the results qualitative rather than quantitative. air

~it +

air

re+:~q~,~r

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................................................ l

Figure 1. Conceptual f l o w s h e e t f o r butane based process.

We now present results obtained from optimization of the butane based process at a nominal power output of 1 W and a nominal operating temperature of 1000 K. Figure 2 illustrates the optimal profile, obtained by applying a piecewise constant approximation with 50 control segments of equal duration to solve the problem. The optimal start-up procedure duration was determined to be around 150 s. The number of time intervals has an insignificant influence on the start-up performance in terms of the objective function.

1096 2

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Figure 2. Time profiles for optimal start-up of butane process.

3.2. Case Study 2: Ammonia Based Process Ammonia is often considered as a potential energy source in fuel cell systems, e.g., Metkemeijer and Achard (1994), because ammonia decomposition produces hydrogen. A drawback of this process is that ammonia is corrosive and toxic and therefore tight constraints regarding the emission of residual ammonia need to be imposed. Also, ammonia decomposition is an endothermic reaction and therefore a heat source is required. While oxidation of part of the hydrogen produced could be used to provide the necessary heat, a more promising approach Mitsos et al. (2004b) is the use of a secondary fuel with a high energy density, such as butane. In Chachuat et al. (2004), we have considered optimal steady-state operation of the process shown in Figure 3 and we now extend this work to transient operation.

1097 air

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Figure 3. Conceptual lTowsheetfor ammonia based process.

The scope of this paper does not permit a detailed discussion of the start-up procedure for the ammonia based process. Instead we present how, for a fixed design, the fuel energy density (in Whr/Kg) changes as a function of the power output. This consideration is very important for the transient operation, since at start-up it is plausible to gradually increase the flow through the fuel cell. Furthermore, the power demand of power consuming devices is time varying and there is a trade-off between running a process away from its optimal operating point and consuming more energy from the auxiliary battery. In Figure 4 the design optimized for a nominal power demand of 10 W (Chachuat et al., 2004) is used and the energy density based on optimal steady-state operation is shown in comparison to the design optimized for the given power output, it should be noted that we do not consider a variation of the operating temperature, assuming that the design was done for the maximal allowable temperature, based on material constraints. The energy density is maximal at a power demand slightly higher than the one for which the system was designed (~ 10.1 W). For power demands lower than the design power output, the heat generation is small, and relatively more butane needs to be burned to compensate for the heat losses. For an increasing power output, the ammonia flowrate is increased and the fractional conversion in the reactor and fuel cell is decreased; the constraints on residual concentrations of ammonia and nitric oxide in the outlets are only met with a largely increased flow of oxygen, which results in higher requirements for heat and a higher butane flow rate. The flow rate for oxygen quickly becomes so large that the pressure drop through the system would become significant, making the process practically infeasible and also violating one of our main modeling assumptions. This case study shows that it is necessary to consider variations in the power demand during the design of the system, and a promising method is stochastic optimization.

1098

.........

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Figure 4. Process performance outside its optimal operating region.

4. Conclusions A methodology for the simultaneous design and operation of fuel-cell based micro power generation devices was presented and demonstrated by considering the start-up procedure for two fuel-cell systems based on fuel processing in conjunction with a Solid Oxide Fuel Cell. The models used are of intermediate fidelity, allowing the optimization of design and operation without the specification of an exact geometry. The formulated methodology allows the solution of the formulated problems using dynamic optimization tools. The case studies show a strong interaction between design and operation. We are currently extending our methodology and case studies to the whole operating cycle as well as varying power demands. We anticipate that using stochastic optimization formulations will allow a significant improvement in process performance.

References Arana L.R., 2003. High-Temperature Microfluidic Systems for Thermally-Efficient Fuel Processing. Ph.D. thesis, Massachusetts Institute of Technology. Chachuat B., A. Mitsos and P. I. Barton, 2004. Optimal design and operation of micro power generation employing fuel cells. Submitted. Lee C. K. and P. I. Barton, 2002. Modeling, simulation, sensitivity analysis and optimization of hybrid systems. ACM Transactions on Modeling and Computer Simulation 12, 256. Metkemeijer R. and P. Achard, 1994. Ammonia as a feedstock for a hydrogen fuel cell; reformer and fuel cell behaviour. Journal of Power Sources 49, 271. Mitsos A., I. Palou-Rivera and P.I. Barton, 2004a. Alternatives for micropower generation processes. Industrial & Engineering Chemistry Research 43, 74. Mitsos A., M. M. Hencke and P. I. Barton, 2004b. Product engineering for man-portable power generation based on fuel cells. AIChE Journal (in press).

Acknowledgements This work was supported by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the Army Research Office under Grant DAAD 19-011-0566. We would like to acknowledge Klavs F. Jensen and the other members of the MIT ~tChemPower team for stimulating discussions.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1099

Performance monitoring of industrial controllers based on the predictability of controller behavior Rachid A Ghraizi a, Ernesto Martinez b, C6sar de Prada a, Francisco Cifuentes c, and Jos6 Luis Martinez c ~Dpt. of Systems Engineering and Automatic Control Faculty of Sciences, University of Valladolid, 47011, Spain bINGAR-Institute of Development and Design Avellaneda 3657, $3002 GJC - Santa Fe. Argentina CRepsol-YPF, Dpt. of Advanced Control Paseo de la Castellana 278, Madrid, Spain

Abstract This study focuses on performance assessment of industrial controllers. A methodology based on the concept of the predictability of controller errors is proposed for performance monitoring. The proposed approach is based on evaluating controller behaviour by analysing the time series of its error and to verify the existence predictable patterns beyond the control horizon in each one of the controlled variables of the process. To favour its implementation in a plant information system a performance index is proposed. For effectiveness of the monitoring algorithm, proper selection of some tuning parameters depending on the type of loop (temperature, level, pressure, etc.) is discussed. Examples using industrial data from a refinery are provided.

Keywords: Process control, controller performance, loop monitoring, performance benchmarking, fault diagnosis. 1. Introduction With the increasing complexity of control structures and the sheer number of controllers in modern process plants, the automation of performance monitoring tasks is a key issue to grasp the benefits of advanced control systems and real-time optimization (Thornhill, et al., 1999). In process plants there are thousands of control loops whose performance demands continuous supervision. Human personnel simply cannot have the budget of attention to handle this overwhelming task which renders many loops to remain open or providing a service much below the required standards. Abnormal operation of control loops can make a significant impact not only in the economy but also in the safety of the process. During the last decade several monitoring techniques have been developed. Desborough and Harris (1992, 1993) focusing on the comparison of the actual controller variance to ideal of a minimum variance controller. Thornhill, et al., (1999), proposed the prediction of the error to determine the performance of a SISO controller. Ghraizi, et al., (2004), suggest a practical index for performance monitoring of a control loop based

1100 on the analysis of the predictability of the error time series emphasizing proper selection of the control horizon using engineering judgment. The contribution of our work is based on the proposal of a procedure to obtain an index that allows the controller monitoring in closed loop and to evaluate its performance using predictions to detect the existence of predictable patterns in the time series of the error associated to each one of the controlled variables of the process. The method was applied to analyze off line some loops of PIDs in a petrochemical plant.

2. Monitoring methodology The performance-monitoring concept revolves around the idea of predictability of controller behavior beyond a chosen control horizon. Assuming the control horizon b has been chosen appropriately, the behavior of a perfectly working controller cannot be predicted beyond the interval of time during which any disturbance entering the loop up to a present time is supposed to be compensated (see Fig. 1 for details). On this ground, there may exist different alternatives to detect patterns of predictability in the time series associated to controller errors and manipulated variable changes. It is worth noting that as seen from time t, the controller error after time t+b of a properly working controller cannot be distinguished from a random walk stochastic process. Over the control horizon, the controller behavior is fully predictable since it corresponds to its own control policy built-in by design.

Figure 1: presentation of the prediction of the error.

It is worth discussing first the meaning of the control horizon b for a regulatory control task. Whatever the internal workings (PID, Predictive, etc.) of a controller, the value of b represents a sound engineering decision that takes into account among other things process dynamics, type of service and acceptable control energy. Let's denote by a scalar e(t) the controller error whereas ;(t) stands for the prediction of such error based on past values of the controller error, and possibly, control actions generated by the controller. The difference between the actual and predicted controller errors is the residue r(t) whose means and variance provide relevant information regarding the predictability of a controller behavior. The calculation of a performance index from a given data set demands some way of estimating future controller errors. The easiest way to do this is to propose a regression model of the following form: e(t + b) - a 0 + a l e ( t ) + a 2 e ( t - 1) + a 3 e ( t - 2) + ... + a m e ( t -

m + 1)

(1)

Where m is the model order and ai are the parameters to be fitted upon data using for example least-square regression. The Predictability Index (PI) is calculated to bear some similarity with the one proposed by Harris (1989) to measure the current

1101 performance regarding the best performance that can be achieved using a minimum variance controller, 2 PI - 1 cr r (2) mse

Where, cy2 is the residue variance and mse is the mean square error. Similar calculations can be used to define a measure of the predictability of controller outputs. For a given interval of time, if a controller does not exhibit a predictable behavior beyond the control horizon, c~ ~ mse gives rising to a near zero value of PI. As the controller behavior is more predictable rose increases relative to o-r2 , which in turn increases PI. For a controller exhibiting an easily predictable behavior (e.g., output saturation) o-j <<mse(t) and PI= 1. It is possible to define confidence intervals for sample estimations of the predictability index, which allows using control charts to detect excursions associated to loop malfunctions. The estimate to the confidence interval is carried out according to the following equation: r

T=11 a/Zn-1 --

~

~;

--

(3)

n

Where t~-a/Z,,-~ is the Student statistic, a is the level of confidence, n and or,. are, respectively, the size of the group of the data and the variance of the noise.

3. Parameter tuning It is necessary to provide some guidelines on how some parameters involved in the calculation of P1 should be selected. Parameter m, represents the order of the regression model. This parameter should have a value that is big enough to capture the characteristics of the time series of the error to reflect the predictable components in the model. As a rule of thumb, m should have a value slightly bigger than the loop settling time. Too high a value for m creates problems of overfitting and poor extrapolation capabilities in the model, which will affect the sample estimation of the PI index. Parameter n, is the size of the data sample and it should to take into account the trade off between index variance and data homogeneity. A very small size of the data set gives rise to big variance in the index distribution, while a too big data set is mixes heterogeneous data, which may mask a lot of important information. Since index calculation uses the error of controller and not the controlled variables, it is not necessary that the loop remains in the same set point, but it is important that the characteristics of the loop are the same throughout (Ghraizi, et al., 2003), such that, sensors, valves, control algorithms should not be altered by calibration or tuning. Regarding the sampling interval tm, is necessary to avoid an excessive or insufficient sampling. If the data are frequently sampled, the impulse response of the closed loop is not established inside the m samples. With low frequency sampling, the impulse response is only established inside a few samples and the important loop characteristics are not captured between the samples (Thornhill, et al., 1999; Stanfelj, et al, 1993). Parameter b represents the control horizon, which coincides with the prediction horizon for the time series model. It has been analysed by different authors like Harris, (1989), Desborough, and Harris, (1992), Harris, et al., (1996), Stanfelj, et al., (1993). In our work, we have observed that b should be equal to the loop settling time, independently

1102 of the type of the loop so that so it can reflect the necessary prediction characteristics in a control loop.

4. Industrial data analysis In order to test the index, several analysis were performed with a Toolbox implementing several monitoring functions. The length of the batches considered was n = 1000 samples of real plant data. The following graphs show the analysis of different loops taken from a petrochemical plant. The parameters were adjusted to the nature of the loops. In this way, we choose tm=5 sec., b = 15 (number of samples), m=30 for flow control loops. For level ones tm=60sec, b=30, m-30, (in this case n=720), for pressure tin-5 sec., b=5, m=30, and for temperature tm=60sec., b = 15, m-30. In the left part of all the graphs, we can observe the batches of data and their analyses, while in the right part we can see a zoom of a certain area of them to visualize some details. The upper graph corresponds to the controlled variable and its set point, while the values of the error and its predictions are in the graph in the middle. Finally, in the lower one, the values of the performance index P I are displayed. In figure 2 one can observe 17 batches of 1000 data of a flow loop which performance deteriorates at the 13 th batch, due to a perturbation that has affected the process. The performance index at the beginning doesn't have high values what indicates that the error has little predictability, as shown in the right hand side, but when the perturbation appears, the manipulated variable saturates and the P I almost is equal to one. Notice the bottom right hand side graph showing that the error can be predicted easily this time. Once the process returns to its normal state, the error, and the index takes a small value again. Data

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In figure 3 one can observe results from a level loop where a change in the behaviour takes place after t=1000 proximately. At the beginning, the PI has a small value but when the change takes place, PI increases reflecting the predictability of the error. By the contrary, the Harris index, shown in the bottom right hand side graph, does not performs equally well remaining in a low value which means bad tuning, not taking into account the special characteristics of an average level control.

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Figure 4 displays data from a cascade loop in which a temperature output is following a changing set point very slowly with a significant steady error. In this case, the P I has high values all the time, and in the extended graph o f the right is seen that the error is completely predictable. In addition, the Harris index is consistent with this result. Data T e m p e r a t u r e

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Finally, graph 5 shows the data o f a pressure loop performing well. In this case, the error is not predictable and the values o f PI are always low. Also, the Harris index is high but shows a higher variability than the PI. Data pressure •

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1104 Figure 6 shows the main window of the developed Toolbox, which allows not only perform analyses of a control loop using the index IP, but also other analyses based on cross-correlation, power spectrum, impulse response, Harris index, etc., that can be used to confirm or perform a deeper analysis in order to detect the possible cause of the controller's bad operation. w~

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5. Conclusions This paper presents results showing a promising way of analysing the performance of industrial controllers using a time series of the error to detect the existence of predictable patterns. An index was computed to achieve this analysis evaluating the residuals between the controller's error and its prediction and some rules have been proposed to adjust the parameters of the method. Finally, it was applied to plant data showing a good behaviour.

References Desborough, L., Harris, T. 1993. Performance assessment measures for univariate feedforward/feedback control. Canadian Journal of Chemical Engineering, 71,605-616. Desborough, L., Harris T., 1992 Performance assessment measures for univariate feedback control, Can. J. Chem. Eng. 70, 1186-1197. Ghraizi R. A., Martinez E., de Prada C, 2004, Anfilisis del comportamiento de los controladores industriales, XI congreso latinoamericano de control automfitico Ciudad de La Habana, Harris T. J., (1989 Assessment of control loop performance, Can. J. Chem. Eng. 67, 856-861. Harris T.J., Boudreau F., MacGregor J.F., 1996 Performance assessment of multivariable feedback controllers, Automatica 32, 1505-1518. Stanfelj N., Marlin T.E., MacGregor J.F., 1993 Monitoring and diagnosing process control performance: the single loop case, Ind. Eng. Chem. Res. 32, 301-314. Thornhill N. F., Oettinger M., Fedenczuk P., 1999 Refinery-wide control loop performance assessment, Journal of Process Control 9 109-124.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1105

A Systematic Approach to Plant-Wide Control Based On Thermodynamics Luis T. Antelo, Irene Otero-Muras, Julio R. Banga and Antonio A. Alonso* Process Engineering Group, Instituto de Investigaciones Marinas-CSIC C/Eduardo Cabello, 6 - 36208 Vigo, Spain

Abstract In this work, a systematic approach to plant-wide control design is proposed. The approach combines ingredients from process networks, thermodynamics and systems theory to derive robust decentralized controllers that will ensure complete plant stability. The proposed methodology will be illustrated on a reactor network exhibiting complex behaviour.

Keywords: Plant-wide Control, Process Networks, irreversible Thermodynamics, Inventory Control.

1. Introduction Over the years the area of plant-wide control has attracted the process engineering community as a challenging problem which drives continuing research efforts. A number of solutions to it were suggested, lying in between the following two extremes: a hierarchical decomposition of the original problem based on heuristic rules (Buckley, 1964; Luyben et al., 1997; Skogestad, 2002) and a mathematically oriented approach based on the solution of a given large scale mixed integer nonlinear programming dynamic optimization problem (see Biegler and Grossman, 2004, for an excellent review). Unfortunately, both lines of attack are hampered by a number of drawbacks which prevent their systematic application to general classes of process plants: the hierarchical approach usually leads to conflicting decisions only unravelled on a case by case basis and the mathematically one is limited by the high dimensionality of the problem and the restrictions imposed by the definition of the objective function. To overcome these issues, we combine previous results that link thermodynamics with passivity and Lyapunov theory (Farschman et al., 1998; Hangos et al., 1999; Alonso and Ydstie, 2001), and apply them to systematically design and/or to analyse stable decentralized control structures for process plants. In this way, the approach leads to hierarchical decentralized control structure which simultaneously ensures convergence of mass and energy inventories and guarantees robust stabilization of the intensive variables. The paper is structured as follows: In section 2, a formal representation of chemical process plants in terms of interconnected mass and energy networks is presented. The thermodynamic formalism and its consequences in designing decentralized controllers are presented in section 3. Finally, in Section 4 the approach is illustrated on a reaction network. *Author to whom correspondence should be addressed: [email protected]

1106

2. The Underlying Structure of Process Networks A process network is defined by a number j = l ..... n of well mixed homogeneous material regions connected by material and energy fluxes we will refer to as nodes, plus an extra region j = 0 which represents the environment. To each node j in the network we associate a state vector zjs R ~+~of the form zj=(n/, .... n~,d) r, where n~ represents the mole numbers of component i, # is the internal energy and c stands for the total number of chemical species. Nodes and environment are connected by a set of n convective fluxes we refer to as f ~ It~+Cand p j ~ ) ~ R +for component and energy, respectively. Since energy is transported through material flows, we also have that pj(O) = 0. Note that the formalism as it stands can easily accommodate multiple connections between modes by defining ~b~ - £ a j k ~ b ~ , where ~. stands for either material or energy fluxes and %~ k=l

represents the fraction of ¢~ directed to the node k so that £ a i k = 1 (Hangos et al., k=l

1999).Dissipative transfer between nodes in the network is included through vectors cpk• R +de (with i=l .... c) a n d ~ E R +d'' which stand for mass and energy respectively. Network dynamics obey standard conservation principles for mole number and energy which, with some abuse of notation, can be formally stated as: h~ - N ¢ f ~ + N ¢CPk + v W

n~. , f k • ~+,. , k _ 1,.. ., c;

(1)

it - N o p + N~,~ + Q

u, p • R +"

(2)

where N¢ •N'×" denotes a convective column conservation matrix (Hangos et al., 1999).Ne ~ N,×Jc , N ~ R "×J'' are matrices which define network dissipative transfer interconnections, and the extra-terms v W and Q in Eqns (1)-(2) have been included to account for chemical reaction units and external heat sources, respectively. Alternative network dynamic representations can be derived from the fundamental network dynamics (1)-(2). In this way, the corresponding mass network representation can be easily obtained by defining transformations m - 2 crknk and ~b= 2 c r ~ f k k =1

with crk

k =1

being molecular weight of the k-specie. Inventory network representations will result from projecting Eqns (1)-(2) onto the linear operators P~ • R "-de×" and P~ • R È-d'×È satisfying P~ I N ~ v 1 - 0

and P~ I N ~ v I - 0, respectively, so that"

n"~I - N o . f ~

n ~l , f ~ • ~ +(,-de) ; k - 1,...,c;

(3)

i~ - Nopz

uz, pz ~ I~ +~"-~''~

(4)

3. Hierarchical Design of Decentralized Controllers 3.1. Thermodynamic foundations of Process Networks To start with, we consider that each node in the process network with volume vj is equipped with a continuous and twice differentiable scalar function Sj (zj, vj )" R +(c+2) ~ R with the following properties"

1107 1. S / ( z , v / )

is a first order homogeneous function in all their arguments so that

Sj - ~ z j +/~v/

(5)

2. S j (z/, v l)is strictly concave with respect to the vector zj. Function ~., as defined, coincides with classical entropy (Callen, 1985). From Property 1, it follows that entropy is an additive function so that for a process network its total entropy is of the form

S- ~S/(z/,v/).

Property 2 ensures that for

(z,v)

,/=1

constants, S has a maximum over the convex set: ,,

/~,

~,/

(6)

v .,

jl

.i--1

This, in fact, constitutes an evolution criterion as any thermodynamic system evolves in C so to maximize S. Finally, concavity also ensures the existence of a well defined oneto-one map between the vector of intensive properties /~j and the vector of densities

p~- v~lz/.

One main implication, of interest in process networks, is that

whenever ~b - 0 network states will evolve so to maximize S. This can be easily shown by noting that ~b - 0 :zz>~ - 0 for k = 1..... c and p(O) = 0 so that Eqns (3)-(4) become .,~

n~ -z~ I - 0 . Since material and energy inventories are constant, we are in the set C and the evolution criterion applies. It is worth mentioning that as the network evolves, entropy is being produced so by computing the time derivative of S along (1)-(2) we obtain: _..I

i

i

Since S is bounded from above by its maximum, we also have that a ( z ] ) - 0

(7*)" --/

,/=1

- MArg ax

C

S

'

the

equilibrium

StClte

for

of the network. The entropy balance

represented by Eqn (7) adopts the following form for open process networks:

dS

---P

+¢~ (,u/,~b)

(8)

where ~ (,u/ , 6) denotes the entropy flow through the network, which by definition becomes zero at the equilibrium state of the network, i . e . .

(~i, 6) - 0.

3.2. Decentralized control design In order to preserve and/or to enforce the stability of extensive as well as intensive plant states, we make use of previous results in system theory that links thermodynamics with passivity and Lyapunov theory (Hangos et al, 1999; Alonso and Ydstie, 2001). The underlying idea is to exploit the concavity of the entropy function to construct natural storage and Lyapunov candidates and to employ them to design stabilizing (usually high gain) controllers. However, as discussed previously, concavity can only be attained once the network states are in the set C defined in (6). This fact, motivates a hierarchical control design decomposition in which mass and energy inventory controllers are first designed to ensure that the network states will remain in the set C. In particular, the

1108 mass and energy inventory control layers consist of linear proportional controllers of the form:

~b1- ~b~+ c% (rnl -m~ )

pl - p~ + co,,(ul -u~ )

(9)

where c% and co are appropriate gain matrices constructed so that Nocom and N~co are negative definite. By applying (9) to the inventory network (3)-(4), it is straightforward to show that mt--4 m~ and u~ ~ u~ exponentially fast. Integral action could be also included in (9) without substantially altering the stability properties of the closed loop network (Farschman et al, 1998). From the thermodynamic properties discussed in Section 3.1, it also follows that since the network states are in the interior of the set C, its entropy will remain upper and lower bounded and consequently, from Eqn (8), we have that: T

Lim ~(P + ~ )dz - O

(10)

T--+~ 0

Unfortunately, condition (10) does not prevent the density states pj = v~lzj, and thus their intensive counterparts from exhibiting complex dynamic behaviour such as multiplicities. However, since the network remains in C, the network entropy is strictly concave and intensive variable control can be designed by, for instance, methods discussed in Alonso and Ydstie (2001) to ensure convergence of the network density states. This will be illustrated next on a representative example.

4. Case Study: A N o n - i s o t h e r m a l C S T R We illustrate the proposed hierarchical control design methodology on a jacketed nonisothermal CSTR in which an liquid phase irreversible exothermic reaction A -~ B takes place. A detailed description of the process model and parameters can be found in Alonso and Banga (1998).

4.1. Mass and energy inventory control Figure 1 depicts a schematic representation of the reactor and heat exchanger as a process network consisting of two nodes connected by a dissipative heat transfer term. The mass and energy inventory control approach discussed in Section 3.2 is diagrammatically represented in Figure 2. As shown in the Figure, mass inventory control results into a LC control loop which fix the residence time in the reactor. In order to implement the energy inventory control, an internal energy observer was designed to estimate the energy content in the reactor, and the estimate used as the measurement for the FC loop acting on coolant flow rate. As discussed previously, the proposed controllers guarantee inventories to converge to the desired set-point. However, the control structure does not ensure control of temperature and conversion in the reactor. Such behaviour motivates the thermodynamic analysis presented next.

4.2. Thermodynamic analysis of the reactor network. The inventory control structure allows us to re-write process network dynamics in terms of intensive variables, which for this case takes the form:

C

1109 where CA and T are composition and temperature, respectively, p is the reaction rate and 0,/7, and ), are dimensionless physical parameters related with residence time and heat transfer areas (see Alonso and Banga, 1998).

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c

Q ........................

/)

2"

Figure 1. Reactor process network

Figure 2. Proposed control structure

The entropy balance associated to this network takes the form given in (8) with entropy production and entropy flow being of the form: R

(12)

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d7 p

7"

dc

rdc (c::' - cA)o- g

Process entropy and its time derivative (which equals ~ + •

) is represented in Figure 3

along the set C defined by (6), which in our case corresponds with the manifold of constant mole number and energy. As it can be seen from the Figure, there are three points in C satisfying the steady-state entropy balance which correspond with an unstable and two stable stationary points. Note that the stability or instability can be easily established from the curvature of the systems entropy. 0.5:

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50 (s)

Figure 4. Concentration and Temperature evolution under intensive variable control

4.3. Intensive variables control In order to ensure stabilization of the intensive variables (reactor concentration and temperature) the inventory control configuration is completed with an intensive variable control loop acting on the coolant temperature To. Although different control structures could serve to that purpose, in this work a PI temperature controller and a non-linear exact linearizing control (Alonso and Banga, 1998) were tested, demonstrating for both

lllO cases state stabilization. The evolution of temperature and concentration under intensive variable control is presented in Figure 4. Finally, some control experiments were carried out in order to test the unstabilizing effect of input constraints on the closed loop dynamics. In this case, the thermodynamic analysis reveals new points in the region C satisfying the stationary entropy balance (see Figure 5) which corresponds with either stable, unstable or even limit cycles caused by total inventory fluctuations. A representation of one of such oscillatory regimes is depicted in Figure 6. a)

........ ~ -~V[.~:~::::.::..::::.: ........................................................................................ ,~....

i

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0.05

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"~ i ;o

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~ ....

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,~

,

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Figure 6.Evolution of the state and manipulated variable in the presence of input constraints

5. Conclusions In this contribution, a systematic plant-wide control design methodology has been presented. The approach, which combines tools and concepts from systems theory and thermodynamics, allows the design of decentralized control structures which ensure stabilization of both plant extensive and intensive variables. The proposed methodology has been illustrated on a reactor network exhibiting complex behaviour.

References Alonso, A.A. and J.R. Banga, 1998, Design of a class of stabilizing nonlinear state feedback controlled with bounded inputs. Industrial & Engineering Chemistry Research, 37, 131. Alonso, A.A. and B.E. Ydstie, 2001, Stabilization of distributed systems using irreversible thermodynamics. Automatica, 37, 1739. Biegler,L.T. and I.E. Grossmann, 2004, Retrospective on optimization. Computers & Chemical Engineering, 28, 1169. Buckley, P.S., 1964, Techniques of process control. John Wiley & Sons. Callen, H.B., 1985, Thermodynamics and an introduction to thermostatistics. John Wiley & Sons. Farschman, C.A., K.P. Viswanath and B.E. Ydstie, 1998, Process Systems and Inventory Control. AIChE Journal, 44, 1841. Hangos, K.M., A.A. Alonso, J.D. Perkins and B.E. Ydstie, 1999, Thermodynamic approach to the structural stability of process plants. AIChE Journal, 45,802. Luyben, M.L., B.D. Tyreus and W. Luyben, 1997, Plantwide control design procedure. AIChE Journal, 43, 3163. Skogestad, S., 2002, Plantwide control: Towards a systematic procedure. In CAPE 10 and ESCAPE 12. Elsevier, 57.

Acknowledgements The authors acknowledge the financial support received from the Spanish Government (MCyT Projects PPQ2001-3643) and Xunta de Galicia (PGIDIT02-PXlC40209PN).

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) cC~2005 Elsevier B.V. All rights reserved.

1111

A Multiple Model, State Feedback Strategy for Robust Control of Non-linear Processes F. Y. Wang a* p. Bahri b, p. L. Lee c and I. T. Cameron

a

a Division of Chemical Engineering, The University of Queensland Brisbane, Qld 4072, Australia ~' School of Engineering, Murdoch University, Rockingham Campus Murdoch, WA 6150, Australia c Division of Engineering, Science and Computing, Curtin University of Technology GPO Box U 1987, WA 6845, Australia

Abstract In order to achieve global stability using well-established linear control theory and techniques, a multiple model approach has attracted increased attention in recent years. In our previous work, a mini-max optimisation strategy was developed within the framework of a multiple model approach, in which a global controller can be designed without the requirement of membership/validity functions used in conventional methods, and the regime division was realised using a gap metric method. The major limitation of the reported methods is that robustness against process/controller disturbances cannot be addressed if the process switches from stable to unstable in operation. Furthermore, the number of local models is still large for highly non-linear processes even though the gap-metric method is incorporated. In this paper, a significantly modified multiple model approach is developed to achieve robust control with global stability. The main new features of the current approach include: (1) stabilization of open-loop unstable plants using a state feedback strategy, (2) incorporation of an adjustable pre-filter to achieve offset-free control, and (3) implementation of a Kalman filter for state estimation where necessary. The improved controller design method is successfully applied to two non-linear processes with different chaotic behaviour, namely a continuous stirred tank reactor and a Zymomonas mohilis reactor. Compared with conventional methods without model modifications, the new approach has achieved significant improvement in control performance and robustness with dramatically reduced number of local models.

Keywords:

Chaos; Localised models; modification; Robust control

Mini-max

optimisation;

Author to whom correspondence should be address: [email protected]

Model

1112

1. Introduction Most chemical processes are non-linear in nature. However, for effective control and operation, low dimensional, linear models are highly desirable. It is not always possible to represent a non-linear process by a single linear model. Consequently, a multiple model approach has attracted increased attention in recent years (Murray-Smith and Johansen, 1997). In the conventional multiple model approach, a complex, non-linear model is reduced to a set of localised, linear sub-models. The overall model is the weighted combination of the local models (Shorten et al., 1999). However, it is not always easy to determine the so-called membership/validity functions used in the reconstruction of the overall model, and to effectively divide the operational regimes. In an attempt to eliminate the difficulties involved in the determination of blended models, Bartholomaus (2002) developed a mini-max optimisation strategy, in which a global controller can be designed without the requirement of membership/validity functions. However, the method leads to a large number of local models due to the lack of an effective strategy for regime division. In order to reduce the number of local models, we have incorporated the gap metric method into mini-max optimisation algorithms (Wang et al., 2003). In spite of the advances witnessed in the field, a major limitation of the reported methods can be identified as: "It is very difficult to achieve desired robustness properties if the process consists of open-loop unstable regimes". It can be shown in the case studies carried out in this paper that, although acceptable control performance was obtained using reported methods for a class of chaotic processes (Morningred et al., 1990; Bartholomaus, 2002; Wang et al., 2003), the robustness criteria have not been reached. This can be demonstrated easily through the observation of chaotic dynamics in the stabilized systems with slightly disturbed controller gains. If the robust issues cannot be effectively addressed, the reported methods have little practical significance for unstable processes. Furthermore, the number of local models is still large for highly non-linear processes. In this paper, a significantly modified multiple model approach is developed to achieve robust control with global stability. In the proposed approach, the original open loop unstable plants are first stabilized using a state feedback strategy followed by the local linearization within a regime classified by a gap metric measure. The smooth transition between regimes, as well as offset-free control can be assured through the incorporation of an adjustable pre-filter in the multiple model control framework. If the feedback states are not measurable, a Kalman filter is implemented for the state estimation. Two case studies, namely robust control of a continuous stirred tank reactor and a Zymomonas mobilis reactor, are carried out to demonstrate the advantages of the proposed approach over conventional ones. It can be shown that the chaotic dynamics are under robust control with a dramatically reduced number of local models.

2. Multiple Model, State Feedback Strategy The proposed multiple model, state feedback control strategy is schematically shown in Figure 1, in which the left part is the mini-max optimiser, and the right part is the nonlinear system.

lll3 Mini-max Opt{mizer ....................................................

Local O:paratior±al C onditions YL.

XL K C

~i

xk

.............

Kf

L . o c ~ e d Lm~.r Models El, L: ..... L~

~)

" -I Ii ' J f(x) [-.

Figure 1. Schematic Diagram of Multiple Model Approach with State Feedback

In Figure 1, E is the global linear controller, Kc and Kf are the state feedback and the Kalman filter matrix, respectively, and P is the pre-filter with adjustable gains. The non-linear model is described by:

k - f (x) + g ( x ) u ; y = h(x)

(1)

where x, y, and u are state, output and control variables, respectively. The non-linear model can be linearised into a set of local linear models L~ in m regimes identified by index i (i = 1, ..., m) with state space matrices {Ai, Bi, Ci} and transfer function matrix Gi(s). It should be noted that the relationship between matrix Ai with and without state feedback is: Ai = (Ai°+BiKc), where Ai ° is obtained before state feedback. The key issue of the control study is the optimal determination of parameters in the global controller E and pre-filter P using mini-max optimisation algorithms. The gap metric method is used as a measure for regime classifications, which was clearly described in Samyudia et al. (1996).

3. Optimal Design of Controller and Pre-filter The optimal controller parameters are determined using mini-max optimisation algorithms. The controller E(Q) consists of n parameters ~ ~ Q G R ", The local objective function in H-infinity norm format can be formulated as:

1114

(2)

W e (I + GiE(Q)) q where i = 0, 1, ..., m with i - 0 as the starting operational point, J is the objective function, W is the weighting function matrix, the subscripts u and e identify control and error relevant functions, respectively. In principle, the mini-max optimisation can be formulated as rain m a x { J 0 , . . . , J m } with respect to Q. Since it is very difficult to determine the starting point for optimisation (Bartholomaus, 2002), a sequential minimax optimisation algorithm is proposed in this paper, which is represented as follows: Qm - 1

min {Jo }_~ min max{Jo, J1 }'..___> min max{Jo,... , Jm } --->Q

(3)

The overall parameter vector Q is applicable to all regimes rather than a single regime. The following equation is used to determine the pre-filter gain for SISO systems:

LimlP s ~ O

(s)(, "

G i (s)E(s))

' G i (s)E(s)] - 1

(4)

"

4. Case Studies A continuous stirred tank reactor model originally proposed by Morningred et al. (1990) and further analysed by Bartholomaus (2002) is selected as the first case study. The model is represented as:

dC~

_ q (Coo _ C~

) - k oC exp(-E' / RT)

dT : q (r o -r)+k,C~ dt V

(5) exp(-E'/RT)+

k2qc[1-exp(-k 3/q~)](r~o-r)

The nominal values of model parameters are available from Momingred et al. (1990). We treat k2qc[1-exp(-k3/qc)] together as the control variable u. The control objective is to drive the concentration Ca from the initial operating point Ca - 0.06 to the final operating point Ca = 0.16 along a specified staged trajectory by adjusting the coolant flow rate qc. The process is open loop unstable with multiple steady states. The conventional (Bartholomaus, 2002; Wang et al., 2003) and improved performances are shown in Figure 2. The system becomes open loop unstable as Ca > 0.140. It can be shown from Figure 2a that the conventional control leads to notable deviations from desired trajectory in the unstable regime. The most unacceptable fact is that when the conventional controller gain increases 10%, chaotic dynamics appear as shown in Figure 2b. This implies that the conventional controllers are of little practical significance due to the robustness concern. The newly developed control scheme allows a broad range of controller gain variations. The control variable profile and its deviations from steady state are depicted in Figures 2c and 2d, and this is easy to achieve. The number of local models is reduced from 10 (Wang et al., 2003) to 5 using

1115

the proposed approach. than 10 were used.

Previous work by Bartholomaus (2002) suggests many more

b: Chaos under Controller Gain Change

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Figure 2. Control of a chaotic CSTR a OynBmics u n d e r T h r e e Control S c h e m e s 2.6.~ ........................,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i:

Improved Performance

!

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:

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o12

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08

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0.2 tit r, t r = 1 0 0 0 0

Figure 3. Control of ZMC with bifurcation behaviour

0.3 (h)

200

1116 The second case study is a Zymomonas mobilis reactor. Its model was fully described by McLellan et al (1999) and further analysed by Zhang and Henson (2001). The model consists of 5 state variables. We choose biomass X as the output and dilution rate D as the manipulative variable. The conventional and modified performances can be seen in Figure 3. Figure 3a shows the performance with three different control schemes with an indication of multiple steady states. Figure 3b shows the oscillatory behaviour using conventional control schemes without state feedback. Similar to the first case study, oscillations become severe with a slightly disturbed controller gain. Both performance and robustness have been improved significantly using the proposed control scheme. Three local models are sufficient for effective control of this process. For both processes, the controller format is" (qls2+q2s+q3)/(q4s2+qss+1), and the pre-filter equation is: pi/(s+l), where q~-q5 are determined through mini-max optimisation, and the regime dependent parameter Pi is computable using Equation (4).

5. Conclusions Through the theoretical development and simulation studies on control of two nonlinear processes with chaotic dynamics, the following conclusions can be drawn: 1.

2.

3.

Although a class of non-linear processes with chaotic dynamics can be stabilised using conventional control schemes, this work has shown that robustness is the main issue preventing the industrial application of the reported methods. State feedback for pole placement is an effective strategy amenable within the framework of the multiple model approach, leading to significantly improved performance and robustness with a dramatically reduced number of local models. The mini-max optimisation techniques enable the design of a global controller without relying on membership and validity functions. An integration of mini-max optimisation, pre-filter design, state estimation using Kalman filter and state feedback leads to the development of robust, offset free control systems for nonlinear, unstable processes.

Reference Balas, G.J., J. C. Doyle, K. Glover, A. Packard and R. Smith, 1995, ~t-Analysis and Synthesis Toolbox For Use with MATLAB, The Math Works, Natick. Bartholomaus, R., 2002, Contr. Eng. Practice, 10, 941. McLellan, P.J., A.J. Daugulis J. and J. Li, 1999, Biotechnol. Prog., 15,667. Morningred, J.D., B. E. Paden, D. E. Seborg and D. A. Mellichamp, 1990, Proc. ACC, 1614. Murray-Smith, R and T. A. Johansen Eds., 1997, Multiple Model Approaches to Modelling and Control, Taylor and Frances, London. Samyudia, Y., P. L. Lee, I. T. Cameron and M. Green, 1996, Comput. Chem. Eng. 20, $919. Shorten, R., R. Murray-Smith, R. Bjorgan and H. Gollee, 1999, Int. J. Control, 72, 620.S. Wang, F.Y., P. Bahri, P.L. Lee and I.T. Cameron, 2003, Proc. PSE 2003, 1065. Zhang, Y. and M.A. Henson, 2001, Biotechnol. Prog. 17, 647.

Acknowledgements The authors would like to acknowledge the financial support from the Australian Research Council (ARC) through a Large Grant Scheme for project A 10030015.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espuna(Editors) ~>2005 Elsevier B.V. All rights reserved.

1117

A Robust Discriminate Analysis Method for Process Fault Diagnosis D. Wang* and J. A. Romagnoli Dept. of Chemical Engineering, the University of Sydney, NSW 2006, Australia

Abstract: A robust Fisher discriminant analysis (FDA) strategy is proposed for process fault diagnosis. The performance of FDA based fault diagnosis procedures could deteriorate with the violation of the assumptions made during conventional FDA. The consequence is a reduction in accuracy of the model and efficiency of the method, with the increase of the rate of misclassification. In the proposed approach, an M-estimate winsorization method is applied to the transformed data set; this procedure eliminates the effects of outliers in the training data set, while retaining the multivariate structure of the data. The proposed approach increases the accuracy of the model when the training data is corrupted by anomalous outliers and improves the performance of the FDA based diagnosis by decreasing the misclassification rate. The performance of the proposed method is evaluated using a multipurpose chemical engineering pilot-facility. Key Words: discriminant analysis, robustness, fault diagnosis, and process monitoring.

1. Introduction Chemical processes experience abnormal conditions that may lead to out-ofspecification products or even process shutdown. These abnormal conditions are often related to the same root causes. Data driven process fault diagnosis techniques are often employed in process industries due to their ease of implementation, requiring very little modelling effort and a priori information. Given that there are multiple datasets in the historical database, each associated with a different abnormal condition (root cause), the objective of fault diagnosis is to assign the on-line out-of-control observations to the most closely related fault class. Fisher discriminate analysis (FDA) is a superior linear pattern classification technique, which has been applied in industry for fault diagnosis (Russell et. al. 2000). By maximising the scatter between classes and minimising the scatter within classes, FDA projects faulty data into a feature space so that data from different classes are maximally separated. Discriminant functions are established associated with the feature space so that the classification of new faulty data is undertaken by projecting it into the feature space and comparing their scores. As a dimensionality reduction technique for feature extraction as PCA, FDA is superior to PCA because it takes into account the information between the classes and is well suited for fault diagnosis. FDA also has better performance than other techniques such as KNN and SIMCA (Chiang, et. al. 2004). to whom correspondence should be addressed: [email protected]

1118 Even through the above advantages, there are still unsolved issues within the application of FDA approaches. One key aspect is the robustness of the approach when dealing with real data. It is known that, in FDA, the most difficult assumption to meet is the requirement for a normal distribution on the discriminating variables, which are formed by measurements at interval level. Practical examination tells us that the real plant data seldom satisfy to this crucial assumption. The data are usually unpredictable having, for example, heavier tails than the normal ones, especially when data contain anomalous outliers. This will inevitably result in the loss of performance leading in some cases to wrong modelling in the feature extraction step, which in turn leads to misclassifications of the faulty conditions. In this paper, a robust discriminant analysis method for process fault is presented. In the proposed approach, without eliminating the data in the training set, robust estimations of with-in-scatter matrix and between-class-scatter matrix are obtained using reconstructed data using M-estimator theory. A winsorization process is applied in the score space, which eliminates the effects of outliers in the original data in the sense of maximum likelihood estimation. The robust estimator used in this work is based on the Generalised T distribution, which can adaptively transform the data to eliminate the effects of the outliers in the original data (Wang et. al. 2003, Wang et. al., 2004). Consequently, a more accurate model is obtained and this procedure is optimal in the sense of minimising the number of misclassifications for process fault diagnosis.

2. Process Fault Diagnosis Using Discriminant Analysis 2.1 Discriminant analysis Let the training data for all faulty classes be stacked into a n by m matrix X ~ 9~..... , where n is the observation number and m is the variable number. The within-classscatter matrices S,,, and the between-class-scatter matrix S b contain all the basic information about the relationship within the groups and between them (Russell et. al. 2000). The FDA can be obtained by solving the generalized eigenvalue problem: Sbu k = 2~Swu k , where 2 k indicates the degree of overall separation among the classes by projecting the data onto new coordinate system represented by u;. After the above process, FDA decomposes the observation X ~ 9~"×m as (1)

X "-- T U T : £ ti~Ti i:1

2.2 Process fault diagnosis based on FDA After projecting data onto the discriminant function subspace, the data of different groups will cluster around their centroids. The objective of fault diagnosis is to assign the on-line out-of-control observations to the most closely related fault classes using classification techniques. An intuitive means of classification is to measure the distances from the individual case to each of the group centroids and classify the case into the closest group. Considering the fact that, in the chemical engineering measurements there are correlated variables, different measurement units, and different standard deviations, the concept of distance needs to be well defined. A generalized distance measure is introduced (Mahalanobis distance): O2(xi [ G, )=(x, - Y,

)vk-l(xi - Xk) T ,

where

1119

D2(x, I G~_) is the squared distance from a specific case x; to 2~, the centroid of group k, where V/, is the sample covariance matrix of group k. After calculating D 2 for each group, one would classify the case into the group with the smallest D 2 , that group is the one in which the typical profile on the discriminating variables most closely resembles the profile of this case. By classifying a case into the closest group according to D -~, one is implicitly assigning it into the group for which it has the highest probability of belonging. If one assumes that every case must belong to one of the groups, one can compute a probability of group membership for each group: P(GI, :"i)= P(xi G k / ~ P ( x i

Gi). This is a posterior

probability; the classification on the largest of these values is also equivalent to using the smallest distance.

3. R o b u s t D i s c r i m i n a n t A n a l y s i s B a s e d on M - e s t i m a t e W i n s o r i z a t i o n The presence of outliers in the training data will result in deviations of discriminant function coefficients from the real ones, so that the coordinate system for data projection may be changed. Fault diagnosis based on this degraded model will inevitably increase the misclassification rate. A robust remedy procedure is proposed here, to reduce the effects of outliers in the training data. After implementing FDA, the outliers in the original data X c 9~...... can manifest themselves in the score space. By recurrently winsorizing the scores and replacing them with suitable values, it is possible to detect multivariate outliers and replace them by values which conform to the correlation structure in the data.

3.1 Winsorization Consider the linear regression problem: y = f ( X , O ) + e ,

where: y is a n×l vector of

dependent variables, X is a n xm matrix of independent variables, and 0 is a p xl vector of parameters, e is a n xl vector of model error or residual. An estimation of parameter 0 (t~) can be obtained by optimization or least squares method. With the parameter

t}

estimated,

the

prediction

or

estimation

of

the

dependent

variable y i ( i - 1 ..... n) is given by ; ' i - If(x,, t~) and the residual is given by r~ = y , - ;,,. In the winsorization process, the variable ),~ is transformed using pseudo observation according to specified M-estimates, which characterizes the residual distribution. The normal assumption of residual data will result in poor performance of winsorization. In this work, we will fit the residual data to a more flexible distribution, i.e. the generalized T distribution, which can accommodate the shapes of most distributions one meets in practice, and then winsorize the variable y, using its corresponding influence function.

3.2 Robust discriminant analysis based on M-estimate winsorization The proposed robust estimator for FDA modelling is based on the assumption that the data in the score space follow the generalized T distribution (GT) (Wang and Romagnoli, 2003), which has the flexibility to accommodate various distributional shapes:

1120 P

f~r(u,'o,p,q)= 2crq,/PB(1/p,q)(1+ i,l,~/qo.,~)~+,,,~

-oo < .
(2)

where: u is the argument, a, p, q are distributional parameters, a corresponds to the standard deviation, p and q are parameters corresponding to the shape of distribution. This density is symmetric about zero, uni-modal, and suitable to describe the error characteristics in most cases. By choosing different values of p and q , the GT distribution will accommodate the real shape of the error distribution. The tail behaviour and other characteristics of the distribution depend upon these two distributional parameters, which can be estimated from the data (Wang et. al., 2003). The robustness of the estimator, based on a GT distribution, can be discussed by investigating its influence function (~,), which is given by

~(u,o,p,q) = (pq + ,)sign(u)lulq-'//(qa " + ul")

(3)

The technique of winsorization will be used in FDA to eliminate the effects of outliers in the following way. The data value y in score space can be transformed into a new value y"' by winsorization. By doing this, the large values exhibited as outliers in the original data set will be brought closer to the other observations after they are transformed fi~om the score space back to the original data space according Eq. (1). A new FDA model is obtained using the new data set. This process is carried out iteratively until there is not much change in the discriminant function coefficient.

4. Case study The proposed robust FDA (RFDA) strategy is applied to a case study of a pilot-scale setting containing two CSTRs, a mixer and a number of heat exchangers (Wang et. al., 2004). A process flowsheet is presented in Figure 1. The total number of measurement variables in this study is 27, including 12 temperature variables, 11 flowrate variables and 4 level variables. Plant data are combined with simulations to generate data with different distributions and outliers. This architecture is used to generate data under normal and faulty conditions. To investigate the proficiency and performance of the proposed robust approach RFDA compared to the conventional FDA (CFDA), training data that consist of three faulty classes are generated when the plant is running under three different faulty conditions, and the data are contaminated with outliers as well as

~

~" ~'"M~'~r:~, • ,'~'~¢,...........~............" ~* "*," '~:~v......... ~", " "-:~ L""~A~" ~, "~ '~v " ~- °~";'--~ " ~,--: i

i

Figure 1. Two CSTR's Flowsheet

Figure 2. Corrupted Training Data (Class 1." Sample 1-150; Class 2." Sample 151-300; Class 3." Sample 301-450)

1121 I:eult~ bUllS nelll,ln

6O0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

SO0

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I

fi15

o

~

too

I~

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~,~

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Figure 3. Uncorrupted Training Data (Class 1" Sample 1-150," Class 2. Sample 151-300; Class 3. Sample 301-450)

m

t

~

Figure 4. The projections Of training data (without outliers) onto the first two loading vectors using CFDA.

normal noise (10% noise) as shown in Figure 2. The training data without outliers are also plotted for comparison (Figure 3). For this corrupted training data set in Figure 2, both CFDA and RFDA are applied to build the model. The calculation results show that different FDA models are obtained by these two different approaches. For the same number of discriminant function retained (for example, 2 in this study), the different discriminating powers of the functions are presented in the two approaches, with the ones in RFDA having larger discriminating power than the CFDA one. This can be illustrated by investigating the eigenvalues from these two approaches tabulated in Table 1. It is custom in FDA that the nonzero eigenvalues are presented in the order of descending magnitude, and the size of the eigenvalue is related to the discriminating power of that function: the larger the eigenvalue, the greater the discrimination. From the table one can imagine that RFDA gives better separation of the faulty groups than CFDA, because the eigenvalues from RFDA are much larger than that from CFDA. By projecting the training data to the reduced discriminant function subspace, one can easily visualize the separation degrees of the approaches. Figure 4 shows the projections of training data (without outliers) for three faulty classes onto the first two loading vectors using CFDA. One can see that there are three clusters of data, which are representing three different faulty groups. The centroids are represented by the cross signs inside the circles. However, when the training data are contaminated with outliers (data in Figure 2), the projected data using CFDA will widely spread in the reduced subspace and there are great overlapping between the group regions (Figure 5). This indicates that the outliers in the training set have a great influence on the FDA model and the misclassification rate based on the less accurate model will inevitably increase. Using RFDA, to the corrupted data set, will reduce the effects of the outliers and makes the model close to the real one. Figure 6 illustrates the projection of training data using RFDA. From the figure, one can see that faulty groups are well separated and the locations and the ranges of clusters are nearly the same as the case when there are no contaminations and CFDA is used (comparing Figure 4). The rationale behind this is that the robust winsorization process in the discriminant functions subspace brings the spread data, those which manifest outliers in the original data space, to the centroids of the clusters, so that this will eliminate the effects of outliers and better model is expected. The misclassification rates of these two approaches are reported in Table 2 when they are used for fault diagnosis using 150 on-line fresh data in each group. From

1122 the table one can see that diagnosis, using CFDA gives a large misclassification rate, while diagnosis based on RFDA has similar misclassification rate with the situation where the model is built by CFDA using uncorrupted data.

5. C o n c l u s i o n s A robust FDA modelling approach (RFDA) based on winsorization in score space using adaptive robust estimator was developed and presented. The effects of outliers in the training data can be eliminated by the method while the effectiveness as well as the robustness is retained by using GT-like estimator. It was shown that the proposed method can obtain a more accurate model when the normal assumption is violated in the training data. Process fault diagnosis by RFDA has better performance than that of the conventional FDA, resulting less misclassification rate. "~ ................... '..................... i ~ ~ ~

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Figure 6. The projections of training data (with outliers) onto the.first two loading vectors using RFDA. Table

eigenvalue)

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CFDA(without outliers) 0.033

References Chiang, L. H., M. E. Kotanchek and A. K. Kordon (2004), "Fault diagnosis based on Fisher discriminate analysis and support vector machines", Comp. & Chem. Eng., 28, 8, 1389-1401 Devlin S. J., Guanadesikan, R. and Kettenring, J. R. (1981), "Robust Estimation of Dispersion matrices and principal components", J. of Amer. Stats. Asso. 76, 354-362 Hoo, K.A., K.J. Tvarlapati, M.J..Piovoso and R. Hajare (2002), "A Method of Robust Multivariate Outliers Replacement", Comp. Chem. Eng., 26. 17-39 Russell, Evan L., L. H. Chiang and R. D. Braatz (2000), "Data-driven Techniques for Fault Detection and Diagnosis in Chemical Processes", Springer.UK Wang, D. and J. A. Romagnoli (2003), "A Framework of Robust Data Reconciliation Based on a Generalized Objective Function", Ind. Eng. Chem. Res., Vol. 42, No. 13, pp. 3075-3084. Wang, D. and J. A. Romagnoli (2004), "A Robust PCA Modelling Method for Process Monitoring", 7th International Symposium on Advanced Control of Chemical Processes (ADCHEM), 11-14 Jan. 2004 Hong Kong, China, 417-422. Wang, D. and J. A. Romagnoli (2004), "Robust Multi-Scale Principal Components Analysis with Applications to Process Monitoring", J. of Process Control. In process

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1123

Learning in Intelligent Systems for Process Safety Analysis Chunhua Zhao, Venkat Venkatasubramanian* {chunhua, venkat} @ecn.purdue.edu School of Chemical Engineering Purdue University West Lafayette, IN, USA

Abstract Process safety analysis is necessary for analyzing and assessing in detail the inherent hazards in chemical processes. We have developed a tool (called PHASuite) to assist experts conducting process safety analysis. PHA is knowledge intensive, and the analysis capacity and quality of PHASuite depend exclusively on the quality of domain knowledge. It is, however, impossible and impractical to encode all kinds of knowledge into the knowledge base during development phase of PHASuite. Thus, the major aim of this work is to address the important practical learning needs. The learning-fromexperience strategy using case-based reasoning methodologies and learning from data using Bayesian learning, are investigated.

Keywords: Process safety, Automated process safety analysis, Intelligent systems, Machine learning, Case-based reasoning, Bayesian learning

1. Introduction Occupational safety and health are very important issues in process industries. As modern chemical plants have become large and extremely complex, it has become very difficult to analyze and assess in detail the inherent hazards in the plants, to effectively and safely manage changes, to perform maintenance safely, to better control of abnormal events online, and to effectively train operators. PHA review is considered as one of the most important safety related activities within the OSHA PSM regulation framework. For chemical process plants, Hazard and Operability (HAZOP) analysis is the most commonly practiced PHA methodology (Kletz, 1999). HAZOP analysis is the study of systematically identifying every conceivable deviation from normal plant operation, and finding all the possible abnormal causes and the adverse hazardous consequences of those deviations. While HAZOP analysis is a thorough, systematic and successful procedure, it is also a difficult, labor-intensive and time-consuming process requiring weeks or months of effort by several human experts. A software system, PHASuite (Process Hazards Analysis Suite, Zhao, 2002) has been developed to assist experts conducting PHA. The most important components in PHASuite are: (1) facilities for entering or gathering from other resources, the information necessary for the analysis; (2) creating a proper representation suitable for Author to whom correspondence should be addressed: [email protected]

1124 automated analysis based on the process information; (3) knowledge for safety analysis, wrapped in models, to model the process; (4) reasoning engine, consisting of the control knowledge which uses the knowledge to perform analysis on the representation of the process; (5) result management facilities for user reviewing the results generated from analysis.

2. Why Learning? Consider the following scenario: when analyzing a particular process, after process information is entered into PHASuite, the reasoning engine is invoked to analyze the process using the safety knowledge stored in the models, and results are presented for users reviewing. Users may find some of the results are not appropriate for this particular process. Users may also want to add or modify some of the results. This is to be expected given the generic models in PHASuite. Without proper mechanism to incorporate this kind of knowledge based on users feedback, if similar situation arises later when analyzing another process, PHASuite would generate similar inappropriate results and users would have to make the same changes to the results again. The mechanism of enabling software programs improving automatically through experience is the research area of machine learning (Mitchell, 1997). The aim of this work is to explore the machine learning methodologies, and investigate how to apply these methodologies in PHASuite, given the prior knowledge in the models. Besides the user feedback, process historical data, which contains real-world information on the relations between process variables, is another resource of learning. The reminder of this paper is organized as follows. Learning from experience using case-based learning methodology is discussed in next section. Learning from data using Bayesian learning is briefly discussed in Section 4. And finally Section 5 gives a conclusion and outlook into future work.

3. Case-Based Learning HAZOP analysis performed by human experts depends largely on their experience. Experience plays two important roles here. Firstly experience contributes to refinement and modification of reasoning process. Successful experience is solidified into causal relationships between process variables and rules for cause/consequence analysis. Experience's second role is equally important. Experience helps analysis of new processes by recalling similar situation encountered during earlier HAZOP analyses. Case-based reasoning techniques provide a formal way to organize the different kinds of experience into a formally organized knowledge base, which is easy to access, easy to modify, and easy to expand. In case-based reasoning, new problems are solved by retrieving and adapting solutions of similar problems encountered in the past. Once a new solution is created, it can be stored in memory for potential reuse in future. Thus, learning capability based on CBR makes it possible for PHASuite to organize its 'experience' obtained from previous analysis, and to reuse such experience to improve quality of analysis on new processes.

1125

All CBR methods have similar operations. From the processes point of view, the major steps in CBR are illustrated in Figure 1 (Aamodt and Plaza, 1994). These steps are: (1) Retrieve the most similar case or cases; (2) Reuse the information and knowledge in those cases to solve the problem; (3) Revise the proposed solution; and (4) Retain the parts of this experience likely to be useful for future problem solving. Accordingly, there are five major challenges in order to apply CBR to solve real problems, including case representation, retrieval methods, reuse methods, revision methods, and retain methods. A very important feature of case based reasoning is its coupling to learning. It enables sustained learning by updating the case base after a problem has been solved. When a problem is successfully solved, the experience is retained in order to solve similar problems in the future. When an attempt to solve a problem fails, the reason for the failure can be identified and remembered in order to avoid the same mistake in the future. "~"';.22 <~;+''~

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In this work, the safety models for operations and equipments are represented as cases. The features that are used to index operation models are: Function type; Subfunction; Physical properties of the processing materials, with values liquid, gas, solid; Processing conditions: Pressure, with values of high, low, normal, or Temperature, with values of high, low, normal; Components (equipments) and the corresponding process variables. The types of functions for device can be divided into: ToMake, ToMaintain, ToPrevent, ToControl (Chandrasekaran, 1994). And for operations, where the functionality is defined on the materials or substance, the functions may be divided into the following types: ToMake, such as reaction related operations; ToSeparate, such as separation related operations; ToMaintain, such as hold; ToMove, such as Transfer; ToChange, such as heat, cool; ToClean: clean, purge; etc. Case retrieval is one of the main steps when selecting models from knowledge base. The task includes selection of candidate models and ordering of candidate models based on their similarity to the current situation. The process to be analyzed is first assessed and the features that are used to index the models are determined. For example, for charge operation, which needs an operation model with function ToCharge, and the things to be

1126

charged are amount of materials, so the generic add material is located. The specific models are determined by process information. Here the index feature is physical state of material added. So the process information about the material added is assessed. If the material added contains solid material, load model is selected. This process is shown in Figure 2. If the functional or structure-behavior specification of the desired case and a stored case match at least partially, then the stored case is judged as potentially useful and is selected as a candidate case. For example, consider a model to be selected for a tank, whose component list contains agitator. However, after searching through the knowledge base, there is no index feature for a component agitator. The closest model, which is a model for a tank without an agitator, is selected as the candidate. ToCharge

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Retrieved operation and equipment models are analyzed to see if they are suitable for the present situation. Adequate modification methods are applied to those models if modification is necessary before they are used. The modifications which can be made to the model include: (1) Process variables: add, delete; (2) Causal relations: modify, delete, add; (3) Rules for cause/consequences: modify, delete, add; (4) Rules for digraph propagation: modify, add. Case modification starts after the easiest to adapt candidate model is selected from the ordered set of candidate models. Though this system supplies aids to this modification task, user interaction is heavily involved, which can be called as "on-site model modification". The aids supported by this system include: commonsense knowledge, and rule-guided repair. Considering the tank example described in last section, when a new component is present in the tank, commonsense knowledge tells that a new process variable should be added to the model to represent the effect of this new component, in the tank example, a process variable agitation_speed is added to the model. The relations between this new added variable and other variables should be decided. The system searches the knowledge base to see if there is index for component agitator and finds the corresponding model. Analysis is then carried out to find out the part of the model which gives information which may help in the construction of relations between agitation_speed and other variables. Similarly, this approach helps modifications of other parts of the model. This corresponds to recalling the experience of only those parts which are useful for the new situation. In the implementation of this module, knowledge builder will be called up for

1127 the "on-site model construction". Further research on this topic will help to reduce the involvement of user. When a new case is created and added into case base, a proper index path needs to be built to store the case into the right position. In most circumstances, the newly added case should have similar index path as the model from which it is created. But new index feature may have to be added to the index path and another depth level may be added to the path. Considering the example of tank, since the agitator is a component, so only index feature needs to be added, without changes to the index path. By changing the index structure and adding the newly created model to the knowledge base, the model can be selected next time when a similar situation is encountered.

4. Bayesian Learning Current models in PHASuite are deterministic models. Consider the partial model of Filtration operation shown in Figure 3. When analyzing the deviation of high duration_ofoperatioH, PHASuite concludes that separation_extent is high. However, the probability of duration_ofoperaiton is high and separation_extent is high given duration_of operation is high, is not analyzed. We argue that process historical data, contain real-world information on relations between process variables. So the problem is how can PHASuite learn from the process historical data, and how to combine prior knowledge in PHASuit with the data. The causal models in PHASuite can be mapped to Bayesian Belief Network (BBN) (Mitchell, 1997) in a straightforward fashion. Similar to the models in PHASuite, BBN is a directed acyclic graph, consisting of nodes which represent variables, and arcs to represent assertion that a variable is conditionally independent of its non-descendants (given immediate predecessors). Direction of the arc represents causality. BBN describes the joint probability distribution governing a set of variables by specifying conditional independence assumptions, and conditional probabilities. Conditional probability table for each variable describes probability distribution for that variable given values of its immediate predecessors. A completely described BBN provides a complete description of the domain. Each entry in the joint probability distribution can be calculated from the information in the network. Since it is practically difficult to specify conditional probabilities for each variable in BBN manually, the solution is to learn the BBN from data. If assuming that network structure is given in advance and all network variables directly observable in each set of process data, learning conditional probability is straightforward by using na]ve Bayes classifier. After the BBN is successfully learned from process data, more detailed analysis such as risk assessment can be carried out by inference on the network, e.g. by calculating the P(cake_mass=low duration_of_operation=high). Moreover, with the probability information, it provides better diagnosis capability when using PHASuite real time for online fault diagnosis. When diagnosis of the possible cause of cake_mass=high, the

1128 probabilities of possible causes of duration_of_operation, pressure, and cloth_porosity are calculated, instead of only listing three deviations as equal probable causes for this problem using the deterministic models.

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~

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5. S u m m a r y and Future Research Plan In this work, possible machine learning methodologies that can be applied to PHASuite were investigated. Two learning sources are identified: experience from users feedback when using PHASuite conducting PHA, and process historical data which provide information for a probabilistic approach to inference. Case-based learning is discussed in details as well as its applications in PHASuite. Currently, model is considered as a case. Using cases to represent knowledge components other than models, and types of knowledge that are difficult to be modeled by relations between local process variables will be further studied. Case-based techniques are also useful to combine different PHA methodologies, such as HAZOP and What-If to improve the quality of analysis. Cases can also be used to represent past accidents to incorporate this experience into the knowledge base of PHASuite. Ontologies can be developed for the cases, and Semantic Web tools can be used to annotate the document based on the ontologies for knowledge representation and acquisition. Bayesian learning is introduced and discussed as a methodology to combine prior knowledge in the models with process data. The benefits of learning from data are also discussed. As next step, real process data will be gathered and the proposed methodologies will be tested. Based on that, efficient learning and inference algorithms will be identified to be incorporated in PHASuite.

References Aamodt, A. and E. Plaza (1994). AI Communications. 7(1): 39-59. Kletz, T. (1999). Hazop and Hazan: Identifying and Assessing Process Industry Hazards 4th Edition. The Institute of Chemical Engineers, Rugby England. Mitchell, T., (1997). Machine Learning. McGraw Hill. Ramakrishnan, R., J. Gehrke (1999). Database Management Systems. 2nd Edition. Zhao, C. (2002), "Knowledge Engineering Framework for Automated HAZOP Analysis", Ph.D Thesis, Purdue University, West Lafayette, IN.

Acknowledgements This project is supported by University of Cincinnati Occupational Health and Safety Education and Research Center Pilot Research Training Program.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1129

Multivariate Decision Trees for the Interrogation of Bioprocess Data Kathryn Kipling, Gary Montague, Elaine Martin, Julian Morris School of Chemical Engineering and Advanced Material, University of Newcastle, Newcastle upon Tyne, NE1 7RU, United Kingdom

Abstract This paper introduces a method for analysing correlated process data to extract useful information with multivariate decision trees. The techniques have been applied to a bioprocess data set and have been shown to provide insight into the causes of process variation. The differences between the univariate and multivariate methods are highlighted and the tree interpretations are discussed. It is observed that there is very little difference in the classification abilities of the tree types from a prediction of the outcome perspective but the information from the multivariate trees is more informative with regard to cause of deviation rather than simply identifying the observed effects.

Keywords: multivariate decision trees; correlated data; bioprocess data 1. Introduction Effective data analysis is key to understanding the causes of variation within process operation. Extracting information from continuous process operation is challenging but batch processes raise further complications. Batch processes are highly interdependent systems and the relationships between variables is an important consideration in data analysis. However, when analysing bioprocess data these relationships are often not considered although they can contribute critical information to data interpretation. Ignoring the interdependencies can lead to unnecessarily complex and possibly incorrect conclusions being drawn from the data. Multivariate statistics provides techniques for analysing dependent and independent variables that are correlated to each other to varying degrees. The techniques that are considered under the banner of multivariate statistics include: canonical correlation, multiway frequency analysis, analysis of covariance, discriminant analysis, principal component analysis (PCA) and partial least squares (PLS). The commonly used techniques are PCA (Francis and Wills, 1999) and PLS (Wold, 1985). Decision trees are a commonly used technique for data analysis / mining and rule induction. In its simplest form, the concept allows the approximation of a discrete valued target function through splitting the data based on information measures and this is presented in a tree structure. It is widely used for inductive inference and the types of applications that have been investigated using decision trees include: the increasing chemical process yield in nuclear power plants by assessing the quality of the pellets (Langley and Simon, 1995); classification of celestial objects (Fayyad et al., 1995);

1130 improving oil and gas separation by suggesting separation vessel dimensions (Guilfoyle, 1986) and making credit decisions (Michie, 1989). There are many algorithms that can be used to perform a decision tree analysis and the choice of algorithm depends greatly upon the application and the type of data that is to be interrogated. It is not the aim of this paper to discuss the relative merits of one technique over another but comparison studies are available in the literature (Lira et al., 2000). The algorithms that have been applied or adapted in this work are ID3 (Quinlan, 1986) and CART (Breiman et al., 1984). These are commonly used techniques that are well understood and are adaptable for multivariate techniques. By using such methods the interpretation of results is simplified and the techniques used are explainable. There are other methods available for classification of a data set and discriminant analysis is one such technique. Here a model is built from a set of training data to form a relationship between the input variables and the target variable. This can then be tested on an unseen data set to verify its ability to correctly classify the data. The main differences between this technique and a multivariate approach is that the models are formed through multivariate linear regression rather than using a method that orthogonalises the data to create independent variables. Orthogonalisation is a critical transformation for information extraction.

2. Multivariate Decision Trees The concept of a multivariate decision tree has been discussed in the literature. Larson and Speckman (2002) considered the use of multivariate regression trees in ecology for the analysis of plant abundance data. They conclude that the resultant trees extract some of the important features that distinguish where species occur. These techniques and other literature (Brodley and Utgoff, 1992) consider the concept of a multivariate response and use methods that delineate between classes in the output. However, there is little consideration given to the idea that the predictor variables may be related and the correlation between variables may be important. This paper discusses these topics. The first method considered was the removal of the correlation between the predictor variables to provide an independent set for analysis. Here the data was pre-processed to remove any missing data or anomalous values, then the data was analysed using the PCA technique. The resultant principal components were used as the inputs into the decision tree program. To assess the results the loadings plots are required: if a variable has a large absolute loading value then it is considered to be influential to the principal component and is a key decision making variable in the tree. The second technique uses the concept of PLS to relate the input values to the outcome to force a significant link between the variables and more accurately assess which variables influence the outcome. Initially the technique is similar to the pre-processed decision tree; the data is analysed using the PLS approach and the resultant information used to feed into the decision tree program. At the end of an iteration the error matrix is considered. The information contained in the errors is unmodelled hence at the next iteration it is this data that is analysed. The error matrix becomes the new data set and the process is repeated until there are no errors or there are no samples to be classified. The split methods that are used to interpret the outcome are the Gini index and entropy technique. There are many techniques that exist and these are discussed in Mingers,

1131 (1989). Many of these methods are based in univariate statistics but since the attributes used in the decision tree algorithm are independent of each other then these are reliable methods to use. Other strategies do exist and have been used in multivariate response decision trees. These include linear machines (Duda and Hart, 1973), the mean structure of the data set and the covariance structure of the data set (Segal, 1992). Since these methods are considered for multivariate response trees they are not discussed here but they do form the basis of a possible extension to the work.

3. Data Analysis The data that was analysed using these techniques was taken from an antibiotic fermentation. The data comprised seed, final stage and biochemical data. Due to the problems of using time series batch data for analysis, point values were taken from the data and used as indicators of the process behaviour. These point values are maxima, minima, time values and rates of change in variable values. In total there were 36 predictor variables and 1 target variable. This target variable is an indicator of the quality of the batch and is classed as "good" or "poor". For comparison purposes the data was analysed using the simple univariate tree. The data that was used for training comprised 66% of the total number of batches and was chosen based on the extremities of the variables values: some of the batches that were chosen exhibited the maximum and minimum values for a variable while other batches were more representative of the whole set. This training set was used for all three tree types. The remaining 34% of the available data was used for validation. The data was analysed using PCA and 9 principal components were retained describing 72% of the data variation. The tree was then built using the CART technique (Breiman et al., 1984) and was trained using the same 66% of the available batches as defined above.The iterative decision tree technique was used on the same 66% of the batches for training. The iterative method uses the ID3 algorithm (Quinlan, 1986). In this technique, the variables are all continuous and to split these values at appropriate points the method described by Fayyad and Irani (1992) is used.

4. Results 4.1 The univariate decision tree Figure 1 shows the univariate decision tree pertaining to the training data. This tree indicates that a lower value of variable 27 suggest a better batch and a higher value of variable 15 produces a poorer batch. The information contained in this tree and Table 1 shows that it can accurately classify the unseen data set although the limited number of batches in this set means that some of the branches are not evaluated. ~Variable 27 1 l Split value -0.00316 I I __ I 1 I SplitVariable15 Good value 430.33 1 I _ I I ooo0

oor

Figure 1- Univariate decision tree for bioprocess data

1132 Table 1- Accuracy of the univariate decision tree

Leaf Number 1 2 3

Number of Samples 12 0 5

Number of Samples Correctly Classified ll N/A 2

% Accuracy 92 N/A 40

4.2 Pre-processed decision tree Figure 2 shows the decision tree produced using the PCA pre-processing technique. It can be that PC1 is the key discriminator of the data for the training set. The loadings plot for PC 1 indicates that variables 6, 18, 26 and 27 contribute most to the variation.

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Larger values of these variables suggest that there is a higher probability of following the right hand branch and ending in a good quality product. However, smaller values of these variables will force the decisions down the left hand branch and the discrimination is then made by considering PC7. Table 2 presents the results of the validation analysis showing that the root node was successful at separating the good from poor batches but again there are issues with the limited number of validation batches. The results in Table 2 are similar to those of the univariate tree but this multivariate approach provides greater insight into the process and which combinations of variables are influential. Table 2-Accuracy o f the pre-processed decision tree Leaf Number of Number of Samples Correctly Number Samples Classified 1 0 N/A 2 3 1 3 14 12

% Accuracy N/A 33 86

4.3 lterative decision tree The iterative approach was used to produce the tree shown in Figure 3. All of the decision nodes of the tree use the first latent variable of the iteration. This is not unexpected since the outcome variable, the quality, has been considered throughout the

1133 process of building the model. Considering iteration l, it can be seen from Figure 3 that variable 18, 26 and 27 contribute most to the model and for iteration 2 variables 10, 21, 22, 33 and 35 show the greatest values in the loadings and for iteration 3 variables 5, 11, 14, 20, 28, 32, and 33 are the most important in the model. Hence for decision 1, if the values of variables 18, 26 and 27 are large then the batch has a greater probability of having a low quality. Similarly for iteration 2, higher values of the key variables lead to poorer batches. Good batches are produced when the values of the key variables in iteration 3 are low. The tree was tested using an unseen data set. Lo~,d,,,~j~,.,,en,v.,,.~,,,,,,,e,a,,on, .....

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Table 3 shows the results of the validation of the iterative decision tree. These results are comparable with both the univariate and pre-processed decision trees but the process understanding that the multivariate approach provides is much more useful to the end user than the univariate tree. The concept of using the errors as input to the next iteration of the tree means that all of the available information can be used in the development of the tree improving the information that is available to the end user.

5. Conclusions This paper has shown that where there are relationships between variables it is beneficial from a process understanding perspective to consider combinations of these variables to eliminate the correlation and assist in the decision making process. The technique suggested here is to pre-process the data using a multivariate technique such as principal components analysis and use the result of this analysis as the input into the

1134 decision tree. The use of such a technique orthogonalises the data and as a result the data fed into the tree is independent of the other variables. The second method described first produces a model relating the input to the output and then using this model, where again the inputs are orthogonal to each other, determines a decision node. The residuals from the model are then used to build another model and another node until the residuals are too small to be considered significant. Three decision tree techniques have been compared on the same data sample and it has been shown that the multivariate techniques are comparable to the univariate method in classification ability but it is important to appreciate that decisions are rarely taken in isolation and that many variables are considered in parallel when interpreting data. The multivariate tree techniques give the user this ability and consider which variables are most influential on the outcome and why this is the case. The results of the analysis indicate that for the technique to be successful there need to be many samples for training and testing and although this is a common disadvantage of using decision tree methods for data mining, the results of the validation presented here are promising.

6. References Breiman, L., J. Freidman, R. Olshen and C. Stone (1984). Classification and Regression Trees. California, Wadsworth International. Brodley, C. E. and P. E. Utgoff (1992). Multivariate Decision Trees. Amherst, University of Massachusetts: COINS Technical Report 92-82 Duda, R. O. and P. E. Hart (1973). Pattern Classification and Scene Analysis. New York, Wileyinterscience. Fayyad, U. M. and K. B. Irani (1992). "On the Handling of Continuous-Valued Attributes in Decision Tree Generation." Machine Learning 8(1): 87-102 Fayyad, U., P. Smyth, N. Weir and Djorgovski (1995). "Automated Analysis of Image Databases: results, progress and challenges." Journal of Intelligent Information Systems 4:1-19 Francis, P. J. and B. J. Wills (1999). Introduction to Principal Components Analysis. in Quasars and Cosmology. eds: G.J.Ferland and J.A.Baldwin. San Fransico, Astronomical Society of the Pacific. CS-162. Guilfoyle, C. (1986). Ten Minutes to Lay the Foundations. Proceedings of Expert Systems User, August, 16-19. Langley, P. and H. Simon, A (1995). "Applications of Machine Learning and Rule Induction." Communications of ACM 38:54-64 Larson, D. R. and P. L. Speckman (2002). Multivariate Regression Trees for Ananysis of Abundance Data. Columbia, University of Missouri: 21 Lim, T.-S., W.-Y. Loh and Y.-S. Shih (2000). "A Comparison of Prediction Accuracy, Complexity, and Training Time of Thirty-three Old and New Classifcation Algorithms." Machine Learning 40:203-229 Michie, D. (1989). Problems of Computer-Aided Concept Formation. in Applications of Expert Systems. eds: J. R. Quinlan. Wokingham, Addison-Wesley. 2. Mingers, J. (1989). "An Emprical Comparison of Selection Measures for Decision-Tree Induction." Machine Learning 3:319-342 Quinlan, J. R. (1986). "Induction of Decision Trees." Machine Learning 1(1): 81-106 Segal, M. R. (1992). "Tree-Structured Methods for Longitudinal Data." Journal of the American Statistical Association 87(418): 407-418 Wold, H. (1985). Partial Least Squares. in Encyclopaedia of Statistical Sciences. eds: S. Kotz and N. L. Johnson. New York, Wiley. 6: 581-591.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1135

On a New Definition of a Stochastic-based Accuracy Concept of Data Reconciliation-Based Estimators M. Bagajewicz University of Oklahoma 100 E. Boyd St., Norman OK 73019, USA

Abstract Traditionally, accuracy of an instrument is defined as the sum of the precision and the bias. Recently, this notion was generalized to estimators. However, the concept used a maximum undetected bias, as well as ignored the frequency of failures. In this paper the definition of accuracy is modified to include expected undetected biases and their frequency.

Keywords: Instrumentation Network Design, Data Reconciliation, Plant Monitoring. 1. Introduction Traditionally, accuracy of an instrument is defined as the sum of the precision and the bias (Miller, 1996). In a recent paper (Bagajewicz, 2004) this notion was generalized to estimators arguing that the accuracy of an estimator is the sum of the precision and the maximum induced bias. This maximum induced is the maximum value of the bias of the estimator used, that is, a result of a certain specific number of biases in the network which have not been detected. This lead to a definition of accuracy that is dependent on the number of biases chosen. Aside from many other shortcomings of the definition, two stand out as the most important: The definition has no time horizon associated to it, nor states anything about the frequency at which each sensor will fail, or the time it will take to repair it. In addition, the definition could be more realistic if expected bias, instead of maximum bias is used. In this paper, we review the definitions and discuss the results of a Montecarlo technique that can help determine an expected value of accuracy.

2. Background Accuracy was defined for individual measurements as the sum of the absolute value of the systematic error plus the standard deviation of the meter (Miller, 1996). Since the bias is usually not known, the definition has little practical value. Bagajewicz (2004) introduced a new definition of accuracy of an estimator (or software accuracy) defined as the sum of the maximum undetected induced bias plus the precision of the estimator:

1136 where

c~i ~i and (~'i are the accuracy, the maximum undetected induced bias and

the precision (square root ) of the estimator's variance Sii, respectively. In turn, the accuracy of the system can be defined in various ways, for example making an average of all accuracies or taking the maximum among them. Since this involves comparing the accuracy of measurements of different magnitude, relative values are recommended. The maximum undetected induced bias is obtained from the assumption that a particular gross error detection test is used. In the case of the maximum power measurement test, and under the assumption of one gross error being present in the system this value is given by"

(2)

g~p,1) __ z~ripl ) M a x [(jr _ s m ) i s ] Vs ~/-mss

where Z crit (p) is the critical value for the test at confidence level p, S is the variancecovariance matrix of the measurements and W = A r (ASA r)-lA (A is the incidence matrix). When a larger number of gross errors are present in the system, an optimisation model is needed. Thus, for each set T we obtain the maximum induced and undetected bias by solving the following problem: ~¢P) ( T ) - M a x (~crit,i -- Z ( S W ) i s Vs~T set

(~crit ~ "

s.t

Z

Wks(~cri', s

(3)

-- -- crit

VsET

Therefore, considering all possible combinations of bias locations, we write

~¢p,,T) _ Max 6~ p) (T)

(4) vr As it was mentioned above, this definition states what the accuracy of the system is, when and ifa certain number of gross errors are expected to take place. In other words,

it represents the worst case scenario and does not discuss the frequency of such scenario. We now discuss a new definition and how to obtain an expected value next

3. Stochastic Based Accuracy We define the stochastic based maximum induced biased as the sum over all possible nr biases of the expected fraction of time (Fn~) in which these biases are present.

gl

- Z

]

/7T

The formula assumes that a) when errors in a certain number of sensors occur they replace other existing set of undetected errors and that b) Sensors with detected errors are repaired instantaneously.

1137 Sensors have their own failure frequency, which is independent of what happens with other sensors. For example, the probability of one sensor failing at time t, when all sensors where functioning correctly between time zero and time t is ~ i - J ; ( t ) l - I [ 1 - f , . ( t ) ] , where f ( t ) i s the service reliability function of sensor / i f sensors are not repaired. When sensors are repaired, one can use availability and write

f~(t) = ri/(r~ + bt~ ), where ri is the repair rate and }_ti is the failure rate. The second issue, the repair time, is more problematic because it also affects the value of o- i , which becomes the residual precision during that period of time.

So, E[F,, ] can only be

estimated by identifying the probability of the state with the frequency of the state in the /

|

case of negligible repair time. However, when repair time is significant E[Fn~ ] i s more difficult to estimate and there are no expressions available. In addition, multiple gross errors do not arise from a simultaneous event, but rather from a gross error occurring and adding to an existing set of undetected gross errors. In addition, problem (3) assumes the worst case in which all will flag at first, but it does not say what will happen if some are eliminated. We now define the stochastic-based expected induced biased as the sum over all possible nT biases of the expected fraction of time (F,, T ) in which these biases are present. I1 T

To understand how the stochastic-based induced bias (and by extension, the stochasticbased accuracy) can be calculated. Assume that a system is bias free in the period [0, tl] and that sensor k fails at time t~. Thus, if the bias is not detected, then there is an expected induced bias that one can calculate as follows:

(k )]- El

- sw],

)dOk

where h(O k "~Sa,Ok) is the pdf of the bias q3a with mean value 8a and variance 9k" Note that we integrate over all values of 13a, but we only count absolute values, as the accuracy definition requires.

Thus, in between tl and the time of the next failure of

I-~(p 1) some sensor t2, the system has an accuracy given by °'i + E[6i ....ij~,(k)] •

In turn, if the bias is detected, the sensor is taken out of line for a duration of the repair time Ra. During this time (and assuming no new failure takes place), the system has no induced bias, but it has a lower precision, simply because the measurement is no longer used to perform data reconciliation. Thus, during repair time, the expectation of the accuracy due to detected biases is given by the residual precision~yiR ( k ) .

After a

period of time Ra. the accuracy returns to the normal value when no biases are present *'R

&i • Thus, in the interval [0, t2), the accuracy is given by [&i tl+ c~i ( k ) R k +°'i *(t2_

1138

t,. Rk)]/t2 when bias k is detected and [ o" i t,+ E[-~ ~,~,~de, ( k ) ] (t2_ t,)]/t2 when bias k is undetected. The expectation is then given by multiplying the undetected portion by the corresponding probability

(s)

P,,,,e,(k) - fa ~''' h(Ok "gk,Pk )dOk k,crit and the detected by its complement [ 1 -

P,,,d~, (k)].

Assume now that the bias in sensor k is undetected at t~ and another bias in some other sensor r occurs at h, which can be in turn detected or not detected. If it is undetected, then the expected induced bias is given by:

E[~f p,R)(k,r)] - ~k,crit ;r,cri, I[i__ SW]i k Ok + [I-- SW]iFOF{ ~k,crit ~r,cri!

(9)

h(Ok," ak,Ok )h(Or," a,.,9, )dOkdO,. where, for simplicity of presentation we have assumed that 6 k,crit and

6r,crit can be

used as integration limits. (in reality, the integration region is not a rectangle). We leave this detail for future work. In turn, if the error in sensor r is detected, then we assume that the induced bias remains. Quite clearly, the scenario shown is one of many, and while one is able to obtain the expected induced errors in each case, the problem of calculating the expected fraction of time in each state persists. Thus, we resort to Montecarlo simulations to assess this.

3.1 M o n t e c a r l o

simulations

Consider a scenario s, composed of a set of n, values of time (tl, t2,..., tns ) within the time horizon 7 ~. For each time ti, one considers a sample of one sensor failing with one of two conditions" its bias is detected or undetected. Sensors that have been biased between ti_l and ti and where undetected at ti, continue undetected. Thus, when bias in sensor k is detected, for the time between t~ and t~ +Rk we write

E[a i ]- cyi ( k ) + E

p,m, , 1,i-1 ' 12,~- , "" "~l mi,i-1

(10)

where the second term is the expected bias due to the presence of m~_l undetected errors. 1,i-1.

, ......

,.i-1

a,,~_,

a,,c,.,

v=l

(11)

1-Ih( O~, a~,p~ )dO~ v

For the interval

(t~+R~ ,ti+l), we write

r[ai ]- 6i + r[~i,undet(ll,i_l,12,i_ l ..... lmi.i_l ) ]

(12)

In turn, if the error was not detected, then we write ti+l, we write (13)

1139 The above formula is valid for k =~l,,i_ ~,v = 1.... m i ~ . Otherwise, the same formula is used, but k is removed from ~i(')...." ) (l 1 . i

1 '

l~_ . i

1 ' ....

l,,,i , i

1

)"

To obtain an average accuracy of the system in the horizon 74' and for the scenario s, the accuracy in each interval or sub-interval is multiplied by the duration of such interval and divided by the time horizon 74'. Finally all the values are added to obtain the expectation for that scenario. The final accuracy is obtained using the average of all scenarios. Finally, scenarios are sampled the following way. For each sensor a set of failure times is obtained by sampling the reliability function repeatedly and assuming that sensors are as good as new after repair (AGAN maintenance). Of these, undetectability is sampled using a pdf given by P,,,,d,,, ( k ) and its complement.

4. Example Consider the example of figure 1. Assume flowmeters with cy/=1, 2

and 3,

respectively. We also assume that the biases have zero mean and standard deviation p x =2, 4 and 6 respectively, failure rate of 0.025, 0.015, 0.005 (1/day) and repair time of 0.5, 2 and 1 day respectively. The system is barely redundant (Only one gross error can be determined, and when it is flagged by the measurement test, hardware inspection is needed to obtain its exact location. This is due to gross error equivalency (equivalency theory: Bagajewicz and Jiang, 1998).

S~

I

$3

r

Figure 1. Example

The problem was run with scenarios containing 20 event samples. A portion of one such sample is for example depicted in Table 1. Convergence is achieved very quickly (see figure 2) to a value of accuracy of 1.89. (The solid line is the average value). Comparatively the accuracy defined for maximum bias of one bias present is 6.30. This highlights the fact that using a maximum expected undetected bias is too conservative

5. Discussion and Conclusions The problems with an existing definition of accuracy have been highlighted and a new definition, which gives a more realistic value, has been presented. In addition a Montecarlo sampling technique was suggested to determine the value of the accuracy. Some shortcomings still remain: The expected value of existing undetected biases is determined using rectangular integration regions, when it is known these regions have other more complex forms. This can be addressed analytically somehow, but one can also resort to sample the bias sizes as well. All this is part of ongoing work.

1140 Table 1. Example of one scenario (Portion)

Time 15.6 43.6 62 90 100 115 150 160 170 185 189 193 208

Bias in sensor S1 S1 $2 $2 $2 S1 $3 S1 $2 $2 S1 S1 $2

Bias detected No No Yes Yes Yes Yes Yes Yes No No Yes No Yes

2.7

2.3

2.1-

1.9-

~.

1.5

.

0

20

.

.

40

.

60

80

Figure 2. Montecarlo Iterations convergence.

References Bagajewicz, M., 2004, On the Definition of Software Accuracy in Redundant Measurement Systems. To appear. AIChE J., (available at http://www, ou. edu/clas s/che- de sign/Unpub lished-p ap ers.htm). Bagajewicz M. and Q. Jiang. Gross Error Modelling and Detection in Plant Linear Dynamic Reconciliation. Computers and Chemical Engineering, 22, 12, 1789-1810 (1998). Miller R. W. Flow Measurement Engineering Handbook. McGraw Hill, (1996)

Acknowledgements Funding from the US-NSF, Grant CTS-0350501, is acknowledged.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) ~ 2005 Elsevier B.V. All rights reserved.

1141

The Integration of Process and Spectroscopic Data for Enhanced Knowledge Extraction in Batch Processes C. W. L. Wong a, R. E. A. Escott b, A. J. Morris a, E. B. Martin a* aCentre for Process Analytics and Control Technology School of Chemical Engineering and Advanced Materials University of Newcastle, Newcastle-upon-Tyne, NE1 7RU, UK bGlaxoSmithKline Chemical Development, Tonbridge, TN 11 9AN, UK

Abstract Batch process performance monitoring has been achieved primarily using process measurements with the extracted information being associated with the physical parameters of the process. More recently, there has been an increase in the implementation of process spectroscopic instrumentation in the processing industries. By integrating the process and spectroscopic measurements for multivariate statistical data modelling and analysis, it is conjectured that improved process understanding and fault diagnosis can be achieved. To evaluate this hypothesis, an investigation into combining process and spectral data using multiblock and multiresolution analysis is progressed. The results from the analysis of an experimental dataset demonstrate the improvements achievable in terms of performance monitoring and fault diagnosis.

Keywords: Multiblock; Multiresolution analysis; On-line monitoring; Batch processes. 1. Introduction Since the introduction of the Process Analytical Technology (PAT) initiative, companies in the processing industries are increasingly aware of the need to attain a detailed understanding of their processes and products. The goal of PAT is to build quality into the process and remove the final step of testing the final product, thereby achieving the ultimate goal of parametric release. To deliver against this objective, an enhanced understanding of the process and the product is required. One approach to realising this objective is through the implementation of on-line spectroscopic analysers. A second aspect is the need for on-line real time process performance monitoring. Traditionally batch process performance monitoring (Neogi and Schlags, 1998; Martin and Morris, 2002) has been performed primarily using process measurements with the extracted intbrmation being associated with the physical parameters and/or inferred chemical parameters of the process. More recently, there has been an increase in the use of process spectroscopic instrumentation for the monitoring of a process (Gurden et al., 2002). Spectroscopy provides real-time, high-quality chemically rich information, but in

Author to whom correspondence should be addressed: [email protected]

1142 most studies, the data is analysed independently of the process data. By integrating the process (physical state) and spectroscopic (chemical state) measurements for multivariate statistical data modelling and analysis, it is hypothesised that improved process understanding and fault diagnosis can be achieved. To evaluate this belief, an investigation into combining the two data forms using multiblock and multiresolution analysis is conducted. The results of the combined analysis are compared with those attained from separate analyses undertaken on the spectral and process data. A number of approaches to combining Principal Component Analysis (PCA) and Partial Least Squares (PLS) with wavelet analysis have been proposed (Bakshi, 1998). Current methods reported in the literature have involved the selection of an appropriate scale as the basis of the monitoring scheme after the application of the wavelet transformation or alternatively applying the projection method to the decomposed scales, complicating the interpretability of the final process representations. To address this level of complexity, multiblock analysis is considered. Multiblock methods can enhance the identification of the underlying relationships between several conceptually meaningful blocks thereby summarising the relevant information both between and within the blocks in a single representation. To demonstrate the potential of the developed methodology, process and UV-visible data from a batch mini-plant is considered.

2. Methodology for Data Integration In a typical batch production environment, process information and spectra are normally acquired in separate data historians thus dividing the data into two distinct data blocks. These two blocks are conceptually meaningful since the same object is measured but the description of the state differs. Two approaches are developed in the subsequent sections and compared for combining the process and spectral data.

2.1 Multiblock Method For the first approach, the spectroscopic and process data are integrated using multiblock analysis, more specifically consensus PCA (CPCA) (Westerhuis et al., 1998). Figure 1 provides a schematic of the proposed integrated on-line monitoring scheme. The process and spectral data are divided into two base blocks and CPCA is applied. More specifically a starting super score tr is selected as the first column for one of the blocks and this vector is regressed on both blocks to give block variable loadings. The block scores tb are then calculated and combined into a super block T. The super scores are then regressed on the super block to give the super weights of the block scores with the super weight being normalised to unit length and a new super score is calculated. The procedure is repeated until the super score converges. Both the super and block scores are then used for the monitoring of the performance of the process.

2.2 Multiresolution Analysis For the second approach, integration is performed as per the first approach but the spectral data is first pre-processed using wavelet analysis. Most data generated from chemical processes is inherently multiscale and multivariate in nature. Spectral data is no exception and usually comprises a large number of wavelengths thus the interpretation of such a large and complex data matrix requires advanced techniques to

1143 reduce the dimensionality and complexity of the problem. Wavelets have been proven to be a useful tool to denoise signals and extract multiscale components (Trygg and Wold, 1998; Teppola and Minkkinen, 2000).

Super Level

Super

/ Block T [

..i.~ .....................

kl k~

............................ 2::................

kl k2

-

I

Base Level ...................

Process

tl

Spectroscopic

Wavelet t: Coefficients

Figure 1. h~tegrated on-line monitoring scheme by CPCA

in the second approach, the spectral data is decomposed using the discrete wavelet transform with the original signal being recursively decomposed at a resolution differing by a factor of two from the previous step. During the decomposition, the smallest features (noise) are first extracted, resulting in an approximate signal. From this approximation, new features are extracted, resulting in an ever more coarse approximation. This continues until the signal has been approximated to the preselected level. The differences are stored as wavelet coefficients. If all wavelet coefficients are used, the original signal can be perfectly reconstructed. In Figure 1, the dotted section is included into the CPCA but not the spectroscopic block. The size of the dataset is significantly reduced however the details are retained with the multiscale components being extracted.

3. On-line Monitoring 3.1 Process Description A simple reaction of nitrobenzene hydrogenation to aniline is considered. Eight experiments were performed of which six batches formed the nominal data set. Seven process variables were recorded every second including reactor temperature, pressure, agitator, H_~ gas feed, jacket inlet and outlet temperatures and flow rate of heating fluid with the UV-Visible spectra being recorded every 30 seconds. Two batches with predefined process deviations were also run. The first of these, batch 7, was discharged with 10% less catalyst to simulate a charging problem and to simulate a series of temperature control problem. The second batch, batch 8, simulates a series of agitator speed and pressure loss problems. The changes reflect both a change to the process as well as to the chemistry. In the application, Daubechies-4 wavelet with five decomposition levels was chosen with the last level of wavelet coefficients being considered as the spectral block as opposed to the original spectra.

1144 3.2 Data Pre-preeessing One of the challenges of data integration is to time align the disparate data sets. The process measurements may be recorded with a sampling interval of seconds but the time frame for the spectroscopic measurements is typically larger. In this study to realise the more rapid detection of a fault, a sampling rate of ten seconds was selected, hence interpolation of the spectral data was necessary. Additional pre-processing of the UVVisible spectra was required since it exhibited a baseline shift therefore a baseline correction was applied to the spectroscopic data. Since the process and spectral data blocks are three-dimensional matrices, X (I x J x K), the first step is to unfold the data to a two-dimensional array. The approach of Nomikos and MacGregor (1994) was adopted resulting in a matrix of order (I x JK). Auto-scaling was then applied to the unfolded matrices for the removal of the mean trajectories. A weighing factor was also introduced at this stage to ensure the variance of each block was unity. The weighting factor to achieve this was 1/n 1/2 where n is the number of variables in a block. The next step was to re-arrange the matrices into a matrix of order (IK x J) to enable the application of the Wold et al. (1998) approach. By adopting this procedure the issue of unequal batch length monitoring and the need to consider how to handle on-line performance monitoring is reduced. CPCA is then applied to the preprocessed data blocks with the principal component scores being used for monitoring. 3.3 Results 3.3.1 Multiblock Approach The process and spectral block scores for the first principal component for batch 7 are shown in Figure 2a and 2b. The temperature control problem is observed from Figure 2a and verified using the contribution plot (Figure 3). It is expected that a slower reaction would occur when less catalyst is charged into the vessel thereby affecting the overall kinetics of the reaction. This effect is observed in Figure 2b (spectral block) where the trajectory is observed to be out of control throughout the whole process.

0

20

40

...... ~a) 60

80

100

120

140

0

20

40

60

80

....... oc~)

100

120

140

Figure 2. Block scores of principal component one. (a) Process," (b) Spectral

1

2

3

4

5

6

7

Figure 3. Contribution plot for the process block scores

Figure 4. Super scores for principal component one for batch 7

1145 The super scores of principal component one were interrogated. Figure 4 illustrates the advantages of the multi-block approach. It summarises the deviations from the process and spectral blocks. Figure 5 shows the super scores of principal component one for batch 8. This batch has mainly process disturbances as observed from the process block scores (Figure 6) since the spectral block scores (Figure 7) revealed no out-of-control signal. Most of the process disturbances are detected from the super scores however the agitator disturbance during the period 43 - 4 9 was not detected as the main source of failure (Figure 8). This result will be compared with the multiblock-wavelet approach.

/~,\

20

40

~0

80

100

120

140

120

~.~o

tl

Figure 5. Super scores of principal component one for batch 8

Figure 6. Process block scores of principal component one Scores

--

;;;s_

20

-

|0

2

6O 80 I1 for b l o c k 2

; 100

Contrlbuhon

plot of PC

1 at Time 43 to 49

-120

1,1Q

Figure 7. Spectral block scores of principal component one

1

2

3

4

5

6

•

Figure 8. Process block scores of principal component one

3.3.2 Multiblock- Wavelets" Approach

For the multiblock-wavelet pre-processing approach, the number of variables (wavelengths) for the spectral data was significantly reduced from the original number of wavelengths, i.e. 216 to 14 wavelet coefficients, resulting in the data being compressed 15-fold. However, the process features are retained as evidenced from the coefficients shown in Figure 9 for batch 8.

21

lO

.5 [ o

20

,1o

/

80

6o

100

120

14(J

0

~ 1

2

3

4

5

6

7

tl

Figure 9. Super scores of principal component one.for batch 8

Figure 10. Contribution plot for process block scores

Interrogating the super scores of principal component one, it was observed that a similar result is obtained. The focus is on the agitator disturbance during time period 43 to 49

1146 where it shows an out-of-control signal that was not observed from the multi-block analysis. The contribution plot of the process block scores (Figure 10) confirmed the finding that the fault was primarily due to the failure of the agitator (variable 3) which consequently affected the reactor pressure (variable 2) and H2 gas feed (variable 4). The approach has been shown to have improved fault detection capability.

4. Discussions and Conclusions The area of integrated data monitoring has become increasingly more important as increased amounts of data from different data structures are recorded. However, the extraction of information and hence knowledge from such combined data structures is limited. The development of an integrated framework can help in the understanding of the process more than that of an individual model. While further fault diagnosis is required, the integrated model allows tracking back to the base models thus to address the problem accordingly. More specifically in this paper, a successful application to data integration has been proposed where the chemical and physical information are incorporated into the model but interpretation is made simpler in a single representation. Multiblock and wavelet transformation are combined providing a powerful combination of dimensionality reduction and data compression. The correlation between blocks and the multiscale nature of data were also considered. The challenges of time alignment, data scaling and weighing between blocks were discussed.

References Neogi, D. and C. Schlags, 1998, Multivariate statistical analysis of an emulsion batch process, Industrial & Engineering Chemistry Research, 37, 3971. Martin, E. B. and A. J. Morris, 2002, Enhanced bio-manufacturing through advanced multivariate statistical technologies, Journal of Biotechnology, 99, 223. Gurden, S. P., J. A. Westerhuis and A. K. Smilde, 2002, Monitoring of batch processes using spectroscopy, AIChE Journal, 48, 2283. Bakshi, B. R., 1998, Multiscale PCA with application to multivariate statistical process monitoring, AIChE Journal, 44, 1596. Westerhuis, J. A., T. Kourti and J. F. MacGregor, 1998, Analysis of multiblock and hierarchical PCA and PLS models, Journal of Chemometrics, 12, 301. Trygg, J. and S. Wold, 1998, PLS regression on wavelet compressed NIR spectra, Chemometrics and Intelligent Laboratory Systems, 42, 209. Teppola, P. and P. Minkkinen, 2000, Wavelet-PLS regression models for both exploratory data analysis and process monitoring, Journal of Chemometrics, 14, 383. Nomikos, P. and J. MacGregor, 1994, Monitoring batch processes using multi-way principal component analysis, AIChE Journal, 40, 1361. Wold, S., N. Kettaneh, H. Friden and A. Holmberget, 1998, Modelling and diagnostics of batch processes and analogous kinetic experiments, Chemometrics and Intelligent Laboratory Systems, 44, 331.

Acknowledgements Chris Wong would like to acknowledge the EPSRC, GlaxoSmithKline, the UK ORS Scheme and CPACT for financial support of his PhD.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1147

A Systematic Approach for Soft Sensor Development Bao Lin a, Bodil Recke b, Philippe Renaudat b, Jorgen Knudsen b, Sten Bay Jorgensen a* a

CAPEC, Department of Chemical Engineering, DTU Lyngby 2800, Denmark b FLS Automation Valby 2500, Denmark

Abstract This paper presents a systematic approach for development of a data-driven soft sensor using robust statistical technique. Data preprocessing procedures are described in detail. First, a template is defined based on a key process variable to handle missing data related to severe operation interruption. Second, a univariate, followed by a multivariate principal component analysis (PCA) approach, is used to detecting outlying observations. Then, robust regression techniques are employed to derive an inferential model. The proposed methodology is applied to a cement kiln system for realtime estimation of free lime, demonstrating improved performance over a standard multivariate approach.

Keywords: Multivariate regression analysis, Soft sensing, Robust statistics

1. Introduction Soft sensors have been developed as supplement to online instrument measurements for process monitoring and control. Early work on soft sensor development assumed that a process model was available. The inferential model is developed using Kalman filter (Joseph and Brosilow, 1978). In case the process mechanisms are not well understood, empirical models, such as neural networks (Qin and McAvoy, 1992; Radhakrishnan and Mohamed, 2000), multivariate statistical methods may be used to derive the regression model (Kresta et al., 1994; Park and Han, 2000; Zhao, 2003). A model-based soft sensor can be derived if a first principle model (FPM) describes the process sufficiently accurately. However, modern measurement techniques enable a large amount of operating data to be collected and stored, thereby rendering data-driven soft sensor development a viable alternative. Multivariate regression techniques have been extensively employed to develop datadriven soft sensors. Principal component regression (PCR) and partial least squares (PLS) address collinearity issues of process data by projecting the original process variables into a smaller number of orthogonal latent variables. Process measurements are often contaminated with data points that deviate significantly from the real values due to human errors, instrument failure or changes of operating conditions. Since Author to whom correspondence should be addressed: [email protected]

1148 outlying observations may seriously bias a regression model, robust statistical approaches have been developed to provide a reliable model in the presence of abnormal observations. This paper presents a systematic approach for building a soft sensor. The proposed method using robust statistical techniques is applied to the estimation of free lime for cement kilns. The paper is organized as follows. Section 2 describes data preprocessing which includes both univariate and multivariate approaches to detect outlying observations. The robust PCR and PLS approaches are presented in section 3, followed by the illustrative application on development of a free lime soft sensor for a cement kiln. 2. D A T A P R E P R O C E S S I N G Outliers are commonly defined as observations that are not consistent with the majority of the data (Pearson, 2002; Chiang et al., 2003), including missing data points or blocks, and observations that deviate significantly from the normal values. A data-driven soft sensor derived with PCR or PLS deteriorates even in the presence of a single abnormal observation, resulting in model misspecification. Therefore, outlier detection constitutes an essential prerequisite step for a data-driven soft sensor design. A heuristic procedure has been implemented in the paper to handle missing data related to sever operating interruptions. A template is defined by the kiln drive measurement to identify missing observations, since near zero drive current data corresponds to a stop of cement kiln operation. During such a period, other process measurements will not be reliable or meaningful. In case a small block (less than 2 hour) of data is missing, interpolated values based on neighbouring observations will be inserted. If a large segment of missing data is detected, these blocks will be marked and not used to build the soft sensor. Both univariate and multivariate approaches have been developed to detect these outlying process observations. The 3a edit rule is a popular univariate approach to detect outliers (Ratcliff, 1993). This method labels outliers when data points are three or more standard deviations from the mean. Unfortunately, this procedure often fails in practice because the presence of outliers tends to inflate the variance estimation, causing too few outliers to be detected. The Hampel ident~er (Davies and Gather, 1981) replaces the outlier-sensitive mean and standard deviation estimates with the outlierresistant median and median absolute deviation from the median (MAD). The MAD scale estimate is defined as: MAD = 1.4826 median

~x i - x ' l }

(1)

where x * is the median of the data sequence. The factor 1.4826 was chosen so that the expected MAD is equal to the standard deviation a for normally distributed data. Since process measurements from the cement kiln system are not independent from each other, detecting outliers using univariate diagnostics is not sufficient, resulting in masking and swamping. Masking refers to the case that outliers are incorrectly identified as normal samples; while swamping is the case when normal samples are classified to be outliers. Effective outlier detection approaches are expected to be based on multivariate statistical techniques.

1149

Principal component analysis (PCA) is a multivariate analysis tool that projects the predictor data matrix to a lower dimensional space. The loading vectors corresponding to the k largest eigenvalues are retained to optimally capture the variations of the data and minimize the effect of random noise. The fitness between data and the model can be calculated using the residual matrix and Q statistics that measures the distance of a sample from the PCA model. Hotellings T 2 statistics indicates that how far the estimated sample by the PCA model is from the multivariate mean of the data, thus provides an indication of variability within the normal subspace. The combined Q and T~tests are used to detect abnormal observations. Given the significance level for the Q (Jackson and Mudholkar, 1979) and T 2 statistic (Wise, 1991), measurements with Q or 7"2 values over the threshold are classified as outliers. In this paper the significance level, a has the same value in the two tests, however finding a compromise between accepting large modelled disturbances and rejecting large unmodelled behaviours for outlier detection clearly needs further investigation. 3. R O B U S T

STATISTICS

Scaling is an important step in PCA. Since numerically large values are associated with numerically large variance, appropriate scaling methods are introduced such that all variables will have approximately equal weights in the PCA model. In the absence of a prior knowledge about relative importance of process variables, autoscaling (meancentering following by a division over the standard deviation) is commonly used. Since both mean and standard deviation are inflated by outlying observations, autoscaling is not suitable for handling data which are especially noisy. This paper applies robust scaling to cement kiln data before performing PCA (Chiang et al., 2003) which replace mean by median and the standard deviation by MAD. There are two types of approaches for rendering PCA robust. The first detects and removes outliers using a univariate approach then carries out a classic PCA on the new data set; the second is multivariate and is based on robust estimation of covariance matrix. An elliposidal multivariate trimming (MVT) (Devlin et al., 1981) approach is used. It iteratively detects bad data based on the squared Mahalanobis distance:

d~-(xi-xi)rS

'(xi-xi)

(2)

where x i is the current robust estimation of the location and S

is the robust

estimation of the covariance matrix. Since the data set has been preprocessed with a Hampel ident(fier, 95% of data with smallest Mahalanobis distance are retained in the next iteration. The ileration proceeds till both

X i

and S* converge. In this paper, the

iteration stops at the 10 th iteration such that at least 60% of the data is retained for the estimation of covariance matrix. Chiang et al (2003) suggested the closest distance to center (CDC) approach that m/2 observations with the smallest deviation from the center of the data is used to calculate the mean value. The CDC method is integrated such that the covariance matrix from the initialization step is not disrupted by outlying observations.

1150 Principal component regression (PCR) derives an inferential model with score vectors and free lime measurements from the lab. During the regression step, zero weights are assigned to outlying observations identified by the PCA model; a weight value of one is assigned to normal data. PLS is a multivariate statistical approach for relating input and dependent data matrices. The input data is projected onto a k-dimensional hyper-plane such that the coordinates are good predictors of dependent variables. The outlying measurements identified with an also downweighted PCA model before PLS analysis. The proposed approaches, robust PCR and weighted PLS, are applied to a data set collected from the log system of a cement kiln. 4. C A S E S T U D Y The product quality of a cement kiln is indicated by the amount of CaO (free lime) in clinker. The direct measurement is generally only available with a time delay of about an hour. In addition, the measurement also suffers from operating perturbations within the kiln and the cooler, which result in uncertain indication of the average quality. It is desirable to develop a soft sensor that is able to accurately predict the content of free lime in real time, and can be employed for effective quality control. The operating data from a cement kiln log system are used to derive a soft sensor of free lime in the clinker. There are 13 process measurements available, including kiln drive current, kiln feed, fuels to calciner and kiln, plus several temperature measurements within the kiln system. The standard measurements are logged every 10 min, whereas the laboratory analysis of free lime content of the clinker is logged approximately every 2 hours. A data block of 12500 samples is selected in this study: 6500 samples to derive the model and 6000 samples for validation. One step ahead prediction residual sum of squared errors (PRESS) between the model and measured lime content is used to select the number of principal components (PCs): Nv

PRESS

- Z

2

(3)

( ~ ( i ) - y,,, ( i ) )

i=1

where N v is the total number of samples during the validation period. It is calculated only when a new lab measurement is available. The PRESS of regression models derived with PCR and PLS are shown in Figure 1. The PCR model with 5 PCs has the minimum PRESS (23.443). The PLS analysis shows a minimum of PRESS for 2 latent variables (LVs), because PLS finds LVs that describe a large amount of variation in X and are correlated with dependent variables, Y, while the PCs in PCR approach are selected only on the amount of variation they explain in X. 6O

45

50

40

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~,~ 40

35

O

C:'

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C:,

25

1

2 (a )

3 4 5 6 7 N u m b e r of Principal Components

O

30 . ~i;,

8 (b)

N u m b e r of Principal Components

Figure 1. P R E S S o f (a) - PCR model • (b) - PLS model during validation period

1151 24

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.

.

.

.

.

.

.

.

"23

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,

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, IU981)

C1996

Significance Level

l-i994

13.992 0.990

Significance Level

0 988

0 986

0984

L-I

0 980

Figure 2. PRESS with sign(lqcance level varied~'om 100% to 98% (a)-PCR (b) PLS mode/

Given the PCA decomposition, weights of 0 are assigned to abnormal points to downweight these observations before a regression model is derived. 95% significance level is commonly used for Q and T-~ tests. The lower the significance level, the higher the chance to reject outlying points. Figure 2 shows the PRESS of robust PCR model of 5 PCs and PLS model with 2 LVs while significance level varies from 100% to 98%. When the significance level is 100%, robust PCR approach is the same as the standard version applied to operating data preprocessed by the univariate approach. As shown in Figure 2, downweighting outlying observations improves the predictability of both models. With the choice of an optimal significance level 99.0% for a PCR model, the minimum PRESS of 21.471 is obtained, which is about 20% less than that of a standard PCR model (25.754). The PRESS of a PLS model drops from 27.435 to 23.786 by incorporating robust statistical components and choosing the significance level of 99.6%. Figure 2 also reveals that an optimal significance level depends on the quality of the modelling data block. Comparisons of the PCR and PLS rnodel with lab measurements during the validation period are shown in Figure 3 and 4 respectively (only 1000 samples during the validation period is shown). PLS model is able to capture more of the relevant information than PCR model with a smaller number of LVs. Although the robust PCR approach has a smaller PRESS than that of the PLS model, it is obtained at the cost of using 3 more principal components and higher noise contents in the regression model. L

..._....~'~-~ 1 5 .

,~

t

=~--

0.5

~:~

~

~

~"~

: ~ ~#~i!,÷~.:: '

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1200

1300

1400

1500

1600

1800

1700

1900

2000

S~Lntple

Figure 3. Validation o f robust PCR model with 5 PCs (* - lab measurements," solid line - PCR) PRESS = 21.471

_2fi I -1.5

--÷~......

........

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.

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Figure 4. Validation o f robust PLS model with 2 L Vs (*- lab measurements; solid line - PLS) PRESS - 23. 786

1152 Although deviations are observed when fast dynamics take place in the process (see Figure 3 and 4), the CaO soft sensors developed with a systematic robust statistical approach capture the slow change and the trend of lab measurements, which are important for process operation and control.

5. C O N C L U S I O N S This paper presents a systematic approach to build a soft sensor using robust statistical approaches. The proposed methodology is applied to predict free lime of cement kiln systems. Due to the low signal-to-noise ratio in operating data, data preprocessing demonstrates to be an essential step for development of a data-drive soft sensor. A case study demonstrates the improved performance of a robust PCA model for the detection outliers. The real-time estimation of free lime can be obtained with the datadriven soft sensor, which shows some potential to be used in closed loop control. Due to contamination of process measurements in operating data, downweighting outlying observations is beneficial to enhance the predictability of a regression model. The case study indicates the existence of a optimal downweighting vector determined by the significance level of Q- and 72 - statistics. The issue of finding the optimal significance levels for regression model development and integrating the information from irregularly-sampled low quality measurements into the weighting vector need further investigation.

References Chiang, L.H., R.J. Pell and M.B. Seasholtz (2003). "Exploring Process Data with the Use of Robust Outlier Detection Algorithms." Journal of Process Control, 13(5): 437-449. Davies, L. and U. Gather (1981). "The Identification of Multiple Outliers." Journal of the American Statistical Association, 88: 782-801. Devlin, S.J., R. Gnanadesikan and J.R. Kettenring (1981). "Robust Estimation of Dispersion Matrices and Principal Components." Journal of the American Statistical Association, 76: 354-362. Jackson, J.E. and G.S. Mudholkar (1979). "Control Procedures for Residuals Associated With Principal Component Analysis." Technometrics, 21 (3): 341-349. Joseph, B. and C. Brosilow (1978). "Inferential Control of Processes." AIChE J., 24: 485-509. Kresta, J.V., T.E. Marlin and J.F. MacGregor (1994). "Development of Inferential Process Models using PLS." Computers and Chemical Engineering, 18(7): 597-611. Park, S. and C. Han (2000). "A Nonlinear Soft Sensor based on Multivariate Smoothing Procedure for Quality Estimation in Distillation Columns." Computers and Chemical Engineering, 24:871-877. Pearson, R.K. (2002). "Outliers in Process Modeling and Identification." IEEE Transactions on Control Systems Technology, 10(1): 55-63. Qin, S.J. and T.J. McAvoy (1992). "Nonlinear PLS Modeling using Neural Networks." Computers and Chemical Engineering, 16(4): 379-391. Radhakrishnan, V.R. and A.R. Mohamed (2000). "Neural Networks for the Identification and Control of Blast Furnace hot Metal Quality." Journal of process control, 10(6): 509. Ratcliff, R. (1993). "Methods for Dealing with Reaction Time Outliers." Psychological Bulletin, 114: 510-532. Wise, B.M. (1991). Adapting Multivariate Analysis for Monitoring and Modeling Dynamic Systems, PhD Thesis, University of Washington. Zhao, Y.-H. (2003). A Soft Sensor Based on Nonlinear Principal Component Analysis. 2003 International Conference on Machine Learning and Cybernetics, Xian China.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1153

Application of Multi-Objective Optimisation to Process Measurement System Design David Brown a'c, Franqois Mardchal a*, Georges Heyen b*, Jean Paris c a Swiss Federal Institute of Technology, Laboratory for Industrial Energy Systems, Institute of Energy Sciences, CH-1015 Lausanne, Switzerland b Department of Chemical Engineering, University of Liage Institut de Chimie, Sart Tilman, B6a, All6e de la Chimie 17, B-4000 Liege, Belgium Ddpartement de gdnie chimique, t~cole Polytechnique, C.P. 6079, succursale Centre-ville, Montrdal, QC, H3C 3A7, Canada

Abstract Multi-objective optimisation (MOO) has been used with an equation solver data reconciliation software to develop a tool for sensor system design based on modifying the sensitivity matrix of a simulated process. MOO enables searching for the best tradeoff between two conflicting objectives: the cost of the system and the precision of key performance indicators (KPI) (variables that have to be measured or calculated). This methodology has been applied to design the sensor system of a two stage experimental air-water heat pump. Proper knowledge of modelling equations and constants helps to improve the estimation of the precision of variables, and lowers the cost of the system. Compared to single objective optimisation, the MOO strategy increases the number of solutions, yet the precision function still relates to different objectives for each KPI, and its formulation is shown to have an impact on the trade-off obtained.

Keywords: sensitivity matrix, reconciled precision, key performance indicators, population based evolutionary algorithm, Pareto optimal frontier. 1. Introduction It is now standard to archive real time control system data which can in turn be used for process follow-up and simulation. A set of measurements, however, is rarely coherent due to process instabilities, unaccounted losses, sensor deviations, etc. Data reconciliation is essential to coherently transform raw data so as to determine the state of a process in operation. This requires redundant measurements, beyond what is strictly needed to solve a system of modelling equations. With insufficient (as is often the case of large scale processes) or unsuitably chosen measurement locations, the state of the process cannot be defined. The many benefits of online data reconciliation, e.g. improved plant production and operation, and early detection of equipment degradation, Author/s to whom correspondence should be addressed: [email protected]

[email protected],

1154 have been discussed by Heyen et al, (2000). From a financial viewpoint, priority may be given to significant process variables designated as key performance indicators (KPI). A sensor system design methodology developed by Heyen et al (2002) combines the use of the equation solver type data reconciliation software VALI III (Belsim, 2001) and genetic algorithm programming. A cost function is minimised in a single objective optimisation by targeting specific precision values for KPI with a penalty function. This type of formulation tends to eliminate inexpensive solutions that do not match precision requirements, or conversely expensive solutions with better than required precision. This paper proposes the use of a queuing multiple objective optimisation (MOO) program (Leyland, 2002) with a non-dominated ranking scheme (Golberg, 1989) to emphasise the trade-off between precision and cost and broaden the array of solutions.

2. Methodology The resolution procedure, is based on the one defined by Heyen et al (1996; 2002). Firstly, a data reconciliation model of a given process is built and solved for nominal operating conditions. The sensitivity matrix M of model A allows calculating reconciled variables and reconciled variances with the variance matrix P, provided as follows, [~]-[P

AO]-~I-Pc] - M - ' [-Pc] with P-[~~22]

var (Y~)~-~ (Mi'~)2 2 j:, or;

(1)

Vi-l,n

(2)

The variance matrix P refers to position, type and precision of sensors that may be installed. The goal of MOO is to optimise P, by systematically selecting from a database the sensors that improve precision at a minimum cost. Unmeasured variables have close to or infinite variance, and for measured variables the variance becomes, 2 or; -

y~,/ 2 O'sensor_ .j

I 1 1 + 2

'v'i-l,n

O'exist_ i

(3)

In MOO evolutionary algorithms the definition of Pareto optimality for a vector (Pareto, 1896) is extended to a search space. If there are no new solutions after a certain number of generations, it is assumed that the trade-off curve coincides with the Pareto optimal frontier (POF). It should be noted that singular matrices need not be penalised.

3. Selection of the Objective Functions The cost objective is the sum of capital costs of the system. Other factors could also be included (e.g. installation, maintenance, variations in cost with the number of sensors). The precision objective has to be global, even if each KPI can be considered as a separate objective function. This is equivalent to a weighting problem. Though there is no theoretical limit to the number of objectives of evolutionary algorithms, Leyland (2002) has nevertheless pointed out that with a greater number of conflicting objectives, • there are fewer dominated solutions, thus optimisation becomes meaningless,

1155 • the required initial population is larger, thus calculation time is increased and, • the interpretation of results becomes increasingly complicated. Moreover, as individual KPI precisions are not always conflicting objectives, we formulated the problem with two objectives. The simplest formulation of the precision objective is to minimise the sum of reconciled variance amongst the list of KPI:

l/' 0.. i

-

JpPCC-- '~i1 Y-/

(4)

It can also be expressed as the least precise reconciled variance within the set of KPI:

max/; '

'"'~'"

(5)

A third alternative, intended as a compromise between the prior two, is a modified Kreisselmeier-Steinhauser (KS) function (Raspanti et al, 2000), for which the variances of the KPI are summed while approximating the value of the least precise variance. exp

./prec - 1 In l--L]57

tTKPI

i

O" i

-Y-

p

l

.

'

p E 9t

+•

O" i

./prec --~ max

-

i=l'nmv

t

when p - ~ oo (6)

4. Application

Example

The method has been applied to design the sensor system of an experimental two stage air-water heat pump (Figure 1) (Iraburu, 2002). Data reconciliation was completed with a list of constant specifications relating to the pressure drops in the transfer lines, the composition of refrigerant and the geometrical characteristics of the compressors and heat exchangers. Other parameters were considered as process variables.

TI

PI '

~ "1"3 !~ P I ' - i'

-

. T3

','2 ..........................................~T 3 ............

........~~i.... • E!

.~

T3

•.

.

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.

.

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.i :

7 ........... T3v~ P i : M 2

~

,

'i:=::7

"..........i = !

TI

i ......................................"!"3 ~..................................... :!~'J::'

Figure 1. Air-water two stage heat pump

There were no installed sensors before system design optimisation. The available sensors are listed in Table 1. At each available sampling point, at most three sensors may be installed to perform a single type of measurement.

1156 Table 1. Available sensors

Type a Range Errorb Units Costc Type a Range Errorb Units Costc P 1 0.1- 400 0.2 % Bar 457 M1 0-0.02 0.2 % kg/s 6 800 P2 0- 0.2 0.2 % Bar 756 M2 0-1.83 0.2% kg/s 10000 dP 0- 0.05 0.2 % Bar 400 V 10- 40 0.2 % L/min 8 000 T1 73- 1173 + 1.5 K 125 H 0- 100 0.8 % % 640 T2 73-1173 +0.3 K 200 E1 0- 10 1.0 % kW 2 000 T3 173- 473 + 0.1 K 250 E2 0- 10 0.3 % kW 18 500 %bbreviations for types of measurements: P: pressure; dP: pressure drop; T: temperature; M: mass flow; V volumetric flow; H" relative hurnidity; E: electrical power. berrors are relative except for temperature sensors. Ccosts are in CHF.

5. Results and analysis 5.1. Importance of adding redundancy by system balance equations At first, a single KPI is selected: the coefficient of performance (COP) of the heat pump, i.e. the ratio of the condenser heat load to the electrical power consumption. Two models are compared: the entire flowsheet and another model in which the condenser and the electrical source are considered separately. The number of equations, constants, and variables, and the results for systems of minimal costs are given in Table 2. Table 2. Optimisation for COP estimations

Model Equations Constants Variables Min cost (CHF) STD (%) Cond./Elec. 60 12 67 10 957" 21.57 Flowsheet 165 31 184 11 571 0.326 aless expensive non singular solutions are found, but the KPI standard deviations exceed

Sensors 7 25 100 %

The trade-off curves are shown in Figure 2, left. Since the problem involves integer variables, each point relates to a specific system, and the POF can be neither smooth nor continuous. Despite the greater number of sensors required for characterising the complete system, closed loops increase redundancy, which improves COP precision and lowers costs. For similar costs, the trade-off curve of the condenser and electrical source subsystem is entirely dominated. Figure 2, right shows one solution from the Pareto set (23,385 CHF, STD: 0.17 %). For the subsystem calculations, a solution with an equivalent precision would cost approximately 100, 000 CHF (cf. Figure 2, left). ...............................

& O

....

:

10 ~

i

......................................................

T~:irJ:

C o m ~ ] e t e m ~ d ~ of heat ~:~::r'np .

.

.

.

.

.

.

.

0

:-El}:

:,TJ: T3

.....

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.-

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.....

el;

IU

L~

i

........

0

0 5

1 C o ~ :o:~s:ys~em.. ( C H F )

15

2

.........

............. ~:>~

x 10 ~

Figure 2. left." Trade-off curves for COP (after I00,000 evaluations), right." sample solution

1157 5.2. Analysis of the formulation of the precision function When several KPI are involved, the precision function may influence the resolution procedure and the results. Let us consider an example with four KPI: the COP and three pressure drop parameters (air side of the evaporator, capillary and expansion valves). For equation 5 (Figure 3, left), the trade-off is located in the low cost/precision part of the search space. The least precise KPI is almost consistently the COP. The precision of the other KPI are equivalent, but sometimes worsen as costs increase. The precision objective can no longer be improved when, for lack of remaining sampling points, a plateau is reached for the evaporator air side pressure drop KPI. This limitation hampers exploration of the high cost/precision region. Conversely, for equations 4 and 6 (Figure 3, right), it is essentially the high cost/precision region that is explored. The KPI precisions all improve somewhat more steadily with costs, but almost asymptotically, which is of lesser interest. Moreover, in the cost region where results overlap with those of equation 5, there is a wider spread in KPI precisions. Consequently, it is more costly to obtain a desired value of the least precise KPI (i.e. the COP). Nevertheless, a full coverage of search space can be assured only by these sum based functions. With equation 6 a compromise could be expected with a higher value of the p factor (set to 1000 in our calculations). However, the use of an exponential operator is an issue of concern in regard to machine precision. This type of function would be more robust should the logarithm operator be applicable first. 025

Capd~a~y va:!ve P D Evaporato~r ai~ ~Je P.D E×pa~]:sio n valve P. D COP

~ ~.

::i

0.2

0.1

0 25

Ca~!!a~:y valve P D Evapo~a~o~ af~ t~;Je P D Expa r~sion~valve P. D COP

:.~-- 0 2

22

~,~" 0 1 .ca

1

2

3 4 C,:3st o~t s,~{em {CHF}

5 × 10 '~

4

6 8 C.OS~of s'~tem (CHF.)

10

12 , t 0=

Figure 3. (left." Eq. 5, right. Eqs. 4 and 6) Trade-off curves forjbur KPI (100,000 evaluations)

With a satisfactory trade-off curve, the choice of a system for implementation can be based on targeted budgets and/or KPI precisions. 6. C o n c l u s i o n A method combining data reconciliation to a queuing MOO program has been proposed for the optimal design of sensor systems, and illustrated with the example of an experimental heat pump. The advantages of adding redundancy with balance and modelling equations has been demonstrated by comparing a model of the entire installation (which yields improved precision and costs) to a model that only includes the units which define the COP. However, the precision objective influences the tradeoff obtained when there are multiple KPI. On one hand, minimising the least precise KPI appears to be the best strategy for minimising investments. On the other hand, the functions that can be expected to assure a fuller coverage of search space should be

1158 based on the sum of KPI. This issue may be solved with further changes to the modified KS function. With independent objectives, the MOO resolution approach has the benefit of yielding a trade-off of solutions with KPI precision as a function of costs. Feasibility criteria can then be used to finally select a system among the proposed solutions. Nomenclature A: Jacobian (incidence) matrix for measured and unmeasured variables C: matrix of constants fprec: precision objective function k: number of sensors selected M: sensitivity matrix n: number of variables nKp~: number of key performance indicators P: inverse variance-covariance matrix s: number sensors available for one type of measurement var (Yi): reconciled variance of reconciled variable i y: vector of measured variables Y: vector of reconciled variables 7i,j: integer decision variable ~ {0,1 } )~: Lagrange multipliers P: weighting factor cyi: standard deviation of measured variable i O'exist i: precision of sensor(s) already installed for measuring variable i O'sensor_j: precision of the additional sensor j References Belsim, 2001, VALI 3 User's Guide, Belsim s.a, St-Georges-sur-Meuse, Belgium. Golberg, D.E., 1989, Genetic Algorithms in Search Optimization and Machine Learning, Addison-Wesley, Reading, MA, United-States. Heyen G., E. Mar6chal and B. Kalitventzeff, 1996, Sensitivity calculations and variance analysis in plant measurement reconciliation, Computers & Chemical Engineering, vol. 20S, 539-544, Heyen, G., 2000, Application of Data Reconciliation to Process Monitoring, Symposium ISCAPE 2000, Carthagena de Indias, Colombia. Heyen, G., M.N. Dumont and B. Kalitventzeff, 2002, Computer-aided design of redundant sensor networks, Proc. ESCAPE 12, ed. J. Grievink, J.Van Schijndel, Elsevier 695-691, The Hague, Netherlands. Iraburu, E., 2002, Mod61isation d'une pompe a chaleur/t haute tempdrature, Diploma project, Ecole Polytechnique Fdddrale de Lausanne (in French). Leyland. G, 2002, Multi-objective optimisation applied to industrial energy problems, Doctoral thesis, Ecole Polytechnique F6ddrale de Lausanne, Switzerland. Pareto, V., F. Rouge ed., 1896, Cours d'6conomie politique, Volume I & II Lausanne, Switzerland (in French). Raspanti, C. G., J. A. Bandoni and L. T. Biegler, 2000, New strategies for flexibility analysis and design under uncertainty, Computers & Chemical Engineering, vol. 24, (9-10), 2193-2209. Acknowledgements This project was partially funded by the EU-Canada Cooperation Agreement on Higher Education and Training Academic Mobility Program (HRD Canada) and MRN Quebec.

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1159

Utilities Systems On-Line Optimization and Monitoring: Experiences from the Real World Diego Ruiz a*, Jorge Mamprin a, Carlos Ruiz ~, David Nelsonb and Gary Rosemeb %oteica Europe, S.L. Pau Riera 2, E-08940 Cornell/t (Barcelona), Spain bNelson and Roseme, Inc. P.O. Box 30024, Walnut Creek, CA 94598 - USA

Abstract Utilities systems at oil refineries and other large industrial complexes such as pulp and paper mills or chemical plants are very big energy users that have many degrees of freedom. Manipulating these degrees of freedom with the advice of a cost based optimization program usually can result in significant savings in operating costs with small investment needs. This is particularly important within the electrical deregulation context. Since the electrical system is the main economic trade-off with a steam system, electrical deregulation provides many new challenges in order to operate the combined systems at the minimum overall cost. This paper will not describe just all the features of the software or fully explain on-line optimization technology. The objective of this work is to present some interesting facts and lessons from the experience of implementing a cost based optimization program at thirty oil refineries and petrochemical complexes, around the world, since 1997. This paper will focus on the key optimization variables and constraints in steam system optimization, how they should be handled and how the human and organizational aspects can be addressed. Several of the key optimization problems found in a typical oil refinery steam system such as boilers, extraction-condensing turbines, co-generation and turbine/motors spare drivers are discussed and how those problems can be handled properly is described.

Keywords:

Energy Optimization, Process monitoring, Utilities systems, On-Line

Optimization

1. Introduction Refineries and petrochemical plants usually operate large and complex utilities systems. For example, they utilize different kind of fuels, several cogeneration units, many steam pressure levels, different kind of consumers and there are emission limits to be observed.

Author to whom correspondence should be addressed: [email protected]

1160 These complex utilities systems have several degrees of freedom. Manipulating these degrees of freedom with a cost based optimisation program usually can result in significant savings in operating costs. This is particularly important within current deregulated electrical markets. Since the electrical system poses one of the main economic trade-offs with a steam system, electrical deregulation provides many new challenges to operate the overall combined system at minimum cost. Other important aspect is that utilities systems are continuously evolving (there are frequent changes) and also, sometimes there is a lack of sensors that need to be addressed properly. Furthermore, utilities systems have several constraints coming usually from the operations side. For example, maximum flows and steam cushions. Finally it is important to mention the difficulties that exist in the coordination among plant areas. In large complexes, operators are generally not concerned about global energy costs reductions but only about the Unit(s) under his/her responsibility. All the items mentioned above have been successfully addressed in more than 30 industrial complexes, since 1997. The purpose of this paper is to comment some facts and lessons learned during the implementation of the on line technology utilized to reduce energy costs. Since the availability of this kind of systems is recent, there is a lack of articles explaining these aspects. This paper will not focus on software features, on-line optimization technology or detail economic results, which have already been reported (Ruiz et al., 2004). Instead this paper will initially review optimization and constrained variables explaining some optimization examples. Finally, some human and organizational aspects are commented.

2. Optimization Variables Optimization variables are those variables where you have a relatively free choice on what that value might be. For example, the steam rate at which a particular boiler operates is a free choice as long as the total steam production is satisfied, thus each boiler flow can be optimized such that the most efficient boilers production is maximized. There are two kinds of optimization variables that can be handled when optimizing a steam system. • Continuous variables, such as steam production from a fired boiler or steam flow through a steam driven turbogenerator. It is also important to determine if the unit should be shutdown recognizing its minimum operating limit. • Discrete variables, where the optimizer has to basically decide if a particular piece of equipment will operate or not. The most common occurrence of this kind of optimization in refinery steam system is spared pump optimization where you have to choose which of two pumps to operate, one of which is driven by a steam turbine and the other by an electrical motor.

3. Constrained Variables Constrained variables are those variables that cannot be freely chosen by the optimizer but must be limited for practical operation. There are two kinds of constraints in steam systems optimization:

1161 Direct Equipment Constraints. An example of a direct equipment constraint is a turbogenerator power output. In a turbogenerator you may optimize the steam flows through the generator within specified flow limits but there will also be a maximum power production limit. Abstract Constraints. An abstract constraint is one where the variable is not directly measured in the system or a constraint that is not a function of a single piece of equipment. An example of this type of constraint is steam cushion (or excess steam production capacity). Steam cushion is a measure of the excess capacity in the system. If this kind of constraint were not utilized then an optimizer would usually recommend that the absolute minimum number of steam producers be operated. This is unsafe because the failure of one of the units could shutdown the entire facility.

4. Optimization Examples This section will describe and discuss several of the important optimization issues found in refinery steam systems. The SQP (Successive Quadratic Programming) optimizer from Lasdon at the University of Texas at Austin (Fan et al., 1998) is used for a great variety of optimizations although it has been significantly tuned and customized for steam system optimization where there are many integer decision variables.

4.1 Boiler Optimization When optimizing dual fuel boilers (boilers burning different fuels, for example fuel oil and fuel gas, at the same time) it is important to capture the following factors in the model: • An on-line line method of measuring efficiency. • A method that independently measures the efficiency of each fuel. • Accurate costs of the respective fuels. • A constraint that accurately limits the total consumption of the respective fuels. These limits may be specified by a "have to burn or fuel gas" limit on the lower limit and an emission limit on maximum limit. These factors are important to capture because dual fuel optimizations are not just controlled by the relative boiler efficiencies but also by the costs of the fuels. They are limited by real constraints in the refinery, which specify that so much of a particular fuel must be burned in the refinery because it is produced as a by-product in the refinery and it cannot be sold, so it must be burned. In the European Union and US refineries, this is typically a fuel gas constraint. There may also be a total limit on the cheap internal fuel source as well. The intersection of all these variables provides a very complex optimization that can have very profound economics.

4.2 Steam Production Cushion When a boiler optimization allows boilers to shut down you must deal with a constraint on the steam production spare capacity (sometimes known as steam cushion). If you don't deal with this an optimizer will tend to aggressively shutdown boilers until you will have very little spare capacity. This may be the minimum operating cost method to operate the steam system but it is not operationally robust. Without some spare capacity built into the system, a small steam failure could cascade into an entire facility

1162 shutdown. Underneath we will see how to deal with the steam production cushion constraint. Here is how to select values for the minimum of the Total Spare Capacity constraint. • This number is basically an insurance policy. The larger the number, the safer the operation. Higher values, however, cost money because it makes you run more equipment then absolutely necessary and typically there are large savings from shutting down your most inefficient steam producers. • A A value of 0.0 indicates no spare capacity. If any boiler trips you cannot supply the steam required by the plant. • A conservative number to use is the maximum capacity of the largest steam generator on-line. Then, if your largest generator fails, you will be insured that you have enough spare capacity on-line to service the facility.

4.3 Extraction/Condensing Drive Turbines Optimizing Extraction/Condensing drive turbines is very common especially in ethylene plants. The compressor drives are typically > 10,000 HP. On a drive turbine the mechanical power of the turbine must remain constant (the process is expecting a constant power output). Figure 1 shows an example: A single condensing extraction turbine is modelled as two separate turbines (one from throttle pressure to the extraction pressure and one from the extraction to vacuum pressure).

.................................q -

7¢ e

k

o

i(i,

............. .

_

__

4 ~.~39

7~. r..e~:.

Figure 1. A condensing-extraction turbine model example

The accumulator component on the far right calculates the total power from the drive turbine. The constraint above it is an equality constraint on mechanical power. This insures that the mechanical power of the unit remains constant at all times during optimization. The correct mechanical power is determined from the simulation results. In many turbine optimizations like this there are two degrees of freedom to optimize but we know all three flows. Selecting which flows to optimize is usually not important for the optimization. In this case we selected the optimization of the high-pressure turbine throttle flow and the low-pressure turbine exhaust flow. The extraction steam is determined by difference and is limited within its operating limits with the constraint block. It is very important on condensing turbines like this on to know the surface condenser pressure accurately. The amount of power produced in the low-pressure section of the turbine is extremely sensitive to this number.

1163 Good efficiency curves are also important to have, especially if there are multiple, parallel drives turbines in the system.

4.4 Spared Pump Optimization Spared Pump optimizations are mixed integer optimizations problems where you must decide which pump to operate for a predetermined process need. The simple and most typical cases is where you have two identical spared drives, one driven by a steam turbine and one driven by a electric motor and you are trying to select the least cost option. This will not be described here. A more complicated case that will be described is when you have several drives, not necessarily the same size, in a shared service and you have to choose the optimal set of drives to operate. First some general comments about this problem: • The drives optimized typically will not be very large (> 100 HP but < 1000 HP) because large process driver like a compressor are two expensive to spare. • There will be lots of drives to optimize. An older refinery that has small turbine drives might have several hundred in the plant. • The turbine efficiencies will be pretty low (in the order of 35% isentropic efficiency) and be very hard to determine because of the size of the turbines • The process will dictate how many drives to operate and the optimizer will only need to select the correct ones.

4.5 Cooling Tower Drives Example Figure 2 shows an example of a set of cooling tower pump drives. There are four 500 HP pumps. One is driven by a high pressure to medium pressure back pressure turbine, one by a high pressure to condensing turbine and two by motors. Currently, three of the pumps are running (the two turbines and one motor). The optimizer can manipulate the pumps but must maintain three in operation. k~ '-'

,;~:~,.

..............

~::.i ~: ~:,.

• .~ 121

a e~ /,5

y/,,.,!

Figm'e 2. A condensing-extraction turbine model example Optimizers are connected to each of the drives. These optimizer icons instruct the overall site optimizer to determine if the respective pumps operate. The icon with an A inside, on the right, represents an optimization group accumulator. It is a special kind of accumulator that adds up the mechanical power of each of the drives and then controls the total power during optimization. It does the following:

1164 • •

•

Based on its specification, it specifies the mechanical power for each drive, the optimizer limits and the constraint limits connected to it It also has the built in intelligence to simplify the optimization. For example if all the drives in a group were operating it would make the optimizers unavailable because there are no options. You must run all drives. The constraint hooked to the accumulator is either an equality or a minimum constraint on the total mechanical power of all operating pumps. In other words, it requires the optimizer to maintain at least as much total mechanical power from all pumps at the end of the optimization as current operation requires.

5. Implementation aspects The most important sensors to implement in the system are those involved directly in optimization, such as boiler flows, letdown and turbo generators flows. Important sensors are those which provide data to the model that is not changed by optimization. Less important are those sensors only utilized for monitoring and that do not participate in the modelling. Pump status is often a manual entry, unless where it is possible to determine the pump status automatically especially for pumps directly involved in optimization. The status can be inferred from many sources (RPM, flow or standby status). It is important to emphasize the high involvement and motivation of plant operators right from the beginning of the implementation project. The complete set of optimization recommendations must be taken into account. Options that cannot be implemented in practice are removed during modelling phase. Coordination among plant areas in order to implement the proposed optimization recommendations is also a critical issue, so management involvement is crucial. The robustness of the tool has helped operators gain confidence in the system. Final user's acceptance and widespread use, for both engineers and operators, is one of the key issues for an implementation to be considered successful.

6. Conclusions In this paper, some key optimization problems from experience of implementing a cost based optimization program at oil refineries and petrochemical complexes have been presented. Typical scenarios at oil refinery steam system such as boilers, extraction-condensing turbines, co-generation and turbine/motors spare drivers have been discussed and how those problems can be handled properly is described. Finally, some implementation aspects have been mentioned.

References Fan, Y., S. Sarkar and L. Lasdon, 1998, Experiments with Sucessive Quadratic Programming Algorithms, Journal of Optimization Theory and Applications 56, 3. Nelson, D., S. Delk and G. Roseme, 2000, Using Visual MESA to Optimize Refinery Steam Systems, AIChE 2000 Spring Meeting, Session T9013. Ruiz, D., C. Ruiz, D. Nelson, G. Roseme, M. Lfizaro and M. Sartaguda, 2004, Energy Costs Reduction By Using and On line Utilities Optimization Tool, ERTC Computing 2004.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1165

A Continuous-Time Formulation for Scheduling MultiStage Multi-product Batch Plants with Non-identical Parallel Units Yu Liu and I. A. Karimi* Department of Chemical & Biomolecular Engineering National University of Singapore 4 Engineering Drive 4, Singapore 117576

Abstract Multi-stage multi-product batch plants with non-identical parallel units are quite common in the batch chemical industry. Scheduling production in these plants optimally is a complex task that has received limited attention in the literature, in this work, we propose a new continuous time-representation using asynchronous slots and report a mixed integer linear programming (MILP) formulation for the short-term scheduling of such plants. Using several examples, we show that our formulation is simpler, tighter, and performs better than previous formulations.

Keywords: MILP; multi-product; batch plant; scheduling; makespan 1. Introduction Scheduling of plant operations is a routine activity in all batch plants. Although the task of optimal scheduling is complex in even simpler batch plant configurations such as serial lnulti-product process, it is even more difficult in the case of multi-stage multiproduct batch plants with non-identical parallel units. However, in spite of their industrial significance, the existing research has paid little attention to the scheduling in plants with multiple stages. Pinto and Grossmann (1995) developed a continuous-time, slot-based MILP formulation for the short-term scheduling of multistage batch plants. They assumed sequence-independent set-ups and unconstrained resources. To assign orders to the time slots on a unit, they used tetra-index (order, slot, unit, and stage) binary variables. This increased significantly the number of binary variables for larger problems. Hui, Gupta, and Meulen (2000) presented a formulation with a set of tri-index binary variables (order, order, stage) instead of the tetra-index binary variables, i.e. (order, order, stage, unit). Although they could deal with sequence-dependent set-up times, they could solve problems with only five orders to optimality in reasonable time. Recently, Gupta and Karimi (2003) developed several improved sequence-based MILP formulations. In contrast to Pinto and Grossmann (1995), they used tri-index variables (order, order, and stage) to handle order-sequence dependencies explicitly. Compared to other sequenceCorresponding author. E-l-nail: cheiak(a:!nus.edu.sg

1166 based formulations in the literature, their formulations used fewer binary variables and constraints, solved faster, and gave better objective values in some cases. All these formulations are still not suitable for larger problems, and more effective formulations and algorithms are badly needed for this difficult problem. In this paper, we develop a more effective approach for this tough scheduling problem. We begin this paper with a detailed problem description and then develop an MILP formulation for this problem. Next, we compare our model with the existing models to demonstrate the superiority of our model with three examples.

2. Problem Description Figure 1 shows a multi-stage multi-product batch process with non-identical parallel units. The plant has S batch stages (s = 1, 2, ..., S) and a total of J batch units (j = 1, 2, ..., J). We define set Us = {l'l unitj is in stage s} and m~ = lUg. I, i.e. J = m l + m2 + . . . + ms. We assume that unlimited intermediate storage (UIS) exists between consecutive processing stages.

m(s_lff l m~s_lff 2

g~ O~ ms

m2

ml

Stage 1

---[ Stage n''- l

2 II o

o

o

Stage S

Figure 1. Structure of the scheduling problem The plant operates in a batch mode, i.e. produces individual batches of products rather than long campaigns of identical batches. Let I denote the number of batches (i = 1, 2, . . . , / ) that the plant must process. Some of these batches may be identical. We assume that each batch follows the sequence 1, 2, ..., S of stages for processing. If a batch skips a specific stage, then its processing time is zero on all units in that stage. When parallel units are non-identical, a unit may not be able to process all batches. To accommodate these preferences, we define/j = {/[batch i can be processed on unit j} and Ji = {/I unit j can process batch i}. A real scheduling problem could involve tens of batches, 2-5 stages, and 20-30 batch units. In addition to the above process features, we assume the following. 1. A unit cannot process more than one batch at a time. 2. Processing is non-preemptive. 3. Processing units do not fail and processed batches are always satisfactory.

1167 4. Start of the current scheduling period is zero time. 5. Neglect transition times. 6. The size of each batch is known a priori. 7. More than one unit cannot process a single batch. 8. Resources are unlimited. With these, we can state a short-term scheduling problem for the above process as follows. Given jr,.,/.i, U,., and the processing times of batches on suitable units, identify the units that should process each batch and the start/end times of all batches on each unit to optimize some scheduling criterion. We use makespan as the scheduling objective. 3. M I L P

Formulation

The main feature of our slot-based formulation is that we define time slots for each stage and each unit separately. Instead of assigning batches to unit-slots, we assign them to stage-slots and then derive their assignments to specific units later. By doing so, we reduce the number of binary variables dramatically compared with the existing slotbased formulations.

1~t Unit ................

I Slot 1 I

Slot i-1

I

. . . . . . . . . . . . . . . .

2 nd Unit

Slot 3

Slot/

UnitiSlots ................ /'/7 th

s

Unit

Stage s

Slot 2 Slotl

i

2

Slot 4

I 3

ooo

SlotI

Time Figure 2. Definition and time-matching o f slots in a stage s

We represent time (Figure 2) on each stage s and each unit j by exactly I contiguous, variable-length slots ( k 1, 2, ..., /). Note that the unit-slots for a stage are asynchronous with their stage-slots and stage-slots are asynchronous across stages. Let T~.,.be the time at which slot k ends on stage s and tjk be the time at which it ends on unit j. As shown in Figure 2, the endpoint of each stage-slot matches with the endpoint of exactly one slot of some unit in that stage. For instance, T3.,.= t_~3in Figure 2. For each stage-slot, we use the following binary variable and constraint to assign exactly one batch, which must exit the stage at the end of that slot. {10 ye,~, -

if batch i exits stage s at time T~,

otherwise

1168

ZYeik~

=

1

(1)

i

Since a batch must pass through each stage once and only once, we have,

Z ye,~ - 1

(2)

k

Having assigned a batch to each stage-slot, we now assign a unit to each batch by defining the following binary variable. z~ -

1 0

i f u n i t j processes batch i otherwise

J • Us

Note that the index s in the above is not free. Fixing j fixes s, as j • Us. Since only one unit in each stage must process a given batch, we write the following for each stage s,

Z z,-1

(3)

jeU s ,./eJ ~

Using the two binary variables yei~ and zo., we define a 0-1 continuous variable YZo.ksyeikszijs. We linearize this by using,

Z jeU

r z ~ = ye,~,,

(4a)

,jeJ i

Z YZ~ - z

j • Us,j •Ji

(4b)

k

Having assigned batches to slots and units, we now determine the completion times of batches and slot times. First, slots on each stage are contiguous and ordered, so

Note that YZo.~ = 1, only when a batch i exits a unit j at some slot k (or time tj-k), otherwise it is zero. Therefore, to ensure that the processing of every batch that exits a unit j at Oh, we use,

t,~ > t,(~_,, + ~ PgYZ,~

j • Us, tjo = URTj

(6)

Where, URTj is the release time of unit j, which is the earliest time at which unit j is ready to accept a new batch. Note that if a batch does not exit a unitj at tjk, then tj.k= tj.(k_ 1). Thus, only the unit-slot from which a batch leaves provides the processing time (PTo.). Now, if a batch does leave a unit j at tjk, then we must register this exit on the time axis of the corresponding stage as well by forcing Tks = tj.k. We do this as follows. L > tj~ Tk~._
j • Us

(7a)

j E Us

(7b)

i

Where, M is a constant larger than the maximum possible makespan. Having ensured that each batch gets sufficient time for processing on a suitable unit, we must ensure that a stage s processes a batch only after stage (s-l) has completed it. To this end, we

1169 define CT:, as the completion time of batch i on stage s, i.e. the time at which it exits stage s. Clearly, this is the time at which the stage-slot to which the batch is assigned ends, therefore,

c~, - Z r~,y<. k

Then, to ensure that a batch processes on a stage only after it has finished processing on the previous stage, we require,

c r > c~ r~

--

: ( ,~

1)

+ ~ PT~ !

Cr, o-BRr,

is

jet.:,

where BRT: is the release time of batch i. Next, we define TY&a.~ = Tksye:~, to linearize the nonlinear expression for CT~, with the constraints below.

CT., _>E , - M(1 -

)

(Sa)

CT _
(8b)

::e,,~,

Lastly, we minimize the makespan (H) given by any one of the following constraints. Although it is sufficient to use just one constraint and most of the following constraints are redundant, we found that using all three reduced the solution time.

(9a)

H > Tk," H >

CT~,,~

(9b)

H > tg.

(9c)

4. Model Evaluation To evaluate this formulation and compare it with those of Pinto and Grossmann (1995) and Gupta and Karimi (2003), we use three examples. Example 1 has two batch stages (S = 2) and process nine batches ( i = 9). Stage 1 has two parallel units (U1 = { 1, 2} and ml = 2} and stage 2 has three (U2 = 13, 4, 5} and m2 = 3}. Table 1 gives the remaining data for this example. Table 1. Processing time (h) of batches on units in Example 1 Batch (i)

1

1

15

2 3 4 5 6 7 8 9

6 12 16 16 12 4 18 11

Unit U) 3 4 5 62 44 2 20 42 14 51 63 12 17 50 12 37 64 8 53 34 19 21 37 17 24 43 2 10 34 2

5 33 70 17 41 24 21 23 39 36

1170 For solving the three examples, we used CPLEX 9.0 in GAMS 21.4 on an hp workstation xw6200 (Intel Xeon 3.40 GHz CPU and 3.00 GB RAM) running Windows XP. Table 2 shows the performances of and statistics for various models. Our model clearly performs much better than the existing two models. From Table 2, we see that only our model finds the optimal solution within 1000 s for all examples. Furthermore, our model also gives higher RMIP values for all the problems, which indicates that our formulation can be tighter than the other two models. In spite of using more binary variables, our model is much faster than the model of Gupta and Karimi (2003). Compared to the slot-based model of Pinto and Grossmann (1995), our model uses almost half the binary variables. Table 2. Comparison of our model with two literature models for the examples

Example 1 (S=2, ml=2, me=3,/--9) Binary Non- Vari- Cons- RMIP CPU Relative MIP Model Variable zeros ables traints (h) Time (s)Gap (%) (h)

Nodes

Ours Gupta Pinto

207 152 360

84 84 84

35390 409994 619954

Ours Gupta Pinto

184 168 504

34 34 34

5244 51720 406222

Ours Gupta Pinto

272 248 720

148 149 148

10646 398600 36881

3669 2456 3524

694 832 64.11 146 0 209 613 41 1000 16.67 473 838 41 1000 0.53 Example 2 (S=2, ml=3, m2--4,/--8) 3633 721 770 22.65 23 0 3112 241 743 22 1000 17.65 4908 649 1154 22 588 0 Example 3 (S=3, ml=3, m2=2, m3=5,/--8) 5273 1041 1134 103.83 72 0 4504 353 1082 66 1000 32.21 7016 929 1652 66 194 0

5. C o n c l u s i o n An MILP formulation using a novel continuous-time asynchronous slot-based time representation was developed for scheduling multi-stage multi-product batch plants with non-identical parallel units. Evaluation on three examples shows that our formulation is simpler, tighter, and at least two times faster than the best existing formulations.

References Hui, C. H.; Gupta, A.; Meulen, H. A. J. A novel MIP formulation for short-term scheduling of multi-stage multi-product batch plants with sequence-dependent constraints. Comput. Chem. Eng. 2000, 24, 2705. Gupta, S.; Karimi, I. A.; An improved MILP formulation for scheduling multiproduct, multistage batch plants, Ind. Eng. Chem. Res.; 2003; 42(11); 2365. Pinto, J. M.; Grossmann, I. E. A continuous time mixed integer linear programming model for short-term scheduling of multistage batch plants. Ind. Eng. Chem. Res. 1995, 34, 3037.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1171

Optimal Scheduling of Supply Chains" A New ContinuousTime Formulation A.C.S. Amaro a and A.P.F.D. Barbosa-Pdvoa bl a|SCAC, Quinta Agricola, 3040 Coimbra, Portugal bCEG-IST, IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Abstract In this paper a new continuous-time mathematical formulation is proposed for the optimal schedule of industrial supply chains. This introduces novel concepts to represent the supply chain instances (sites, equipment units, transportation facilities, etc) suitable events (transforming operations, transportation tasks, storage) and material states. Furthermore, it establishes a better commitment between the events allocation and the time scale associated. A single level formulation is obtained that allows the computation of the optimal supply chain schedule for a defined economical or operational performance criterion while accounting simultaneously for the explicit integration of different topological and operational characteristics of the supply chain dynamics. The formulation is a Mixed Integer Linear Programming (MILP) that is solved using a standard Branch and Bound (B&B) procedure. The applicability of the proposed formulation is illustrated through the solution of a practical example involving an industrial pharmaceutical chain.

Keywords: supply chain, schedule, optimization, continuous-time.

1. Introduction For many years companies managed their logistic processes, procurement, production and distribution in a non integrated way. However, due to increasing competition, this attitude has been changing and companies do now consider the integration of their supply chain as a key business issue. Consequently, the accessibility to tools that will allow an integration of such structures both at the design and operational levels is crucial (Goetschalckx et al, 2002). Some important contributions within the supply chain modeling and optimization have been proposed recently. Two important research strategies were followed, a stochastic and a deterministic approach. The former, results frequently into complex non linear optimization problems requiring strong assumptions to achieve an optimal or nearoptimal solution. On the other hand, the deterministic counterpart results typically into large mixed integer linear problems based essentially in a discrete time approach to represent the time domain. The main drawback of these formulations is that the resulting problems can become hard to solve within a reasonable margin of optimality. 1To whom correspondence should be addressed: [email protected]

1172 Furthermore, in the works published few authors considered the different supply chain activities integration and a lack of models generality exists (Shah, 2004). This work tries to address some of these limitations and presents a continuous time model for the integrated supply chain operation. Novel concepts are introduced that allow the complete representation of supply chain structure and its operability while keeping the mathematical formulation linearity. The resulting MILP problems are solved using a standard Branch and Bound (B&B) procedure. The model is characterized below and some considerations are made on the assumptions made. A real case-study is then solved showing the model applicability.

2. Model Characterization A supply chain is an operational structure that produces and distributes a set of materials using its internal resources (production, storage and transportation facilities) and some external resources (raw-materials, utilities). The resources are distributed amongst sites that guarantee a supply chain specific task (production, storage, distribution, etc.). These sites can be grouped into different clusters based on their operational functionality: (a) supplying, (b) transformation, (c) packing and (d) distribution. The latter supplying a set of aggregated customer regions (Amaro and Barbosa-Pdvoa, 2004). The supply chain sites and the associated connectivity structures form the supply chain topology. Each site and connectivity structure is then characterized by the associated resources (e.g. facility, warehouses and trucks) availability, suitability and capacity amongst other requirements. In terms of operation two major set of events describe the supply chain operability. These are respectively transforming and transportation events. The former represents general processing operations involving a material "transformation" (e.g. reaction step, filling operation, storage) and are referred as tasks, i=1 .... NT. The latter describes the materials transportation and are named as transportation flows or simply flows, 1=1 .... NL.

The linkage between the chain topology and the events occurrence is derived automatically based on the suitability criteria. For the task events a single suitable linkage is assumed. Does for a given transforming operation that can be performed at N E independent resource instances, a set of N E distinct event tasks is generate. Nevertheless, the same resource can be suitable to perform more than a task (at different time domains) and a compatibility set is generated to represent the set of task events that can be performed at each resource. For the transportations events, each transportation flow is defined by a material state, a path and a connectivity structure (Amaro and Barbosa-Pdvoa, 1999). Each connectivity structure may have a set of transportation resources to perform every suitable event. The suitability criterion establishes the linkage between the transportation flow and the connectivity structure. Any transport event (e.g. transport of material A from S1 to $3 site) is represented by a single transportation flow with N V suitable resource allocations belonging to the same connectivity structure, or by a set of Nl transportation flows defined over an equal number of available connectivity structures. To account for the multipurpose nature of the transportation resources (a resource may be shared by more than a material state during a specific time domain) a compatibility criteria is also defined and evaluated for each pair of transportation flows, 1 and l', defined over the same connectivity structure. The sets of compatible flows defined over each connectivity structure are grouped into a

1173 novel modeling instance called a family. The supply chain transport operations are then represented by the whole sets of compatible and incompatible family flows. Finally, the material existence along the supply chain is modeled by a set of material states. These represent the linkage between each material and the associated chain location.

3. Mathematical Formulation In the present model a continuous time formulation is developed where a common time grid for all resources is assumed (Castro et al, 2001). The time horizon is divided into several intervals (slots), with events taking place only at the interval boundaries. Each slot has an a priori unknown duration that will be determined by the time limiting event. This limiting time can result from different occurrences: (1) the allocation of a single processing task or transportation flow to a given resource; (2) the allocation of a set of batches of the same processing tasks (replication of the same batch) to the same resource; (3) the occurrence of a linear combination of different task events allocated to the same processing resource instance (assemble of batches) and (4) a linear combination of transportation events allocated to suitable transportation resources. Note that, cases (2), (3) and (4) can only occur if the required material to process or transport, during the slot time, is available at the beginning of the slot. The same availability is applied to the resources used. Furthermore, the products obtained through the processing tasks or transportation flows will only be available at the end of the slot. Therefore occurrences of any of these situations imply a non requirement, during the slot time, of the material and resources involved (see case-study below). Also, associated storage capacity must exist during the slot so as to account for eventual releases of material. Furthermore, as in Castro et al (2001), and for points (1), (2) and (3) the concept of non-limiting task is used. Tasks are allowed to last longer than their processing times if no demand exists on the associated material and/or resource. Additionally, point (4) may represent the occurrence of different transport flows performed by the same family or the allocation of different transport families to a given suitable transport resource defined within a connectivity structure. A sharing mode of operation is allowed for the allocation of each transportation family to a given transport resource (each transport equipment may be shared by the whole set of flows defined within a family, during a specific time domain). Overlapped and the non-overlapped operation modes are considered. The former represents a sharing mode of operation were the limiting time describes the time usage of a transport resource by the simultaneous occurrence of a set of transport flows belonging to the same family. In the latter, the limiting time accounts for the linear combination of transportation times characterizing the allocated set of compatible (single family) or incompatible (different families) transportation flows. These new concepts allow a reduction on the number of event points required to describe the global time horizon and does a reduction in the global model may be obtained. In terms of variables the model considers both binary and continuous variables. The binary variables represent decisions within the supply chain (e.g. allocation of transportation flows and transforming tasks to suitable resources) while the continuous variables describe operational requirements (e.g. task dimension, amounts transported and material amounts).

1174 In terms of constraints these are of different forms and account for various situations such as: time slot bounds and linkages with events allocation, capacity requirements and limitations, equipment instances suitability and allocation, transportation policies, events pre-conditions and compatibilities, material supplies, demand levels and due dates, amongst others. Due to the lack of space the mathematical model will not be presented in this paper. As objective function the maximization of the supply chain profit is adopted. This involves processing, storage, transport and raw-materials costs as well as product values. The final model solution optimizes simultaneously the slot dimension and the scheduling objective while accounting for the explicit integration of different topological and operational characteristics of the supply chain.

4. C a s e S t u d y A supply chain is considered where different pharmaceutical solutions are produced for hospitals as well as ambulatory use. The supplying cluster is characterized by a main production structure, plant P1. This has four operational sections, two of them performing water treatment operations (WT1 and WT2) followed by a mixing step (MH) where chemicals additives are homogenised with treated water. A filling section follows where a blow, fill and sell process is carried out (BFS). The water treatment produces two water types, W_I and W_2, and some water wasted solutions, WW. W_I is sterile water and is used for general nursing purposes and to produce the water solution (W_2), suitable for injection purposes at the second treatment section. Chemical sterile additives are then mixed and homogenised with W_2 and the resulting solution goes to the filling section. Four different solutions are obtained: IS 1, IS2, IS3 and IS4 at different capacity containers: 100, 250, 500 and 1000 ml. The P1 rawmaterials, water treatment chemicals and additives as well as the polymer, are fulfilled by external suppliers based on pre-defined supplying capacities and time scales. The water required is an inner resource (locally explored). ~+i!~Plants:P1, P2 ~

I CP|

~

Airport and Sea Port

WH1 ....

!

~ ~

* EEC

Z,," : +,:, /

:

/

7t-~

%1 / L+. ........... ~L)

\\

k

Table 1 - Family flows description

Sites

P1 Flows

H Hospital

i~ FinalProducts

::

~

:

:-:

H1

fl

WH1 WH2 WH3 P2 SP AP H2

f2 f3

EEC1 EEC2

flO

f6

P2

WH2

j7

f5 f4

or°9

fl2 2°8

fI1

Figure 1 - Supply chain structure. In terms of country distribution P1 supplies different points in the supply chain: P2 a generic drug plant with IS3 and IS4; a hospital site with IS1 and IS4; and three

1175 distribution sites (warehouses WH1 to WH3) located at different country regions, figure 1 and table 1. Furthermore, IS 1 and IS4 are also delivered to an African distribution partner using a free on board strategy for the material fulfilments carried at the sea port. Finally, delivers to EEC partners are performed. Two of them involve a road distribution and a latter one a free on fly strategy carried out at the airport site, figure 1. The former EEC partners (EEC1 and EEC2) demand respectively, IS1 and IS2, and IS3 and IS4 while the later one (EEC3) requires IS 1 and IS4. The above distribution network is guaranteed essentially by P1 dedicated transport resources ~=1 and [=2 (see Figure 1) that involve respectively resources v l,v2, v3 (in-house) and v4,v5 (contracted). Furthermore, WH2 and P2 also have their own transport resources (~=3 and ~=4). The former may transport materials to the sea port while the later may send the materials to the WH3 distribution site and to the south hospital site, H2. This is allowed based on a crossdocking strategy. Concerning the storage policies, it is assumed that at the beginning of the time scheduling all supply chain sites have a storage level of 25% of capacity dedicated to each suitable material state. Also, no storage level less than 5% is allowed. Based on the above characteristics the supply chain schedule is optimized for five days of operation so as to maximize its profit while guaranteeing pre-defined demands and due dates. Some of the results obtained are shown in figures 2 and 3. In terms of operation it can be seen from figure 2 that only IS4 and IS2 are produced. This is explained by the fact that the available storage levels of IS1 and IS3 are enough to guarantee the amounts required for distribution. On the other hand, the high level of production of IS4 is due to its high market requirements that are not supported by the available storage levels. Within the plant schedule (figure 2) different time limiting occurrences are observed such as: the replication of the same task (task 7 in slot 1, from 0 to 4) and a combination of different tasks (tasks 7 and 5 in slot 5). Also, the occurrence of non-limiting tasks is observed (represented by task horizontal lines, task 1 in slot 1 and task 3 in slot 5, etc.) PI

,,,,,,,,,,~

2

Mt

fi'

~

~ ,

'3 £~.~ ,2 ~ . m ~

v3

~

~t

3

m

.flo

.flo'

~a

ij~

l]]s

~,,,. ~,,,~.~

::~i~

fl~

I

.flo

#

! ]

ISI 4

i

Irtl7

:

I'-q

, I

fl/ ./zo

I !

~25 Fi36

[]

~,~17

/

II

4

8

B

21i

34

Figure 2 - Plant P 1 Schedule

28

~

~

41

0

4

Figure 3-Supply Chain distribution schedule

For the distribution activity (figure 3), structure P 1 guarantees most of the distribution requirements since it is the main linking point in the supply chain. P 1 supplies directly warehouses WH1, WH2 and WH3, the airport and the associated plant P2. On the other hand, warehouse WH3 is also supplied through P2 and the sea port is supplied by warehouse WH2. Analyzing in more detail the use of the vehicles it can be seen that

1176 due to its higher capacity transportation equipment v2 is fully used during the week. Furthermore, vehicles vl and v3 that have the same capacity but different variable transportation costs (v3 has a lower cost) are used accordingly and does the later is more used. On the other hand, vehicles v7, v8 and v9 are used occasionally when required to perform some cross-docking operations. These different occurrences combine various transportation policies (see point 3). For instance at the second time slot (from 4 to 8 hours) family flow f2 is allocated twice to vehicle v3 and two non replicated transport operations are done. In the former three different materials are transported (compatible flows of IS 1, IS2 and IS4) while at the latter only two of these materials (IS2 and IS4) are transported. Events are overlapped during each family allocation and a sharing mode of operation is observed. In slot 8 to 16, family f3 is allocated to different transportation equipments (v2 and v3) performing in each case different flow tasks. The transport of IS 1 and IS2 is performed by v2 using a sharing mode of operation, while IS4 uses fully the capacity of vehicle v3. Finally, at the first Friday slot (32 to 38 hr) a single transport event uses v3 capacity and a non overlapped operation is performed. The final model was solved using the GAMS/CPLEX solver. It is characterised by a maximum profit of 139982,37 currency units and involves 15261 constraints, 9306 variables, 2719 integer, and took 2605 CPU sec. to solve in a Pentium III.

5. Conclusions A novel continuous time model was proposed for the optimal schedule of supply chains where an integrated approach of different supply chain activities such as supply, production, storage and distribution is considered. Structural and operational characteristics are model simultaneously where variable tasks and transportation times are allowed. Different storage policies, transportation resources sharing and pre-defined demand requirements are also considered. As final result a detailed operating plan at both the production and transport levels is obtained where processing, storage and transport occurrences are identified. The continuous nature of the mathematical formulation allows a closer linkage between supply chain major events and the modeling space used to represent it. In this way time dependent events can be easily modeled and novel concepts are considered. This is the case of the non-limiting tasks concept and the occurrence of different combination of processing tasks as well as transportation flows. Furthermore, a transport sharing policy exploring the family concepts is also developed. These novel concepts allow the reduction of the number of events points in the global model resulting in a flexible but quite compact formulation. A real case study taken from a pharmaceutical industry was studied and the results obtained were promising. Further studies are under development where different supply chain structures and characteristics are being analyzed.

References Amaro, A.C.S. & Barbosa-P6voa, A.P., 1999, EJOR, 199, 461-478. Amaro, A.C.S. & Barbosa-P6voa A.P., 2004, Comp. Aided Chemical Eng,18,877-883. Castro, P., Barbosa-P6voa A.P. & Matos H. (2001), Ind. Eng. Chem Res.,40,2059-2068. Goetschalckx, M., Vidal C.J. & Dogan K., 2002, EJOR, 143, 1-18. Shah, N. 2004, Computer Aided Chemical Engineering,18, 123-138.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1177

Effect of pricing, advertisement and competition in multisite capacity planning M. Bagajewicz University of Oklahoma 100 E. Boyd St., Norman OK 73019, USA

Abstract The multi-site capacity planning problem with a long term time horizon, with transportation constraints is expanded to consider pricing of the product, the effect of advertisement and competition. We use a modification of the Cobb-Douglas model for consumer utility and include the effect of advertising.

Keywords: Capacity Planning Problem, Planning, Pricing. 1. Introduction The investment capacity planning problem has been so far formulated for enterprises where the demand and price were considered as parameters, sometimes uncertain (Sahinidis et al., 1989, Liu and Sahinidis, 1996, iyer and Grossmann, 1998, Ahmed and Sahinidis, 1998, etc.). Recently, Guillen et al., (2003) showed that elementary pricing decisions can be added to scheduling problems. Extensions of Guillen et al. (2003)'s model to capacity planning are straightforward. This approach, however, does not take into account the effect of advertisement, or the influence of competition. This paper addresses the simultaneous addition of pricing, advertisement cost and competition to investment and capacity planning problems. A microbrewery capacity planning problem (Spencer et al., 2004) is used as basis for illustration

2. Background Spencer et al. (2004) considered the typical capacity planning problem with expansions, with different potential locations and transportation costs for the plants and applied it to the location of beer microbreweries. The model, which maximizes NPV, was crafted so that reinvestment is allowed by using portions of proceeds and no new capital. The model output provides the expansions through the time horizon, the anticipated sales, and the advertising strategies and expenses. The novel aspect of the model was that sales in each potential market were connected to advertisement expenditures and the effect of competition was considered. Competition was modeled in the following way: Sales< Market Demand *(Market share without competition- Effect of competition)

1178 Thus, the effect of competition is to reduce the market share in proportion to the number of breweries in the market. Advertisement was considered as follows: Market Share = Market share without competition + b * Advertisement where b is the constant relating market share increase per dollar spent in advertisement. The assumption is that the sales to advertisement efforts behave linearly. In advertisement theory (Rao, 1970), sales grow linearly with advertisement until they reach saturation (they level off) after which there is a small decline (over-saturation phase). When advertisement is not present, Spencer et al (2004) showed that location changes to places where a larger market share can be obtained with less advertisement efforts and/or a location closer to more markets. Spencer et al (2004) considered prices fixed. This paper relaxes this assumption and also considers competition and advertisement in a different way.

• Saturation SalesT , Oversaturation [ Thresh°ld 1 ]

p, Advertising Rate / Year Figure 1. Sales vs. advertising effort.

3. Pricing and Competition Assume first that there is an established market for the new product (in this case, beer) and that the total demand is assumed constant. The question is what price will be the right one and what level of advertisement efforts is needed to attract the optimal number of customers and the new demand associated to it. Let Pl be the targeted new product selling price, dl its demand, p2 the average competitor's product price, and d 2 is the corresponding competitor demand. We start assuming the following relation as valid: Pldl = C P2d2

(1)

In this relation c is a constant. This relation can be derived using the concept of indifference curves (Hirshleifer and Hirshleifer, 1998), which express how much equal utility (happiness) a combination of product 1 and 2 will provide to a customer. Such an expression, compatible with (1) is d ( 1d~~ - U ,

where U is the utility and c = rl/r2.

This form of the utility function is known as the Cobb-Douglas utility, which requires rl +r2=l. Thus, (1) is obtained by maximizing U subject to a budget constraint

P l dl + p zd2 <- Y, where Y is the total consumer budget. In the case where the prices

1179 of the competition (p2) and d 2 are fixed, the expression reduces to Pldl = const, which corresponds to a market structure of monopolistic competition, (Dixit and Stiglitz, 1977) which is in turn based on two assumptions: a) the firm maximize its own profit by choosing an optimal price for given prices by other firms, and b) each demand is small relative to entire market. The use of the above formula for pricing is sometimes conflictive. For instance, if d2 >> d~ if an equality is used, Pl will be very small, and likely incompatible with the economics. If one uses an inequality (e.g. p~d~ < c p2d2 ) the restriction becomes meaningless and the price chosen will be too high. To overcome this, it is proposed to use the plant capacity instead of d2. This is equivalent to assuming that the market size is of the capacity of the plant. Indeed, if such a market is shared 50/50, then prices will be equal (for c = 1).

4. Advertising Equation (1) does not express the dynamics of the competition process, but rather the state of equilibrium among competitors at some point in time. When c=l, equation (1) reveals that equal prices of the new product and that of the competitors' product, results in an evenly shared market. Such outcome would be realistic if the following conditions are met: a) The new product and the existing ones have been in the market for a long time. b) The quality of each product is the same. c) Advertising campaigns are equally effective, and d) Production capacities of all competitors can satisfy the demands. Since these conditions are hardly met for a new product, the above model needs to be improved. First, the competitors will have a clear advantage over the new product because they will have been established in the market for a number of years. They will have earned loyal customers and will have successful advertising campaigns in place. On the other hand, the new product will have the advantage of being a superior product, which will either increase convenience of use or save money and time to the customer. To account for influences from advertising, the model is modified as follows: (2)

~(t,a). p,d, = c p2d2 • ot(t,a)

This still corresponds to an indifference curve of the form d[ "~d( ~ - U , where now rl and

F2

are functions of ot(t,a) and f 3 ( t , a ) . The function ~ ( t , a )

is a function of time

and the advertisement campaign efforts for the new product. This function ranges between zero and one. At the beginning (t=0), o t ( O , a ) = ot 0 (a small number) indicating that the demand of the new product d~ is small, no matter what the price is. As time goes by, the function approaches one, reflecting equal opportunities for all competitors in terms of advertisement. Thus, before the value of o t ( t , a ) reaches one, the competitors have a competitive advantage by virtue of their longer standing in the market, with an established customer base. Thus, we call o t ( t , a ) Function for the new product.

In turn, ~ ( t , a )

the Inferiority

is also a function of time and the

advertisement campaign of the new product (a). At the beginning (t = 0), ~ ( O , a ) = 1

1180 indicating that there is no initial advantage for the new product. As time increases, 13 approaches zero asymptotically, becoming zero only if the competition disappears. It represents the superiority of the new product and ultimately its competitive edge. Therefore, we call it the Superiority function. We envision these two functions to have concave and convex forms as shown in figure 2. 1 ............................................................................................................................................... 0,9 O8

0.7 0.6 0.5

..~.,.,~,.__,,.__--4

0.4 O.3

0~ / /

--....

01

"~-~

o ...........................................................................................................................................................................................................................

2

4

6

8

10

12

time [years]

Figure 2. Inferiority and superiority functions. One gets some estimated values for

c~(t,a)and

~(t,a)using

data from the

performance of similar novel products in the past. We note that this is a simplified model ignores the advertisement efforts of the competition. The assumption that the inferiority and superiority functions are linear with advertisement efforts is first made. For simplicity, we also assume ~ ( t , a ) - 1, that is the existing product is as good as the new one in the consumer minds for a long time The following form of the inferiority function can be assumed: or(t, a ) - or 1 - ~ 1 - ot o J~

! j, where ot 0 and ~l are

the inferiority function values at time zero and infinity, respectively. It is also assumed that within the time horizon, [Yt + 7 , , a ~ << 1. Under these conditions, (2) renders a linear relationship between dl and advertisement efforts consistent with figure 1. This inferiority function does not penalize higher prices and therefore, it leads to answers where the price chosen is always the highest. This can be easily verified by substituting (2) in the following simplified profit function Profit=-pldl -(gl + g2 dl)-a where (gl + g2 dl) is the operating cost and realizing that reducing d~ and increasing p~ leads to higher profits. One needs to realize that as much as advertisements changes consumer attitude towards buying the product, price has the adverse effect, so we propose to use

cz-

a(t,a, pl ) - e

yp(pl-p2) [13,1 --(Oil--¢Z0 ) e-[v'+v"'a]t ]" Thus, if the price is higher

than the market, then revenues are higher, but the inferiority function is also lower.

5. Model The model is presented succinctly because of space reasons. As stated above, the Spencer et al's (2004) model is used, which considers multiple potential sites for plants. Each plant can send its products to different markets. We also consider several different locations for raw materials. The transportation costs of raw materials as well as products are taken into account. Budgeting constraints are set so that the capital investment is used at the beginning and all the expansions are financed by the proceeds of the project. Thus, the model decides if it is profitable to reinvest. Finally, the following pricing

1181 model

is

used:

p~d~ - cp2Cap[cz ~ + ( o t ~ - c z 0 X T , + 7 ~ , a ) t e r''{p~-p')], which

assumes monopolistic competition. (p2 and d2 fixed) and includes a linearization of the inferiority function using the assumption that [7, + It ,air << 1 over the time horizon. Although time is already discretized into periods in this model, the expression

p~d~ is

non-linear. To linearize the expression and use MILP solvers prices were discretized. Thus, assuming that a set of nm values of prices per market m are chosen (pro.i, i=1"" nm), the following equations are used:

['

Z ieP,,~

z ....i - I

(4)

ieP,,,

where Cap is the final capacity, p~.,,, is the average price of the competition, and Zm.i a binary variable that forces the model to choose only one price. This price stays constant through the life of the project (although this condition is also easy to relax). This is the same strategy as the one used by Guillen et al. (2003). Linearization of (3) is straightforward. Notice that sales instead of demand is used in eq (3) together with an inequality, because sales (which are lower than demand) may be limited by capacity.

4. Example Microbreweries are defined by the industry as small breweries that produce less than 15,000 barrels of beer per year and distribute the product for consumption off-premise. A pale ale has been chosen for the recipe of the beer to be produced because it is lighter in taste than other microbrews, but it has more taste than the watered-down national brands. The main raw materials used in the production of micro brewed beer are hops, malted barley (yellow dots in figure 3), and yeast (blue dots). Several locations in the US were considered (black dots). The Markets are each of the 48 US contiguous states. Using a maximum of 1.5 million of initial investment, fixed prices and the aforementioned advertisement and competition model, Spencer et al. (2004) found a solution that chooses to build only one brewery (Phoenix, AZ) for only one market (AZ), with expansions in year two, three and four. For a $3 million initial investment, two breweries are built (Phoenix, AZ and Las Vegas, NV) and expanded afterwards.

Figure 3. Raw materials and potential plant locations

1182 When the effect of competition was eliminated and the advertisement was eliminated and the market share considered fixed (slightly higher than the one without advertisement) the model used by Spencer et al (2004) chose to build only one brewery in Milwaukee, Wisconsin. Since the model was not allowed to increase its market percentage through advertising, it was forced to sell to more markets than before. The net present worth came out to be about half of that with advertising included. The new model

was

run

using

c~1

=0.95,

~0

=1/7,

7t =0.029,

7p - l n { p z l ' 5 / P , m ~ } / ( P , ma~--P2)' which corresponds to 66% of the maximum potential achieved if pl=p2, and ~/~t such that the negative effect of the highest price (Pl=Pl,max) is equivalent to a=$50,000 at year 10. Only 3 choices of price were given (0.975p2, P2 and 1.025p2). With these parameters, when considering Phoenix, the model puts one plant with a small capacity at first, building up to full capacity (15,000) in year 7, using only about 1.25 million of the 1.5 million available. It sells and advertises in Arizona with the lowest price possible, and decides to sell in New Mexico at a highest price without any advertising, for only two years, after which it abandons that market. One interesting result is that it advertises in Arizona until year 9, time at which decides to stop, because of the natural growth of the inferiority function. When ~tt was halved, Nevada was added as a market for a few years to later abandon it: the investment is slightly lower (1.175 million).

5. Conclusions A multi-site capacity planning problem recently developed, which contained location dependent transportation costs and budgeting constraints as well as sales, prices and advertisement costs as variables, was developed. A combination of low prices and advertisement can be a good strategy coupled with capacity planning expansions. Future work will include larger initial investment, uncertainty and risk. References Ahmed S. and Sahinidis N.V., "Robust process planning under uncertainty", Industrial & Engineering Chemistry Research, 37(5):1883-1892, (1998). Dixit, A. K. and J. E. Stiglitz, "Monopolistic Competition and Optimum Product Diversity." The American Economic Review, 67, pp. 297-308 (1977). Guill6n G., Bagajewicz M., S. E. Sequeira, R. Tona, A. Espufia and L. Puigjaner. Integrating Pricing Policies and Financial Risk Management into Scheduling of Batch Plants. PSE 2003. 8th International Symposium on Process Systems Engineering. China, June, (2003). Hirshleifer J., D. Hirshleifer, Price Theory and Applications. Prentice Hall, New Jersey, (1998). Iyer R.R. and Grossmann I.E., "A bilevel decomposition algorithm for long-range planning of process networks", Industrial and Engineering Chemistry Research, 37:474-481, 1998. Liu M.L. and Sahinidis N.V., "Optimization in Process Planning under Uncertainty", Industrial Engineering and Chemistry Research, 35:4154-4165, 1996. Rao, A G., Quantitative theories in Advertisement, Wiley, New York, (1970). Sahinidis N.V., Grossmann I.E., Fornari R.E., Chathrathi M., "Optimization Model for Long Range Planning in the Chemical Industry", Comp. and Chern.Eng., 13: 1049-1063, 1989. Spencer N., J. Godwin, M. Bagajewicz, S. Powell and S. Hodge Simultaneous Modeling of Location, Advertisement and Competition in Investment/Capacity Planning With Risk Management. AIChE Annual Meeting, Austin, Nov. (2004).

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1183

Multi-objective Optimization of Curds Manufacture N.G. Vaklieva ~*, A. Espuna b, E.G. Shopova a, B.B. Ivanov a and L Puigjaner b a

Institute of Chemical Engineering, Bulgarian Academy of Sciences, Acad. G.Bontchev Str. Bl.103, 1113 Sofia, Bulgaria

b Chemical Engineering Department, Universitat Politecnica de Catalunya E.T.S.E.I.B. Av. Diagonal, 647,E-08028 Barcelona, Spain

Abstract In this paper, an important profit/environmental impact trade-off problem in dairy is presented as a multi-objective optimization problem. A Genetic Algorithm (GA) is used to find the conditions leading to the best compromise between both objectives. Two cases, at different weighting coefficients are considered to illustrate an enhanced effect of the environmental impact on the multi-objective function.

Keywords: Multi-objective Environmental impact.

optimization,

Genetic

algorithms,

Dairy,

Profit,

1. Introduction A number of business and environment programs, initiated for Central and Eastern Europe, aim to assist the environmental performance of companies. Many of them, involving small and medium-size enterprises, promoted the use of innovative policies and instruments to deal with local and global environmental issues. The problem discussed in this work focuses in the necessary trade-off between plant profit and environmental impact in dairy products manufacturing. The aim is to find the best compromise between plant income for a given demand of two types of curds and the BOD load generated in their manufacture. The effect of the amount and composition of processed milk, processing unit's assignment and number of processed batches is taken into account in both objectives. Additionally, the BOD load is formulated so as to account for the inherent losses, which are considerable in dairy plants. Both targets are in a conflict and the search for a best trade-off between them entails formulating the multi-objective optimization problem and the application of an appropriated solution technique.

2. Process Description Curds are milk products containing about 80% water and 20% solids (casein, fat, minerals, microelements and other milk components). They are produced by acidification of the skimmed standardized whole milk with lactic acid bacteria or acidifiers. Author to whom correspondence should be addressed: [email protected]

1184 A description of the main production tasks ( l E L, L =3 ) (Baltadzhieva, 1993) and related information (Stefanis et al. 1997) are presented in Table 1. Table 1. Processing tasks description, where CY1 (x)* is a yield o f curds by-product with x milk fat content in the skim milk.

Processing tasks

Task Duration 30 min.

Task 1 Pasteurization Task 2 Acidification

240 rain.

30 rain.

Task 3 target products processing

Draining

-

Input/Output

Fractions

In. Skim milk Out. Pasteurized Skim milk In. Skim milk In. Culture Out. Curds by-product Out. Whey In. Curds by-product Out. Curds target product Out. Drained Whey

1 1 0.88 0.12 CY1 (x) * 1-CY1(x)

1 0.9 0.1

The particular case study under investigation involves the manufacturing of two types (i e l , I = 2) of curds: low fat-P1 (0.3%) and high fat-P2 (1%). The products composition and values of recovery factors are presented in Table 2. Table 2. Products composition and values o f the recovery factors.

Products P1 P2

Composition of target products

Recovery factors values

Moisture % 80 81.58

R S - solids

R C - casein

recovery factor 1.724 1.386

recovery factor 0.96 0.96

Fat % 0.3 1.009

Solids % 20 18.42

Both products manufacture cyclically in a single campaign (TC i = 4 hours). The dairy comprises the equipment units listed in Table 3. Table 3.

Plant data.

Type No

Pasteurizers 1 2

3

4

Vat reactors 5 6

7

Drainers 8 9

10

11

V [m3]

300

150

1oo

300

250

80

60

1oo

250

400

60

The production demand for each product is 7000 kg and must be manufactured into the horizon H of 400 hours. The cost of input milk C M is 0.25 BG Lv per kg, whereas the target products are sold at CC1 = 1.10 and CC2= 1.42 BG Lv per kg. Short Time High Temperature pasteurization by steam takes place in task 1 followed by cooling with chilly water. The heating energy required per kg of skimmed milk E H is 300 kJ/kg, while that required for cooling E C is 228 kJ/kg (Baltadzhieva, 1993). The costs per kJ of steam and chilly water are respectively CS=6, 32.10 -6 and C W = 1, 55.10 -5 BG Lv. The plant has two operators at a labor cost of L C = 1, 08 BG Lv per hour.

1185

3. Waste Analysis Wastewater generated after process cleaning has a considerable BOD. The B O D load depends on both, the composition and amount of processed milk, and spillage and losses of raw material, by-product and product as follows (Carawan at al., 1979, Overview of Dairy Processing, 2000): I) the B O D load of 1 kg skimmed standardized whole milk is determined as follows: B O D M (x) = 0.89.x + 1.031.MP%(x) + 0 . 6 9 . M L % ( x ) ,

where: - x is a milk fat in %, and M P % ( x )

and M L % ( x )

(1)

are protein and lactose

presented as functions of the milk fat in a skimmed standardized whole milk, II) The B O D load of associated to the processing tasks inherent losses are: Task 1. The waste is due to glued coagulated milk on the pasteurizer's walls. The B O D depends on the mass of processed milk: The B O D load of 1 kg of pasteurized milk is: B O D p - 1.5.10 -3 [kgO2/kg pasteurized milk].

(2)

Task 2. The pollution results completely from a spilled whey. The inherent leaks are WL%=1.6% of the processed whey mass. The B O D load of 1 kg of acid whey is: B O D w - 32.10 -3

[kg O2/kg acid whey].

(3)

Task 3. The polluting is due to both:

i) ii)

Discharge drained from the curds whey. The B O D load of 1 kg of acid whey is the same as in Task 2; Inherent losses of the target products gluing on the drainer's wall. They depend on the curds fat content F C % (Table 2)- CL% = 0.0017.FC%. The B O D load of 1 kg of curds is:

B O D c (x) = C Y ( x ) . B O D M (x)

kg 02

(4)

kg cheese

4. Formulation of the Multi-objective Optimization Problem 4.1. Variables Continuous variables x i , i ~ I, I - 2, are introduced to account for the fat skimming of the used standardized whole milk. A set of binary variables (p,i is used to structure production routes for each product i , as follows: (p,i - 1 if unit p ~ P, P - 11, is used for product i and 4"p,i-0 otherwise. Integer variables n i i E I , to account for the number of produced batches.

I - 2 are introduced

4.2. Mathematical model of curds processing The mathematical model that describes target products manufacturing comprises: a) The F D M (Fat in Dry Matter) equation. It keeps for the quality of target product (Johnson, 2000). The F D M value is determined using the product composition data listed in Table 2 and fat recovery factors RFi calculates accordingly FDM i =

RFixi , (RFix i + RCiMC% i )RS i

Vi ~ I

(5)

1186 where:

MC%i, is the casein content presented as a function of the milk fat content in

skimmed standardized milk. b) The Van Slyke balance equation. It is used to target product yield calculation as functions of fat content in the used milk: CY i =

[RFi.x i + R C i . M C % i ]RSi

, Vi E I

(6)

SC% i

c) Constraint keeping positive and less or equal to 1 value of the respective fat recovery factor: O < R F i <1,

(7)

VieI.

d) Constraint determining technological boundaries for milk skimming for the product: 0.05 < x i < 1.4,

Vi e I .

(8)

4.3. A d d i t i o n a l c o n s t r a i n t s

A) Structural constraints. They support structuring the feasible (at least one suitable units to be assigned to each task) and compatible production routes. The identification of appropriate units-p for tasks-/is carried out using the following array of binaries:

ID(i)-

Ii

000 1 1 1 0 0 00' 000 0 0 0 1 1 1 1

1

Vi.

(9)

Production routes' feasibility is kept by the following constraints:

/=1 /k,.p=l

(10)

)

while their compatibility requires" I

~_,(p,i < l

(11)

Vp, p e P .

i=l

B) Production constraints. They aim to ensure manufacturing the planed amounts within the time horizon H. The products batch size is given by" ~., Vp .ID( i) tp . ( p,i Batch i - m i n ,

p

, Vl, l e L i , Vi, i e I ,

s(i)~

(12)

where the size factors -s(i)t depend on the milk fat. A number of batches, considering queuing times, must be chosen so as to ensure demand fulfillment into the time horizon: min max n i <_ n i <_ n i ,

ni.Batchi > Qi,

Vi, i

e

I,

Vi, i e I ,

(13) (14)

1187 n~.TQ + ~ (T~,~ - T Q ) _ H ,. Vi, i ~ / .

(15)

1

4.3. Multi-objective function Because the target is to find the best trade-off between the environmental impact and the profit, the multi-objective optimization criterion must have both into account. A) The environmental impact. The Global B O D "processed" from the plant is used as an environmental impact assessment, Stefanis at al. (1997). It is defined by the B O D "generated" in the tasks, due to determined pollutants- w ~ W, W = 3 : GBOD - Z

rt i Batchi

i

w

where: m(i)w/

(16)

Z Z re(i)w,/BODw, l

[kg/kg] are the pollution indices related to pollutants in the tasks,

determined on the basis of pollutants mass balance (Hilaly and Sikdar, 1995). The environmental impact assessment must be subjected to minimization or maximization of its negative value: ~ l - m a x [ - Z n , B a t c h , Z ~-'~m(/) w,/ BODy ]. ) x,(,n\ i w I

(17)

B) The income function. It is formulated to present the production profit accounting for the products selling costs, milk cost, energy cost and labor cost. It is subjected to maximization. • 2 - max ~" rIi . ( - T C x,(,,,

i .2.LC

i

+ Batch i (CC i -

1

CM - EH.CS - EC.CW)).

(18)

CY i

The corresponding weighted multi-objective function is: MAX(al.O1 + a 2 . ~ 2 ) ,

(19)

where: c~l and a2 are weighting coefficients. The multi-objective optimization problem thus formulated is solved by using Genetic Algorithms developed in IChE-BAS, on the basis of the approach proposed in Handbook of Evolutionary Computation (1997), at the following settings: p o p s i z e 300; generations - 600; selection - linear rank; crossover - uniform and mutation - nonuniform. A dynamic penalization is used to transform the resulting constrained optimization problem to an unconstrained one. Pareto Frontier is generated by applying a methodology proposed by Messac and Ismail-Yahaya (2003).

5. R e s u l t s The problem above is solved at two different values of weighting coefficients a. In the first case the values of both coefficients are taken equal to 0,5, which results in the optimal solution of 250,163 at B O D load of-242,753 and being the plant income 743,077 Lv. In the second case the 691 weight is increased to (zl=0,7 then c~2=0,3. This results in the optimal solution of 53,098 at -233,147 B O D load and 721,002 Lv plant income. The values obtained of controlled variables for both cases are listed in Table 4.

1188 For comparison purposes, the problem solution has been run separately for the particular objective functions eq. (15) and eq. (16). Then, the optimal B O D load obtained in-183, 6, while profit is 835,61 Bg Lv. Table 4.

Values of controlled variables at the optimal solution.

Product Batch size [kg]

P1 P2

85,56 111,24

P1 P2

99,82 103,42

Milk fat %

Number of batches

Units

Task l Task 2 al=0,5 a2=0,5; Optimal solution of 250,163 0.075 82 1 6 0.233 99 2, 3, 4 5, 7 al=0,7 a2=0,3; Optimal solution of 53,098 0.079 72 2, 4 6 0.237 99 1, 3 5, 7

Task 3 11 8, 10 8, 9 10, 11

6. C o n c l u d i n g R e m a r k s This paper deals with a trade-off problem between profit and environmental impact in a dairy plant. A Genetic Algorithm technique is found as an appropriate solution approach. The amount and composition of processed milk and inherent losses are accounted in the Global B O D assessment. The conditions at which is attained the best compromise between both objectives are found. The effect of overweighting of the environmental issue on the solution is also shown.

References Baltadzhieva, M.A., 1993, Technology of Dairy Products (in Bulgarian), Zemizdat, Sofia. Carawan, R.E., J.V. Chambers, R.R. Zall, 1979, Spinoff on Dairy Processing Water Management, Extension Special Report No AM-18.B, January, The North Carolina Agricultural Extension Service. Handbook of Evolutionary Computation, 1997, IOP Publishing Ltd and Oxford University Press. Hilaly A. K., Sikdar S. K., 1995, Ind. Eng. Chem. Res., 34, 2051-2059. Johnson M., 2000, Dairy Pipeline, 12, No 2 (July), 9-11 Messac A., Ismail-Yahaya A., Mattson C. A., 2003, Structural and Multidisciplinary Optimization, 19 (No 2), 86-98. Overview of Dairy Processing, Cleaner production Assessment in Dairy Processing, COWI Consulting Engineers and Planners AS, Denmark, for UNEP and Danish EPA, 2000, 7-11. Stefanis S.K., A.G. Livingston, E.N. Pistikopoulos, 1997, Computers&Chem. Eng., 21, 10731094. http ://www.rec.org/REC/Programs/SofiaInitiatives/SI.shtml Acknowledgements This study is carried out by financial support of Bulgarian NCSR- contract X-1108 and VIII Commission for Scientific and Technical Cooperation between Spain and Bulgaria - Research Project "Waste minimization and reliability operation of Batch Plants".

European Symposiumon ComputerAided Process Engineering- 15 L. PuiNaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1189

Global Supply Chain Network Optimisation for Pharmaceuticals Rui T. Sousa a, Nilay Shah a* and Lazaros G. Papageorgiou b a

Centre for Process Systems Engineering, Imperial College London London SW7 2AZ, UK

b Centre for Process Systems Engineering, Department of Chemical Engineering, UCL (University College London) Torrington Place, London WC1E 7JE, UK

Abstract In the pharmaceutical industry, the historically high margins of profit are harder to come by so it has become vital to look at each enterprise as a whole and try to extract the maximum value from its supply chain. In this work we address an optimisation problem for the product allocation-distribution structure of a pharmaceutical company supply chain, from primary (active) ingredients production to final product distribution to markets. Given the multi-period demand profile of the company's portfolio, the model tries to allocate the products to sites and to address other issues that supply chain managers usually face. The objective is set as the maximization of the company's NPV. The full space model is not tractable in a reasonable time, so two decomposition algorithms have been developed: a heuristic method where frames of products are optimised sequentially and a Lagrangean decomposition method. The first algorithm reduces the CPU substantially while maintaining the quality of the final results.

Keywords: supply chain networks, large-scale optimisation, pharmaceuticals

1. Introduction In the past, the large R&D in full based multinationals have always enjoyed a very important economic status. This comfortable position was possible due to: a) high productivity of the R&D activities, b) long effective patent lives of new compounds and ability of these to provide technological barriers to entry, c) limited number of substitution products that could compete with drugs in a given therapeutic area (leading to high demands of these compounds) and d) low price sensitivity due to separation between prescribing and paying responsibilities. The corporate strategy was to explore the price inelasticity ensuring high margins of profits and investing a significant proportion in R&D. In the past 30 years, the operating context of this industry has evolved and become much more challenging. Nowadays, R&D productivity is declining and costs rising due to new regulatory requirements, increasing the time to market. This leads to effective Author to whom correspondence should be addressed: [email protected]

1190 patent lives shortening, which, in addition with product substitutes in many therapeutic areas (either alternative products or off-patent generics), has shortened the market exclusivity period of new drugs. Simultaneously, healthcare payers are exerting strong pressure on prices and prescription policies.

1.1 Previous works in supply chain in the pharmaceutical industry Rotstein et al (1999) model the supply chain of a pharmaceutical industry, from the drug development stage until final manufacture. The demand forecasts are uncertain, dependent on the clinical outcomes. This paper is the first to approach the problem in a holistic perspective by considering production issues and capacity investment together. The expected NPV is estimated for a composition of scenarios. Papageorgiou et al (2001) take the same initial model, insert a higher degree of detail in the production process and take into account the trading structure of the company. However, this time the problem is formulated as a deterministic, multi-site, multi-product and multi-period problem. Levis and Papageorgiou (2004) introduce an uncertainty factor, where the demand forecasts are dependent on the results of the clinical trials for each product. Gatica et al. (2003) address the issue of product development and uncertainty in clinical tests outcomes, but from a different perspective of the previous works. They consider several pharmaceutical drugs in different stages of the development process. The multistage, multi-period, stochastic problem gives rise to a multi-scenario MILP model. 1.2 Solution methods for large MILP models Gupta and Maranas (1999) formulate a problem, characterized by the production planning of multiple products, in multiple sites, with deterministic demands due at the end of a finite number of time periods. The authors develop a decomposition algorithm based on Lagrangean Relaxation in conjugation with a specific heuristic procedure. The main strategy is to decompose the original model into a collection of smaller, more tractable sub-models. Jayaraman and Pirkul (2001) address a supply chain design/ product allocation problem. In order to solve it, they relax three blocks of constraints that allows them to decompose the original problem in three different sets of subproblems. The first two ones, after a minor heuristic procedure, are converted in sets of independent knapsack sub-problems. The third sub-problem is a trivial one that can be solved in linear time. Maravelias and Grossmann (2001) introduce a good example of a model composed of two (or more) independent sub-models with one linking constraint. Making use of this feature, the authors duplicate the linking constraint variables and build a Lagrangean decomposition scheme, resulting in two independent sub-models. Iyer and Grossmann (1998) and Levis and Papageorgiou (2004) give two examples of hierarchical algorithms. In the first step, an aggregated version of the model, with a reduced variable space, is solved in order to make the "here-and-now" decisions. In the second step, a detailed model is solved subjected to the decision variables estimated in the previous step. Rotstein et al (1999) execute a similar procedure in a reduced scenario space in the first sep. 2. P r o b l e m D e s c r i p t i o n The participants in the enterprise's supply chain are primary sites (active ingredient manufacturers) and respective storage facilities, secondary sites and respective

1191 warehouses and final product market areas. The distribution network within each market area is out of the scope of this work. Each primary site may supply the active ingredient to any of the secondary sites and be located in any place around the world. There are five geographical areas for secondary sites and markets. Since the transportation costs are very significant at this end of the supply chain, material flows between two different areas are not allowed. Each secondary geographic area produces and consumes some product families, but not all, from the company's portfolio and a single sourcing policy is followed, i.e. each product (both primary and secondary) will be produced in one and only one site on each time period. The model assumes an initial allocation of products to sites. Due to several events, such as organic growth or merges/acquisitions, this configuration may not be optimal anymore, so the model allows the assignment of products to sites to change between different time periods ("allocation transfer"). For secondary products, this can only take place between sites in the same geographical area.

3. Mathematical Model Indices and sets: i primary products, c primary sites, l primary sites resources, p secondary products, s secondary sites, r secondary sites resources,./geographical areas, m market locations and t time periods, p/, ~ and Mi are the sets of secondary products (produced and consumed), sites and markets belonging to areaj. Parameters: Dt~,,,, demand forecasts, MT,./'MTPi/ manufacturing requirements of secondary and primary products, A,.JAPi,< availability of secondary and primary resources, CPSi~.,/CPPi~, secondary and primary products production costs, CTS,,,,, transportation costs of secondary products between sites and markets, CTP< average transportation costs between primary and secondary sites, PF~i, secondary product composition, V2t,, selling price, CTAz~.,/CTAP~< secondary and primary products allocation transfer costs, TFp secondary product yield, Vli internal selling price of primary products, TRS,/TRP< secondary and primary sites location tax rates, CUt~ indirect costs of unattended demand, K,7~ equals 1 if product p uses resource r, CIV inventory costs, Max upper limit of production rates. Continuous variables: Z NPV (objective function), PRt~.,/PRP~,, production rates in secondary and primary sites, /Vt,.,t inventory of secondary products in secondary sites, IVP~, inventory of primary products, TS~.......,secondary products flow from sites to markets, TP~.,, primary products flow to secondary sites, SLy,,,, secondary product sales, Up,,~ unattended demand. Binara, Variables: Xt~.,,/XPi<, allocation of secondary and primary products, XTt~.~/XPT~,, secondary and primary products allocation transfers decisions. The key constraints of this model are the ones concerning allocation of products. Constraint (1) accounts for the single sourcing option, constraints (2) and (3) state that the effect of allocation transfers will only occur O periods after the decision has been taken and constraint (4) limits the number of transfers that can happen in each time period. In this paper, only the secondary products allocation constraints are shown, but the formulation is the same for the primary products.

~-'Xf~,, -1 .~eS i

Vt, p ~ P / , j - 1,2,3,4,5

(1)

1192 o

XTp,_ o > Xp,, - ~-'Xps,_~

Vp,s,t > 0

(2)

- [1,o]

(3)

4=1

-< l ~ XTp, t < 3

W,t

(4)

p~PjseSj

The capacity constraint for secondary resources (5) states that the resources utilization needed to meet the desired production rates has to be lower than their availability. The Primary resources availability constraint has the same formulation without the changeover term.

Other constraints are production, (6) and (7), flow balances between echelons, (8) and (11), sales, (9), unfulfilled demand (10) and inventory, (12) and (13).

PRp,, <_Max Xp,, PRP~a < Max XP~a SLpm,

= ~ TSp ...., seSj

SLpm t ~ Dpm,

p

(6)

V i, c, t

(7)

Vj = 1,2,3,4,5, p ~ P i , m ~ M j , t

'v'j - 1,2,3,4,5, p ~ Pj,m c M j , t

Upmt = D pmt - S L p m :

T P,i "-~

Vp, s,t

PRpstPFip TF

(8)

(9)

'v'j = 1,2,3,4,5, p ~ Pj, m ~ m j ,t

(10)

Vi, s t

(11)

p

IVps , = IVmt_ 1 + p e p s , - ZTSpsm,

Vj - 1,2,3,4,5, p ~ Pj ,s ~ Sj

(12)

Vi, t

(13)

m~Mj

lye,

- Iv,.,_, + Z c

-

Z s

A special set of constraints is also included to account for forbidden flows between the secondary geographical areas as well as a set of non-negativity constraints. The objective function is the NPV, as mentioned before. The income is provided by sales of secondary products. The costs term includes secondary and primary production, inventory and transportation costs as well as tax costs in both locations. Z = sales revenues - primary products/sites costs - secondary products/sites costs (sales revenues - secondary products/ sites costs) T R S s - (internal sales revenues of primary products - primary products/sites costs) TRPc (14)

1193

4. Solution Methods Two algorithms were developed to tackle the problem: Lagrangean decomposition and product frames algorithm (PFA). The first method makes use of the intrinsic structure of the model matrix. The problem can be described as two separated sub-problems (concerning primary and secondary sites and products) with one binding constraint, (11). Doubling one of the two variables in the binding constraint, PRp.~,, a decomposition scheme based in Lagrangean relaxation is built, as described in Reeves (1993). The two sub-problems obtained are independent and easier to solve than the original problem. The sum of the optimum solutions will constitute an upper bond to the original problem while the set of values of binary variables will provide a lower bond, through a heuristic method. The values are used to update the Lagrangean multipliers. The iterative cycle is repeated until the convergence criterion is met. In the PFA, the list of secondary products is separated in several groups (frames) that are allocated sequentially instead of simultaneously. During this process, all the variables concerning the products outside the frame being optimised (both binary and continuous ones) are not modified. In the modified version of this algorithm (PFA modified) the products demanding higher resources usage are optimised first, and all the binary allocation variables of the secondary products that are still to be allocated are relaxed. This provides a partial solution for each frame that will be closer to the full space solution, while keeping a reduced binary variable space. An aggregated version of the model (AM) has also been developed, where dimension m is removed. The demand profiles, transportation costs of secondary products and final market prices are calculated as average quantities over the dimension m. The variable block TSp,.~,,, is deleted, the sales block is modified to SLp.~,, constraint (8) is substituted by constraint (15) and the objective function, constraints (9), (10) and (12) are modified. This reduces significantly the number of continuous variables (---30%). ~ P R , _<~ t

.s'~Si

DJ~,,/ V/-

1,2,3,4,5,p ~ Pj

(15)

t

5. Illustrative Examples Two examples motivated by an industrial situation were generated to test the model. The first set contains 6 primary sites, 6 primary products, 33 secondary sites, 30 secondary product families, 10 market areas and 12 time periods. This results in a model with 29,880 continuous and 12,480 binary variables. The second set has 10 primary sites, 10 primary products, 70 secondary sites, 100 secondary product families, 10 market areas and 12 time periods. This model contains 185,760 continuous variables and 84,096 binary ones. The algorithm performances are shown in Table 1. The Lagrangean decomposition method did not provide good results because the secondary product allocation sub problem alone demands a high computation time to solve. This is aggravated by the weak dependence between the primary sub-problem and the PRp.,.~variable, which increases the number of iterations needed for convergence. All the tests were performed on Unix based machines with 2 GB RAM and 1.8 GHz Pentium IV processor, running CPLEX 9.0 solver.

1194 Table 1. Performance and results obtained with the different solution methods, a not solvable in 250,000 s CPU, b two cycles, c one cycle, A M - A g g r e g a t e d version o f the model.

First Example LP LP (AM) Full Space 1 Full Space 2 Full Space (AM) PFA (AM) PFA modified (AM) PFA modified

Opt 475,847 486,130 469,190 467,190 473,909 448,224 473,120 474,118

Gap (%) 1.4 1.9 2.5 6.1 0.6 0.4

Second Example CPU(s) 100,002 7,111 29,714 1,927b 447 c 450 c

Opt Gap (%) 1,006,351 1,057,058 a a 16.2 909,546 2.1 1,035,799 a

CPU(s)

6,973 b 75,911 c

6. Conclusions and Future W o r k The full space model of the large problem is solvable neither for the detailed model nor for the aggregated version. The PFA on its simplest version is fast to solve but does not provide good quality results, especially with the large problem. Clearly, the modified version allows obtaining better results than with the first one. For the smaller first example, it is even faster since it only demands one complete cycle to find a good solution. With these methods only the aggregated model of the second example is solvable with reasonable result quality. Future work on algorithm design is required to solve large problems. This may be attained trough decomposition/hierarchical procedures or via hybrid approaches of mathematical programming and heuristic methods.

References Gatica, G., Papageorgiou, L. G., & Shah, N. 2003, Chemical Engineering Research & Design, vol. 81, A6, 665-678. Gupta, A. & Maranas, C. D. 1999, Industrial & Engineering Chemistry Research, vol. 38, 5, 1937-1947. Iyer, R., Grossmann, I.E, 1998, Industrial & Engineering Chemistry Research, vol.37, 2, 474-481. Jayaraman, V., Pirkul, H. 2001, European Journal of Operational Research, vol. 133, 2, 394-408. Levis, A. & Papageorgiou, L. G. 2004, Computers & Chemical Engineering, vol. 28, 5, 707-725. Maravelias, C. T. & Grossmann, I. E. 2001, Industrial & Engineering Chemistry Research, vol. 40,26, 6147-6164. Papageorgiou, L. G., Rotstein, G. E., & Shah, N. 2001, Industrial & Engineering Chemistry Research, vol. 40, 1,275-286. Reeves, C. R., Modem Heuristic Techniques for Combinatorial Problems/edited by Collin R. Reeves 1993, Blackwell Scientific, Oxford Rotstein, G. E., Papageorgiou, L. G., Shah, N., Murphy, D. C., & Mustafa, R. 1999, Computers & Chemical Engineering, 23, $883-$886. Shah, N. 2004, Computers & Chemical Engineering, vol. 28, 6-7, 929-941. Acknowledgements The first author acknowledges the Portuguese agency FCT through fellowship POCTI, SFRH/BD/12177/2003.

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1195

Linear Quadratic Control Problem in Biomedical Engineering Irma Y. Sfinchez Chfivez a*, Rubdn Morales-Mendndez b, Sergio O. Martinez Chapa c aMechatronics and Automation Department, bCenter for Industrial Automation and CElectrical Engineering Department, ITESM Campus Monterrey Eugenio Garza Sada 2501 Sur, 64,849 Monterrey NL, Mdxico

Abstract Optimal control allows the incorporation of functional constraints and requirements as a departure point for the design process. The glucose continuous control problem in a diabetic patient is addressed with the linear quadratic optimal control design principles. A glucose control system is proposed. The glucose-insulin dynamics is represented by the Ackerman's model. This model considers the glucose level as the single output, so a state space observer is used to estimate the blood insulin level. The cost function is defined in quadratic terms of the exceeding glucose level and the amount of supplied insulin. An optimal control law is generated under servocontrol and regulatory approaches. Robustness of the control law in each case is examined by a Monte Carlo simulation. Results demonstrate the suitability of the optimization and regulatory approaches in biomedical engineering problems.

Keywords: glucose optimal control 1. Introduction A control system for continuous drug delivery can reach or keep a desired physiological condition in a sick person. Diabetes mellitus is a chronic disease that affects the ability of the body to produce insulin or to be sensitive to insulin. The insulin allows the absorption of glucose in the cells to be used as energy. There are two major types of diabetes mellitus: juvenile-onset diabetes (type I) and maturity-onset diabetes (type II). In type I diabetes the cells of the pancreas that produce insulin are destroyed, which suggests a treatment based on introduction of insulin (Seeley et al. 1995). Insulin infusion can be done subcutaneously and intravenously. The subcutaneous route is easier and safer to manage, which is an advantage for closed systems implementation since it is the route used in traditional open loop diabetes treatment. The intravenous route avoids time delays to reach blood stream and to produce body response, which is convenient for continuous closed loop performance. Both insulin delivery types have been considered in closed loop treatment systems (Bellazi et al. 2001, Parker et al. 2001). Lispro insulin may combine the advantages of both routes because of its fast absorption after subcutaneous injection.

* Author to whom correspondence should be addressed: [email protected]

1196 An open loop treatment system may be seen as a partially closed loop system because medical prescription of insulin is based on home glucose monitoring among other information of the patient (Bellazi et al. 2001). Decision support systems have been designed for diabetes management for this kind of therapy systems. PID type controllers have been used for blood glucose control. A PID based on a sliding scale approach, tested in patients in intensive care unit, is reported (Chee et al. 2003). A PD controller has been derived with a pole assignment strategy and tested in patients (Bellazi et al. 2001). Robustness of closed loop systems has been achieved by adaptive and predictive mechanisms to account for sparse glucose measurement (Woodruff et al. 1988) and time variations of the glucose-insulin process. The model predictive control algorithm implements a self-tuning controller that has been studied by simulation (Parker et al. 1999) and tested in vivo (Dudde and Vering 2003). A quadratic performance criterion is usually considered in glucose advanced control algorithms in terms of glucose deviation and amount of exogenous insulin. In this work, a Linear Quadratic Control (LQC) problem is stated for designing an optimal controller in such terms. The formulation approach of this criterion may lead to tracking problems (Parker et al. 2001). Servocontrol and regulatory approaches are discussed. The paper is organized as follows. Section 2 presents the LQC problem and the Ackerman's glucose-insulin model. In section 3, the blood glucose level optimal controller is designed. Section 4 presents simulation results. Section 5 discusses the results. Finally, in section 6, the paper is concluded.

2. Fundamentals 2.1 Linear quadratic control problem The LQC problem consists of determining a control law u(t) to minimize the cost function given by equation (1):

J(u)--~1 e~ (ts)Se(t~)+-~1 ~0r [eV(t)Q(t)e(t)+u(t)R(t)u(t)~t

(1)

where S is a constant matrix; Q and R may vary with time; Q, R and S are symmetric matrices; S and Q are positive semidefinite, and R is positive definite. The control law u(t) is the input of the state-space model ~c(t)= A(t)x(t)+ B(t)u(t),

x(O) = x o defined in [to, tJ where A(t) is the state transition matrix and B(t) is the input matrix. An optimal control law u*(t) is assumed to exist for this problem in [to, t~. An optimal trajectory x*(t) is associated with u*(t). The control signal and the state vector are u(t) = u*(t) + ev(t) and x(t) = x*(t)+ ey(t) where e is a small positive number and v(t) is arbitrary. The optimal control law is obtained when c=0, which makes dJ(g)/dc =0. The control law is specified as u(t)=-Kdc(t)+K, Kc=R-1BrP, K=-R-1Br/~ (Naidu 2003, Vinter 2000) where P is a symmetric positive semidefinite matrix and la is a column vector, both used to define a costate vector 2(t)=Px(t)+~.

1197

2.2 Ackerman glucose-insulin model Research on glucose control in diabetic patients depends on the development of accurate models. Models based on mass balances between different organs or compartments have been combined with models for gastric absorption of food and subcutaneous absorption of insulin to form a high order non-linear model. However, a parsimony principle leads to the management of simpler models in order to obtain a closed solution to the optimal control problem (Parker et al. 1999). The Ackerman's model is widely known because of its simplicity, since it considers one compartment that represents the global glucose-insulin dynamics in the human body (Ackerman et al. 1965). This model is based on the glucose tolerance test where the basal level is disturbed by the intake of glucose. The Ackerman model can be used as a single input single output (SISO) system for the discussion of control issues, which can be solved before using broader models. The non-linear interaction between glucose and insulin is described by

G ( t ) - f l ( G , H ) + p ( t ) and t:t(t)-f2(G,H)+u(t) with G(t=O)=Go, H(t=O)=Ho, p(t=O)=O and u(t=O)=O, where G(t) is the glucose level, H(t) is the hormone level, p(t) is the external glucose supply rate and u(t) is the insulin infusion rate at time t. Considering the deviation variables g(t)=G(t)-Go and h(t)=H(t)-Ho, and applying a standard

linearization

procedure,

g(t)--mlg(t)-m:h(t)+p(t),

the

linear

representation

of

model

is

and / ¢ t ) - m4g(t)-m3h(t)+u(t). Parameters ml,

m: ,m 3 , and m4 have been obtained from experimental data (Yipintsol et al. 1973). In the case of a type I diabetic patient, m4=O. The term p(t) is not considered. The final state-space model is given by it(t) - Ax(t) + Bu(t), x(O)=O, y(t)=Cx(t)+Du(t) where x(t)=[x~(t) x:(t)]T=[g(t) h(t)]T,A=[-ml-m: O-ms], B=[O 1]~ C=[1 O] and D=O.

3. Optimal controller Under the servocontrol approach, let Xd be the desired glucose change in a diabetic person (Xd = Gd- Go ). Deviation of blood glucose level from its desired value (xl--Xd = G - Gd) and insulin infusion must be minimized. The objective function is" )2

2

where p is a positive weighting factor. By comparing equations (1) and (2), it can be identified that S - [ 0 0, 0 0], 0 - [ 2 0," 0 0], R - Z p , t 0 - 0 a n d t / , - o ~ . The optimal control law is u(t)=-K~x(t)+K, where K~.=[K1 K:] and K=m:xd/(p~). The tbllowing Ackerman model parameters in rain -1 are used: ml-0.0009, m:=0.0031 and ms=0.0415 (Yipintsol et al. 1973). With p - 1 0 rain 2 and xd =-200 mg/dl (according to the simulation problem presented in section 4), the parameters of the control law are ~=-9.8101x 10 -4 min -2, K1=-0.2991 rain -1 and K~=0.0183_ min -1. For the regulatory approach, a normal glucose level is referred as the initial steady state. Any deviation from this value is a disturbance. Therefore, x l is the deviation of glucose level from the desired value. From the performance criteria represented by equation (3), the control law is u(t)=-K~x(t) with K, =[-0.2991 0.0183].

1198

The control law in both approaches is a function of the two states of the system, glucose

(xl(t)) and insulin (x2(t)) concentrations. The glucose concentration measurement is supposed to be available while the insulin concentration needs to be estimated. The design of the control law and the design of the state observer are independent. The state observer is designed according to classical control theory. The Ackerman's model is an observable system. The observer model is given by

~(t) - A'Y(t) + Bu(t) + Ke[y(t )- CY(t)] where y(t)- CY(t) is the observation error. The gain vector Ke=[0.2021 -2.1023]~ produces a faster observer response with respect to the closed loop behaviour.

4. Simulation The simulation problem consists of a situation of hyperglycaemia in a type I diabetic patient with an initial glucose level of 300 mg/dl. The closed loop system should reach a desired steady state level of 100 mg/dl. The sensor and actuator are assumed to be ideal systems and the open loop dynamics is supposed to be dominated by the model of the patient or physiological process to be controlled. Under a servocontrol approach, the initial deviation value is zero assuming an initial stable state in hyperglycaemic condition (300 mg/dl). The glucose change to be achieved is -200 mg/dl. Simulation results are shown in figure 1. The transitory elapses 4 hours (left-top graph); a steady state error of 0.3 mg/dl is detected (right-top graph); estimation of insulin concentration is reliable (left-bottom graph), and the cost function grows indefinitely (right-bottom graph). For the regulatory approach, the reference steady state is the normal condition of glucose level at 100 mg/dl, so the initial deviation of 200 mg/dl is considered a disturbance to the closed loop system. No offset error is obtained, and the cost function converges.

5. Discussion The stated simulation problem has been presented in the literature (Kikuchi et al. 1978). Glucose levels at 1 and 2 hours with the servocontrol approach are very similar to reported values. Glucose levels of 185.98 and 119.86 mg/dl are obtained while previous works report = 183 and = 119 mg/dl at these times respectively. For the regulatory approach, glucose concentrations of 166.8 and 112.57 mg/dl are reached at 60 and 120 min. These results differ more from the reported results, however the performance is more satisfactory. The situation simulated for performance comparison between the servocontrol and regulatory control approaches consists of an initial hyperglycaemic condition, instead of a meal disturbance managed in recent works (Parker et al. 2000, Kienitz and Yoneyama 1993) as enough proof for the adequacy of the regulatory formulation.

1199

3oo.~

102 101.5

25o \ ea, O,ucose,eve,

2oo~

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Real glucose level

100.5 100

E

Desired glucose level

99.5'

lo0i

Desired glucose level

99 98.5

Insulin supply °o

50

100

150

200

Time (min)

250

300

93800

350

400

200

400

450

500

550

600

600

800

1000

1200

Time (min)

3 x 106 "(D

0

E ~_~ -0.01 0

E ._o

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0

o

00 O

-0.04 050!

-0050

50

100

150

Time (min)

200

250

300

Time (min)

Figure 1. Servocontrol approach results

A linearized and low order glucose-insulin model may cause uncertainty as non-linear high order models do. Although a more complete model may be suitable to manage characterized uncertainty (Parker et al. 2000), all effects may not be represented, which justifies a random variation of model parameters to analyze controller robustness. Monte Carlo simulation proofs the robustness of the control system. To illustrate the variability, figure 2 presents box and whisker plots for different percentages of variation. These graphs were computed by 30 independent runs. Beyond 60% parameter variation, the servocontrol system shows unacceptable performance. The regulatory design performs with no significant difference with more than 50% variation.

6. Conclusions Blood glucose control in a diabetic patient is an example of a biomedical problem where optimal control theory (LQC) can be applied. The servocontrol system gives results similar to those reported for the same simulation problem. A small offset is observed in the final steady state in this work. The regulatory control approach is more appropriate for this biomedical problem because no specification of a desired change is required; instead, any blood glucose deviation fiom its normal value is managed as a disturbance to be solved to recover the normal state. The regulatory system is more robust to variations in plant dynamics since the offset does not appear. Given the natural time variation of physiological processes, predictive or adaptive control laws can have superior performance (Parker et al. 1999, Morales-Men6ndez et al. 2004). Closed loop diabetes treatments tend to be bloodless, painless and more precise than conventional treatments consisting of insulin injections with certain frequency and doses. Implementation of proposed closed loop treatments requires microsystems with reliable continuous sensors and actuators and embedded control algorithms.

1200 .o_ O t-=3 ~_

o o o

o r)

° 1!f 8

5

~

.la_

10

20

O 40

60

5

10

20

40

50

5

10

20

40

50

m

'*- - 1 0 I

I

82 5

10

20

40

60

°VoAckerman's model variation

0

% Ackerman's model variation

Figure 2. Robustness tests. Left-graphs for servocontrol, right-graphs for regulatory approach

References Ackerman, E., Gatewood, L., Rosevear, J. & Molnar G. 1965, 'Model Studies of Blood-Glucose Regulation', Bull. Mathem. Biophys., vol. 27(suppl). Bellazi, R., Nucci, G. & Cobelli, C. 2001, 'The Subcutaneous Route to Insulin-Dependent Diabetes Therapy', IEEE Eng. in Medicine and Biology, vol. 20, no. 1, pp. 54--64. Chee, F., Fernando, T. & Van Heeden, P. 2003, 'Expert PID Control System for Blood Glucose Control in Critically Ill Patients', IEEE Trans. Info. Tech. in Biomed., vol. 7, no. 4, pp. 419-425. Dudde, R. & Vering, T. 2003, 'Advanced Insulin Infusion using a Control Loop (ADICOL) Concept and Realization of a Control-Loop Application for the Automated Delivery of Insulin', 4 th International IEEE EMBS Special Topic Conf on Info. Tech. App. in Biomed., pp. 280-282. Kienitz, K. & Yoneyama, T. 1993, 'A Robust Controller for Insulin Pumps Based on H ~ Theory', IEEE Trans. on Biomedical Eng., vol. 40, no. 11, pp. 1133-1137. Kikuchi, M., Machiyama, N., Kabei, N., Yamada, A. & Sakurai, Y. 1978, 'Homeostat to Control Blood Glucose Level', Int. Symp. Med. Inf. Syst., pp. 541-545. Morales-Mendndez, R., Mutch, J., de Freitas, N., Poole, D. & Guedea-Elizalde, F. 2004, 'Dynamic Modelling and Control of Industrial Processes with Particle Filtering Algorithms', Barbosa-P6voa and Matos H editors ESCAPE-14, Lisbon Portugal, pp. 721-726. Naidu, D. 2003, Optimal Control Systems, CRC Press, Boca Raton, F1. Parker, R., Doyle III, F. & Peppas, N. 1999, 'Model-based Algorithm for Blood Glucose Control in Type I Diabetic Patients', IEEE Transactions on Biomedical Eng., vol. 46, no. 2, pp.148-157. Parker, R., Doyle III, F. & Peppas, N. 2001, 'The Intravenous Route to Blood Glucose Control', IEEE Eng. in Medicine and Biology, pp. 65-73. Parker, R., Doyle III, F., Ward, J. & Peppas, N. 2000, 'Robust H~o Glucose Control in Diabetes Using a Physiological Model', AIChE Journal, vol. 46, no. 12, pp. 2537-2549. Seeley, R., Stephens, T. & Tate, P. 1995, Anatomy & Physiology, St. Louis. Vinter, R. 2000, Optimal control, Birkh6user, Boston, Ma. Woodruff, E., Gulaya, S. & Northrop, R.1988, 'The Closed-Loop Regulation of Blood Glucose in Diabetes', Proc. of the 14th Annual Northeast Bioengineering Conference, pp. 54-57. Yipintsol, T., Gatewood, L., Ackerman, E., Spivak, P., Molnar, G., Rosevear, J. & Service, F. 1973, 'Mathematical Analysis of Blood Glucose and Plasma Insulin Responses to Insulin Infusion in Healthy and Diabetic Subjects', Comput. Biol. Med., vol 3, pp. 71-78.

Acknowledgements The authors thank Dr. Graciano Dieck Assad and Prof. Oscar Miranda Dominguez for their valuable comments and the Consejo de Ciencia y Tecnologia del Estado de Nuevo Le6n for financial support.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1201

Using Structured and Unstructured Estimators for Distillation Units" a Critical Comparison Fabrizio Bezzo*, Riccardo Muradore, Massimiliano Barolo DIPIC - Dipartimento di Principi e Impianti di Ingegneria Chimica Universit~t di Padova, via Marzolo 9, 1-35131 Padova PD, Italy

Abstract The paper discusses the use of several structured and unstructured estimators for the control of a binary distillation column. An extended Kalman filter, three multivariate regression-based estimators, and a novel subspace identification-based estimator are compared in terms of design effort, on-line computational demand and control performance. Keywords:

inferential sensors, subspace identification methods, distillation columns.

1. Introduction Modem production control methods require the availability of reliable and timely information on product quality. When hardware quality measurement instrumentation cannot be used on-line, a common practice is to make use of the available process knowledge (first-principles models and on-line "secondary" measurements) to estimate the desired "primary" variables. Quality estimators based on first-principles models are usually denoted as structured. If a reliable physical model of the plant is not available (or is too burdensome for on-line use), unstructured estimators are preferred, which use some form of multivariate statistical methods to relate the secondary measurements to the primary ones. Following the work of Roffel et al. (2003), in this paper a structured estimator and several unstructured estimators are developed and critically compared to assess their effectiveness for the control of a distillation column. An extended Kalman filter, three multivariate regression-based estimators, and a novel subspace identification-based estimator are compared in terms of design effort, on-line computational demand, and performance in closed-loop operation.

2. Case Study A continuous distillation column model will be used as a case study; this model will be referred to as "the plant" in the following. The 12-tray column separates an ethanol/water mixture. Column design and operating parameters can be found in Bezzo et al. (2004). The column is described by a detailed tray-to-tray model taking into account mass and energy balances, with nonlinear tray hydraulics based on the actual Author to whom correspondence should be addressed: [email protected]

1202 tray geometry. Vapour-liquid equilibria are described by an NRTL model. The control objective is to keep the distillate and bottoms compositions close to their setpoints in spite of unmeasured disturbances on the feed. The LV control configuration is used. It is assumed that tray temperature measurements are available on-line in order to reconstruct the product composition values that are used as controller inputs. Note that, since the purpose of this study is to evaluate the performance of different composition estimators and not to devise the best control strategy for this column, we are not considering the (simpler) control approach where two pilot tray temperatures are considered as the controlled variables.

3. E s t i m a t o r D e s i g n The vector of estimated compositions at sampling time k will be indicated with :?(k)=[~D(k ) ~B(k)] r , where the x~ and xB are the ethanol mole fraction in the distillate and bottoms (respectively), and A indicates an estimated property. It will be assumed that only two tray temperatures (whose optimal locations are to be determined) can be made available to each estimator. A set of closed-loop data (under conventional temperature control) is also supposed to be available; these data are used to select the optimal temperature locations for each estimator, and to calibrate the estimators. 3.1 Extended Kalman filter (EKF) The structured estimator considered in this work is the well-known extended Kalman filter (S6derstr6m, 2002), whose formulation requires a state-space model of the plant. In order to keep the on-line calculation time reasonably low, this model must be a simplified representation of the plant. Therefore, several simplifications were made, such as constant vapour flows in each section of the column, piecewise linear vapourliquid equilibria, linear tray hydraulics. A discrete-time representation of this model was then obtained, so that the EKF can be written as: ~(k+ 1)-IF(~c(k))-K(k)Copt(x(k)) 1 So(k)+ K (k) y°pt (k)

,

(1)

2(k): L ~(k) where ~ is the state vector estimation, F(.) and Copt(') are the Jacobians of the nonlinear functions of the model, K is the Kalman gain, L is the matrix relating the full state vector to the distillate and bottoms compositions, Yopt is the optimal set of temperature measurements. A two-step procedure was devised to select the elements ofyopt. The first temperature measurement location is selected in such a way that an EKF using this single measurement provides the largest explained variance of the vector of estimated compositions. A similar approach is used to select the second location, with the EKF now employing two measurements (with the first one determined in the previous step).

3.2 Static linear estimator (SLE) The static linear estimator takes the form:

~(k) : Ayop , (k) + b

,

(2)

1203 where matrix A and vector b are computed using a least-squares regression approach. Note that if more (than two) temperature measurements were available, an alternative approach could be to rely on all the available measurements and use partial leastsquares regression to eliminate the input measurement collinearity and to design the estimator (Mejdell and Skogestad, 1991). In order to select the optimal temperature measurement locations, a procedure developed by Muradore et al. (2004) was used. Let Y and Z be the matrices containing the temperatures on each tray and the compositions XD and xB for a sufficient large time interval (calibration data), respectively. The procedure selects the optimal locations in a sequential manner using the sample correlation matrix between Y and Z, and the explained variance of the Z-block as a stopping rule.

3.3 Dynamic linear estimator (DLE) Augmenting the input matrix Yov, with past temperature measurements produces a dynamic linear estimator in the form: f ( k ) = A [ y o p `(k)

Yopt(k-1)

..-

)'opt(k-v)]+b

.

(3)

In this case, the A and b matrices are determined via least-squares regression, while the number "~ of past measurements is selected by trial and error. The optimal temperature locations are calculated in the same way as done for the SLE.

3.4 Static nonlinear estimator (SNLE) The static nonlinear estimator uses a nonlinear mapping between the optimal selected temperatures and the estimated concentrations. A second-order polynomial function is used to relate the input and output data: ..~( k ) - Al yop~ ( k ) + A~_.v 2o;,(k)+b

,

(4)

where the polynomial coefficients are determined via least-squares regression. The optimal temperature locations are selected as done for the SLE.

3.5 Subspaee identification (SID) based estimator The last unstructured estimator considered in this work is based on a subspace identification approach (Van Overschee and De Moor, 1993). The advantage of this approach is that the identification algorithm directly provides the dynamic model order, so that the problem related with the determination of z in the DLE is circumvented. The first step in SID is to identify a linear state-space dynamic model for concentrations and temperatures. With reference to equation (5), calibration data matrices Y and Z are used to compute matrices F, K, L, C. These matrices allow mapping the innovation [e:(k) e,,(k)] r, which is strictly related to the process and measurement noise in the plant, into compositions and temperatures. Therefore, the identified model takes the form: x(k + 1) = F x(k) + K[e: (k) z(k) = L x(k) + e_ (k) _

e,, (k)]

(5)

y ( k ) = C x(k) + e,, (k).

The analysis of the observability Gramian allows to select the temperature locations that are more related to the state vector. Finally, a Kalman filter is designed:

1204

.~(k + 1)- F ~(k)+

G(k)[Yop,(k)-Cop,fc(k)l (6)

~.(k)= L.;c(k)+ J[Yopt(k) - Cop,fc(k)l where G(k) is the Kalman gain and matrix J takes into account the covariance between ey and ez. 0.7837 0.780

3000

I

- - -ideal

---idealrea

.................r e a l

"E" 0.777 o o 0.774

%'- 2500 o 2000

0.771 o vE x

0.765

1500 .._4 m 1000 x

0.762

500

0.768

0.759

,[

F

0

.

500

1000 time

1500

2000

2500

0

(min)

250

,// 500 2000" time

22'50

2500

(min)

Figure 1. Product composition responses to a feed flow disturbance for the ideal and real case.

4. Simulation Results A closed-loop test is used to compare the estimator performances when a +10% step feed flow disturbance is delivered to the column. All simulations are compared to an "ideal" case, where it is assumed that the product compositions are available in real time and the quality controllers' inputs/outputs are continuous. Figure 1 compares the control responses of the ideal case to a "real" case where the composition signal is sampled and delayed to take into account the analyser delay (which is assumed equal to 10 min). The quality loops are tuned according to the relay-feedback procedure suggested by Shen and Yu (1994). Note that the performance of the real case is quite unsatisfactory and advocates the use of on-line composition estimators. Table 1. Selected temperature sensors and accuracy indices for different estimator designs. XD

EKF SLE SNLE DLE ( r = l min) DLE (r=2 min) SID

Selection RMS [x 103] T2, T 7 0.436 T3, T7 1.76 T3, T6 1.68 T3, T8 T3, T8 T2, T9

1.57 1.42 1.13

XB

ExVar 99.14 63.13 66.18 70.48 75.96 84.92

RMS [x 105] 1.38 2.06 1.96 1.53 1.30 2.06

ExVar 90.10 77.22 79.27 87.43 90.95 77.69

Table 1 shows the optimal temperature sensors for each estimator, and compares the estimation accuracy in terms of root mean square (RMS) error and explained variance (ExVar) as obtained in the estimator design stage (the bottom tray is tray number 1).

1205

Even if the ExVar and the RMS are the most sensible indices to assess the optimal sensor location, they appear to be less significant in order to compare the closed-loop performance of different estimators. In fact, Figure 2 shows that, although the EKF explains a considerably larger variance of the design data, all the other estimators exhibit a good performance in the closed-loop simulations (note that the profiles of the actual product compositions are reported on each graph). 0.772 ,

380 - - -ideal ................EKF .......... SID

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0.766 --

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<

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2000

2500

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,

,

250

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~:

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Figure 2. Product composition responses to afeed lTow disturbance using d(fferent estimators.

The SLE causes a not completely satisfactory control performance on xB. Making the estimator nonlinear or dynamic greatly improves the performance. However, a potential issue arising in the design of SNLE's and DLE's is that a systematic method would be desirable to choose either the order of the polynomial function (SNLE) or the sampling delay and the number of past measurements (DLE). The SID-based estimator overcomes the shortcomings of the DLE, although it appears that the control response is

1206 quite noisy in this case study. A way to counteract this problem could be to slightly detune the composition controllers. Anyway, the results achieved with this novel approach are promising, and further investigation is called for. The above estimators exhibit important differences in terms of design effort. The SLE, SNLE, DLE estimators are all very easy to design. The SLE does not need any tuning parameter, whereas the SNLE and DLE require the tuning of the polynomial order and of parameter -c, respectively, as previously commented on. On the other hand, the "standard" EKF design is much more demanding since a sufficiently reliable model must be available, and a time-consuming filter tuning is necessary. The SID-based estimator is a Kalman filter, too, but the identification procedure generates a low-order black-box model that does not require tuning, thus greatly simplifying the design of the estimator. As far as the on-line computation time is concerned, it is quite obvious that SLE, SNLE, DLE are very little demanding. On the contrary, the computational burden of the EKF is quite heavy because of the Riccati equation update and of the fast sampling for robustness. The SID estimator appears to be a good compromise, since a low-order linear model is used.

5. Conclusions Several structured and unstructured estimators have been compared in terms of design effort, on-line computational demand and effectiveness in a closed-loop test for composition control in a distillation column. The nonlinear and dynamic unstructured estimators proved to be a sensible choice for quality control. A subspace identificationbased estimator (where a reasonably simple, easy-to-identify dynamic model is used within a Kalman filter framework) proved to be a promising alternative.

References Bezzo, F., S. Varrasso and M. Barolo, 2004, On the controllability of middle-vessel continuous distillation columns, Ind. Eng. Chem. Res., 43,2721. Mejdell, T. and S. Skogestad, 1991, Estimation of distillation compositions from multiple temperature measurements using partial-least squares regression, Ind. Eng. Chem. Res., 30 2543. Muradore, R., F. Bezzo and M. Barolo, 2004, A sequential method for optimal location of measurement sensors in tubular reactors, Proceedings GRICU, Ischia (Italy), 12-15 Sept., 1383. Roffel, B., B.H.L. Betlem and R.M. de Blouw, 2003, A comparison of the performance profile position and composition estimators for quality control in binary distillation, Comp. Chem. Eng., 27,199. Shen, S.H., A.M. and C.C. Yu, 1994, Use of relay-feedback test for automatic tuning of multivariable systems. AIChE J., 40, 627. S6derstr6m, T., 2002, Discrete-time stochastic systems. Springer-Verlag, London. Van Overschee, P. and B. De Moor, 1993, Subspace algorithm for the stochastic identification problem, Automatica, 29, 649.

Acknowledgements This research was carried out in the framework of the MIUR-PRIN 2002 project Operability and controllability of middle-vessel distillation columns (ref. no. 2002095147\002).

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1207

Modeling of complex dynamics in reaction-diffusionconvection model of cross-flow reactor with thermokinetic autocatalysis Tereza Trfivni~kovfi a, Igor Schreiber a and Milan Kubi~ek b* aDepartment of Chemical Engineering bDepartment of Mathematics Prague Institute of Chemical Technology, 166 28 Prague 6, Czech Republic

Abstract We examine wave patterns occurring in a simple reaction-diffusion-convection model describing a tubular cross-flow reactor with exothermic first order reaction. First, only reaction-diffusion equations are solved by numerical integration to find characteristic spatiotemporal patterns. Then the effects of convection on these patterns are examined. It is found, that most of the resulting patterns are either steady state non-moving waves, or upstream traveling periodic waves. The analysis of this system includes determination of stability and bifurcations of spatially homogeneous steady state, which leads to a dispersion relation, and a direct application of numerical continuation method to the spatially distributed model.

Keywords: reaction-diffusion-convection systems, cross-flow reactor, chemical waves, nonlinear dynamics, bifurcation 1. Introduction Traveling chemical waves appear due to interplay of autocatalytic chemical reaction and diffusion (Kapral and Showalter, Eds., 1995). Pulse waves can travel through spatially homogeneous but excitable medium, while traveling front waves represent a switch from one homogeneous steady state to another. Near the borderline of excitability and bistable steady states in a parameter space, there may be a zone where more complex dynamics occur, including spatiotemporal chaotic structures (Merkin et al., 1996). Also, periodic phase waves may occur, when the homogenous system is spontaneously oscillatory. All these phenomena are present in the simple model of a cross-flow reactor with exothermic first order reaction studied in this paper when the longitudinal convective flow is absent (Vani~kovfi et. al., 2003, Trfivni~kovfi et. al., 2004]. We have also partly examined effects of added convective flow (i.e., advection along the reactor) (Kohout et al., 2003, Trfivni~kovfi et. al., 2004), in particular when the Lewis number Le is equal to 1. This corresponds either to a homogeneous reactor (Chang and Schmitz, 1975) or to a packed bed reactor with reaction in liquid phase. When Le is different Author to whom correspondence should be addressed: [email protected]

1208 from one, a differential convective flow occurs (Yakhnin et al., 1994) leading to convective instabilities (Yakhnin et al., 1995). On the other hand, interaction of reaction and convection in the absence of diffusion/dispersion generates steady state patterns (Nekhamkina et al., 2000), which become dynamic and complex as the dispersion is added (Nekhamkina et al., 2001, Sheintuch and Nekhamkina, 2001). The aim of this paper is to further examine effects of added convective flow on spatiotemporal reactiondiffusion structures for varying values of Le.

2. Model Equations We use a simple one-dimensional model of a cross-flow reactor with exothermic first order reaction (Yakhnin et al., 1994, Nekhamkina et al., 2000). The cross-flow reactor is a membrane tubular reactor (tube within a tube), which enables continuous supply of the reactant not only at the inlet but also through the membrane that forms the outer shell. The reactor is cooled through its inner shell. Although not used in current applications, this arrangement holds a promise of better control over the course of the reaction. The dimensionless mass and energy balance equations govern the spatiotemporal dynamics of the conversion x and dimensionless temperature y as follows, 0x OZ"

0x O~

L e oOy ,r

d c)~ O2y :2

a~

~

(x

)+Da(1 )e y+v ~' -x w -x -,

v -Oy ~

~

(1)

c~v ( y - y , ) + BDa(1 - x)e ~'-. 7+

v

(2)

The parameters in Eqs. (1-2) are: the dimensionless convection velocity v, the dimensionless thermal diffusivity d, the Damk6hler number Da, the Lewis number Le, the mass and heat transfer coefficients ~ and ~ , respectively, the dimensionless reaction heat B, and the dimensionless activation energy 7. The parameters Xw and yw are ambient values of x and y. We set c~ = 0.5, Xw = Yw = O, B/Le = 1O, d/Le = 1, 7 = 1000 and use v, ~ , Da and Le as variable or adjustable parameters. The system in the presence of flow is subject to Danckwerts boundary conditions,

~:-0" x-O,d °3y =vY; 04

4-L" °3Y=o,

Le

(3)

04

while Neumann boundary conditions are used in the absence of the convective flow, --0"

°3y = 0 ;

o4

~:-L"

°by = 0 ,

o4

where L is the dimensionless length of the reactor.

(4)

1209

3. E f f e c t o f v a r y i n g v at L e = 1 The homogeneous system (equivalent to a stirred packed bed reactor fed through the membrane only) shows a bifurcation diagram in D a - ~, plane where the region of bistability meets the region of excitability along a Hopf bifurcation curve (Vani~kovfi et al., 2003). Here a chaotic spatiotemporal structure occurs, which we call triangular chaos. The effect of the flow is shown in Fig. 1. At first, the chaotic pattern persists (Fig. l a), but as the flow is increased, a high-conversion steady state occurs which is nearly spatially homogeneous (Fig. 1b) with the exception of a narrow zone at the input. Next, this steady state develops small waves near the inlet (Fig.lc) that become regularly spread along the reactor as the flow is increased (Fig. 1d). For still higher v, the pattern breaks, and the low-conversion steady state is observed (not shown).

0 i 0

200

0

a) v = 0 . 5

20~)

b) v = 1.5 20(':

1 I

J[ J

4 do (~

0 0

40 ~

c) v = 3.0

0

d) v = 4.0

Figure 1. Effects o f convection on triangular chaotic pattern Le = 1.0, Da = 0.039558, ~, = 1.0, shades o f grey code conversion f r o m dark (x=O) to light (x = 1)

To understand the nature of these transitions we used continuation method and linear stability analysis of Eqs. (1-3), followed the steady state as v is varied, and generated a solution diagram (e.g., Kohout et al., 2002) in Fig. 2. It turns out that there are two Hopf bifurcations on the branch delimiting a range where the steady state is stable. The first one corresponds to the transition from Fig. l a to Fig. l b, and the second one corresponds to disappearance of the wavy pattern. Within the range of stable steady state the wave number is decreased as the convective flow is increased.

1210 0,9 0.8 0.7 0,6 0,5

'i

0.4

0,3 unstable stable Hopf bifurcation.................. , o.! 6 0 2 4 ................

0,2

............. 8

/]q !0

12

14

Figure 2. Dependence o f the conversion x at position ~ near the inlet on the convection velocity v shows effects o f convective f l o w on the stability o f high conversion steady state

4. E f f e c t o f v a r y i n g L e at v = c o n s t The effect of changing the Lewis number is studied for conditions that keep the same phase portrait in the reaction-diffusion system, that is, ~ / L e , B / L e and d/Le have to be kept constant and equal to the values for L e = 1. We chose to study the front wave at v = 3. For Le = 1 there are two coexisting fronts, the faster one is an ignition front, the slower one is an extinction front (Fig. 3a). Initially, the change in L e does not affect the ignition front, but has a drastic effect on the extinction front, which is converted into a steady state wavy pattern (Fig. 3b). Next, the ignition front is frozen, and the steady state pattern exists only in a part of the reactor (Fig. 3c). Finally, the ignition front is reverted and becomes an upstream extinction front, which pushes the wavy pattern toward the inlet so that only a narrow high-conversion zone remains (Fig.3d). By performing a linear stability analysis of the homogeneous steady state in an unbounded system we obtain a dispersion relation (Yakhnin et al., 1995, Nekhamkina et al., 2000) implying existence of a neutral curve corresponding to appearance of periodic waves with certain wave number k at various flow velocities v, see Fig. 4. When the frequency of these waves becomes zero, standing waves appear, indicated by a HopfTuring point in Fig. 4. This observation suggests, that even in the bounded system the steady state pattern in Fig. 3b occurs due to this Hopf-Turing point. 200

o~,

0 0

200

i ~iii!~i::~i;i;i;iiil;iZ:;i;i ........................... ....................... '7':%::'11:................................ ;;;7;11111:;11;1711;;;71;i~iiii;"~%! %~ ~i~11;7;;i;;i~iii:;;; ~ i~iiiii;!i;:...................... ¸. . . . . . . . . , . ..

0

200 "{:

a) Le = l.O, ~, = 0.99, d = l, B = lO

b) Le = 1.2, ~. = 1.188, d = 1.2, B = 12

1211 200

0i

{.~ +

c) Le = 1.5, c~. = 1.485, d = 1.5, B = 15

d) Le =2.0, Q = 1.98, d = 2, B = 20

Figure 3. Effects o f Lewis number on f r o n t wave D a = 0.04, v=3.0

5. E f f e c t of v a r y i n g v at Le = 600 The last case examined here is the effect of convective flow on reaction-diffusion patterns when L e is large. The parameters D a , B and ai+, are adjusted so that the corresponding homogeneous system is near the borderline between a high-conversion steady state and limit cycle oscillations, and the reaction-diffusion system displays chaotic dynamics that we call an undulating pattern (Fig. 5a). When the flow is slightly increased, this pattern is still chaotic and takes the form of upstream moving ripples (Fig. 5b). Then, after a transient, the moving waves become periodic (Fig. 5c). Further increase in velocity (Fig. 5d) causes the upstream waves to move faster, and an alternating pattern of one- and two-packet waves form during the transient, which eventually evolves into regular periodic waves. These waves have lower wave number as well as frequency than the earlier ones. 25

F

t

20

15

10-

+ \_____ 0

0

0.5

,,

1

Le = 1.2 T u r i n g point

1.5

2

k

Figure 4. Neutral curves corresponding to case b).from the Figure 3

6. C o n c l u s i o n s We have shown that the effect of convection on reaction-diffusion waves in a crossflow tubular reactor may lead either to a steady state wavy pattern for the Lewis number close to one or to periodic waves for large values of L e . It is known that reaction-

1212

:.i~ :N :N~ :::®:. ::N :: ~ N :;N! W

!iii i I

0

e i~ii :N~ ;::i~ ;~?: i:l

IIN:

:i!Ii:iN i~i @

:iii:

lik:$!

II :~!: ! ;~Ii:'i!::,iii?~!:)~; i~:,s:!!! i!iilt; ii:tS!!!;iiBiR!!iilt@i;)
:?i::k::~!!i::::~

200

0

" }0 g

:~0(1:

0

200

' ~ ; N N N " 7 7 N N N N N T ; :

0

", ~ , ~ "

i: :I

:it

~i

::

:

200

F i g u r e 5. Effects o f convection on undulating chaotic pattern Le = 600, D a = 0.064, ~ = 690. a) v = O.O, b) v = O.1, c) v = O.5, d) v = 1.5

convection steady state wavy patterns are related to periodic oscillations of the homogeneous system with L e = 1 (Nekhamkina et al., 2000). Since the reactiondiffusion patterns examined here are far from this condition when L e is large, convection cannot contribute to steady state pattern and periodic waves occur instead.

References Chang, M. and R. A. Schmitz, 1975, Chem. Eng. Sci. 30, 21. Kapral, R. and K. Showalter, Eds., 1995, Chemical Waves and Patterns. Kluwer Academic Publisher, Dordrecht. Kohout, M., Schreiber, I. and M. Kubi6ek, 2002, Comp. and Chem. Eng. 26, 517. Kohout, M., Vani~kovfi, T., Schreiber, I. and M. Kubi6ek, 2003, in Proc. of the ESCAPE 13, Kraslawski, A. and I. Turunen, Eds., Elsevier, Amsterdam, p. 725. Merkin, J. H., Petrov. V., Scott, S. K. and K. Showalter, 1996, Phys. Rev. Lett. 76, 546. Nekhamkina, O., Rubinstein, B. Y. and M. Sheintuch, 2000, AIChE J., 46, 1632. Nekhamkina, O., Rubinstein, B. Y. and M. Sheintuch, 2001, Chem. Eng. Sci. 56, 771. Sheintuch, M. and O. Nekhamkina, 2001, Catal. Today 70, 383. Trfivni6kovfi, T., Kohout, M., Schreiber, I. and M. Kubi6ek, 2004, Proc. of the 31st Int. Conf. of the SSCHE, Markog, J. and V. Stefuca, Eds., Slovak Univ. of Technology, Bratislava. Vani6kovfi, T., Kohout, M., Schreiber, I. and M. Kubi6ek, 2003, Proc. of the BOth Int. Conf. of the SSCHE, Markog, J. and V. Stefuca, Eds., Slovak Univ. of Technology, Bratislava. Yakhnin, V. Z., Rovinsky, A. B. and M. Menzinger, 1994, Chem. Eng. Sci. 49, 3257. Yakhnin, V. Z., Rovinsky, A. B. and M. Menzinger, 1995, Chem. Eng. Sci. 49, 2853.

Acknowledgements This work has been supported by the grants MSM 6046137306 of the Czech Ministry of Education and 104/03/H 141 of the Czech Science Foundation.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1213

A Design and Scheduling RTN Continuous-time Formulation Pedro M. Castro a*, Ana P. Barbosa-Pdvoa b, Augusto Q. Novais b aDepartamento de Modelag~o e Simulag~o de Processos do INETI 1649-038 Lisboa, Portugal bCentro de Estudos de Gest~o do IST 1049-001 Lisboa, Portugal

Abstract This paper presents a general mathematical formulation for the simultaneous design and scheduling of multipurpose plants. The formulation is based on the Resource Task Network process representation, uses a periodic, uniform time grid, continuous-time representation and originates mixed integer nonlinear programs (MINLPs) or mixed integer linear programs (MILPs), depending on the type of tasks and objective function being considered. Its performance is illustrated through the solution of two batch-plant example problems that have been examined in the literature.

Keywords: Resource Task Network, Uniform-time grid, Event points

1. Introduction Multipurpose plants are general purpose facilities where a variety of products can be produced by sharing the available plant resources (raw materials, equipment, utilities and manpower) properly in time. The production of a particular product involves a sequence of operations that can be batch, semi-continuous or continuous in nature, where a particular unit is usually suitable for more than a single operation. As a consequence, multipurpose plants are more flexible and suitable for the production of small quantities of high value-added products with short life cycles, the current trend of consumers' demands in today's competitive global market. These same special characteristics however, introduce extra degrees of complexity into the design and operation of such plants. In particular, it is not possible to design a plant without considering how it will be operated, neither it is possible to schedule all the required operations without knowing the plant configuration. Hence, design and scheduling must be considered simultaneously to avoid over or under design. Several authors have addressed the design and scheduling problem of batch plants. Few, however, have based the mathematical formulations on general process representations. Barbosa-Pdvoa and Macchietto (1994) presented a discrete-time formulation that uses the maximal State Task Network (mSTN). Examples of continuous-time formulations

Author to whom correspondence should be addressed: [email protected]

1214 are the work of Lin and Floudas (2001) for the STN and of Castro et al. (2004) for the RTN, with both assuming a short-term mode of operation. This work follows that of Castro et al. (2004) but now a periodic mode of operation is assumed. In addition, both batch and continuous tasks can now be handled. However, to avoid generating MINLPs, only equipment items characterized by size (not processing rate) will be considered. Thus, the two example problems chosen to illustrate the performance of the formulation involve the design and scheduling of batch plants.

2. Fundamental Concepts In the proposed formulation, the time horizon of interest (H) is divided into a fixed number of time intervals/slots. The interval boundaries are called event points (set T) and their exact location (Tt), as well as the cycle time (H) is unknown a priori. A single time grid keeps track of all events taking place (see Figure 1). In periodic problems, the beginning and end of the time horizon are the exact same event point. The wrap-around operator defined in eq 1 is used to overcome the problem of modelling the execution of tasks that span across two cycles and to facilitate the formulation of some constraints. i

i Cycle N

,~1 "-] 1

Slot 1

~

Slot 2

I

Slot T-1

I

2

3

/~/

I

-1--1

Slot T

I

T

l

Cycle N+I Slot 1

I

I

2

>

T+1-1

0

H

Figure 1. Uniform time grid for periodic scheduling problems ~ ( t ) - t - I T l if t > T , ~ ( t ) - t if l <_t <_ T l, ~ ( t ) - t+ T / f t < l

(1)

The quality of the solution returned depends greatly on the number of event points considered, ITI. For MILP models, the returned solution is a global optimum solution only if the pre-specified number of ITI is sufficient and does not act as a hidden constraint. The search for the global optimum usually involves solving the problem for different values of ITI until no increment is found in the objective function. To account for the fact that the majority of process tasks does not span across the whole time horizon, the number of event points allowed between the beginning and end of a task must not exceed At. A global value is assumed for all tasks belonging to the same type (e.g. batch, continuous, storage), with the requirement that At must equal 1 for continuous and storage tasks. Again, the use of an exceedingly low At value can also work as a hidden model constraint, so a similar procedure to that of ITI should be used. The RTN process representation regards all processes as bipartite graphs comprising two types of nodes: resources (set R) and tasks (set I), the latter being operations that transform a certain set of resources into another set. Two variables are used to characterize the instance of task i starting at event point t and ending at t'. The binary variable Ni,t, c identifies the occurrence of the task, while ~i,t,t' (positive continuous variable) gives the total amount of material processed between t and t'. The other required variables are the excess resource variables Rr.t, the existence variables for equipment resources ( R,.° _<1Vr ~ R eQ), the net consumption/production over the cycle & (for raw-materials, r ~ R

TM

or final products, r~RFP), the capacity V~ ( r ~ R Be) or the

1215 processing rate ,o,. ( r e R cE) of equipment resource r (depending on whether the equipment processes batch or storage tasks, I b or F, or continuous tasks, f ) . The task processing time is assumed to be given by a constant (c~) plus a term proportional to the amount of material being processed (fl~). The amounts of each resource consumed/produced at the start/end of a task are assumed to be proportional to the binary (~i..i / fi,..i) and/or continuous (v,.i/v,.,i ) extents of the task. The former parameters are usually linked with equipment resources, while the latter are typically linked with material resources. The other required parameter ( s f ) allows the amount processed by task i to be lower than the minimum design capacity of the equipment. Note that a 1:1 correspondence is assumed between tasks and equipment resources. Z / a , . , = Z,a,.., = 1 V i e i reR

(2)

reR

3. Mathematical Formulation The objective function considered (eq 3) minimizes the capital cost of units, which consists of a fixed term (if,,.) plus a term (fl,.) proportional to the size or processing rate of the unit. Other performance criteria can also be incorporated. In particular, one can maximize the profit of the plant for product demands between given upper and lower bounds. In the following constraints, R Tc represents all equipment resources with the exception of storage tanks. Note that batch tasks producing materials subject to zerowait policies (I zw) or continuous tasks subject to a predefined minimum rate (I EAtR) require two additional set of constraints (eqs 6 and 7). min Z

{d,-R,° +/TiV,I,.~R BE +/~,P,l,.~e (T)

(3)

reRnO

r,,-r,

->

r -1 Z

' ie//'

T~-T r < - H-

~-'fi,.,(%X-~.,., ' +fl,~'-~.,.,,)iel/' Z

-~r,iNZ,',' ' -

i e I ~' , I z~s"

'

R

(4)

, t , t ' e T , t < t'< A t + t

t'=~+l-IrlVreR rc ,t, t' < A t + t -

T I (5 )

Z

-~r,iNZ,t,t']t'=t+l)+ £.,t1R

i __1,

(6)

T

Z-fi,.i(~z,N---~.,.,, + fl , ~ , . , ., , ) + ieI h ,I z'"

Z

¢t ,. , ~ , ,, .,

iel' ,I E'~IR

> H-Hma~(1-

•

tot

ie I", I

- -

~,=~+~V r

max i

T t, - T l _< H max ( 1 -

Tt-Tt'

max

/Or

/el'

Z~,,iN--i.,., ' ieI ~ ,I zlr

t'=t+i

Vr e R TC , t , t < t'<_ A t + t

ioirain

Z~,-.iN--/.t.t'[,'=,+, ITI)-ieI' ,I £'~4R

(7) Z~r,i(o£iNZ,,,, ic1 ~ ,1 z~"

' + ~,~2,,,,')-

Z icl" ,1E~'~m

]d2'i¢i't't'

t'=t+l Irl Vr e

R Tc ,t,t'<_ At + t - I T [

Dr

TI - 0AHmin _
(8)

1216

Rr't = Rr'f~(t-') + ie, bZI

t'eT~"~(~r"N--~'t't' +Vr'i~"t't')+ t,~T~.~(~r,,Ni,t,,t+V_r,i¢.~,t,,t)l+ t _t-At+lTI

[/'/r,/N2,',~(TM) + -~r,iN2,f~(t-1),' + (Vr,i~-~,t,f~(TM' + V-r,i~i,f2(,-1,,,)l,~,

Z ielSviei

c

]+ieIz C"~r,/~:~,f~,,-l),, +

(9)

Z[(jLlr,i -~-~r,i)Ni,t @ (Vr,i +Vr,i)~i,t]-k- mrlt:l,r~RR M -- Arlt=l,r¢RFP ~/Iz E R, I E T ieI t B

Rr ,T - R O + Z Z ( idbtcT

Z flr ,i NZ ,t ,t ' + E -flr,i N i,, ,' ' ) + t'cT t'eT t
(10)

Z Z (flr,iN2,t,D(t+l) +/'l--r,iN2",t,TM ) V r ~ R EQ icI CvicI ~ toT R max Rrm i n -< R r,t -< -'r

~'r

R, t

E

(11)

T A A,. = d ,.max H V r e R FP

~

NL,t,t'sfi Z ,i'lr,iVr ~,-min <- ~i,t,t' ---~Vr , - m a x V i e i b ,t,t < t' < At + t v t' <_At + t - [ T I <- Ni,t,t' Z,Hr,i reR reR -

--

ATmin

Ni,t,f2(t+l)--

--

min

Z ~tr,iPr rcR

-

~

<- ~i,t,f2(t+l) <- Ni,t,n(t+l) H

max

--

max

Z ]lr,i [3r rcR

Vi e I c , t

e T

(12) (13)

Ni,t,D(t+l)Sfi Z ~ r , i V r min ~ ~:-~,,,fl(,+l) -< ~[i,t,fl(,+,) Z ~ r , i Vmax V i ~ I S , t ~ T rcR rcR

(14)

Ni,tsfi Z/lr,iVr-..min < ~i,t --- ,,-max < Ni,t _E_ /.lr,iV r V i e I t ,t • T rcR rcR

(15)

¢-i,t,t' <- Z ~ r , i V r V i ~ I b , t ~ T , t ' ~ T , t < t'<_ At + t v t'<_ At + t - I T I r¢R

(16)

~-~,,,~(,+,) <_(T,+,I,~ITI + HI,:IT I -Tt)Z~r,ilO r Vi

(17)

-

-

~ IC,t ~ T

rmR ~--~,t,g2(t+l) -< Z

(18)

-~r,iVr Vi ~ I S,t ~ T

reR ~i,t <- Z ~ r , i V r rcR

VieIt,teT

(19)

° V r e R EQ ~r e R sE --t . <. .V r. < v mr a x R--r

VrminR

m i n ,-, 0

,Or

max

1~r <_,Or <_t9 r

0

R r Vr •

R

EQ

,r e R

CE

(20)

(21)

4. C a s e Studies Two example problems taken from Barbosa-P6voa and Macchietto (1994) are used to illustrate the capabilities of the proposed formulation. The resulting MILPs were solved to optimality on a Pentium IV-3.4 GHz machine, running Windows XP Professional, by the commercial solver GAMS/CPLEX 8.1.

1217 In the first example (EX1) two raw-materials (S 1 and $2) are transformed into two final products ($5 and $6) through a sequence of processing steps. A maximum of four different equipment items (R1-R4) can be used, together with a storage vessel (V4) to store the intermediate material $4. The complete RTN representation of the process is given in Figure 2 while the resource data is given in Table 1. The maximum demand of $5 and $6 is equal to 8.333 t/h. It is assumed that the cycle time can vary between 6 and 10 h and that all intermediates are subject to ZW policies. As can be seen from Table 2, the problem is solved rather rapidly despite its relatively high integrality gap, and features an optimal cycle time of 6 h. The optimal schedule, together with the required capacities of the chosen equipment units (R1, R2 and V4), is given in Figure 4. The second example (EX2) involves three raw-materials (FeedA-FeedC), 5 intermediates, 2 final products (P1, P2), 4 main equipment units (Heater, R1, R2 and Still) and 4 storage vessels (V4-V7). The RTN representation of the process is given in Figure 3, while the problem data is given in Table 3. The maximum demand of P 1 is set to 3.3703, while that of P2 is set to 6.5 t/h. It is assumed that the cycle time lies between 5 and 15 h and that ZW policies apply. The optimal solution is given in Figure 5 and features a plant worth kS 400.87 with an optimal cycle time of 6.994 h. The plant consists of four pieces of equipment, where R2 and V6 are designed at their minimum capacities (70 and 10 tons, respectively). These values are still higher than the maximum amount of material being processed by all tasks taking place in those vessels (58.933 and 5.051, respectively) so there is still some unused capacity. @

i-: -

...... o. . . . TI_R4

:

;

0_

o..... o. . . . T4 R3

1

,

....

_~Yi~i~__~?_ .

.

.

Table 1. Problem data for EX1

-

....

"

....

.

Resource ',

,

_

Duration

2 h

T2_Ri

Duration= 2 h

/

~, . . . . Duration=

,,~ o.4

(~__~

R1 R2 R3 R4 V4

4 h

T3_R2. Duration= 4 h

stsa Dur.= Whate~r

/,7;. rain

/ V,max

40/70 70/120 70/120 40/70 10/60

~;.//~,. 150/0.5 120/0.2 121/0.2 151/0.5 20/0.2

Figure 2. RTN representation for EX1

Table 2. Computational statistics

Problem

T

I.V.

C.V.

5 6

85 240

246 716

EX1 EX2

C. 409 1220

Obj rel. MILP 202.3 149.5

Obj MILP 330.6 400.9

H (h)

Nodes

CPUs

6 7.00

2300 42353

3.5 149

Table 3. Problem data for EX2

Resource g min / v max

Heater 20/50

50/70

70/70

~,r/fir

100/0.2

150/0.5

1 2 0 / - 150/0.3 30/0.1 15/0.1 10/0.1 20/0.2

R1

R2

Still

50/80

V4

V5

10/30 10/60

V6

V7

1 0 / 7 0 50/100

1218 m2ff_ ....... I React2_R2 1 / ~

_ _ ~1 Heat L__ ~ 1 D.... l+0.0067*Si~e / -'%22J ' ! ' StriA ~_ . . . . . =, I D____* .... w ...... ,

I ..... ', L-:::::::_--::-f:::'? ..... i

~'C~__o?_

~.~(~5

4 . ~ D.... 2. . . . . . . . . . ..... 0.4 1 React2 RI r0.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . / D.... 2+0.057*Si~e .._t.. ,.~1 StlAB I _ _ _ ~ . . . . ..~lntAB'~l j | D.... Wh. . . . . I ',' ~, 0.8N@J ~__* @

',

Reactl_R1

'1~

Reactl_R2

"

......

;0.6 --b~.~)-

Dur.=2+0.0167*Si;~

,

, [

i

i ........

React3_R1

L t D 1 ~ [ Dur.=1+0.0083*Size

___._~' '.i t

"M_2)

..... -' .... I DbrS:~p°nb:l

I~- - @ 0 . 1

- ~.....~ - ,, ~ D .... 1Y0e.g233*Sizet . . . . . . I - ; 3 @ ,

,z

[

Figure 3. RTN representation for EX2

. V4 (28)

.

.

.

StS4; 28

.............................................................................................................................................. i 5.051 StlAB; 5.051

V7 (0)

StS4; 28

StlAB;

V6 (10)

I R4 (0)

v5(o)

i

:

R3 (0)

Still

T4

1

i

:

TI_RI" 42 0

1

T2 RI" 28 2

3

TI_R1; 30 4

5

Time (h)

Figure 4. Optimal solution for EX1

i

(50.51) 35.36

R2 (70) R1 (0)

R1 (42)

i

V4 (0)

:

Heater 6

React2_R2;58.933

• 50.514

Reactl_R2;

Heat;

23.573

(23.57) 0

2

4 Time

6

(h)

Figure 5. Optimal solution for EX2

5. C o n c l u s i o n s This paper presents a new continuous-time formulation for the simultaneous design and scheduling of multipurpose plants featuring batch and/or continuous tasks with fixed or variable duration. The formulation employs the Resource Task Network process representation making it entirely general and directly applicable to virtually any process. The efficiency of the proposed formulation was tested by solving two well known example problems. The results show that by solving a single model, one is informed of which equipments to buy, their size, the optimal cycle time and operating schedule. Although this is rather convenient, bear in mind that with current computers only small problems can be handled by this continuous-time formulation. Thus, there is still need for improvement and further developments should be expected in the forthcoming years. References Barbosa-P6voa, A., Macchietto, S. (1994). Detailed Design of Multipurpose Batch Plants. Comp. Chem. Eng., 18, 1013. Castro, P., Barbosa-Pdvoa, A., Novais, A. (2004). Design and Scheduling of Multipurpose Plants using a RTN Continuous-time Formulation. In Proceedings of the Sixth Conference on Foundations of Computer-Aided Process Design, Cache Publications: Austin, 2004; p 431. Lin, X., Floudas, C. (2001). Design, Synthesis and Scheduling of Multipurpose Batch Plants via an Effective Continuous-time Formulation. Comp. Chem. Eng., 25, 665.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1219

Use of Perfect Indirect Control to Minimize the State Deviations Eduardo S. Hori a, Sigurd Skogestad b* and Wu H. Kwong a aFederal University of Sgo Carlos Sgo Carlos - SP - Brazil bNorwegian University of Science and Technology N-7491 Trondheim - Norway

Abstract An important issue in control structure selection is plant "stabilization". By the term "stabilize" we here include both, modes that are mathematically unstable (modes with RHP poles) as well as "drifting" modes that need to be kept within limits to avoid operational problems. By this definition, we can include states x as variables that should be "stabilized", i.e., we want to avoid them to drift too far away from their desired (nominal) values. An advantage of this approach is that we are able to avoid problems resulting from nonlinear effects. Therefore, as the objective function can, usually, be considered as a combination of states, the control system obtained by this approach is not tied too closely to a particular primary control objective (which may change with time) because it allows the designer to change the control objective. This paper presents a way to reduce the effects of disturbances and measurement errors in the states and the results show the effectiveness of this approach.

Keywords: perfect indirect control; minimization; state deviations 1. Introduction In the regulatory control layer, the main objective is to "stabilize" the plant. Here we put the word stabilize in quotes because we use it with the same meaning as used by Skogestad (2004): "stabilization" includes both modes which are mathematically unstable (modes with RHP poles) as well as "drifting" modes which need to be kept within limits to avoid operational problems. Doing this we are able to avoid problems resulted from, for example, nonlinear effects. By this definition, we include any states x as variables that should be "stabilized", i.e., we want to avoid them to drift too far away from their desired (nominal) values. An advantage of keeping all states close to their nominal values is that we are able to avoid problems resulting from nonlinear effects. Therefore, an important point in the control structure selection is the choice of the operational objectives (Skogestad, 2004). The problem is that the operational objectives may change with time, according to necessities, e.g. market, safety constraints, etc. Due to these changes, we don't want to tie the control system too * Author to whom correspondence should be addressed: [email protected]

1220 closely to a particular primary control objective. As, usually, the objective function can be considered a combination of states, a good approach would be to define the objective function in this way (y~ = Wx). This approach has the advantage of allowing the controller designer to easily change the control objective only changing the combination of the states. Another advantage is that the minimization of Wx includes both stabilization of RHP-poles and disturbance rejection. In summary, the good of this paper is to discuss in more detail the approach introduced in Skogestad (2004) of selecting secondary controlled variables (e = Yz ) such that we minimize the effect of disturbances ( d ) on the weighted states ( y~ - Wx ).

2. Perfect Indirect Control Consider that we have the following linear model: Ay I - G1Au +GdlAd

(1)

Ay - GYAu +G~Ad + n y

(2)

where Gs are steady-state models. By definition, indirect control is when we cannot control the primary outputs (y~) and, instead, we aim at indirectly controlling y~ by controlling the "secondary" variables c (Skogestad and Postlethwaite, 1996). If the number of measurements ( # y ) is equal or larger than the sum of the number of inputs ( #u ) and the number of disturbances ( #d ), it is possible to obtain a combination of these measurements ( c ) that ensures a perfect indirect control of the "primary" controlled variables (in this case c is used as "secondary" controlled variable). Then we have" Ac = HAy -

HG y Au + HG y Ad + Hn y G

Gd

(3)

nc

where H is the combination of measurements. Solving Equation 3 with respect to Au • Au - G-1Ac- GlGdAd - G l n ~ In Eq. 4 we will consider

Ac-

(4) 0 because we want to keep these variables constant. In

this way, Eq. 4 becomes: Au - - G l n c - G-1GdAd

(5)

Substituting Eq. 5 into Eq. 1 gives: Ay I

-(Gd,-G,G-'Gd)Ad-G~G-J

nc

(6)

Pc

where the "partial disturbance gain" P~ gives the effect of disturbances on y~ with closed-loop (partial) control of the variables c, and Pc gives the effect on y~ of changes in c (e.g., due to setpoint changes in c~ or control error). As we want to reject perfectly the effect of the disturbance in the primary variables, we will select a set of controlled variables such that the matrix Pd is equal to zero. As was

1221 said before this objective can be reached if we have enough measurements y. The matrix P is a degree of freedom which can be arbitrarily specified ( P - P 0 ) by the designer, for example, when P - 1 we have a decoupled response from e s . To find the linear combination of variables we will make some additional assumptions: 1. # c = # y ~ = # u ; 2.

#y=#u+#d;

3. The matrix P0 is invertible. Then, we want to find a matrix H that gives us P~ - 0

and Pc - Pc0. Joining Eq. 3 and

6 results in: HEGY

G ~ ] - P c , I[GI

Gd,]

(7)

By assumption number 1 we have that the matrix IG y

GY 1 is square and, as the

measurements are independent, the matrix is invertible, then, finally: n - P-' co[G i

1

Gd, -.~ 1[ Gy

(s)

G aY, Y

When P0 - 1 and using c as secondary controlled variables, from Eq. 6 is easy to see thatG=G~ andGd=Gd~. 3. M i n i m u m

State Deviation

To keep the states close to their desired (nominal) values in the presence of disturbances and implementation error, we will define a matrix W , which represents a linear combination of the states. It can also be interpreted as the objective of the controller defined by the controller's designer. Consider the following linear model: x

Ax - GXAu + GdAd

(9)

Substituting Eq. 5 into Eq. 9: Ax - ( G ~ -GKG-IG~, ) A d - G K G -' n c -,,-

(10)

pX

Matrices px and pxd represent the effect of the disturbances and implementation errors in the states when we control combinations of variables. To avoid problems related to non-linearities, it is important that these matrices be as small as possible. Then, to minimize the effect of the disturbances ( d ) and the implementation errors (n c), we

want to minimize

norms PXrl, I1 ;11' and Px

important to emphasize

that we will not control the states x directly but, instead, we will "control" them using indirect control as presented in section 2. When we have perfect indirect control and when P~0 = 1, matrices G and G d become equal to G~ and Gd~, respectively. Defining the primary variables as linear combinations of the states ( Yl = Wx ):

1222 Ay, - W A x - WG._..__~Au+ WG~ Ad Gdl

(11)

Eq. 10 then becomes"

/'~X---(Cd- CX (WCX) -I W GXd)] a d - Gx (WCX) -`jn c

(12)

Important point to be discussed: what is the optimal choice of W that minimizes the value of I'd in Eq. 12? Assuming that W - G XT, results in: Ax= G ~ - G ~ GxTG x -'GX~G~ A d - G x GxTG x

(

( (

) 1 )_l

The matrix G x GXrG x

(

)'

n~

(13)

G x~ in Eq. 13 is called projection matrix (Strang, 1980). It

means that the product G x (GX~G x )-1 G xTG X d is the closest point to G dX , i.e., there isn't any other matrix W that can result in a smaller value of P2 than W = G x~ . Then we conclude that the choice of W - G

XT

gives us the minimum value of Pd" This will be

demonstrated in the example below. It is important to notice that this is not the only optimum choice because any matrix W = RG x" is an optimum solution, where R is any non-singular square matrix with apropriated dimensions. The choice of W = G xT is optimum for any choice of Pc0 non-singular, i.e., this result is not restricted to Pc0'- I. It is also important to notice that the matrix W can be arbitrarily chosen by the designer according to the objective of the process. For example, he can choose to make a combination of only some states or use all of them. In summary, the main result in this paper can be summarized as follows: Theorem: Let P~ denote the steady-state transfer function from d to x with e - Hy

kept constant. Then I'd 2 is minimized by selecting H = G xTG1G y~, where 7 indicates the pseudo-inverse.

4. Application to Distillation The proposed theory is applied to a distillation column with 82 states (41 compositions and 41 levels). As the levels don't have steady state effect, we considered that the objective function is a combination of the compositions only. This example has, after stabilization, 2 remaining manipulated variables (reflux flow rate ( L ) and vapor boilup ( V ) ) , and 2 disturbances (feed flow rate ( F ) and fraction of liquid in the feed (qF))" Having 2 manipulated variables, we are able to control perfectly 2 combinations of the states. The measurements ( Ay ) are the flow rates ( L , V, D , and B ). In this example we compared the effect of the disturbances in the states using, as primary variables, 3 different combinations of states (3 different matrices W ). The combinations used were:

1223 •

Combination 1: W was selected in order to select the bottom and top compositions as primary variables. This is the most common choice in distillation studies.

•

Combination 2: W was selected as being the transpose of G x ( W = G x' ). Combination 3 W was calculated solving ln~n [~px P~II2

For each combination we obtained the best combination of measurements (matrix H ) using Eq. 8. Then matrices px and pxd were calculated. The values of the 2-norm If P x II II Pat , and [px

p2]

,.

are presented in Table 1.

of

IP ll, 0" lieP" Pd311.to," a,',' 4

combinations.

1 3 4

" 11

E; I

48.8289 0.0252 0.2560

2.5182 1.0886 1.0886

liE

P:;ll

48.8817 1.0886 1.0886

Although the choice of the top and bottom compositions as primary variables (combination 1) is able to control perfectly these two variables (the closed-loop gains relating the disturbances to the bottom and top compositions are zero), the gains of the states in the middle of the column are very large (above 0.7) (see Table 2). And also this choice doesn't give good rejection of the implementation error (see matrix px in Table 2). As expected (session 3), the results presented in Table 1 confirm that the use of W - G x' is an optimum choice (it has the same value of lIP x

P:~I[I d as obtained by

optimization). As we can see in Table 2, combinations 2 and 3 (obtained by minimization) are equivalent in relation to matrix P] (are exactly the same in both cases). But when we t

analyze only px, we see that the use of W - GX gives us a better result. The reason is that, in the minimization, we are only interested in the norm liP X P×lld and, in this case, the norm of the matrix P~d is much more important than the matrix P~ This can be easily seen when we analyze Table 1 more carefully. Although the value of px I' for combination 3, is quite large (0.2560), the value of IlIP ~

PXll I d is almost the same

as

the value of IlP~ (it is important to emphasize that although the values of IP~[I and II Px

Pd~II presented in Table 1 for combinations 2 and 3 are the same, in reality the

values°VII Px

P:~IId are slightly larger than IPdx , the difference does not appear due

to truncation). As we can see in Table 2, the choice of W - G x' doesn't give perfect control for the top and bottom compositions, but it reduces the sensitivity of the states in

1224 the middle of the column (about 0.4) to variations in the disturbances. This point is important to avoid the effects of non-linearities in the process.

Table 2.

Valuesof the matrices px and P2 for the four combinations.

Combination 1 px PaX 1.00 1.49 i 12.13 12.50 12.43 :

0 0.00 : 2.21 2.72 3.23 !

6.51 4.93 4.85 5.02 4.82 6.63 0.01 1.41 1.00

]

Combination 2 px PaX _

0 0.00 " 0.32[ 0.40~

0.001 0.001 0.001 0.001

0.005 0.005 0.005 0.005 0.004 0.004 : !

0.0 -0.134 0.0 -0.088 0.0 -0.028

0.0 0.72[ I0.0 0.74[

0.001 0.001 0.000 0.000 -0.001 -0.001

0.0 0.351 0.0 0.413 0.0 0.354

-0.001 -0.001 -0.000 -0.000

0.0 -0.048 0.0 -0.034

0.0 '0.0 i 0.0 0.0 i

o.o;o.47/

Lo.o,0.73/ 0.0 0.00~ o . o o.oo/

_

Combination 3 px PaX

_

-0.0 -0.0320.0 -0.047

0.007 -0.0020.010 -0.003 i 0.081 -0.008 0.082 -0.005 0.081 -O.OO2 !

-0.0 -0.032 1 0.0 -0.047

0.036 0.020 0.024 0.024 0.021 0.035

0.0 0.351 0.0 0.413 0.0 0.354

-0.003 0.009 -0.002 O.007

0.0 -0.048 0.0 -0.034

•

0.0 -0.133 0.0 -0.088 0.0 -0.028

_

5. Conclusions In this paper we showed that it is possible to control perfectly (having perfect disturbance rejection and minimizing the implementation error effects) any combination of the states if we have enough measurements available. Therefore, it is shown the importance of the use of the combination of states as primary variables. Although the choice of the top and bottom compositions of a distillation column is good to reject perfectly the disturbances, it fails in the rejection of the implementation error and also it doesn't give a good control of the states in the middle of the column. The choice of W = G ×~ proved to be the best choice if the objective is to keep the states as close as possible to their desired (nominal) values. It rejects very well both disturbances and implementation errors, although it doesn't give perfect control of the top and bottom compositions. References Skogestad, S, 2004, Control structure design for complete chemical plants. Comp. Chem. Eng. 28, 219. Skogestad, S., and I. Postlethwaite, 1996, Multivariable Feedback Control. John Wiley & Sons, London. Strang, G, 1980, Linear Algebra and its Applications. Academic Press, New York. Acknowledgments The financial support of The National Council for Scientific and Technological Development (CNPq/Brasil) and [email protected] de Aperfeigoamento de Pessoal de Nivel Superior (CAPES/Brasil) is gratefully acknowledged.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) <>2005 Elsevier B.V. All rights reserved.

1225

Constraints Propagation Techniques in Batch Plants Planning and Scheduling Maria Teresa M. Rodrigues a and Luis Gimeno b* State University of Campinas aDESQ/FEQ, bDCA/FEEC - U N I C A M P - 13083-970 Campinas S.P., Brasil

Abstract The problem considered is make to order situations where products due dates and raw materials delivery times are constraints that the user must try to satisfy or negotiate. Those constraints, coupled with recipe and resource constraints, can be conveniently handled through constraints propagation techniques both in planning and scheduling. An interactive planning system is discussed where the user gets, after each decision, a feedback in terms of batches processing time windows, equipment units load and estimated resources utilization. APS-like scheduling heuristics exploit these measures to implement internal procedures to select batches in the sequential scheduling procedure.

Keywords: Constraints propagation, Planning, Scheduling 1. Introduction In planning and scheduling problems any solution must respect some set of hard constraints and additionally the user would like some other set of soft constraints to be satisfied or violated to some acceptable extent. Typically the user will begin with the full set of constraints and if no feasible solution is obtained will proceed to relax some constraints evaluating the cost of its violation. Scheduling techniques have always dealt with constraints enforcement in the form of constraints formulation in mathematical programming approaches or logical conditions to be enforced in direct search approaches. In a mathematical programming approach constraints must be formulated as equations before the problem is solved, so that they must be valid equations no matter what decisions are taken during the solve procedure. This can be a difficult or heavy task as for example when cumulative resources constraints must be introduced. On the other side direct search procedures like Branch & Bound, metaheuristics or other heuristics can trigger a specific constraint analysis only when a decision involved in the constraint is taken, e.g. capacity on a specific equipment unit is analyzed only if a task is scheduled on that unit. Combination of the two approaches, called hybrid approaches, has been an active field of research. Time constraints are a very frequent type of constraints in planning and scheduling problems, they impose time limits within which a task can be processed, defining task's earliest starting time (est) and latest finishing time (lfl) or in other terms a time window for task processing (e.g. input materials arrival, due dates, equipment units maintenance). Moreover some other constraints can have some of its consequences translated in constraints on tasks time window limits as far as they impose some Author to whom correspondence should be addressed: [email protected]

1226 ordering among tasks. This is the case for example with shared unary resources which can handle only one task at a time like equipment units or limited intermediate storage units. Shared cumulative resources like manpower can also impose constraints on time windows. In this work direct and indirect time constraints are utilized both in planning and scheduling problems. At the planning phase they allow to analyze equipment units load and plan feasibility in terms of planned due dates and input materials availability. For scheduling purposes an APS-like scheduling heuristic is proposed which utilizes updated time windows to select and schedule a task at each step. Constraints analysis and propagation is a maintenance procedure of tasks time window limits to be all together coherent. In planning problems this procedure enforces constraints on equipment units utilization and intermediate storage and transfer policies. During the scheduling procedure it is a maintenance procedure of time window, which modifies its limits to be coherent with the scheduling decisions already made. The term constraints propagation emphasizes that a task time window modification can trigger modifications on other tasks time windows if its consequences are conveniently propagated. The objective of this paper is to discuss some of the propagation mechanisms and constraints analysis tools existing in the literature, basically constrained based search literature in the computer science area, and present some new propagation mechanisms developed by the authors. Those propagation mechanisms, coupled with tools for estimating equipment units load, have been implemented in an interactive planning & scheduling system for short term batch problems and in an APS-like scheduling system utilized in a chemical industrial plant.

2. Constraints propagation procedures Constraints propagation techniques over tasks time windows have been developed by several authors (Erschler et al., 1976; Fox, 1983; Keng et al., 1988; Sadeh, 1991; Caseau et al, 1994; Cheng et al., 1997) and have been utilized in commercial software systems (ILOG, 1997). Main mechanisms are discussed below. In a scheduling problem its utilization supposes that a previous planning system has determined all the batches that have to be scheduled, precedence relationship among them, equipment unit(s) assigned to each batch and an initial time window for each batch (that can be the entire scheduling horizon). In this way each batch b of a task t has a time window given by its earliest starting time est(t,b) and its latest finishing time lft(t,b) and a processing time pt(t,b). For two batches one can have to precede the other by mass balance constraints prec(t~,b~,t2,b2)=true. Two time instants in a batch time window are derived from est and lft: its earliest finishing time eft = est + pt and latest starting time 1st = l f t - pt. 2.1 Constraints induced by precedences. (Erschler et al., 1976) If there is a precedence between two batches, prec(tl,b~,t2,b2)=true then the following conditions must be enforced: est(t2,b2) >- eft(tl,bl) and lft(t~,bl) <__ lst(t2,b2). If any of such conditions is not satisfied est(t2,b2) has to be increased and/or lft(h,bl) has to be reduced thus reducing respective time windows. A similar constraint propagation can be enforced over batches of the same task assigned to the same equipment to avoid equivalent solutions. Obligatory precedence relationships are deduced from mass balance considerations. The user as is usual in constrained based search may establish other precedence relations.

1227

2.2 Constraints induced by zero wait transfer policies. (Rodrigues et al.,2000) If there is a zero wait transfer policy between two batches (tl,bl) and (t2,b2) then the following conditions hold: eft(tl,bl) > est(t2,b2) and lst(t2,b2) < lft(tl,bl). If any of such conditions is not satisfied est(tj,b~) has to be increased and/or lft(t2,b2) has to be reduced thus reducing respective time windows.

2.3 Constraints induced by limited intermediate storage. (Rodrigues et al.,2000) Time windows for batches producing and consuming an intermediate with limited storage capacity can be utilized to calculate storage time profiles in two limiting scenarios: i) production time allocation at eft and consumption at est and ii) production time allocation at lfl and consumption at 1st. in the first case if storage capacity is exceeded some production batches have to be delayed through est increases, in the second some consumption batches must be anticipated through lft reductions (which will reduce 1st consumption times). Which batches must have its time windows reduced is not entirely fixed but starting with the first/last batches involved in the problem allow producing lower reductions.

2.4 Constraints induced by equipment units. If a batch (t,b) is assigned to an equipment unit its time window can induce a forced occupation during a time interval. In Sadeh, 1991, the concept of slot of total reliance is introduced as the time interval (lst, eft) which necessarily will be utilized by the task if eft > 1st that is if the time window is lower than twice the processing time. Intervals of total reliance (by a batch) are not allowed to other batches assigned to the same equipment unit. This "hole" in a time window would make necessary to work with multiple disjoint time windows, which is not supported by actual constraint propagation mechanism. Nevertheless they can be taken into account in special conditions, for example when heads and/or tails originated by intervals of total reliance are useless because their extent is lower than processing time; in this case they can be eliminated thus leading to time windows reductions. In Caseau et al., 1994, conditions are presented in order to analyze in which situations a set of batches assigned to the same equipment unit lead to obligatory precedence relationships among some of them. Given a set S of batches i and a batch (t,b) not contained in S, conditions are obtained to conclude if (t,b) does not precede the entire set S, does not follow the entire set S, precedes S or is preceded by S. Earliest starting time (estS) and latest finishing time (IriS) for set S are defined as minimum est and maximum lft among the batches in the set, set processing time ptS as the sum of batches processing times. If IriS - est < ptS + pt then (t,b) does not precede the entire set and the condition est _<min(efti) holds, if additionally IriS - estS < tpS + tp then (t,b) cannot be processed among tasks i and it follows that S precedes (t,b) so that the condition est > estS + tpS can be imposed, in the same way if l f l - estS < ptS + pt then (t,b) does not follow the entire set and the condition lfl _< max(lsti) holds, if additionally I r i S - estS < tpS + tp then (t,b) cannot be processed among tasks i and it follows that (t,b) precedes S so that the condition lfl _< IriS - tpS can be imposed.

2.5 Equipment units load imposed by time windows. In Keng et al., 1988 and Sadeh, 1991 similar concepts are presented to represent the load imposed on an equipment unit by the batches assigned to it. Keng defines batch criticality as the ratio between processing time and time window span, and equipment unit cruciality function as a time function obtained summing up batches criticalities. Sadeh introduces the batch individual demand as a time function representing the likelihood that a discretized time interval be used by the batch, and the equipment unit

1228 aggregated demand summing up batches individual demands. Both authors utilize these concepts to guide constrained based search scheduling algorithms. These time functions are related to slack measures utilized by Cheng et al., 1997. The authors have proposed to utilize equipment units load as useful insight in the planning phase to evaluate plant loading and possible bottlenecks (Rodrigues et al.,2000). On the other side it can be used during the scheduling procedure to reduce the burden of the constraint propagation mechanisms, which look for possible ordering among batches in the same equipment unit discussed in the previous section. In fact forced ordering among batches is likely to occur when equipment unit load is high or in the time intervals where load is higher. Equipment unit load has been used to filter out units and time intervals where the constraint propagation mechanism is launched reducing significantly the computer effort.

3. Simple planning problem A very simple planning problem is used to illustrate time windows utilization. Four products A, B, C and D are manufactured through two stages (tasks) each. First tasks A1 and B1 share the same equipment unit U1. Tasks A2 and B2 utilize U3, C1 and D1 utilize U2, C2 and D2 utilize U4. Demand for products B, C and D is located at the end of the horizon (t = 432). There are three demands on product A at times 144, 288 and 432. Raw materials are available at t = 0. Given batchsizes the planning system leads to 8 batches for tasks A1 and A2 and 3 batches for all the other tasks. Tasks processing times are: Al(31), A2(33), B1(32), B2(32), C1(27), C2(16), Dl(21) and D2(19). Batches time windows and equipment units load (aggregated demand) are given in Figure 1. ....................~

............ ~ ~ ~ : ~ i i i : : i : : i

~ii~::i::::::~::i:;iii i:.:~

!...../.";i:; . '.~.../..:....Yi;7;i; .~ ..........................................~i....~

'. . . .~. . . . .:. . . .' . . . . . . .....................:.~..:~..:~..................=.. ..........t.......... ...:ii tl d e m a n d s for

~

i................

i

~

~

~......~ ..:~ 288

...

C1C2 t

i!

Figure 1. Equipment units load and batches time windows. Intermediate demands for product A lead to shorter time windows for initial batches of tasks A1 and A2 which leads to higher load on units U 1 and U3 at the beginning of the horizon. Suppose that the user wants to analyze if product B can be scheduled after product A as far as its batches time windows are large. With this objective earliest starting time - est of the first batch of task B1, B1/1 is modified from t = 0 to t = 280. Constraints propagation leads to the scenario of Figure 2. It can be observed that the increase in est

1229

of B 1/1 is propagated to the other batches of B 1 and to the batches of the second task B2 as could be expected. What is less evident is that that same increase leads to reductions in lft of all the batches of tasks A1 and A2. This results from propagation of capacity constraints in the utilization of equipment units U 1 and U3. Some other time windows modifications by the user can be introduced. For example as load in units U2 and U4 are low the user may want to analyze if products C and D can be delivered early or started later with a postponed delivery of raw materials. Figure 3 shows the result when due date of product C is reduced to t = 160 and for product D raw materials are made available at t = 160 and due date is reduced to t = 300. ......~ r

2._...i.. ............ ~:.: ~ . ° ' ~ . ~ i " ~

~ ........ I-I

lO0

........

~

~

~

~

~'00

:

-

-

-iI:ll:l

J

~

!

~

41:10

500

7 A1 •

III

II~?|I

I

| I]ll.'l~i

........................................ ~

I

I

~B2, .......................................................~%~;;i~,

C1

............... ,

i I._~C34~-

I @

i

!

........................... .. E : . : ......

. . . . . . . . . :. .: .'" . . .

:

'

' ,:,C2 I

:~42 I o.~ 4 ~ ! I LA i rI :~ i,~i j IIl~ ~,~l,,~iI

,

t N

a~~lRlWlJigN~ii',Niii',iii'iiiiii~!i~!ii'~

ii~{~ii~:::::::::::::::::::::::::::::: . ::/::

. ......... :. L._.22_2

. . . . .

, D2

'

................. 22_22_._._..__2

...................................'...'.2.......... 2 _ ........... 3

::~:::

i

1

[

A1

A2 ~:

~

:~

'

I B1 B2

I

c/ ~::::!+~i2&i& . . . . . . I

D1 'D2 ..................................................................................................................................................................................................... i

Figure 3. Scenario after modification of due date (C) and delivery time (D)

4. Time windows based scheduling heuristic Many existing scheduling heuristics have been introduced in recent years into commercial Advanced Planning and Scheduling systems (APS). In general they utilize a constructive or simulation approach where, at each step, a batch is selected and a start time is defined. The constructive approach of the Gantt chart allows taking into account a great number of plant and recipe constraints as far as the actual situation of the plant is known at each step. In this way a convenient/feasible start time can be defined. The

1230 main problem is batch selection. Selection often relies on a batch/task priority order defined by the user from the beginning of the scheduling procedure and/or a priority order in the choice of equipment units to treat bottlenecks first. Again bottlenecks are selected at the beginning. Batches time windows, and its maintenance through constraints propagation, allow developing scheduling heuristics with internal batch selection based on characteristics such as batches criticality, equipment units load and time interval spanned by each batch time window. Heuristics focusing on bottlenecks can benefit from updated equipment units load thus selecting at each step the unit and time interval where batches scheduling is likely to be harder. Heuristics aimed to schedule batches as soon/late as possible select the batch considering the batches whose time windows start/end earlier/later, without using the time instants where equipment units become available as the unique information for batch selection. This selection procedure coupled with candidate batches criticality allow picking up first batches with lower schedule possibilities. This in turn reduces the possibility of undesirable solutions, in the sense that some batches cannot be scheduled inside their time windows, thus implying that some due dates will not be fulfilled or raw materials deliveries must be anticipated. A heuristic aimed to schedule batches as soon as possible has been developed. The procedure utilizes a rolling time horizon and unscheduled batches criticality. Rolling horizon starts at the minimum earliest starting t i m e - est among the unscheduled batches and has a duration established by the user. Batches with est inside the rolling horizon are candidate batches for selection. One batch is selected according to equipment units' load and batch criticality. After batch allocation time windows are updated through constraints propagation as well as equipment units load. For the scenario in Figure 3 computer time was 5 seconds and all the batches were allocated inside its time windows.

5. Conclusions Interactive and/or heuristic planning and scheduling techniques in short term problems can benefit from constraints propagation over batches processing time windows. They allow to visualize and take into account the consequences of decisions that often are complex and difficult to infer. References

Erschler J., Roubellat, F., and Vernhes LP.,1976, Finding Some Essential Characteristics of the Feasible Solutions for a Scheduling Problem. Operations. Research., 24(4). Fox M.S.,1983, Constraint-directed search: a case study in job shop scheduling. Ph.D.Thesis, Carnegie Mellon University, Computer Science Department, Pittsburgh, USA. Caseau Y., and Laburthe F.,1994, Improved CLP Scheduling with Tasks Intervals. Proceedings Eleventh International Conference on Logic Programming. Santa Margherita Ligure, Italy. Keng N.P., Yun D.Y.Y., and Rossi M.,1988, Interaction Sensitive Planning System for Job-Shop Scheduling, in Expert Systems and Intelligent Manufacturing, Ed. M.D.Oliff. Elsevier. Sadeh N.,1991, Look-Ahead Techniques for Micro-Opportunistic Job Shop Scheduling. Ph.D. Dissertation, CMU-CS-91-102, School of Computer Science, Carnegie Mellon University. Cheng C., Smith S.F.,1997, Applying constraint satisfaction techniques to job shop scheduling. Annals of Operations Research (70). ILOG,1997, ILOG Solver White Paper. ILOG Inc.,Mountain View, CA, USA. Rodrigues M.T.M., Latre L.G., Rodrigues C.A.,2000, Production Planning Using Time Windows for Short-Term Multipurpose Batch Plants Scheduling Problems. Ind Eng Chem. Res., 39.

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) g5 2005 Elsevier B.V. All rights reserved.

1231

Information Logistics for Supply Chain Management within Process Industry Environments Marcela Vegetti a, Silvio Gonnet ~, Gabriela Henning b* and Horacio Leon& INGAR/UTN Avellaneda 3657, 3000 - Santa Fe, Argentina b INTEC Gfiemes 3450, 3000 - Santa Fe, Argentina

Abstract This contribution proposes the design of an ontology that provides the foundations for the specification of intbnnation logistics processes in extended supply chains associated to process industries. The proposed ontology includes concepts and relationships that are necessary to formally describe, measure and evaluate a supply chain (SC), thus simplifying the visualization and analysis of networks. A SC ontology is a first step towards achieving a standard description of SC design and management processes.

Keywords: Supply Chain Management, Ontologies, SCOR Model 1. I n t r o d u c t i o n Nowadays, process industries are usually involved in '~extended" supply chains (ESCs), therefore they are tbrced to leave aside the traditional supply chain (SC) companycentric view (Shah, 2004). There is a real need to track and trace product-related information in extended multi-company SCs, either for management or optimization purposes or just for the observance of products liability requirements. The ESC context emphasizes the importance of information logistics (IL) as a key issue for integration. iL processes make accessible to the business management, task-specific and relevant information coming from production, management and business processes as well as from external sources (e.g. suppliers' and customers' data). The role of IL processes is to interlink business process management cycles and to mainly support the monitoring and communication activities in a SC. Thus, the supply chain management (SCM) poses not only the problem of the efficient administration of material inventories and flows but also the challenge of the efficient storage and flow of the associated information. The Supply Chain Council (Stewart, 1997) presented a general framework for the SCM, named SCOR ("Supply Chain Operations Reference Model"). It is based on the consideration that all supply chain tasks and activities can be assigned to five fundamental processes -plan, s o u r c e , m a k e , d e l i v e r a n d r e t u r n - and thus simplifies the visualization and analysis of networks. Theretbre, SCOR is a good starting point for the communication among SC stakeholders. However, it has some limitations and it is necessary to extend it in order to obtain a system of consistent concepts that could be used by all the actors and components of an ESC in a process industry environment.

author to whom correspondence should be addressed: [email protected]

1232 In order to tackle the consistency problem, this contribution proposes the use of the ontology technology, which is discussed in the next section. The proposed ontology, called SCOntology, provides the foundations for the specification of information logistics processes in ESCs associated to process industries. It is introduced in Section 3, where the concepts and relationships that are necessary to describe, measure and evaluate a SC are discussed.

2. Towards a Supply Chain Ontology Even though many ontology definitions exist, the classical one was proposed by Gruber (1993): "an ontology is a formal, explicit specification of a shared conceptualization". A conceptualization refers to an abstract model of some phenomenon in the world, which identifies the relevant concepts of that phenomenon. Explicit means that the type of concepts used and the constraints on their use are explicitly defined. Formal refers to the fact that the ontology should be machine-understandable. Shared reflects the notion that an ontology captures consensual knowledge; so, it is not restricted to some individual, but accepted by a group. Therefore, the construction of an ontology for SCM would provide a framework for sharing a precise meaning of information exchanged during the communication among the many stakeholders involved in the SC. Although many methodologies have been proposed to build ontologies, each having different principles, design criteria and development stages, the approach of Grtininger and Fox (1995) has been selected for the development of the SCOntology. According to this approach a set of natural language questions, called competency questions, must be defined to determine the ontology scope. These questions and their answers are employed in the following step of the methodology, called conceptualization, which consists in extracting the ontology main concepts and their properties as well as relationships and axioms. IL processes have as premises to access the right information, with the right content and quality, at the right time and at the required place. But which is the right information, the right content and quality for it, as well as the right time and place to access it? In order to define the scope of SCOntology, the previous generic competency questions are reformulated as follows: i) which is the required information for each supply chain process?; ii) which is the structure and content of each piece of information?; iii) which is the place to access it?; iv) which are the processes that provide it?; v) which are the processes that consume it?; vi) when is each information piece supplied?; vii) when is it consumed?, etc. Having posed and answered these questions, the conceptualization stage will help to organize and structure the acquired knowledge using a representation language that must be independent of both the implementation language and environment. In this contribution, the well-known UML language will be employed for conceptualizing the SCOntology.

3. Defining the Conceptual Model The relevant concepts of SCOntology that arise when posing and answering competency questions are directly linked to the information associated to the ESC and the processes using it. They can be summarized as follows: (i) Information resources,

1233 defining the information and its structure; (ii) SC Processes, acting as information suppliers and clients; (iii) Locations, where processes are performed and the required information is needed, (iv) Relationships among processes and information resources, such as provider, consumer; (v) Relationships among processes, which allow tracing the information flow associated with particular workflows. A good starting point to represent a framework able to answer competency questions is to consider an enterprise model. Though there are several models available, Coordinates (Mannarino, 2001) has been chosen because it allows representing the process and product views in an integrated fashion. The main concepts are shown in Fig. 1. According to this model, a Process is employed to represent a set of activities in terms of a set of resources that participate in different ways in order to achieve the process' goals. As only certain aspects or characteristics of a Resource may be of interest to a given process, a particular perspective of the Resource (ResourcePerspective) is actually viewed by such P~'ocess. This fact is modelled by means of the Use Mode relationship that reflects the role that the Process plays in relation to the Resource Perspective. The following roles have been considered in this contribution" creates/ eliminates (non-renewable resources), produces/consumes (renewable resources), modilies, uses, and employs (exclusive usage). The incorporation of these role types extends the SCOR original approach, which only considers input and output roles. As can be interred from the previous paragraphs, processes relate among themselves indirectly by means of the resources they operate on. However, two processes can be directly linked through explicit temporal relationships. Furthermore, a Process can be described at different abstraction levels, according to the complexity of the activity that is being modelled. Hence, a process can be decomposed into subprocesses. Other concepts that take part in the model are: (i) the Organisational Unit one and (ii) the specialization of the Resource concept into Material and Information Resources. Temporal Relation ship

UseMode *

InitialState IntermediateState R e s o u r c e State FinalState

sul~process

1. *

.

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Process 1..*

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*

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Resource 1 * i

'!

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,

Material Resource

Figure 1. Supply Chain Conceptual Model Elements This basic conceptual model is extended with the concepts introduced in the SCOR framework, which includes three levels of process detail. At Level One (see Fig. 2), SCM is defined in terms of the following integrated core processes" Plan, Source, Make, Deliver, and Return, spanning from the suppliers' supplier to the customers' customer, and all aligned with each company's operational strategy, work, material, and information flows (Bolstorff and Rosenbaum, 2003). These processes, with the exception of Plan, are considered as Execution type of processes (Execute); thus, they are the ones that represent raw materials acquisition (Source), transformation (Make) and product distribution to customers (Deliver). Return processes are associated with receiving any returned products, having two perspectives built into them" Delive W Return- returns from customers, and Source Return- returns to suppliers. It can be seen

1234 that Plan processes cover all activities for the preparation of future material flows; thus they perform the Planning of the SC and the Execution processes. In addition, SCOR includes a series of Enable elements for each of these processes. An Enable process is a one that prepares, maintains or manages information or relationships on which planning and execution processes rely.

rocess Plan

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Figure 2. Supply Chain: Level I Model

The five basic elements are further divided into process categories at the next level, called Level Two or configuration level. It defines the configuration of planning and execution processes using standard categories, like make-to-stock, make-to-order, and engineer-to-order, employed by companies to fulfil customer orders. The configuration is defined by the specification of which processes are used to move materials from location (organizational unit) to location. Thus, at Level Two, the five Level One process categories (Plan, Source, Make, Deliver, and Return) are decomposed into thirteen supply chain execute process types and five plan process types (P1." Plan the whole supply chain," t:'2." Plan Source; P3: Plan Make; P4: Plan Deliver," 1,5." Plan Return). Furthermore, at this second level, Enable is also extended into five processes (EP." Enable Plan," ES: Enable Source," EM." Enable Make," ED: Enable Deliver; ER." Enable Return), one for each basic process. This decomposition is shown in Fig. 3, including the aggregation association over the SCOR process class, which specialises the processsubprocess link introduced in Fig. 1.

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L

Plan

] p2 t

l

Planning

,

Execute

[ Sou~rce

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Enabling__~E~_~~_EM I

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Figure 3. Supply Chain: A Partial View of the Level I1 Model

Fig. 3 shows the specialisation of Plan and Source processes. The Source Level Two process types (S1 - Source stocked product, $2 - Source make-to-order product, $3 Source engineer-to-order product) attempt to characterize how a company purchases raw materials and finished goods. A level two Source process is guided by the planning made by a P2 process, therefore such 1'2 process has to be performed before the execution of the corresponding Source process. This temporal relationship is refined by the Planning link. The specialization of the Make, Deliver and Return processes was done in a similar fashion, though it is not shown due to lack of space.

1235 Fig. 4 illustrates a partial view of the P1 and P2 processes and their relationships with the associated information resources. In particular, P2 is the process of comparing total material requirements (a Supply Chain Plan Information Resource) with the constrainedjbrecast (another Information Resource) created by the P1 process and generating a material requirements resource plan (Sourcing Plans information Resource) to satisfy landed cost and inventory goals by commodity type. This translates into a material release schedule that lets the buyer know the amount of product that must be purchased based on current orders, inventory and further requirements. ~ !i p2 ~ --i i

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v

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.

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t

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ti ChainSupplyPlans I Constrained Forecast

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Figure 4. A Partial View of Relevant hd'brmation to Perform some Level H Activities

Level Three defines the business processes used to transact sales, purchase and work orders, return authorizations, replenishment orders, and forecasts. Fig. 5 shows a new class, Process Element, that represents those processes. A set of Process Elements defines a level two SCOR process. In the figure, it is possible to see the definition of the S1, and $3 particular ones. At this level, the SCOR model defines work and information flows. Thus, the workflow is specified by temporal relationships. As can be seen in Fig. 5, this link type is represented by customer-supplier relationships that define the roles of the associated Processes; and the information flow is specified by the set of data that are inputs and outputs of the Process Elements. As it was mentioned before, this is included in the proposed ontology by the Use Mode relationship, that allows specifying the semantic of a process in relation to a related information resource. The proposed SCOntologv was implemented by adopting the OWL ontology language (http://www.w3. org/TR/owl-features/) and the Protdg6 2000 ontology editor (http://protege.stanford.edu/). In order to test SCOntology, a refinery industry supply chain process (Julka el al., 2002) has been modeled. Figure 6 shows a partial view of the three SCOR representation levels for the crude procurement process treated in this work. • I

~"~

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-

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Figm'e 5. Supply Chain. A Partial View of the Level III Model

4. Conclusions and future work The SCOR model is a business process reference model that provides a standard description of SC planning and operational activities. Thus, these tasks could be

1236 unambiguously described and communicated among supply-chain partners, providing the basis for SC improvement. However, in its current version, the SCOR model provides partial and very abstract answers to the competency questions that could be formulated in real situations. One of its main drawbacks is the weak representation that information and data have, as well as the lousy modelling of their usage by means of the actual SC processes. Moreover, the sources of most information flows are Enable type of processes; but the SCOR model does not explicitly specify which are those processes and which information is employed in such data creation. The SCOntology presented in this contribution formalizes and extends the SCOR model in order to overcome some of these limitations. Future work will involve specifying the information flows participating at levels IIi and IV and testing the model with other case studies.

Oil supplier: OrganizationalUnit

containlr eleme~2~ eleme~

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Figure 6. Case Study: A partial view of a Refinery Supply Chain model.

References Bolstorff, P., and R. Rosenbaum, 2003, Supply Chain Excellence: A handbook for dramatic improvement using the SCOR model, Amacon. Gruber, T.R., 1993, A translation approach to portable ontology specifications, Knowledge Acquisition, vol. 5, 199- 220 G~ninger, M. and M.S. Fox, 1995, Methodology for the design and evaluation of ontologies. Workshop on Basic Ontological Issues in Knowledge Sharing. Julka, N., R. Srinivasan, and I. Karimi, 2002, Agent-based supply chain management- 2: a refinery application. Computers and Chemical Engineering, 26, 1771-1781. Mannarino, G., 2001, Coordinates, Un lenguaje para el modelado de empresas. PhD Thesis, Universidad de Buenos Aires, Argentina. Shah N., 2004, Process industry supply chains: Advances and challenges, ESCAPE 14, 123-138. Stewart, G., 1997, Supply-chain operations reference model (SCOR): The first cross-industry framework for integrated supply chain management; Logistics Information Management, 10, 62-67.

Acknowledgements This work was sponsored by ANPCyT, CONICET, Universidad Tecnol6gica Nacional and Universidad Nacional del Litoral. Authors gratefully acknowledgehelp received from these institutions.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1237

Plant Structure Based Equipment Assignment in Control Recipe Generation Considering Conflicts with Other Batches T. Fuchino* and H. Watanabe *Department of Chemical Engineering, Tokyo Institute of Technology 2-12-1, Oookayama, Meguro-ku, Tokyo, 152-8552, Japan

Abstract This paper describes the equipment assignment in a control recipe design. To produce a batch in a batch plant, equipment assignments to each task of a batch are carried out on the basis of the equipment requirement information of the master recipe. However, the equipment units satisfying the equipment requirement are not necessarily connected topologically with each other, especially in the lnultiple-path and/or the network structural batch plants. Furthermore, there is no guarantee that the assigned equipment unit does not compete with other batches on a production schedule. In this study, plant structure based equipment assignment system considering conflicts with other batches is developed.

Keywords: Control Recipe Generation, Equipment Assignment, Plant Structure, Conflict between Batches

1. Introduction The process industries are confronted with competitive situation in these days that requires production of high value added products with higher productivity and quality. Batch processes are suitable for producing such products, and their operation should be designed to realize the property of batch processes. In batch processes, the necessary information to produce a product is specified in the recipe, which is hierarchically categorized into four types; general, site, master and control recipe. To produce a batch in a batch plant, the control recipe corresponding to the batch is generated by assigning equipment to the batch and sizing the master recipe to meet the quality requirement, and it is imputed to the operating system for execution. The assignment is carried out on the basis of the equipment requirement information of the master recipe. However, even though the equipment units satisfying the equipment requirement are assigned, it does not ensure that they are topologically connected with each other. Especially, in the multiple-path and/or the network structural batch plants, there exist plural production paths and alternative equipment units for flexible operation, but certain equipment units may not be connected with pipe each other originally or temporally, if such equipment units were assigned for a batch in the control recipe, * Authors to whom correspondence should be addressed: [email protected]

1238 production interruption, abortion of unfinished product and/or unexpected release of hazardous material would occur. It is necessary to consider the plant structural connectability on real-time in generating the control recipe to maintain productivity and safety. Furthermore, in general, multiple products and/or multiple batches are produces in a batch plant, and the equipment units are assigned to these batches simultaneously or time is shifted. When a new batch is planed to be produced in a batch plant, assignment of equipment units to the new batch can not be decided independently, because it is restricted by the other batches, to which equipment units have already assigned, and their occupancy time. Therefore, it is necessary to consider such conflicts with other batches in generating the control recipe. There are several previous studies about recipe design support environment based on ANSI/ISA-S88.01 which is an international standard (Aoyama et. al. (2002), Hoshi et. al. (2002), Kaneko et. al. (2003), and so on). These studies paid attention to the relation between plant structural properties and the operation (recipe), but not to the conflicts with other batches. On the other hand, although batch scheduling systems based on ANSI/ISA-S88.01 have been developed (such as Nortcliffe (2001)), they are not taken into consideration about the plant structural connect-ability. In this study, the control recipe generation is considered based on ANSI/ISA-S88.01 ($88.01), and plant structure based equipment assignment system considering conflicts with other batches is developed.

2. Control Recipe Generation The control recipe is generated based on the master recipe by assigning equipment to tasks and sizing the batch. In the master recipe, equipment requirements to carry out recipe procedures are specified, and the equipments satisfying these requirements should be assigned. However, in order to consider the plant structural connect-ability, not only the main equipments, but also piping and a valve should be considered as an object to be assigned. Therefore, to enumerate alternative equipment assignment, the master recipe representation and the plant structure (P&ID) representation are necessary. On the other hand, the conflicts with other batches can be detected by comparing the plant schedule and the individual batch schedule. The occupancy time of assigned equipment is calculated by their sizing, and the batch schedule can be obtained by ordering of the occupancy time of the assigned equipment. In order to avoid conflicts with other batches, dispatching rule becomes effective. Based on the above consideration, this study aims at developing the control recipe generation environment shown in Figure 1 as IDEF0 activity model. The plant structure, master recipe and scheduling information are put into the system as control of this IDEF0 model and their XML representations are provided at A5 subactivity in this study. In the plant structure representation, equipment, piping and valves are defined as objects, and the structural connections are represented by their associations. The property and specification of the objects are defined as their attributes. The master recipe representation is based on ANSI/ISA-S88.02, and the entities to describe occupancy time for respective equipment unit are defined in the recipe representation in this study. Furthermore, the schedule information is represented by the production order and time of starting the respective batches, so that the plant schedule is

1239 obtained by correlation of the schedule information and occupancy time here. On the basis of these XML representations, the control recipe is generated. In the A2 sub-activity, the alternative equipment units are enumerated by mapping the equipment requirement in the master recipe representation and properties of equipment units in the plant structure representation, and the available paths are searched to check the connect-ability by tracing the associating piping and valves, and mapping the equipment requirements and properties of piping and valves, in the A3 sub-activity. The candidate of connect-able equipment assignment is informed to A4 sub-activity, and the occupancy time is calculated. The conflict with other batches is checked and a very simple dispatching rule; time of starting is delayed if the task conflicts, otherwise reassign equipment, is applied here. Although not only conflicts with other batches but evaluation to quality, safety, etc. should be performed in this activity, only the conflict is considered here. ~-'r-':-,I:-tLICf iC,FI 12:1 B:ec+ij i r-er,I,er-,f i [:er-t if i,::at ior, ,

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Figure 1. The ESCAPE styles used in this document

In case that the equipment, which is connect-able and satisfying the equipment requirement without conflict with other batches is found, the result is informed to A1 sub-activity, and certified. Information of the assigned equipment, scaled formula and the batch schedule information are added to the XML master recipe representation, then the control recipe is generated. The time of starting and associated control recipe ID and so on are revised on the XML schedule information representation. In the next section, the XML representation (plant structure, master recipe and schedule information) and implementation environment are explained, and an application to an example test case is described in the further section. 3. I m p l e m e n t a t i o n

and XML

Representation.

In this study, MS Visio is used "Resources to Represent Related Information" shown in Figure 1 of mechanism for A5. The plant structure, master recipe and schedule

1240 information are described by using its GUI interface, and their XML representations are converted by using VBA. The each sub-activities; A2 to A4, shown in Figure 1 are implemented as external XML parser, and Ruby; the interpreted scripting language for object-oriented programming, is adopted. 3.1 Plant Structure

In this study, the two stage polymerization plant, which is provided by The Japan Society for the Promotion of Science, Process Systems Engineering 143 (JSPS PSE143) committee, is considered. I&PD for the plant is shown in Figure 2, and is converted into XML code. The property data for each object are defined by using Custom Property function of Visio, and XML code only for the plant structure is extracted as shown a part bellow.

N

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easure

Mixer

C

l!

L_

Figure 2. Plant(Process)Structure of Two Stage Polymerization Plant

In assigning the equipment, it is necessary to ensure not only the consistency with the equipment requirement in the master recipe, but also the connect-ability with other equipment units which constitute the process. To ensure the consistency with the equipment requirement, the attribute of the equipment should be described within the "UnitAttributes" tag using the same manner with that describing the equipment requirement in the master recipe. In this study, the property of equipment is specified by using predefined property class as shown following underlined XML tag. Furthermore, to ensure the connect-ability, the precise connection information, which is not the connection of equipment to equipment basis, but that of equipment phase to equipment phase basis. In this study, not only the main equipment but also valves, tee, pipe and so on, appeared in the P&ID are defined as objects, and their connections are

1241 defined using equipment ID, connection port ID and connecting object ID. For example, when the connection port "1" of the equipment "E-01" is connected with the connection port "1" of the valve "MV-01" via the pipe "Pipe-001", then the relation between "E01" and "MV-01" is described as follow. E-01.1, MV-01.1, Pipe-001

3.2 Master Recipe The master recipe is described hierarchically on the basis of procedure. The formula, equipment requirement and so on are defined as property of the procedure, in this study. In order to assign the equipment which satisfies the equipment requirement, the specifications on equipment are described by using predefined property class as same as the equipment properties in the plant structure representation. On the other hand, in assigning equipment, not only the consistency with equipment requirement, but also the conflict between other batches should be checked. To detect the conflict, the occupancy time of the assigning equipment for the scheduled batches and the necessary time for the task should be compared. However, the necessary time for the task is depending to the assignment. Therefore, in this study, the necessary time is modelled as a function of equipment capacity, in this example as shown a part at "ProcedureAttribute" tag, below.

3.3 Schedule Information There are two types of scheduling information are used in this study; the plant schedule information and the batch schedule information. The former specifies sequence of batches and their preferable time of starting and finishing. The assignment of equipment is to be performed according to this order. According to the plant schedule information, the provided external XML parser generates the batch schedule information, i.e. enumerate candidates of equipment for assignment, assign feasible equipment, calculate necessary time for each task, and decide the time of starting the batch not to conflict with other scheduled batches. In the batch schedule information, finally the time of starting and finishing the batch is generated, as shown as follow. <EndTime EndTime="Wed Dec 24 09:12:00 JST 2003"/> Based on the batch schedules, the Gantt chart for the batches appeared in the plant schedule information is provided.

4. Illustrative E x a m p l e To illustrate performance of developed method to assign equipment in control recipe generation, an example problem is solved. Six batches (No l to No. 6), which are specified by the same master recipe, are scheduled for the forgoing two stages

1242 polymerization plant as shown in Figure 1. The production priority is in that order, and equipment assignment is decided one by one according to the priority specified in the schedule information. The result shown in Figure 3 as a Gantt chart of main equipment is obtained successfully. 0000 Mixer

Mixer.22

0100

0200

0300

0400

0500

0600

0700

0800

0900

1000

Batch1

0002.00

:

c2z7.30 n~

nn

Mixer,23 Reactor.2

Batch 1 0209.30 0434.30

Reactor.6 Reactor.8

B=tchl

Reactor

I

!

0434.30

i

Reactor.4

i .

.

.

.

ii i~

.

BatchE 0720.0(~ 0907.30

Reactor,5 Tank.280

Batch5 0710.00 0857.30

i

Tank

i

Tank.278

Figure 3 Result of Assignment for six batches

5 Conclusions In order to assign equipment to tasks in generating control recipe, plant structural connect-ability of equipment units and conflict with other batches should be considered. In this study, plant structure based equipment assignment system considering conflicts with other batches is developed. References ANSI/ISA-S88.01-1995 Batch Control Part 1: Models and Terminology, ISA (1995). ANSI/ISA-S88.02-2001 Batch Control Part 2: Data Structures and Guidelines for Languages, ISA (2001). Aoyama, A., I. Yamada, R. Batres and Y. Naka, Multi-dimensional object oriented approach for automatic generation of control recipes, Computers and Chemical Engineering 24 (2000) 519524. Hoshi, K., K. Nagasawa, Y. Yamashita and M. Suzuki, Automatic Generation of Operating Procedures for Batch Production Plants by Using Graph Representations, J. of Chemical Engineering of Japan 35 (2002) 377-383. JSPS PSE- 143 committee, Technical Report No.20 (1999). Kaneko, Y., Y. Yamashita, and K. Hoshi, Synthesis of Operation Procedure for Material and Energy Conversions in a Batch Plant, Lecture Notes in Artificial Intelligence 2773 (2003) 12731280 Nortcliffe, A. L., M. Thompson, K. J Shaw, J. Love and P. J. Fleming, A framework for modeling in $88 constructs for scheduling purposes, ISA Transactions 40 (2001) 295-305

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) (C22005 Elsevier B.V. All rights reserved.

1243

IMC Design of Cascade Control Mario R. Cesca a and Jacinto L. Marchetti b* a Chemical Engineering Department- Universidad Nacional de Tucumfin Av. Independencia 1800 - (4000) Tucumfin - Argentina b Institute of Technological Development for the Chemical Industry (INTEC) Gtiemes 3450, (3000) Santa Fe, Argentina

Abstract Cascade control is one of the most successful methods for enhancing single-loop performance. However, the literature about synthesis methods for designing and tuning cascade control systems appears to be rather limited. In this contribution, a model-based procedure using internal model control (IMC) approach is proposed for synthesizing the controllers transfer functions. The suggested tuning procedure determines the controller filter time constants such to assure robust stability. Simulation examples are provided to demonstrate the goodness of the synthesis method and to compare its performance with those of PID-PID cascade configuration tuned with already accepted rules.

Keywords: Cascade Control, Robust Control, IMC Design, Model Based Control 1. Introduction The robust process control has received considerable attention in the last twenty years. The IMC structure, as base for the robust controller design, is treated with great detail in Morari and Zafiriou (1989) where robust control is associated with IMC design. When addressing cascade control, the authors mention the utility of this control configuration when the secondary process is dominated by an important uncertainty. Skogestad and Postlethwaite (1996) analyze different cascade control structures, but they do not present any particular robust synthesis method. The paper of Tan et al. (2000) is one of the few contributions of robustness analysis for series cascade systems, where they propose conventional PID controllers for the inner and outer loops. Lately, Brosilow and Joseph (2002) used IMC design approach employing the Mp parameter and considered both stability and robust performance simultaneously. In this framework, the contribution by Hahn et al. (2002) presents a procedure to obtain the uncertain information in order to design robust IMC controllers. In this work, the IMC Series Cascade Control structure is studied (see Figure 1). The analysis includes robust stability conditions for tuning both controllers. Finally, the closed-loop performance and robustness of the synthesized system are compared with cascaded PID regulators tuned according to Lee et al. (1998), one of the few systematic tuning rule for cascade systems reported in the literature.

Author/s to whom correspondence should be addressed: [email protected]

1244

d=J

d,]

r*(

Y2

y

....

Figure 1. IMC Series Cascade Control Structure

2. IMC Cascade Control Synthesis 2.1 Nominal Perfornace The primary disturbance d~, and the secondary disturbance d2 are typically analyzed when dealing with cascade control systems. In particular, the effect of the secondary disturbance on the main output Yl is considered for synthesizing the inner controller q2. Thus, the IMC design proceeds by minimizing the H2 norm of the yl error according to ~'

n nfe?dt- nll II;-nnlJ (l-G2 q2

"

q2

0

q2

2

q2) G1 d2112

(1)

On the other hand, the optimum primary controller q l is obtained by minimizing the H2 norm of the error el, caused by the primary disturbance ,:,o

min ql

f2e,

,,2

aft - min e 1 il2 Z/1

;

n i (1 - q~(if8) d~ !1i

(2)

o

Under nominal conditions (plant equal model), the time constants of the IMC filters should be chosen as small as possible. To avoid excessive noise amplification, the filter parameter should, be chosen so that the controller high frequency gain is not greater than [3 times its low frequency gain. This criterion can be expressed as

-sup] q(jm)l

~o, [q(O)J

(3)

where q(s) is the transfer function of the IMC controller. Brosilow and Joseph (2002) proposed max fl = 20, however, factors between 5 and 20 are encountered in practice. In this work, f l - 10 is adopted, which follows the standard industrial practice of limiting the high-frequency gain of PID controllers. If the controller does not have complex poles in the left-half plane, equation (2) can be transformed in the limit: [3- lim [q(jco)]

~,-,= [q(O) I

(4)

1245 2.2 Robust Stability

In order to evaluate the robust stability conditions a multiplicative description of the uncertainty is assumed. Thus, two families of models with uncertain parameters are defined as"

Hi-{Gi"

Gi (.lo~) - O~(joJ)

I

-I

i - 1,2

(5)

where in each family set, G; is the nominal model, ~.i(jo)) is the multiplicative uncertainty, and (,mi (co) stands for the largest module. The robust stability condition (Skogestad and Postlethwaite, 1996), for the inner loop is

[

I-I

I<-~:me(co)

Vco

(6)

where ~ is the complementary sensibility function under nominal conditions. The primary controller observes the dynamics the transfer function composed by the inner loop and the primary plant connected in series, namely

Ge =

q2G2

Gi

(7)

1+%(G2 -Ge) Thus, the controller q~ must stabilize the following set of equivalent plants

FI~ -IG~ " G,~ (.ico) - d, (.ioJ) -I~:.(.i~o) <_~m.(co) 1

(8)

d, (.ico)

where

r:'~(,/~o)] -]~:',(./~o>~e(./~o)-qe(./oo>Oe (.Soo) e e (.7oo)

(9)

I 1+ qe(j~o) d~ (./co) ~'e(./co) l Finally, the robust stability condition for the primary loop may be expressed as

~ (jco) - q~(jo)) GB(jco ) - ql (jo)) q2 (jo)) G2 (j6o) G, (j6o) l < - -

Vco

(10)

3. Controller Synthesis for Low-Order Plant Models A frequent simplified dynamic characterization of chemical processes consists of a firstorder-lag plus dead-time transfer function. In this way, most of the systems can be represented with enough accuracy for controller tuning (Shinskey, 1996). Thus, this low-order modeling is used for both, the primary and secondary plants

~j~(s)_K~ exp(-0,s) (r,s+ 1)

(72(s)-K2 exp(-O2s) (z2s +1 )

(11)

1246

3.1 Nominal Performance When a unit step is considered as secondary disturbance d2, the ideal controller resulting from equation (1) is q2

O2 , a = 1- exp(---)

- ('~'2 S + 1)(a r, S + 1) K2

(12)

~'1

Note that the synthesized controller contains dynamic parameters from both inner and outer plants. Thus, the realizable controller is obtained including a second order filter q2 -

q2 F2 -

1 ('r 2 S nt- 1)(a 'r 1 S nt"1) K2

(13)

(/~'2 s + 1) 2

where the IMC filter time constant X2 that verifies equation (3) is ANP _JV2 a

V,

(15)

Similarly, assuming a unit step in the primary disturbance d~, and including a second order IMC filter in equation (2), the primary controller results q,

_ q, Fz =

1 (r, S nt- 1) K, (a ~~ s + l )

(16)

(/~2 S + l) 2

(X, s+1) 2

Finally, the noise amplification constraint in equation (3) implies

1

;C- 2

(17)

3.2 Robust Stability When the structure of the secondary transfer

function

G2, and the synthesized

secondary controller q2 are considered, the condition (6) for robust stability becomes 4(a~lO..)) 2 q- 1 (/~ER(_o)2 -t" 1

1 _ < ~

v co

~m2 (09)

(18)

Besides, the minimum value for the IMC filter time-constant 2~ER, that assures robust stability is obtained from equation (10)

1

<

1

V(o

(19)

+ 1

Although it is not explicit, tuning the primary controller depends on the secondary controller through the global uncertainty ~B.

4. C o n t r o l l e r s T u n i n g Notice that the IMC concept allows the controller transfer function synthesis, namely, it determines the controller form. Then, the filter time constant is the tuning parameter used to obtain stability and the desired performance. The proposed tuning approach is"

1247 ~ - m a x ( 2 i ' P , 0 ~ R,s)

i =1,2

(13)

The factor 0 must be greater than 1 to assure an appropriate damping of the controlled variable response; its role is similar to the gain margin. Several simulated cases show that 4~values between 1.2 and 1.5 produce satisfactory results. Notice that the secondary controller must also satisfy the robust stability condition, because if the primary controller is set to manual operation, the inner loop has to remain stable.

5. Simulation Study A large number of numerical cases have been simulated to test the proposed synthesis procedure. Because of space reasons however, only two examples with opposite dynamic plant characteristics are presented. The parameters used in theses examples are shown in Table 1. Case A is a typical cascade control system with secondary dynamics faster than the primary dynamics. On the contrary, case B is an example where the use of cascade control is not recommended because the inner dynamics are slower than the primary one (Shinskey, 1996). Table 1. Plants parameters o f the simulated cases.

Parameter K - Gain r -Time constant 0- Dead time

Case A Primary 1.000 0.490 0.245

Secondary 1.000 0.176 0.088

Case B Primary 1.000 0.116 0.058

Secondary 1.000 0.547 0.273

Figure 2 shows the transient responses for a unit-step change in the secondary disturbance at time 0, and unit-step change in the primary disturbance at time 10. In order to establish a fair evaluation, a conventional cascade control system with PID controllers tuned according to Lee et al. (1998) is considered. This is one of the few systematic tuning rule reported in the literature for cascade PID controllers. The referenced tuning however produces unstable responses in Case B and with others similar dynamics. Consequently, the controller parameters must be readjusted to achieve a reasonable damping in the controlled response. Changes in dead-times of about + 30 % regarding the nominal model are considered to test the proposed tuning procedure. This uncertainty datum is used basically to find the bounds Cm,((_o) and ,Pm2((_O ) . Figure 2 shows the simulation results where two transient responses to changes in both the primary and the secondary disturbances are presented. The upper plots give the responses under nominal conditions, while the lower ones correspond to plants with extreme dead-time values. Notice that cascade IMC gives always better responses under both, nominal and perturbed plants conditions. Furthermore, it yields good performance to both, secondary and primary disturbances, when using on plants like Case B, despite of its usually unfavorable conditions for cascade control. The control effort of cascade IMC remains inside acceptable limits (Marlin, 1995).

1248 :: w: ii::::::........................~.......................................................................... " ....................................~....................................... ~....................................... ~.........................................................................................................................................................

: ......................................... ........... ¢.) :

t.

.................................................................................................................. 71..................................................................:i.......................................

. . . . . .

.

.

.

II .

.

i ~,.

~.~

:i

~.~.:~

i~:~ Ii .....

~,.

~, [ i)~lll'iitl~:.l I,it<';

: ~:"i" :::::' ::' i~i ~ ..........

....

t::-it~ bil~ . . . . . . . . .~. . . . .

".........

l

:i :::' ~ i

~:;;

Figure 2. Closed-loop responses for cases A and B, to step changes in d: (t = O) and d/ (t = 10)

6. C o n c l u s i o n s This contribution revises the synthesis of cascade controllers with IMC structure, and provides a tuning procedure that accounts for nominal performance and robust stability. The approach is developed using low-order models with available estimated limits for the uncertainties; in particular, first-order lags and dead times transfer functions are used to represent both the primary and the secondary plant dynamics. The convenience of tuning the secondary controller first is confirmed by analytical relationships leading to robust stability. A large number of simulation results confirm that IMC cascade control yields better performance than the conventional cascade structure where PIDPID controllers are adjusted following standard procedures. References Brosilow, C. and B. Joseph, 2002, Techniques of Model-Based Control, Prentice Hall, New York, USA. Hahn, J., T. Edison and T.F. Edgar, 2002, Adaptive IMC Control for Drug Infusion for Biological Systems, Cont. Eng. Prac. 10, 45. Lee, Y., S. Park and M. Lee, 1998, PID Controller Tuning to Obtain Desired Closed Loop Responses for Cascade Control Systems, Ind. Eng. Chem. Res., 37, 1859. Lewin, D. and C. Scali, 1988, Feedforward Control in the Presence of Uncertainty, Ind. Eng. Chem. Res. 27, 2323. Marlin, T., 1995, Process Control, McGraw-Hill, New York, USA. Morari, M. and E. Zafiriou, 1989, Robust Process Control, Prentice-Hall, Englewood Cliffs, New Jersey, USA. Shinskey, F. G., 1996, Process Control Systems, McGraw-Hill, New York, USA, 4 th Edition. Skogestad, S. and I. Postlethwaite, 1996, Multivariable Feedback Control: Analysis and Design, John Wiley & Sons, Chichester, UK. Tan, K.K., T. H. Lee and R. Ferdous, 2000, Simultaneous Online Automatic Tuning of Cascade Control for Open Loop Stable Processes, ISA Trans. 39, 233.

Acknowledgements The support from CIUNT of Universidad Nacional de Tucum/m through the Process Systems Engineering Project is gratefully acknowledged.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1249

Robust model-based predictive controller for hybrid system via parametric programming A. M. Manthanwar a, V. Sakizlis a, V. Dua b, and E. N. Pistikopoulos a* aCentre for Process Systems Engineering, Imperial College London, London SW2 2AZ, U.K. bUniversity College London, London WC1E 7JE, U.K.

Abstract In this paper we present an algorithm for the design of robust model-based predictive control for hybrid system under uncertainty via parametric programming. The proposed min-max hybrid control scheme guarantees feasible plant operation for the maximum violation of uncertainty scenario. The key advantage of the proposed hybrid controller design is reduction in expensive, repetitive in nature on-line computations by providing the entire map of optimal robust control policy in given state space. The resulting piecewise affine optimal control law as a function of states can then be implemented online as a sequence of simple function evaluations. An example is presented to illustrate the details of the proposed robust hybrid parametric controller design.

Keywords: Hybrid systems, MPC, robust control, parametric programming, feasibility. 1. Introduction Parametric programming is the state-of-the-art technology to find optimal solution of optimization problems under parametric uncertainty without exhaustively enumerating the entire parameter space, [1,2,3]. Application of parametric programming to the control of dynamical systems led to the development of off-line parametric controller, [4], also known as explicit model predictive control (MPC), [5,6]. The major advantages of explicit parametric controller is reduction in expensive, repetitive in nature online computations of MPC by performing "you solve only once" off-line computation, [3]. Thus, the forefront of "decision-to-policy" making parametric controller design is envisioned to encompass much wider range of applications including control of hybrid systems. Modelling, optimization and control of hybrid systems, [7,8,9], is one of the most active areas of research in process systems engineering. Many practical engineering applications are inherently hybrid in nature that involve interactive combination of logic, dynamics and constraints; also known as mixed logical dynamical (MLD) systems, [10], or simply hybrid dynamical models, [11]. |n the MPC framework this naturally leads to the mixed integer formulation of the MPC problem, where logical decisions are modeled as integer variables, [10,12]. Authors to whom correspondence should be addressed: {amit, e.pistikopoulos}@imperial.ac.uk

1250 Additionally, many process systems are under the influence of uncertainties arising due to parameter variations and exogenous disturbances. Influence of uncertainty causes infeasible plant operation. Therefore one of the key control objectives for hybrid systems is to achieve robust stability and robust performance while guaranteeing economics and operational safety. However, the issue of robust controller design for hybrid systems under uncertainty is not completely addressed in the open literature. For recent review and progress in this area refer to [9]. Mayne and Rakovic, [13] have proposed on-line MPC for hybrid systems. In the current work, we apply the off-line optimization tools via parametric programming to design explicit MPC for constrained linear hybrid systems, which is robust in face of bounded input uncertainty, [6]. The next section 2 presents problem formulation for the multiparametric robust hybrid control (mpRHC). In section 3, Lyapunov based stability is achieved by using principles of linear matrix inequalities, [14], and robust feasibility is guaranteed by using the flexibility analysis theory of Pistikopoulos and Grossmann, [15]. Section 4, presents the min-max control problem. Finally, section 5 presents an example.

2. Hybrid System Model 2.1 S y s t e m r e p r e s e n t a t i o n

Consider the following discrete multi-model dynamical system:

x(k + 1)

-

Alx(k ) + Blu(k ) + Gw(k)

if

Slx(k ) + Tlu(k ) < E 1

Azx(k) + B2u(k) + Gw(k)

~

Szx(k ) + T2u(k ) < E 2

A~x(k) + B~u(k) + Gw(k)

if

S~x(k) + T~u(k) <_E~

.

(1)

where x ( k ) ~ ~ " ,u(k)~ 9~" and w(k)~ 9~t are state, control and disturbance variables with x(0) = x 0 and corresponding system matrices A i ~ N,,x,, , Bi ~ 9v, xm , G ~ 9V'xt " Vi = 1..... s. Furthermore, we enforce x ( k ) , u ( k )

and w(k)to be enclosed inside the

bounded polyhedral sets i.e., Vk > 0, x(k)~ X, u(k)e Y, and w(k)~ 0

representing

operating limitations. Si,T i, and E i defines the convex polyhedra in the state space. 2.2 R e f o r m u l a t i o n

to M i x e d - l n t e g e r

Form

Consider a binary variables 6i(k)~ {0,1} corresponding to each of the ith system dynamics, by defining the non-linear terms xi(k ) = [Aix(k ) + Biu(k)]Si(k ) system (1) can be reformulated as,

x(k + 1) - ~ zi(k ) + Gw(k) i=1

zi(k) < m6i(k); zi(k) > mSi(k)

(2)

zi(k ) < Aix(k ) + Biu(k ) - m(1 - 5i(k)); zi(k ) > Aix(k ) + Biu(k ) - M(1 - 5i(k)) E i < Aix(k ) + Biu(k ) - M* (1 - S i ( k ) ) where ~ i=1

i(k)-l,while

m - - M , M* are appropriately dimensioned large numbers.

1251

2.3 Problem Formulation The finite-horizon MPC problem for the hybrid system is given by, f.,

.

-I

u( 0 ) [ -=

P

s.t. x(k + l)= Aix(k)+ Biu(k)+Gw(k) ([" Six(k)+ Tiu(k) < E i

(3)

x ( k ) s X,u(k) s Y,w(k) s ® , x ( N ) s O~ c_ X;Vk > 0;Vi = 1 v 2 v ...s where Q >- 0 and R >- 0 are the weighting matrices for state and control while positive definite P is the stabilizing terminal cost for the prediction horizon N . The objective is defined over

p=l,2oroobased

on

ll,12orlooperformance criterion and

disjunction denoting logical "or" for i = 1..... s systems.

v

is

After the N ~/' time step we

enforce the solution of constrained and unconstrained problem to coincide, [17,18], by defining O~ as the positive invariant set containing origin in its interior:

O~ = I x(k)~ N",u(k)~ ~'" Kx(k)E Y, 1 [(A i + BiK)x(k)+ Gu'(k)~ X;Vw(k) e ®;Vk > 0 J

(4)

where K is the optimal feedback gain. Rewriting the system (2) in terms of constraint sets X,Y and substituting x(k) into the objective function of equation (3) and can be reformulated as tbllowing multiparametric mixed integer quadratic program.

E [~(U,Z,D,W,x(O)]

F ( x ( 0 ) ) - min U,Z,D

~,~(-)\

.~,.t. g { = : { a - ) . a : { k ) , , , ( k ) . . , { k ) , x { O ) )

(5)

~ 6i(k) - 1;6:(k) ~ {0,1} Vi - 1v . . . v s; i=l

x ( 0 ) e X , U e y X , w ( k ) e ® , x ( N ) e O~ where

the

column

vector

Z=[[zl(1),...,z,.(l)]Y,...,[zl(N-1) .... ,z~,(N-1)] r]

D = [ [ 6 l ( l ) , . . . , 6 , ( 1 ) ] r ..... [ 6 1 ( N - l ) ..... 6 , , ( N - I ) ] r] are

the

optimization

and

vectors.

W = [[wl(1 ) ..... u:,,(1)] r ..... [u,l(N - 1 ) ..... w , ( N - 1)] r] is the expected disturbance vector and U = [[u(0) r ..... u(N - 1)] r]y while x(0) are the current states treated as parameters.

3. T h e o r e t i c a l D e v e l o p m e n t s 3.1 Stability and Terminal Cost for /2 Criterion Definition 3.1.1 Assuming pait:s'(Ai,Bi) are both stabilizable and detectable, system

(Ai,Bi) is a,wmptotically stable (/there exists quadratic Lyapunov jimction given by v~¢)-¢Tp~ >o. Using this definition, we find P >- 0 from the following theorem.

Theorem 1 (Lyapunov Stability)According to Lyapunov stability theorem, an openloop system is stable i.f and only !/ Vi - 1...... s~;3p _ pT >_0 such that Ai r PAi - P < 0 and

1252

closed-loop system pairs (Ai,Bi) are stable if and only/f Vi = 1,...,s;3P = pT >_0 such that (A i + BiK) ~ P(A i + BiK ) - P < O. With o~ - p-1 and fl - K a it is converted to LMI, {

a

(Ai + BiK)T ] >. O.

(A i + BiK )

a

After N th time step control law u(k)= Kx(k)with gain K - fla -1 is implemented.

3.3 Feasibility Definition 4.3.1 The robust polytopic parametric predictive controller steers the plant into the feasible operating region for a specific range of uncertain variations• According to the flexibility analysis theory of [15], maximum constraint violation defines the feasible operating region. This feasible region is depicted by the feasibility constraints, ~(U,Z,D,x(O)) < 0 given by, I gi(U'Z'D'W'x(O) } ~/(U,Z D,x(0)) < 0 ¢:~ max ' w,j Ix(0) e X,U e y N , w e o N , D e {0,1}Ns;'v'j = 1,...,J

(7)

Equation (7) can be solved by identifying critical uncertainty points for each maximization as, if Ogj > 0 ~ w(k) C" - w(k) "b or if Ogj < 0 ~ w(k) ~" - w(k) tb . Ow(k)

~w(k)

Thus, by substituting the sequence of critical uncertainty, w(k) c" in the constraints set g(.), a multiparametric linear program is formulated as,

Ilt(U,Z,D,x(O)) = max{gi(U,Z,D,W,x(O)} w,j • [E >__gi(U,Z,D,W,x(O) ] = mln~ N e [x(0)e X , U e Y ,We O N , D e {0,1}xs;vj = l , . . . , J

(8)

Equation (8) can then be solved using the formal comparison procedure of [ 1].

4. Design of mpRHC The feasibility constraints (7) from section 3.3 are incorporated in problem (5) to obtain the following open-loop robust predictive control problem, min ~ 0E ~ [~(U,Z D,W,x(O)] F(x(O))- U,Z,D

s.t. g(zi(k),~i(k),u(k ), w(k),x(O)) <_0

£ ~i(k) = 1;6i(k)e {0,1};Vi = 1v . . . v s

(9)

i=1

x(O)e X,U e y N , w ( k ) e O , x ( N ) e 0oo min{e > gi(U,Z,D,W,x(O)} 8

This open-loop robust predictive control problem is a bi-level optimization problem. Note that the inner minimization problem is equivalent to equation (8), which can be solved separately resulting into a set of linear feasibility constraints ~ ( . ) < 0 . Substituting it into equation (9) results in following single-level optimization problem:

1253

E[~(U,Z,D,W,x(O)]

F(x(0)) - min U.Z, D

~,~

s.t. g(zi(k),~i(k),u(k),w(k),x(O)) < O;~(U,Z,D,x(O)) < 0; ~i(k)-l;~Si(k)E

{O,1}Vi-lv...v

(10)

s;x(O)E X , U ~ y N w(k)~ 6)

i=1

R e m a r k 4.1 The solution obtained in section 4. is obtained as a piecewise affine optimal robust parametric predictive control policT as a fimction of states U(x(O))for

the critical polyhedral regions in which plant operation is stable and feasible Vw(k).

5. Design Examples Example

1: Consider the following dynamical system

x(k+l)_lll.5X(k)+z,(k)

i[

x(k)>O

.lx(k)+u(k) ~/' x(k)<0 -lO<_x(k)<_lO;-1.2<_u(k)<_2.2.

withQ=l,R=l, andN=2,

using

Theorem

1, P = 0.0054,K = - 1 . 3 5 . For l~ performance criterion, the open-loop computations are performed and the resulting piecewise affine optimal parametric predictive control p r o f l e s as a function of initial state are tabulated in Table 1.

Table 1. Open-loop parametric solution for example 1 CR #

CR

u(k)

u(0) = 2.2

1

- 10 = x ( O )

= -4.2

u(1) = 2.2

2

-4.2 = x(O) = -2.2

u(0) = 2.2

3

-2.2 = x(O) = 0

u(O) = -x(O) z~(1) = 0

4

0 = x(O) : 0.88

u(0) = -1.3636 x(O)

5

0.88 = x(O) = 1.4667

6

1.4667 = x(O) = 5.9111

u(1) = -1.1 x(O) 2.42

u(1) = 0

u(0) = - 1.2

t1(1) = -2.0455 x(O) + 1.8 u(0) = - 1.2

u(1) = -1.2

6. Conclusion This paper presents an explicit solution to the robust MPC for linear hybrid systems via parametric programming. A min-max based feasibility analysis is described to deal with the worst-case uncertainty. The controller performance guarantees system stability and feasible operation. The resulting controllers yield a piecewise affine control law which can be implemented on-line by simple function evaluations.

References [1]

J. Acevedo and E. N. Pistikopoulos, "A multiparametric programming approach for linear process engineering problems under uncertainty," Industrial Engineering and Chemistpy Research, vol. 36, pp. 717 728, 1997.

1254 [2]

[3] [4] [5] [61

[7] [8]

[9]

[10] [11] [12]

[13]

[14]

[15]

[16] [17]

[18]

[19]

[20]

V. Dua, Parametric programming techniques for process engineering problems under uncertainty. Ph.D. Thesis, Imperial College London, Lonodn, U.K., 2000. E. N. Pistikopoulos, N. A. Bozinis, and V. Dua, POP: A MATLAB (the Math Works, Inc.) implementation of multi-parametric quadratic programming algorithm. Center for Process Systems Engineering, Imperial College London, London, U.K. SW7 2PP, August 2003. E.N. Pistikopoulos, V. Dua, N.A. Bozinis, A. Bemporad, and M. Morari, "On-line optimization via off-line parametric optimization tools," Computers and Chemical Engineering, vol. 24, pp. 183-188, 2000. A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, "The explicit linear quadratic regulator for constrained systems," Automatica, vol. 38, pp. 3-20, 2002. V. Sakizlis, N. M. P. Kakalis, V. Dua, J. D. Perkins, and E. N. Pistikopoulos, "Design of robust model-based controllers via parametric programming," Automatica, vol. 40, pp. 189-201, 2004. M. S. Branicky, Studies in hybrid systems: modeling, analysis, and control. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1995. P. Antsaklis, "A brief introduction to the theory and applications of hybrid systems," in Proc. IEEE, Special issue on hybrid systems: theory and applications, vol. 88(7), pp. 879887, July 2000. P. J. Antsaklis and X. D. Koutsoukos, Software-Enabled Control." Information Technology for Dynamical Systems, ch. Hybrid Systems: Review and Recent Progress. Wiley-IEEE Press, April 2003. A. Bemporad and M. Morari, "Control of systems integrating logic, dynamics, and constraints," Automatica, vol. 35, pp. 407-427, 1999. W. Heemels, B.D. Schutter, and A. Bemporad, "Equivalence of hybrid dynamical models," Automatica, vol. 37, pp. 1085-1091, 2001. V. Sakizlis, V. Dua, J. D. Perkins, and E. N. Pistikopoulos, "The explicit control law for hybrid systems via parametric programming," in Proceedings of the American Control Conference, (Anchorage, AK), pp. 674-679, May 8-10 2002. D. Q. Mayne and S. Rakovic, "Model predictive control of constrained piecewise affine discrete-time systems," International Journal of Robust and Nonlinear Control, vol. 13, pp. 261-279, 2003. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory. Philadelphia: SIAM, 1994. E. N. Pistikopoulos and I. E. Grossmann, "Optimal retrofit design for improving process flexibility in linear systems," Computers and Chemical Engineering, vol. 12, no. 7, pp. 719-731, 1988. V. Sakizlis, Design of Model Based Controllers via Parametric Programming. Ph.D. Thesis, Imperial College London, Lonodn, U.K., 2003. E. G. Gilbert and K. T. Tan, "Linear systems with state and control constraints: the theory and application of maximal output admissible sets," IEEE Transactions on Automatic Control, vol. 36, pp. 1008-1020, September 1991. I. Kolmanovsky and E. G. Gilbert, "Theory and computation of disturbance invariance sets for discrete-time linear systems," Mathematical Problems in Engineering." Theory, Methods and Applications, vol. 4, pp. 317-367, 1998. V. Dua and E. N. Pistikopoulos, "An algorithm for the solution of multiparametric mixed integer linear programming problems," Annals of Operations Research, vol. 99, pp. 123139, 2000. A.M. Manthanwar, V. Sakizlis, and E.N. Pistikopoulos, "Design of robust parametric MPC for hybrid systems," in accepted for publication to the 2005 IFAC World Congress.

European Symposiumon Computer Aided Process Engineering- 15 L. PuiAjanerand A. Espufia (Editors) ,~c)2005 Elsevier B.V. All rights reserved.

1255

Model Based Operation of Emulsion Polymerization Reactors with Evaporative Cooling: Application to Vinyl Acetate Homopolymerization S. Arora ~*, R. Gesthuisen t~, and S. Engell a ~Process Control Laboratory, University of Dortmund Emil Figge Strasse 70, 44227-Dortmund, Germany bDeutsche British Petroleum AG Chemical Production K61n, Germany

Abstract In this work, a dynamic model of emulsion polymerization processes is extended by the inclusion of vaporization from the liquid phases in the reactor to the gaseous phase. The multi-component gas-liquid mass transfer phenomenon is described by a set of algebraic equations which are solved by an iterative procedure. The vaporization fluxes are described by MaxwelI-Stefan's diffusion equations. Based upon the extended model, a novel operation strategy is developed. By controlled vaporization, additional heat is removed from the reaction system. This makes it possible to extend the restrictions imposed by the limited heat removal by the cooling jacket considerably. Simulation results are presented tbr the homopolymerization of vinyl acetate in an industrial scale reactor operated in semi-batch mode. The results show that a significant amount of heat can be removed by evaporative cooling.

Keywords" emulsion polymerization; vaporization" modelling; operation" control

1. Introduction Emulsion polymerization is an important multiphase process for the production of a wide range of polymeric materials. The polymerization proceeds as a classical double bond addition reaction initiated via a free-radical mechanism. The reaction is highly exothermic in nature and therefore industrial reactors are often operated under starved conditions. This is due to the limited heat removal capacity of the jackets. In this paper, we investigate the emulsion polymerization of vinyl acetate, taking into consideration the afi~ct of vaporization of the different species from the liquid phase to the gaseous phase. Since the vaporization reduces the heat content of the reacting medium, it has been termed evaporative cooling. The reaction is carried out at temperatures less than the boiling temperature of the liquid in order to avoid bubbling. The vaporization fluxes are computed by the product of the mass transtEr coefficients m

Author/s to whom correspondence should bc addressed: [email protected] s.engell(~bci.unj-dortmund.de

,

1256 and the concentration gradients in the two phases. The mass transfer coefficients (which are functions of concentrations) are estimated by solving the multicomponent MaxwellStefan diffusion equations and by the application of film theory. An algorithm based on the approaches by Burghardt (1983 and 1984) has been developed for this purpose. The model developed here is an extension of our earlier approach, Arora and Gesthusien (2004), where we formulated and analyzed the evaporative cooling model for emulsion polymerization processes. The aim of this paper is to present a model based operation strategy in order to exploit the vaporization phenomenon for the extraction of additional heat out of the system. Further, this approach can be extended to other highly exothermic processes (esp. involving highly viscous systems), where the overall heat transfer coefficient is low, leading to inefficient cooling by the reactor jacket.

2. M o d e l D e v e l o p m e n t Modelling of emulsion polymerization processes has been extensively researched in recent years. Since the process is quite complex and requires complex models, it is beyond the scope of this paper to discuss the various approaches used for modelling of emulsion polymerization process in detail. Only the main equations are described here. The process diagram for which the model is developed is shown in Figure l.

2.1 Emulsion Polymerization Model Emulsion polymerization is a multiphase process involving primarily three liquid phases (the monomer or droplet phase, the water or aqueous phase, and the oil or particle phase). The reaction starts in the water phase where the initiator disintegrates to form free radicals, which then combine with the dissolved monomer in the aqueous phase to form oligomers. These oligomers either precipitate or are trapped by emulsifier micelles to form particles. The polymerization reaction then mostly takes place in the particle phase. The mole balance equations for monomer and for water can be described as: • nSvkp[M] p ]w w k ]w i i ° dM = Min-ERT V [M - ~, N M A + Mrec dt NA P dW dt

i Ai = m i n - Y', N W + + m rec

(1)

(2)

where n denotes the average number of radicals per particle, N T the total number of particles, k

P

the propagation rate, N A Avogadro's number,

RT

the concentration

of oligomers in the water phase and V w the volume of the water phase. ~ N i. A i stands J for the total amount of vaporization of species j from phase i. The subscript in denotes the feed to the system and rec denotes the recycle stream from the condenser. The energy balance for the liquid phase in the semi batch reactor is written as:

1258 a function of existing film and bulk conditions. It is calculated based on the approaches by Burghardt (1983 and 1984) and by Taylor and Krishna (1993). The gas phase component mass balance equations are derived considering the vaporization from the liquid phase and the flow of the gas from the vapour phase to the condenser. The above equations are explicit in nature and require no iterations if the interface compositions are known. It is assumed that there exists thermodynamic vapour-liquid equilibrium at the liquid side of the interface. Thus, the determination of the gas interface composition, which satisfies the two conditions (vapour liquid equilibrium and flux of inert component being zero) based on the existing conditions of temperature, pressure and compositions in the bulk phases is the key to the solution. An algorithm is proposed (Table 1) that uses an iterative procedure to find the interface composition and thus the overall fluxes.

2.3 Operation Strategy The basic idea is to regulate the concentration of the vaporizing species in the gas phase to a setpoint value. If this set point value is below the thermodynamic equilibrium, then vaporization will take place. The farther the setpoint is away from the equilibrium point the greater is the vaporization flux. This property can be exploited here using the nitrogen flow as a manipulated variable for altering the gas phase compositions. Two independent decoupled feedback loops are constructed to implement the above idea. The first loop controls the pressure in the reactor by regulating the outflow, whereas the second loop maintains a desired mole fraction of water in the gas phase by regulating the inflow of nitrogen. Both controllers are PI-controllers.

Table 1. Algorithm for the calculation of vaporization fluxes when intetj'ace compositions are unknown Given

(Xo),(yo),p,[D ]

Step 1

Assume xc~ = x 0 for the liquid interface

Step 2

Calculate Y6" by estimating interface temperature

Step 3

Compute Yavg andcalculateIAav 1

Step 4

Compute (1), using the values of step 1 and step 2

Step 5

Compute ~ (non linear bootstrap coefficient)

Step6

Calculate ( N ) (initial guessof flux)

Step 7

Recalculate (I) (using calculated molar fluxes)

Step 8

Recalculate Yc~ using q) from step 7

Step 9

Check for convergence of Yb" and calculate ( N ) converged, else return to step 2

when

1257

art

+

where ( Y~nicpiT ) rate, AH

rxn

represents the total amount of energy in the reactor, r the reaction

the enthalpy of reaction and AH FXH

vap

is the enthalpy of vaporization.

<Mo-L-@@ Figure 1. Process diagram 2.2 Evaporative Cooling Model The extension of the emulsion polymerization model is performed by the inclusion of the gas phase. Nitrogen is used as an inert gas for manipulation of the gas phase concentrations. The dynamics of the gas-liquid mass transfer is considered by estimating the vaporization fluxes from the three liquid phases (droplet, water and panicle). The vaporization fluxes are described as:

c

V(yO_yfi)

E ----1 ~ exp • + 1 , where • - In ~=Yn8 2 exp~-I Yno

(4)

ny~-1 Nk 1 cD/1 t

Here, ( N ) i s the column vector of vaporization flues.

(5)

(yO-Y6) isthecolumn vector

of difference of mole fractions in the bulk and interfacial conditions in gas phase. [A] denotes the inverse diffusivity matrix, c t the overall concentration and I the film thickness. The subscript n denotes the inert component which is nitrogen. E denotes the nonlinear Bootstrap relation (that makes the flux of nitrogen equal to zero), which is

1259

3. Results and Discussion A seeded emulsion polymerization reaction was simulated for an industrial scale reactor in semi batch mode. The vinyl acetate emulsion polymerization model was tested with experimental and simulation results of Sayer et al. (2002). The simulation results are shown in Figure 2 (subfigures A-F). The reaction rate increases in the beginning and then remains almost constant during the whole reaction profile, see subfigure A. This is typical for semi batch reactors where a constant feed rate is used. The reaction starts slowly, thus accumulating some amount of monomer, which then leads to a peak in its concentration (and also in the reaction rate). Instantaneous and global conversion curves are drawn in subfigure B. The initial dip in instantaneous conversion can also be explained by the same argument as the accumulation of monomer in the initial phase of the reaction. x 10 .5

Subfigure A

15[

:

Subfigure B I

Reaction R a t e ~ 0.8

--

....

"

--

O

.~ 0 . 6

......

(1)

F

0.4

,

o

~ Instantaneous

Global

i i

0.2

[

0 0

100 200 Time (min)

300

0

Subfigure C

15 10

...~..

- _

I

gen

o61 %.

. ........ Hva p

(1)

/!

5

..................................................................................................................................... i...................................... }

/

v

i

60

! ..... E

0

i

!

i

0

100

J

200

58 57

300

0

T i m e (min)

x 10 .5

Subfigure E

12 I ! o

1

0

-

E

6 . . . .

m6

v

,-

"

C .mO

8

n O

-

I

I

F

I

L

I

100 200 Time (min)

i

0.02

I

~ 0.015 VaPw }

------

.....

........... ~

i

"

300

Subfigure F

0.025

I ]

-

"~

I¸ I

t~

:1=

,~ o

300

Subfigure D

62

................ H

I

L k 100 200 Time (min)

>

x

I_i

s_0j

.......

X

:-

0.01 O

4 . . . .

~

r

I

I

--

-

0.005

I

0

0

100 200 T i m e (min)

I

I

300

I

0

I _ _

[

100 200 Time (min)

300

F i g u r e 2. S i m u l a t i o n r e s u l t s f o r 1 0 0 0 litre r e a c t o r

The rates of heat generation and removal by evaporative cooling are shown in subfigure C. It can be noticed that a significant amount of heat is taken out of the system by the proper usage of the vaporization phenomenon. The simulations clearly show the

1260 advantage of evaporative cooling in addition to the jacket cooling which is limited for highly viscous systems and for large reactors that have relatively small heat transfer areas. The temperature of the reacting mixture is maintained around 60 °C and the pressure is kept at 1 atmosphere. The vaporization rate for water is shown in subfigure E. It is observed that vaporization flux is strongly dependent on the temperature. As soon as the reaction is over, the vaporization causes the temperature to fall thus leading to its sharp decline. Since the mole fraction of vinyl acetate is very low in the gas phase due to the high rate of reaction, it was not considered in the control strategy. The value of set point (mole fraction of water in the gas phase) was chosen based on economic considerations (depending on the usage of nitrogen and increment in vaporization flux) of the reaction. Simulation runs were performed for that purpose. The set point along with the actual mole fraction of water in the gas phase is plotted in subfigure F.

4. Conclusions and Future Perspective Emulsion polymerization process offer great challenges with respect to industrial operation, optimization and control. Since the reaction is highly exothermic, the process operation is often restricted by the heat removal constraint. One of the major issues is to run the process at safe conditions but at higher reaction rates. Evaporative cooling can be used for this purpose. A model has been developed here that describes the effects of vaporization on the process conditions. The exact estimation of the molar fluxes requires knowledge of the mass transfer coefficients and the interfacial composition, area and temperature. The approach used in this work is based on Burghardt's approach. Since Burghardt's solution can be applied only when the interface and bulk compositions are known, the vapor-liquid equilibrium calculations together with diffusion equations are solved by an iterative procedure. This model was used to determine the operating set point. Two decoupled control loops are implemented to take advantage of the vaporization phenomenon. The simulation results clearly indicate the advantages of using evaporative cooling over the usual jacket cooling, which is restricted in highly viscous systems and in big reactors (due to the lower heat surface area to volume ratio). In the future, we plan to validate and to improve the results by the experiments.

References Arora, S. and R. Gesthusien, 2004, 8th International Workshop on Polymer Reaction Engineering, DECHEMA Monographs, Vol. 138. Burghardt, A., 1983, Int. Comm. Heat Mass Transfer, 10. Burghardt, A., 1984, Chemical Engineering Science, 39. Sayer, C., M. Palma and R. Giudici, 2002, Ind. Eng. Chem. Res., 41. Taylor, R., and R. Krishna, 1993, Multicomponent Mass Transfer. John Wiley & Sons, Inc., USA.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1261

Event-based Approach for Supply Chain Fault Analysis Ramon Sarrate a*, Fatiha Nejjari a, Fernando D. Mele b, J. Quevedo a and L. Puigjanerb a

Dept. d'Enginyeria de Sist., Aut. i Inf. Ind., Universitat Polit6cnica de Catalunya Rambla de Sant Nebridi, 10, E-08222, Terrassa, Spain bDept, d'Enginyeria Quimica, Universitat Polit6cnica de Catalunya ETSEIB, Av. Diagonal 647, E-08028, Barcelona, Spain

Abstract This work is a contribution to fault propagation analysis in a supply chain network. An event-based fault detection method is applied to fault propagation analysis validation. The goal of this methodology is to discover and validate fault propagation effects on system variables. This knowledge could be used to improve corrective action design in order to compensate negative effects. The methodology has been applied to supply chain fault propagation analysis over inventory data. Once validated, fault propagation effects on inventory level could be compensated by adapting the inventory control policy. Thus, unnecessary inventory holding could be reduced.

Keywords: supply chain management, discrete event system, fault detection, process monitoring, fault propagation analysis

1. Introduction Supply chain productivity and economic benefit strongly depend on the correct behaviour of each unit or activity involved. A raw material supply transport interruption or a production machine breakdown in a manufacturing plant can bring the supply chain to a decrease in efficiency, leading to unexpected economic costs. These undesired situations can be regarded as supply chain faults or incidents. Due to the interconnected nature of supply chains, fault effects usually propagate through the system, degrading, as time goes on, the overall performance. After a production machine breakdown, a manufacturing plant will lately service orders posted by a distributor. Consequently, the distributor could also be forced to delaying orders posted by its costumers, and so on. Anticipating the fault propagation effects could be beneficial in reducing the overall economic loses. Global corrective actions could be designed and planned beforehand off-line. As soon as a fault occurs, these corrective actions could be applied, compensating for fault propagation effects and thus minimizing economic loses. In the machine breakdown example, the manufacturing plant would decide to repair the damaged machine, whereas at the same time the distributor would decide to

Author/s to whom correspondence should be addressed: [email protected]

1262 immediately post its pending orders to another manufacturing plant while production is re-established in the former. This should be preferable to just waiting for repair. In the literature, the analysis to determine how certain fault effects propagate through a system is known as fault propagation analysis. Blanke et al. (2003) propose a methodology for fault propagation analysis based on structural analysis, a technique which analyses the structural properties of mathematical models. However, whenever models are not available, their approach is not applicable. The approach proposed in this paper is based on the observation of system signals. Faults modify the normal behaviour of system signals. Discovering temporal patterns originated by faults on these signals should help in anticipating negative fault effects. Candidate fault propagation patterns could be generated by applying well-known data mining techniques as time series pattern recognition (Berndt et al., 1996) or clustering methods (Piera et al., 1991). These techniques allow for knowledge discovery. However, the observation of system signals by an expert could be enough to produce a candidate fault propagation pattern. In this paper, candidates are generated from the observation of inventory levels. Inventory data is commonly registered by companies, so it will probably always be available for analysis. A methodology has been developed that allows for checking the correlation of a fault occurrence with a candidate fault propagation pattern. This validation methodology is based on a process monitoring technique which has been previously applied to other domains such as biotechnological process supervision (Sarrate et al.,1998) or tool machine monitoring (Aguilar et al., 2001). In this work, its application has been extended and adapted to supply chain fault detection. In Section 2, a brief description of the process monitoring technique applied to fault detection is presented. Guidelines to apply this technique to fault propagation analysis validation are given at the end of this section. Section 3 is devoted to illustrate the methodology on a supply chain network. Two fault scenarios are studied and results are discussed. Some concluding remarks on this methodology are given in Section 4.

2. The Fault Analysis Methodology 2.1 Event-based fault detection Fault detection aims at determining faults present in a system and the time when they have occurred. A lot of research has been done in this field (Isermann, 1997). In Sarrate (2002) a methodology for process monitoring is proposed and applied to tool machine fault detection. This fault detection rrethodology is organized in to stages: the Interface and the Supervisor.

2.1.1. The Interface The Interj'ace analyses system signals following the sliding window paradigm, in order to detect relevant events. Under this approach, data is processed in sets con"prising a time window. A window slides over time, and is periodically sampled. For each sample, all window data is analyzed in order to produce a window attribute which constitutes new data. Output data produced by this sliding window mechanism could be analysed again following the same procedure. Applying this algorithm recursively with different kinds of analysis, the required significant information can be abstracted. For instance,

1263 signal trends can be generated by first applying a linear regression window-based analysis to obtain the slope. Next, the slope is classified over a set of intervals applying a statistical window-based analysis to obtain the mode, which represents the most probable signal trend. Interface configuration is needed to adjust window parameters. Expert system knowledge is applied for lntec/ace design and configuration.

2.1.2. The Supervisor The Supervisor is build upon an automaton which models the system behaviour. It must describe normal operation as well as all faulty situations that should be able to detect. Expert system knowledge is needed to discover which event sequences are associated to faulty situations. In the automaton, states model system states whereas transitions are associated to events.

2.2 Fault propagation analysis validation The Supervisor automaton models system behaviour as event sequences. Events are associated to relevant signal dynamics. Thus, the observation of a sequence of relevant signal dynamics allows a faulty situation to be detected. In fact, the auton~ton stores the fault propagation knowledge. Fault propagation effects are often clearly visible on system variables. Thus, the observation of signals by a system expert should provide temporal patterns that a fault originates on them. Once this information is available, the automaton can be built. Since fault detection methodology is based on fault propagation knowledge, the fault detection procedure can be used for fault propagation validation as follows" 1. A set of design signals must be available. These must correspond to normal as well as faulty behaviour. The design set could be generated by a simulation model or obtained by measurements in the real system. 2. Through expert observation of the design set, the fault detection system must be designed and configured a. Relevant signals dynamics are to be identified. The Interlace must be designed accordingly, so that it is able to detect these significant events. b. Fault propagation patterns are to be discovered. The automaton must be build, so that it models these patterns. 3. A set of validation signals must be available. The same considerations given for the design set apply. 4. The fault detection system is run on the validation set. A fault detection success validates the fault propagation knowledge. However, wrong fault detection performance indicates that the fault propagation knowledge was badly inferred.

3. Application to Supply Chain Fault Propagation Analysis 3.1. Problem statement The fault analysis methodology will be applied to a supply chain. The model interconnects 6 entities, as illustrated in Figure 1. Two types of flows are present. On the one hand, there is a material flow (raw material P and finished products A and B) from the supplier to costumers. On the other hand, there is an information flow (order) from costumers to the supplier.

1264 Supplier

Plant

Distribution centers

Retailers

]D1B~RIB~

~No,"

/

Figure 1. Supply chain network

Demand pattern has been simulated following a certain distribution probability. Given the discrete event nature of the supply chain, its model has been simulated in Matlab using Simulink and Stateflow tools. Two faulty scenarios were studied applying the fault analysis methodology developed in section 2: • Scenario 1 : A transient transport interruption of product B from P1 to D1B. • Scenario 2 : A transient production delay of product A. The goal is to discover how these events have an effect on the inventory levels of the supply chain entities. Excess inventory incurs unnecessary holding costs, while the inability to meet the costumers needs results in both loss of profit and potentially, the long term loss of costumers. The fault propagation knowledge can be used to design adequate corrective actions. For instance, once a fault has occurred and has been noticed, fault effects could be compensated adapting inventory control policies. 3.2. Results

Three design simulations were provided for the fault propagation analysis: the fault-free case, a transport interruption at 4000 s.u. for 65 s.u. and a production delay at 5000 s.u. during 700 s.u., where s.u. stands for simulation units (1 s.u. = 5 min.). Figure 2 shows the inventory levels for some relevant supply chain entities under faultfree as well as faulty conditions. Apparently, the effects that both faults have on them can be easily appreciated. Both result in a transient increase of inventory levels for different supply chain entities. The transport interruption significantly affects D1B inventory level, whereas the production delay slightly modifies D 1B and D 1A inventory levels. In order to validate these fault propagation statements, the fault propagation analysis validation methodology has been followed. For Scenario 1, the fault detection system illustrated in Figure 3 was designed a tuned. The trend detector implements the Interface. Significant trend events sequences are characterized in the Supervisor by a Stateflow automaton. Fault detection results for the design set are illustrated in Figure 4. The first plot corresponds to the D1B inventory data. It shows also the fault detection at 4160 s.u.. Trend events are detected following the sliding window paradigm, as illustrated in section 2.1.1. The second plot corresponds to slope data obtained through a linear regression window-based analysis. And the third plot corresponds to the mode obtained from a statistical window-based analysis.

1265 100 [- Fault-fre4

l

f

_i

__=:[ ............... ]". . . . . . .

D1B invi "i

. . . . . . . II'l '", "ill ""l"l .... "]t' "i "i "" " T....... r,[ .... 0 2000 4000 6000 8000 10000 ,~,~[[~. Fault'fre~ [[[[[~, i , ~ 'm [ Ill ~NIm[Wll'[

] .... _~.L

'1 "ll~ii "'i 'll"l"i 12000 14000

~~~~~~~~~[

~ i ]

"i -' p" i ' '' "' "[ 16000 18000

IIl~[

/mmmml~~~--1[

1

a 1A

inv.t 1[ Ill W'IIV~II"I'ql*lI'I~1rlll iI'f'l~t~'ll'rl"~ ~,r,llrlq '!~ I ,lrq rn1""!"11'~'f"'l'l ' ~"l 0

2000

100[

4000

T . . . . po~t int. . . . pticlltl

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6000

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6000

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14000

10000

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6000

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8000 10000 12000 Time (s.u., 1 s.u 5 rain.)

14000

16000

18000

Figure 2. Design set

EUi~j~{~ZEll CJock I I

worFspace ~

I ...........

~ ___L_l-a--z-'-*r--_-____-3___ I r -it 71

/ %e~,f

Trenddeteetor .......

:~ '~-- Su;ervisor --

* start

'Normal/ r_,estat=O .

D1B_incr. 'Fmtl estat=l D 1B_decr

Figure 3. Event-based fault detection system and automaton for Scenario 1 Once designed and tuned, the fault detection system was used as a validation tool. A validation set was generated via simulation, varying fault time and duration. Table 1 summarises the validation results. As expected, the longer the fault, the better the fault detection: over 250 s.u duration success is granted. This confirms the influence of this fault on the D 1B inventory level. For Scenario 2, a similar study was developed. Another fault detection system was designed but validation results were not so satisfactory. This confirmed the slight influence of this fault on supply chain entities. In this case, fault propagation effects were not generic applicable.

4. Conclusions This work describes a methodology for fault propagation analysis and validation. Fault detection systems are designed for validation purposes. They are built from expert system knowledge, so no mathematical system descriptions or models are needed. As this fault detection system is built from fault propagation knowledge, it can be used for fault propagation validation.

1266 D1B Inventory 150

I'I

l'IIll

.~,,

o

) !.,,,,

-~,

'q

'

ll'~Ill l

~'II I 'I

"

r~-~,'~~

~" 0

2000

6000 8000 10000 12000 14000 Linear regression window-based analysis: Slope

16000

18000

0.6, :. 0.4

1 •

°iil.rr..l~f~,f.r. _o.21 0

2000

i

[~ ,'.... ,, ,n,,.n.h, ....... ~'.~w .n,a ~ , . ~ , r l~..t w ~ ¢"'pu""oW'*" 4000

[

[!

6000 8000 10000 12000 Statistical window-based analysis: Mode

[

[ ..... i

14000

[ .... r

!111 I I 11111It Ill,illill °~oI i lllll I llUli I i llill 2000

4000

6000

16000

18000

!

II IIIIlJl! ,ll Iil[i[lI!

8000 10000 12000 Time (s.u., 1 s.u. = 5 rnin)

14000

16000

18000

Figure 4. Event-based fault detection results for Scenario 1 design set Table 1. Validation results for Scenario 1 (X." wrong, ~" success)

Fault time (xl0 ~ s.u.) = ,

O ,,..~

a,

3

4

5

6

7

8

9

10

11

12

13

14

65

X

x/

X

X

X

X

X

X

X

X

X

X

]oo

x

~/ x

4

4

4

x

x

x

x

4

x

250

x/

x/

q

~/

x/

x/

~/

x/

x/

x/

x/

x/

i

An application to supply chain fault analysis has been done. Results demonstrate the usefulness of this approach. Once fault propagation analysis is validated, adequate corrective actions could be planned to compensate for fault effects. References

Piera, N. and J. Aguilar, 1991, Controlling selectivity in non-standard pattern recognition algorithms, IEEE Trans. In Syst., Man and Cybernetics, 21, 1, pp. 71-82. Berndt, D.J. and J. Clifford, 1996, Finding patterns in time series: a dynamic programming approach, In: Fayyad, U.M. et al., Eds., Advances in Knowledge Discovery and Data Mining, pp. 229-248, AAAI Press/MIT Press. Isermann, R., 1997, Supervision, fault-detection and fault diagnosis methods - an introduction, Control Engineering Practice, 5, 5, pp. 639-652. Sarrate, R., J. Aguilar and J. Waissman, 1998, On-line event-based supervision of a biotechnological process, 3'd IFAC Workshop on On-line Fault Detection and Supervision in the Chemical Process Industries, pp. 359-364. Solaize. Aguilar, J., R. Sarrate and J. Waissman, 2001, Knowledge-based signal analysis and case-based condition monitoring of a tool machine, Joint 9h IFSA World Congress and 20 th NAFIPS International Conference, pp. 286-291. Sarrate, R., 2002, Supervisi6 Intel.ligent de Processos Din~mics Basada en Esdeveniments, PhD Thesis, Universitat Politbcnica de Catalunya (in Catalan). Blanke, M., M. Kinnaert, J. Lunze and M. Staroswiecki, 2003, Diagnosis and Fault-Tolerant Control, Springer-Verlag, Berlin.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) {~:2005 Elsevier B.V. All rights reserved.

1267

Back-off Application for Dynamic Optimisation and Control of Nonlinear Processes Silvina I. Biagiola ", Alberto Bandoni b and Jos6 L. Figueroa ~* aDepartamento de Ingenieria Eldctrica y de Computadoras, Universidad Nacional del Sur-CONICET Av. Alem 1253, 8000 Bahia Blanca, Argentina bPlanta Piloto de lngenieria Quimica-CONICET La Carrindanga Kin.7; 8000 Bahia Bianca, Argentina

Abstract The operating point of a process plant is obtained through optimisation of an objective function subject to certain constraints. Typically, the resultant point lies in the boundary of the operative region. Therefore, in the presence of disturbances, the constraints may be violated and the process may be obliged to operate in an infeasible region. The goal of this paper is to present an efficient back-off algorithm to determine the operating point which guarantees feasibility even under disturbances effects. The proposed method is especially oriented to diminish the computational time associated with nonlinear processes. For this purpose, the nonlinear process is approximated by means of a piecewise linear (PWL) model which allows a substantial computational time reduction. Finally, an example is dealt with to show the application of the proposed approach. For this purpose, a nonlinear steam generating process is modelled, optimised and controlled. Keywords: back-off, canonical piecewise linear approximations, dynamic optimisation, process control

1. Introduction Applications of nonlinear optimisation problems have become very common in the process industries, especially in the area of process operations. To achieve the optimal design and operation of a process, one seeks the best design and operation which will result in a maximum profit. Therefore, in a first design stage, the operating point is usually determined to maximize (or minimize) an objective function. This cost function is normally a weighted combination of various utility costs, material costs, production costs and penalties of environmental emissions. The process model and constraints describe the interrelationship of the key variables. These constraints define a feasibility set for the possible operating points, and in most cases, the optimal operating point lies in the boundary of the set. Therefore, in the presence of disturbances, the current operating point (i.e. optimum point) might exceed some constraint value for the changed conditions. This would lead to undesirable or even unsafe operation of the plant. To avoid operating the process in an infeasible region (Figueroa et al., 1996), it is possible

Author to whom correspondence should be addressed: [email protected]

1268 to move the operation point away from the one determined in the optimisation level and to oblige the new point to satisfy the constraints under the disturbed operation. The movement of the operation point due to the likely effect of disturbances is referred to as back-off, and was originally calculated from the desire for evaluating and comparing control strategies on the economical basis (Perkins and Walsh, 1994). Because in the process industry there is a great number of strongly nonlinear processes, the accomplishment of the back-off algorithm may become very slow or even impossible to perform. To avoid this obstacle, the optimisation problem can be turned into a linear one. In the present paper, we propose to use a canonical piecewise linear (PWL) approximation (Julifin et al., 1999) to the problem. This formulation allows the systematic description of any nonlinear function. Then, the whole procedure, i.e. the dynamic back-off analysis, the steady-state calculations, the closed-loop output predictions, are accomplished on the basis of the PWL representation of the process. The main advantages of the proposed approach are the problem simplification and the substantial calculation-time reduction. In a following stage, a controller is designed to regulate the behaviour of the plant around the designed steady-state value. The underlying idea is that the controller provides perfect control, so that the plant remains very close to its nominal operating points against disturbances and parameter variations and uncertainties on the plant characteristics. Finally, an example is presented to show the application of the introduced method. For this purpose, a nonlinear steam generating process is modelled, optimised and controlled. Computer simulations are developed for showing the performance of the optimised and controlled nonlinear process. The results obtained with the exact nonlinear approach and the approximating PWL one, are compared.

2. Back-off problem formulation The mathematical formulation of the closed-loop back-off problem can be posed as follows:

(1)

%bj[USo,%] subject to

g[Us,X(t),d]
J[x(O,Us,X(O,d]=O, x(O)=xO, u L
S

S

x L_~x_<.U x where x(t) are the process states, u

are the optimisation variables; d(t) are the s disturbances, f are the state equations of the process and g is the set of algebraic inequalities. It is assumed that vector d belongs to a set D which contains all the

possible disturbances"

D-{d:dL
where d L and d H are the extremes of the set.

1269 In this formulation, the model includes the complete description of the process and the controller information. Usually, the back-off technique is used to achieve the process operation feasibility, even under unmeasurable disturbances influence. The solution of this problem implies the solution of a dynamic optimisation under uncertainties and the method by Figueroa et al. (1996) can be followed.

3. Piecewise linear approach In the back-off formulation there is a significant computational complexity associated to the solution of the nonlinear problem. Hence, it is a bottleneck in the on-line application of the back-off algorithm to many nonlinear processes. For this reason, the use of a PWL description to approximate the nonlinear model of the process appears as an appealing strategy to reduce the computational time. A PWL function f.'DcC~'n,--->c~ 1 with D a compact set, is defined as follows"

Definition. Let the domain D be divided into a set of regions or convex polyhedrons~(i)

'

i c {1,

" "

" ~

k~ } such that D _k, ~(i) --i=l

This partition is performed

through a set of hyperplanes ( H "- { H i c D;i E {1,..., k, }}) with dimension (m o- 1). They

are

also

called

limits

[ H i - {v c ~"'" "2"i ( v ) " - a ' i v - fli - 0}],

wherei~ {1 .... h } , a ' i c 9~"'" and f l / ~ ~ 1 V i .

Hence, a PWL functionfis defined by

the local functions [ f ( i ) ( v ) - Ji')v + w(i)], with region ~(;), w (i) ~ ~ /

and

f(V) _

j(i) E

~1×,,,,,

the Jacobian of the

.f(i) (V) for any V C ~(')

Theorem. The components of the PWL functions of A calculated by Julifin (1999) are a base of the linear vectorial space PWLH[D ]. Then, every PWL function f E PWLH[D]can be uniquely represented (Julifin et al., 1999) as a linear combination of the elements in A as [ E ~ A ( v ) - f ( v ) ] . A relevant property is that, under certain conditions (Lussdn Cervantes et al., 2001 and references therein), there exists the inverse function [EYA] -~ that performs the inverse transform to obtain v from fly). This aspect is very important and must be taken into account for evaluating possible models of the static nonlinearity, because when the model is to be used for control purpose, the function must be invertible (Norquay et al., 1998).

3.1 Approximation using PWL functions As described above, the PWL functions have shown to be an appealing approach for modeling and analysis of nonlinear processes. The nonlinearities in the differential equations that describe the process dynamics can be approximated using a piecewise linear representation. In such a way, the operative region can be divided into several domains that constitute the simpleces. Hence, in each domain there is a linear model

1270 which approximates the real one. The operation point can change making the system leave a simplex to enter another one. In such a case, the linear approximating model changes. This model can be represented as follows" i

(2)

2 - A),wL x + B~,wLh-

where A p w L and B p w L are the model parameters that stand for the simpleces i and uis an extended vector which includes the control inputs and the disturbances d: ~--[u'

d'l]'

(3)

The representation given in Eq.(2) is dealt with as a linear system. Therefore, the system's output can be calculated using the solution for linear dynamics.

4. Simulation example To illustrate the algorithm proposed above, the 200 MW drum type boiler of a steamgenerating unit is considered. Ray and Majumder (1983) developed the following model for this nonlinear unit:

dP

= - 1 . 9 3 1 0 -3 S P ~/8 + 0 . 0 1 4 5 2 4 F -

7 . 3 6 1 0 -4 Wc + 1.2110 -3 L

(4)

dt dS

= lOcvP 1/2 - 0 . 7 8 5 7 1 6 S

(5)

dt dL

= 0 . 0 0 8 6 3 W c + 0 . 0 0 2 F + 0 . 4 6 3 c v - 610 -6

dt

p2

_

0.00914L (6)

-8.210-5L 2 - 0.007328S The pressure P[Kg/cmZ], the steam flow to the turbine S[Kg/sec] and the drum level L[cm] are the state variables of the process which is disturbed by the feed water temperature Te[°K] and the control valve setting (cv). To keep P and L in their setpoints, both fuel F[Kg/sec] and water Wc[Kg/sec] flows are manipulated. The operation constrains due to the physical process features are: 120
1271 0.280 < Te < 0.320 0 . 7 0 0 < cv < 0 . 9 0 0

The following objective function is proposed in order to minimize the operating cost and to maximize the steam production" F~,~i - - 0 . 6 S -

0 . 5 P + 0 . 8 F + 0.1Wc

(7)

To provide the back-off algorithm a linear representation of the process, the nonlinear plant was approximated using a PWL description. For this purpose, the nonlinearities

Sp1/8 , cv Q-~, p2 and L2 in Eqs. (4-6) were replaced by piecewise linear functions. A simple controller structure to keep P and L in their desired values was used in both cases: the nonlinear model and the PWL approximation. For these purposes, two PI controllers were designed and their parameters were set to: K=300, Kc = 1, T~,,t = 50 for the pressure regulator and K = 100, K~= l, Tint = 70 for the level regulator, respectively. Table 1 shows the simulation results for both cases: the real nonlinear process and its PWL approximation.

Table /. Optimisalion results. Nonlinear vs. PWL

Nonlinear model PWL model

Fob.i

F

131.01 131.17

40.2318 40.2319

Wc

Calculation time[sec]

158.4186 159.4192

6840.6 156.4

Figures 1-4 illustrate the performance of the proposed algorithm when applied to the nonlinear process and the PWL approximation. The simulations were accomplished using MATLAB 5.3 optimisation Toolbox. A solver to deal with the algebraic equations was embedded in the optimisation program used to carry out the simulations. The algorithm was performed on a 550 MHz Pentium III processor. .

.

.

:!

:

Figure I. Fuel flow

~

.............

] ........

~::

Figure 2. Waterjlow

::!:i ¸

.....

.

.

1272

;::2

.............

ii! i:

i:

..,+:~ :$

:.

ii:

iii

:~:,~

.......................................................................................................................................................................................

:~:~ ~:'~:~:iii........... ii::iiiiiiiiiii..............ii:iii)iiii......... iiiiiiiiiiii................:~iiiii~ii............:i~iiiiiiiiiiiil ......... i:~i~;;~ ........ :i:::iiiii~i~:i..... ~i~:i:ii::i...... ii:iiii~:~i~:~: ...........

Figure 3. Pressure

Figure 4. Level

5. Conclusions In this work, the problem of dynamic simulation and optimisation was tackled in the back-off formulation. The proposed approach is generic and it can be applied to any nonlinear process. The calculation algorithm involves approximating the real nonlinear dynamics by means of a piecewise linear model. This modelling approach allows finding the process response by using the solution for discrete-time linear systems. The primary benefit of this method is a substantial reduction of the computational time. References Figueroa, J.L., P.A. Bahri, J.A. Bandoni and J.A. Romagnoli, 1996, Comp. Chem. Eng. 453, 20(4). Figueroa, J.L. and A. Desages, 2003, Optimal Control Applications and Methods 103, 24. Julifin, P., 1999, High level canonical piecewise linear representation: Theory and applications. Doctoral thesis, Universidad Nacional del Sur, Argentina. JuliAn, P., A. Desages and O. Agamennoni, 1999, IEEE Trans. Circuits Syst. 463, I(46). Perkins, J.D. and S.P.K. Walsh, 1994, Optimization as a Tool for Design/Control Integration. In Interactions Between Design and Process Control, Ed. J.D. Zafirou, Baltimore, Maryland, USA, 1-10. Luss6n Cervantes, A., O. Agamennoni and J.L. Figueroa, 2003, Journal of Process Control, 655, 13. Ray, K.S. and D. Dutta Majumder, 1983, Proceedings of the International Conference on Systems, Man and Cybernetics 705, I. Acknowledgements This work was financially supported by the CONICET and the Universidad Nacional del Sur, Bahia B lanca, Argentina.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1273

Operational Planning of Crude Oil Processing Terminals Anibal M. B lanco a, c, ~ Amdrica B Morales Diaz

a

Alejandro Rodriguez Angeles a and Arturo Sfinchez b a Instituto Mexicano del Petrdleo Eje Central Lfizaro Cfirdenas 152, M6xico, D.F. 07600, M6xico b Cinvestav-Guadalajara, Guadalajara 44520, M6xico PLAPIQUI (UNS-CONICET), Bahia Blanca, Argentina

Abstract A typical crude oil supply chain consists of production oilfields, processing terminals, storage facilities and refineries, interconnected by means of pipelines. In processing terminals, different varieties of base crude-oils are received, processed and blended in order to produce commercial varieties which are exported and/or sent to refineries, in the last decade, very few contributions have addressed the operational planning of processing terminals. In this work, an operational planning scheme, which realistically addresses the typical operation of such processes in the context of crude oil supply chains, is proposed.

Keywords: Operational planning, Processing terminals, Blending processes, Global optimization

1. Introduction Within any process industry, from a planning view point it is possible to identify several instances of decision making which can be hierarchically classified as "supply chain tactical planning", "process operational planning" and "process control" (Shapiro, 2001). Tactical planning seeks to coordinate the operation of the nodes that conform the supply chain, while operational planning focuses on the detailed operation of each node taking into consideration the tactical planning level decisions. Tactical and operational planning of crude oil supply chains have been largely addressed in the last decade due to the considerable potential economic benefits from improving the whole business operation (Kelly and Mann, 2003). At the tactical level, the petroleum supply chain has been modelled and optimized using different approaches (e.g. Neiro and Pinto, 2004 and Aires et al., 2004). At an operational level, several instances of the supply chain have motivated academic and industrial contributions. This is the case of the short term scheduling of refinery operations due to the economic impact of such systems within the supply chain (e.g. Chandra Reddy et al., 2004). Oilfield production planning and scheduling have also received considerable attention (e.g. Ortiz-Gomez et al., 2001). However, to the best of our knowledge, no 1Author to whom correspondence should be addressed: [email protected]

1274 contributions regarding the detailed operational planning of Processing Terminals (PTs) have been published in the open literature. PTs are key instances within petroleum supply chains. In PTs, different base crude oils are received, processed in order to adjust their quality parameters (water, salt, sulphur contents, etc.) and blended in adequate proportions to produce commercial crude oil varieties for local refineries and overseas trade. In this article, an operational planning scheme is proposed, which realistically addresses the operations of PTs within petroleum supply chains. The proposed scheme, which consist of a blending optimization model and an inventories simulator, is designed to be part of a "Control and Management System" of crude oil blending processes. The considered blending optimization model is inherently nonlinear due to the bilinear terms arising in the mass balances (Quesada and Grossmann, 1995) and in this work it is solved to global optimality with "state of the art" global optimization solvers. This article is structured as follows. In Section 2 the operations of a typical PT in the context of the petroleum supply chain of a large oil company is described as well as the information flow between the tactical and operational planning levels. In Section 3 the proposed operational planning scheme that addresses both, the "processing and blending section" and the "storage and crude oil transfer section" of the PT is presented. The detailed mathematical programming model for the "processing and blending section" is described in Section 4 and its performance is illustrated by means of a real study case. Section 5 closes the article with some conclusions.

2. General description of PT operations Consider the petroleum supply chain of a large oil company roughly depicted in Figure 1. Its relevant components are production oilfields (both on and offshore) which feed PTs through pipelines. In PTs the different base crude oils are received, processed and blended, and the produced commercial varieties pumped to refineries and/or exported to the overseas market through tankers. The principal process in PTs is the blending of base crude oils of different qualities, in order to produce blends that meet contractual quality specifications. Important crude oil quality parameters are density, salt, water and sulphur contents among others. The main objective of PTs' operations is to maximize the contribution of low quality crude oils (heavy, high sulphur content oils) to the blends. Previous to the blending, crude oils are stabilized, dehydrated and desalinated in appropriate equipment in order to adjust their volatiles, water and salt contents to quality specifications. The blending is performed in blending nodes, in which low quality oils are injected to higher quality oil streams. Different types of commercial varieties can be produced in this way through different blending arrangements. The produced commercial varieties are allocated to local refineries through pipelines and transferred to tankers for international trade. PTs are required to process all the crude oil produced in oilfields. In other words, they must not constraint the income crude oil flow-rates. This is usually feasible since crude oil is continuously leaving the system to refineries and through tankers. However, it may happen that due to unfavourable climatic conditions, crude oil can not be uploaded to tankers and starts to accumulate in the system. A programmed shut down of

1275 production oilfields is usually implemented if the storage capacity of the PT is about to be exceeded.

Offshore

J

~~

Cm~ ~ fml~ Figure 1. Typical crude oil supply chain

From a logistics point of view, the operations of PTs are tightly restrained to the tactical planning decisions taken at the supply chain management level. In this sense, PTs periodically receive the required amounts of the different crude oils to be sent to refineries. In the PTs, the adequate proportions of the different crude oils are implemented in the blending nodes to meet the specified refinery flow-rates. The remaining crude oil is sent to tanks where the different varieties are stored to attend international commitments. PTs periodically communicate the availability of crude oil to the tactical management level which decides "on spot" crude oil sales or establishes longer term contractual obligations. According to the above description it is concluded that a realistic operational planning scheme for a PT should address the following aspects: • • • •

Accomplish production levels for refinery provision in terms of quantity and quality Accomplish quality levels for export crude oils Maximize the contribution of low quality crude oils to the blends Monitor crude oil inventories

In the following section an operational planning scheme that fulfils the above requirements is presented.

3. Proposed operational planning scheme As mentioned in the previous section, the operational planning level at the PT daily receives the amounts of the different oils varieties that have to be sent to refineries. Each week, the PT is also informed of the daily program for uploading batches of export oils (type and volume) to tankers. Regarding flow-rates and quality parameters of the crude oil streams entering the system, periodic measurements are performed in several points of the supply chain and made available at the information systems of the company. In order to design a tool that explicitly considers such an operative context and realistically adapts to the needs of the PY's operators, a planning scheme is proposed whose information flow structure is depicted in Figure 2.

1276 Flow rates and quality parameters measurements of base crude oils data

ll_

Tactical level decision flow-rates to refineries

Exportation crude oil schedule

I PLANNING MODULE

Mathematical Programming model for the "Processing and Blending" section of the PT

Inventory level simulation

Crude oil uploading management I

]

Process Control

]

PROCESSING AND BLENDING I

Figure 2. Planning Scheme of the PT

The general philosophy consists in splitting the planning module in two sections: 1. 2.

A mathematical programming model to optimize the blending process A dynamic simulation system for inventory levels prediction

Because of the high degree of uncertainty in quality parameters and flow-rates of the crude oils entering the PT, and the fact that the outputs of the systems (flow-rates to refineries) are fixed by the tactical planning level, a "snap-shot" optimization model is considered as adequate for the operational planning of the process. The model is intended to be run each time the operating scenario significantly changes in terms of entering crude oil parameters (quantity and quality) and tactical decisions about flowrates to refineries. Such information is fed to the model from the company's information systems (Figure 2). A detailed description of the model is presented in Section 4. The resulting "blending plan" is downloaded to the "process control" module to be implemented at process level (Figure 2). In order to continuously predict the evolution of export crude oil inventories in storage tanks, a simulation tool is also proposed. Simulation results provide to the transfer operation manager a criterion when to start the crude oil transfer process to the tankers within the assigned "time window", according to maximum and minimum safety inventory levels. In case of unfavourable climatic conditions impeding the uploading process, simulation results can predict storage capacity saturation. The "simulation module" is fed from the "blending optimization module" and from the "crude oil uploading management module" as shown in Figure 2.

4. Mathematical model of the blending section PTs are mainly arrangements of crude oil processing equipment, stream splitters and blending nodes. Processing equipment consist in stabilizers, where gas is removed from the oil, and dehydrators, where water is separated by gravity. Crude/water emulsions are

1277 also broken in dehydrators by means of chemicals promoters. The desalination process also occurs at the dehydrator since the water leaving the unit contains a large part of the salts originally present in the oil phase. Once the base crude oils are set up regarding volatiles, salt and water contents, they are blended in adequate proportions in the blending nodes. The main purpose of PTs is to produce blends with the largest amount of low quality oil as possible while meeting contractual quality specifications. In the following, a general model for the processing and blending section of a PT is presented. O

1

p~..~,= P (p,.,, , 0 ), Vi ~ f~I, Vst ~ f~ST (7)

1

P,.,, =P~.d(P,.d '0a )' V i e f~I, Vd e f~D ' C'b

P,.b

,

,, = p

,

Cb

'

Vi ~ f~I, Vb ~ f~B

pl. C'=p,)C ° ' ~. . . . +p°(C° , V i e hi, Vs e nS >C .Di ' V J

Ci -

D

~ •J

Pi.j -< Pi:i' Vi E F2I, Vje g2J

(1) (2) (3)

(4) (5)

(6)

where p denotes a general property and C a general stream, both in appropriate SI units. f~I represents the set of quality parameters: density, water content, salt content and sulphur content, f~ST, F~D, ~2B and ~S represent the sets of stabilizers, dehydrators, blending nodes and splitters respectively. Super indices I, i~,2 and O, O~.2 denote input and output streams respectively. Process units are modelled as input-output relations in terms of the relevant quality parameters (eqs. 1 and 2). P(.) denotes a function which models the operation of each particular unit. 0 represents the operating parameters vector of each unit. Splitters as well as blending nodes are modelled through the corresponding mass balances (eqs. 3 and 4). Eqs. 5 and 6 stand as production and quality constraints on output streams (set f~J). Super index D denotes desired value. The considered objective function to be maximized is the "blending benefit": (I)=E, c AS, r e f~R. Set F2R represents the streams of low quality crude oils which are fed to higher quality crude oil streams and ASr is the difference of price between both crude oils. The proposed model was applied to an existing PT which receives three base crude oils of high, medium and low qualities, regarding density and sulphur content. It produces five commercial varieties (two for refineries and three for export). The plant possesses one dehydrator, two stabilizers, nine blending nodes, six stream splitters and several storage tanks for the export oil. The resulting model consists of 148 constraints and 172 optimization variables. It was programmed in GAMS (Brooke et al., 2003) and solved to global optimality with the global optimization solver BARON (Sahinidis and Tawarmalani, 2003). In order to illustrate the benefits of the proposed approach, comparison of planning results with historical operating data for a single node is presented in Figure 3. As can be concluded from the graphics, the advantage of the blend planning is twofold: first, substantial increments up to 20% can be achieved regarding low quality crude oil

1278 contribution to the blend (Figure 3 a); second, the downstream variability in crude oil quality is minimized by producing crude oils in tight contractual quality specifications, which positively impacts in refinery operations (Figure 3 b). a) Low quality crude oil contribution

b) Density of the blend

300000

34.50 34.00

250000

33.50 33.00

>, 200000

~

-- 32.50

~ 32.00

150000

31.50

100000

31.00 30.50

50000

30.00 0

29.50 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829

1 2 3 4 5 6 7 8 91011121314151617181920212223242526272829

Period

Period • Historic data • Planning

Figure 3: Historic vs. Planned Operation

5. C o n c l u s i o n s The proposed operational planning scheme for PTs realistically addresses the operations of such systems from a planning standpoint. A major advantage of such a scheme is the optimization of the blending process, which has a meaningful economic benefit since quality giveaway is minimized. Furthermore, the reduction of quality variability can convey a positive impact in downstream processes such as refineries. The monitoring and prediction of crude oil inventory levels through the simulation module aids in the proper management of the crude oil uploading process and in the operation of the storage facility within safety margins.

References Aires M., A. Lucena, R. Rocha, C. Santiago and L. Simonetti, 2004, Proc. Escape 14, 871. Brooke A., D. Kendrick, A. Meeraus and R. Raman, 2003, GAMS: A User's Guide. Chandra Reddy P., I. A. Karimi and R. Srinivasan, 2004, AIChE J. 50 (6), 1177. Kelly J. D. and J. L. Mann, 2003, Hydrocarbon Processing, June 2003, 47. Neiro S. M. S. and J. M. Pinto, 2004, Comp. Chem. Eng. 28, 871. Ortiz G6mez A., V. Rico Ramirez and R. Vfizquez Rom/m, 2001, Proc. Escape 11,907. Quesada I and I. E. Grossmann, 1995, Comp. Chem. Eng. 19 (12), 1219. Sahinidis N. and M. Yawarmalani, 2003, BARON, GAMS: The Solvers Manual. Shapiro J., 2001, Modeling the Supply Chain, Duxbury Thomsom Learning.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) g) 2005 Elsevier B.V. All rights reserved.

1279

A Hierarchical Approach to Optimize LNG Fractionation Units Hassan E. Alfadala ~*, Bilal M. Ahmad a, Abdulla F. Warsame b a

Department of Chemical Engineering, University of Qatar P. O. Box 2713, Doha Qatar b Qatar Liquefied Gas Company P. O. Box 22666, Doha Qatar

Abstract The objective of this paper is to optimize the thermal performance of a fractionation unit within a liquefied natural gas (LNG) facility. Typical fractionation units in an LNG facility consisting of three distillation columns, namely de-ethanizer, de-propanizer and de-butanizer were used in this study. A hierarchical approach is developed to optimizing the system. In this approach, increasing levels of model complexity are used and various thermal targets are set and implemented. The column targeting tool available within the simulation package of Aspen Plus '¢ software was used to optimize a fractionation unit in an LNG facility. First, integrated thermal analysis was used in identifying design targets for improvements in energy consumption and efficiency. The column targeting tool is used in the design of distillation columns by setting targets to reduce utility cost, improve energy efficiency, reduce capital investment and facilitate column debottlenecking. Starting from a short-cut distillation design calculation using the DSTWU method which is based on the well-known Fenske-Underwood-Gilliland correlations, the minimum and actual reflux ratios, minimum and actual number of stages, optimum feed location and condenser and reboiler duties were estimated. These estimates were used as starting points in the rigorous fractionation column design method RADFRAC available in Aspen Plus 'c. The column Grand Composite Curve (CGCC) for each column was generated to give an insight of the actual operation and guide the optimization process. Starting with appropriate feed placement, the CGCC will show the scope for reflux ratio modification by increasing the number of stages. Feed would be either preheated or precooled due to the availability of sharp enthalpy change in the condenser or reboiler side. Finally, the scope for a side condensing or side reboiling can be identified from the area beneath or above the CGCC pinch point.

Introduction Today in the chemical process industry, distillation is considered to be one of the most used unit operation. Such operation consumes the highest amount of energy compared to the rest of the unit operations in any facility. This is due to the fact that distillation is based on boiling temperature difference between the light key and the heavy key. Thus Author to who correspondence should be addressed, e-mail: [email protected]

1280 any attempt to investigate and understand the energy flow in distillation columns would benefit the overall process economy and reduce product cost. In particular, distillation units are core elements in an LNG facility. About a decade ago Dhole and Linnhoff, 1993, had introduced the concept of Column Grand Composite Curve (CGCC). Since then, this concept has been extended (e.g., Gadalla et al., 2003). The CGCC is based on the Practical Near-Minimum Thermodynamic Condition (PNMTC) approximation. These curves could be generated using Aspen Plus Column Targeting tool, Aspen Technology Inc., 2003. This work employs Aspen Plus simulation package capabilities to optimize LNG fractionation unit.

Overall optimization approach In order to strike a proper balance between computational efficiency and result accuracy, we develop a hierarchical approach as shown in Figure 1. Starting with the short-cut column model DSTWU available within Aspen Plus model library, which is based on the well-known Fenske-Underwood-Gilliland correlations, Seader and Henly, 1998, the minimum and actual reflux ratios, minimum and actual number of stages, feed location, condenser cooling requirement and reboiler heating requirement were estimated. Specify feed / Specify | Specify key . | operating conditions~ condenser type ~ components' recovenes~,

Short-Cut Distillation Design (DSTWU) Min. reflux ratio or min. # of stages~ r

Feed location Estimated condenser 'r & reboiler heat duties~r

Rigorous Distillation Design (RADFRAC)

Design Temperature profile ,r

Composition profile ,r

Condenser & reboiler heat duties ~r

Optimum feed location

Column

Reflux modifications

Targeting Approach

Feed preheating/cooling !

Side condensing/reboiling

Optimum Distillation Column Design Figure 1. Overall optimization approach

1281 In order to use the DSTWU model, feed operating conditions, condenser type, key components and their recoveries must be specified. Outputs from the short-cut model will include the minimum reflux ratio, minimum number of stages, feed stage location, and the estimated condenser and reboiler heat duties. All of the above data is required to start the rigorous RADFRAC model which is also available within Aspen Plus model library. The user should specify the required design specifications at this stage. As an example of a design specification would be the targeted purity of the light key in the top product. For each design specification, there must be a variable which will have an upper bound and a lower bound. The condenser duty could be used as an example for the vary type in the RADFRAC model. In order to demonstrate the advantages of the column targeting tool, the following case study has been worked out as an example.

Case study An LNG facility fractionation unit was optimized as a case study using the above mentioned overall optimization approach. The specifications of the feed and products for the case study are given in Table 1. These are representative data of a typical LNG fractionation unit. Table 1. Feed and product specifications for the case study

Properties Mass Flow rate (kg/hr) Temperature (°C) Pressure (bar) Vapor fraction Mole fractions

Feed 25736.0 77.4 6.62 0.38

Top product 13476.4 48.3 6.52 0.00

Bottom product 12259.6 124.2 6.76 0.00

Propane i-Butane n-Butane Methyl-Butane n-Pentane n-Heptane Benzene Toluene

0.05388 0.14808 0.29493 0.13301 0.12368 0.23114 0.00941 0.00587

0.13260 0.27648 0.55049 0.03696 0.00347 0.00000 0.00000 0.00000

0.00000 0.00002 0.00033 0.26470 0.29627 0.40624 0.02122 0.01122

As mentioned above, in the overall optimization approach, as a starting point a converged simulation for the distillation column using the DSTWU must be obtained first. Thereafter, such outputs are fed into the rigorous RADFRAC model in order to construct the column grand composite curve as shown in Figure 2. The following are the four steps for column targeting approach.

1. Feed Location Inspecting the CGCC shown in Figure 2 the feed is appropriately located due to no distortions in the CGCC. If the feed misplaced otherwise, the CGCC would be shifted towards either the condenser or the reboiler side.

1282

125 120 115 110

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0.5

1

1.5

2

2.5

3

3.5

4

4.5

~ t h a l p y Deficit (MMKcal/hr)

Figure 2. Debutanizer Column Grand Composite Curve ( T - H) 2. R e f l u x

ratio adjustment

The horizontal distance in Figure 2 between the y-axis and the pinch point shows the scope for reflux ratio modification. Of course, this is a trade-off between capital cost and operating expenditure, which is due to the fact that whenever the reflux ratio is changed the operating cost gets affected, thus changing the number of stages of the distillation column, which accordingly will have an impact on the capital cost.

135

...........................................................................................................................................................................................................................

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j

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A c t u a l Profile

J

85

75 65

-.-._._.__

55 45 0

0.5

1

1.5

2

2.5

Enthalpy Deficit (MMKcal/hr)

Figure 3. Debutanizer Column Grand Composite Curve after reflux modification

1283 Figure 3 shows the CGCC after the reflux ratio has been reduced to minimize the distance between the pinch point and the y-axis, in order to meet the same design specifications, the number of stages had increased in this case from 25 to 33 stages.

3. Feed conditioning Sharp enthalpy changes on the CGCC will determine the need for pre-heating or precooling the feed. Figure 3 shows that there is a sharp enthalpy change on the condenser side, which determines the requirement for a pre-cooler. The resulting CGCC after the pre-cooling effects is shown in Figure 4.

115

-

Actual

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85

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75

55 45 35 25

....................... 0

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Figm'e 4. DebutanizeF Cohmm Grand Composite Cm've afierjeed pre-cooling

110

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90

7'0 ' E ~

6o

5O 40 30 20 ........................................................................................................................................................................................................................... 0

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1 Enthalpy

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2

Deficit (MMKcal/hr)

Figt#'e 5. Dehutanizer Column GFam/ Composite Cm've after side-reboi/ing

2.5

1284 4. Side condensing or side reboiling

The significant area above the pinch as shown in Figure 4, dictates the need for a side reboiler, which accordingly was added to the column at stage 26, as shown in Figure 5. 5. Conclusion

A hierarchical approach has been introduced to optimize fractionation systems for LNG facilities. Comparing condenser and reboiler duties after applying the column targeting approach with those before, it is obvious that there was a big difference in the heat duty values. The condenser duty decreased from 3.98 MMKcal/hr to 2.13 MMKcal/hr after applying column targeting with a pre-cooler that has a heat duty of 0.44 MMKcal/hr. The reboiler on the other hand decreased also from heat duty of 3.46 MMKcal/hr to 1.09 MMKcal/hr after column targeting with a side reboiler of 0.6 MMKcal/hr. Figure 6 shows the column design after applying the four optimization steps. It is worth mentioning that this process is a trade off between capital and operating cost, therefore, such saving should be incorporated into the overall system cost after adding the new equipment cost, like pre-cooler, side reboiler and the addition of the new stages.

35 30 25

=

Ideal Profile

-

Actual Profile

20 o~

10

0

0.5

1

1.5

2

2.5

Enthalpy Deficit (MM Kcal/hr)

Figure 6. Debutanizer Final Design (Stage- Enthalpy) Column Grand Composite Curve References

Aspen Technology Inc., 2003, Aspen Plus 12.1 Unit Operations Models Reference Manual, Cambridge, USA. Dhole, V.R. and B. Linnhoff, 1993, Distillation Column Targets, Computers Chem. Engng, 17, 549-560. Gadalla M, Jobson M, and Smith R, Optimization of heat-integrated refinery distillation systems, Trans IChemE, January, 81(A) 147-152 (2003) Seader, J.D. and E.J. Henly, 1998, Separation Process Principles, John Wiley & Sons, Inc. New York.

European Symposium on Computer Aided Process Engineering- 15 L. Pui~janer and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1285

First Principles Model Based Control •

a*

Manuel Rodrlguez , David Pdrez a aUniversidad Polit6cnica de Madrid Jos6 Gutidrrez Abascal, 2. Madrid 28006, Spain

Abstract Model Based Control is an important and widely used (mainly MPC) technique. This paper provides a new control architecture based on the use of physical models. In this preliminary work the architecture is applied for unconstrained multivariable control. It has been applied on several standard process units obtaining encouraging results. It has some advantages over MPC as it can use non linear rigorous models and it doesn't need any identification step.

Keywords: Model Based Control, Model Predictive Control, Internal Model Control. 1. Introduction The interest in Model Predictive Control (MPC) started to increase after the presentation of IDCOM (Identification and Command) (Richalet, 1978) and DMC (Dynamic Matrix Control) (Cutler, 1979). After 25 years MPC has become a widely used technology in process control. Nowadays, a new crude distillation unit in a refinery is not conceived with other control scheme but MPC (and the same happens in many other processes). The technology applied is usually based on a previous identification step (which is of the most importance) to get a linear model of the unit and, then, on an implementation step (usually more simple and less time consuming). Although a lot of research has been done regarding Nonlinear MPC using different approaches, differential equations, neural nets (Temeng, 1995), Hammerstein models (Fruzzetti, 1997), Volterra equations (Manet, 1996), fuzzy models (Sousa, 1997) ... it is still an open area where many problems arise. The purpose of this work is the use of first principles models for model predictive control. To achieve this goal, a new architecture has been developed and tested on some simulated process units. The remaining paper is organised as follows: Section two describes in detail the new architecture, how it works and its components, and explains the software implementation. Section three shows the results obtained when it is applied to control some operation units. Finally, section four presents the conclusions and future steps of this work. Author to whom correspondence should be addressed: [email protected]

1286

2. Physical M o d e l B a s e d C o n t r o l A r c h i t e c t u r e . The PMBC architecture is composed of two modules" the Physical Model Based (PMB) Controller Module and the PMB Model Module. Figure 1 shows the proposed architecture: Controlled

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Figure 1. PMBC Architecture

The models used in the components of the architecture have been developed with some degree of error with respect to the process, as it is impossible to get a perfect model of a real process. To this purpose, some parameters have been slightly changed.

2.1 PMB Controller Module This module is the core of the architecture, it predicts the values of the manipulated variables that provide the desired performance (set point change or disturbance rejection). This module has a model of the unit to control. It has a first principles model comprised of a set of DAEs. This module has the following variables as inputs: • The error of the controlled variables, it can be referred to the controlled variable directly or to its derivative. It is the desired response or the target curve. • Measured disturbances. The outputs of this module are the set of manipulated variables (which are commonly inputs in a model of the process). If the controlled variable is at its set point, the input of the module will be the derivative set to zero or the value set to that constant (so it remains in that value). If a disturbance happens, the controller will produce an output to compensate that disturbance and keep the controlled variable at the desired set point value. If a set point change is desired, the input will be an exponential (softened step) in the controlled variable. If the controlled variable acts like an integrator, such as controlling the level with an output stream, a ramp has to be used instead of a step. The time used for the step or ramp is an adjustable parameter. The time scale of this module is the simulation execution time of the model in the selected platform. It is an adjustable parameter, it can be slowed down to avoid excessive control actions that sometimes will provide a worse system performance.

1287

2.2 PMB Corrector Module This module has a model of the unit to be controlled. The model is exactly the same as above except for which are the input variables to it. This model is used in the standard way, so the inputs to it are the disturbances and the inputs to the real process. The outputs of the model are the controlled and output variables of the process. The purpose of this module is to correct, in some way, the prediction made by the Controller Module. As no model is perfect, the controller output will lead to a control action that doesn't set the controlled variable to the desired value. This means that some feedback corrections are necessary. In order to accelerate this procedure, this module compares its output with the actual process output and sets a correction factor to be applied to the control action. So, this module has two components: the model component and the comparison component. The final output of this module, with the correction factor, is the control action to be applied to the real process. The time scale of this module has to be that of the real process, so it has to be synchronized to it as accurate as possible, in order to be able to compare the same variables.

2.3. Software implementation The implementation has three components, the Controller Module, the Corrector Module and the Process Module. All the components have been implemented in the same machine, a PC running under Linux OS. The model used in the Controller and Corrector Modules is not perfect, some changes have been made in several paralneters of them in order to check the proposed architecture. The models have been developed using the ABACUSS II simulator (Barton,2003). This software allows to embed the simulation code in other application. Using the C÷+ programming language, different executables have been generated for every component of the architecture. The information flow has been implemented through shared memory procedures.

3. A p p l i c a t i o n s In this section the results of the application of this architecture are presented. Set point and load changes are applied to all the tested units and the performance of the controller is evaluated.

3.1. Stirred tank heater This unit is a perfectly stirred tank heater with a jacket. It has two input streams and one output stream. There are level and temperature control loops. The manipulated variables are the tank input flow and the jacket input flow. These two variables are calculated in the Controller Module. This module has as inputs the heater temperature and the tank level. To achieve a good control on the tank, the following control equations are used: _

C

d H _ ( S P H - P H )× dt t

t

t

SPH: Level set- point, H: level of the model, PH: level of the actual process.

(1)

1288 __

t

e t

(2)

tiT° - X ~(SPT- P T ) × art t

SPT: Temperature set - point, To" jacket temperature of the model, Pt: temperature of the actual process. The jacket temperature is used as the forcing equation of control instead of the tank temperature because the use of the latter poses a 2 - index problem. Due to this problem, the gain between the two variables needs to be added to the control equation. In this model some parameters are changed about 5% with respect to the actual process. Figure 2 shows the control of the unit in the presence of a flow disturbance and a level set point change. Tout

Tout

i i

.....

/!

/

/ //'/'/"

j - J ~

Level /

Jacket Flow

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/ f J

Flow in

Flow in

/

/

,f

Level

f

Jacket Flow

~0 ......... (

.....................................................

~-~._____~ 5:-.¢~

Flow disturbance C.N~

i[£{~"

Figure 2. Heater response after a flow disturbance on the left. Heater response after a level set point change on the right.

In these tests both loops are affected as the temperature changes with a change in any of the stream flows. 3.2. Continuous Stirred Tank Reactor (CSTR) This unit has the same equations as the heater but a first order reaction, following the Arrhenius expression, is added. In this case, the same two loops (level and temperature) are controlled. But, in this case, the level is controlled with the output stream, which means that the control action has to be changed. An exponential (step) cannot be used and a ramp is used instead. The following equation shows the level control action implemented:

1289 dH

SPH-

dt

t

PH

(3)

The temperature control equation is the same as in the heater application. Figure 3 shows the performance of the system in the presence of concentration and temperature disturbances. In this model, the parameter that is changed with respect to the actual process is the Arrhenius pre-exponential constant in 5%. ::~,:~ i:'ii({

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Figure 3. CSTR response qfter a concentration disturbance on the left. CSTR response after a temperature disturbance on the right.

3.3. Distillation Column

This unit is a binary distillation unit. It assumes equimolal overflow, 20 theoretical trays, simple liquid tray hydraulics and constant relative volatility (ideal mixtures) for the vapour- liquid equilibrium in every stage. Feed enters above 10th tray (feed stage). Total overhead condenser and partial reboiler. The implementation of this unit for a continuous test is not finished at the time of this paper. The only implementation available is just the first control action to be applied to the process. The model in this initial implementation is assumed perfect (this means that just a single control action gets the controlled variable to the desired value). The control equations used are similar to the ones presented in the previous applications. Next figure shows that this control architecture can be applied to the distillation column as well.

4. Conclusions This paper has presented a new architecture for model based control. Regarding the obtained results, this physical model based control seems to be a usable technology for

1290 60

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any process unit. This new approach has some clear advantages over the ones used currently in the industry. It uses a first-principles model that is suited to any operating region, so, it is a non-linear MPC. It doesn't need any identification step which is very resource consuming for any process unit. Although the results presented are promising, a lot of work still has to be done to establish the availability of this technology. First of all, the initial approach taken is for unconstrained predictive control, additional steps taking into account constraints (like valve range,...) have to be made. N e w issues have to be studied as dead-time, stability,... The next step in this work will be to test this architecture with a real system. References Barton, P.I, 2003 http://yoric.mit.edu/abacuss Cutler, C. R. and Ramaker B. L., 1979. Dynamic matrix control--a computer control algorithm. AIChE 86th National Meeting. Houston,TX. Fruzzetti et al., 1997. Nonlinear control using Hammerstein models. J. Proc. Control, 7, n l, 31-4 Maner et al, 1996. Nonlinear model predictive control of a simulated multivariable polymerisation reactor using second order Volterra models. Richalet, J., Rault, A., Testud, J. L., and Papon, J. ,1978. Model predictive heuristic control: applications to industrial processes. Automatica, 14(5), 413428. Sousa et al, 1997. Fuzzy predictive control applied to an air conditioning system. Control Engineering Practice, 5. nl0, 1395-1406. Temeg et al, 1995. Model predictive control of an industrial packed bed reactor using neural networks. J. Proc. Control, 5, n 1, 19-27 Acknowledgements The project is sponsored by Repsol-YPF foundation.

European Symposiumon ComputerAided Process Engineering- 15 L. PuiNaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1291

On-line Oxygen Uptake Rate as a new tool for monitoring and controlling the SBR process Sebasti/t Puig a*, Lluis Corominas a, Joan Colomer b Maria D. Balaguer ~ and Jesfls Colprim a Laboratory of Chemical and Environmental Engineering (LEQUIA). Environmental Institute (IMA-UdG). Campus Montilivi s/n. Facultat de Ci6ncies. University of Girona. E-17071 Girona (Spain). bControl Engineering and Intelligent Systems Group (eXiT). Institute of Informatics and Applications (iiiA). Campus Montilivi s/n. Escola Polit6cnica Superior. University of Girona.E-17071 Girona (Spain).

Abstract This paper focuses on the on-line Oxygen Uptake Rate (OUR) as a new tool for identifying the state of the plant during the aerobic phases of the SBR cycle and as a control parameter to optimize the SBR process. A real-time control system has been designed to adjust the aerobic phases length using on-line OUR as the endpoint of the aerobic phase. The control system implementation has permitted the aerobic phase length reduction around 11% implying significant savings in management costs.

Keywords: On-line Oxygen Uptake Rate (OUR), Sequencing Batch Reactors (SBR), real-time control, wastewater.

1. Introduction Wastewater treatment facilities can be designed to operate in continuous flow mode (i.e. the classical activated sludge process) or in a cyclic or sequenced batch mode such as the Sequencing Batch Reactor (SBR). One of the consequences of operating under batch conditions is the possibility to treat the wastewater using a separate cycle following a fill-react-draw basis (Irvine et al, 1979; Mace and Mata-Alvarez, 2002 and Vives, 2004). Biological treatment can be performed in SBR reactors under a combination of aerobic, anoxic and anaerobic conditions. Under these conditions, the on-going biological reactions during one cycle are conducted in an unsteady state from a high initial concentration of pollutants (mainly organic matter, nitrogen and phosphorous) to the final treated wastewater, which the pollutants concentrations have been reduced to the desired level. The aerobic biological reactions are responsible for the oxidation of ammonia to nitrite and nitrate (the nitrification process), as well as, the biological conversion of organic matter into carbon dioxide. Author/s to whom correspondence should be addressed: [email protected]

1292 To achieve the aerobic conditions, an injection of oxygen (i.e. compressed air) must be supplied in order to transfer and maintain the desired dissolved oxygen level in the biological reactor. The oxygen consumption in the liquid phase or the Oxygen Uptake Rate (OUR) could be a useful tool for knowing the state of the plant. In recent years, the OUR analysis has demonstrated that it is a useful off-line tool for wastewater or biomass characterization in terms of biodegradable fractions, biological nitrification tests or modelling purposes (Brouwer et al, 1998; Gutierrez, 2003; Spanjers and Vanrolleghem, 1998). In this paper, an on-line OUR measurement has been developed and applied to a pilot plant SBR treating urban wastewater as new tool for indicating the state of the plant in real-time and as a control parameter to optimize the aerobic phases length of the SBR cycles.

2. Methods 2.1 Pilot Plant SBR and operational cycle The 1 m 3 Pilot Plant SBR was set up at the Cass/t Wastewater Treatment Plant (Girona, N.E. Spain). The Pilot Plant treated 600 liters of influent wastewater per day. Figure 1 presents a schematic overview of the plant. PC

....................................................................................................................

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~

~

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LL4.::-:: ........

LEVEL

X

AT,O

.~ VALVE

CHANNEL

PUMPIN ,

~

~ EFFLUENT ~

~UMP

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Figure 1. Schematic overview of the Pilot Plant SBR.

The Pilot Plant was equipped with a monitoring and control scheme consisting of interface cards (PCI-6025E and SC-2062 from National Instruments®). On-line monitoring of pH, Oxidation-Reduction Potential (ORP), Dissolved Oxygen (DO) and Temperature was achieved by data acquisition from Endress-Hausser ® probes (CPF81, CPF82 and OXYMAX-W COS-41, respectively) and transmitters (CPM 223). The Pilot Plant was controlled by means of a data acquisition and control software developed using LabView ® (Puig et al., 2004). An eight hour SBR cycle, repeated continuously over time, was adapted from Vives (2004) and is presented in Figure 2 as a sequence of anoxic-aerobic phases and, a step-feed filling strategy to enhance nitrogen removal. Aerobic phases were controlled at 2.0 mg DOoL -1 by means of an ON/OFF control strategy applied to the air injection flow.

1293

I'''

0

I1 ' ' '

I2 ' ' '

I3 ' ' '

I4 ' ' '

I5 ' ' '

I6 ' ' '

I7 ' ' '

I8 hours

Fill ~

Draw ~

Anoxicreaction 1

Aerobicreaction I ]

Figure 2. Operational periods of the SBR Pilot Plant with.filling strateg?'..

2.2 On-line OUR calculation During the aerobic phases of a cycle, when no influent wastewater is added to the SBR and assuming a complete mix reactor, a dissolved oxygen mass balance could be represented by equation 1. 0 UR =K LA( D 0~., - D O) -

dDO dt

(])

where OUR is the calculated Oxygen Uptake Rate (rag.L-I-h-I), DO the dissolved oxygen in the SBR (mg.L-~); DOsat the saturation or maximum dissolved oxygen as a function of temperature (rag.L-J); and, KLA the oxygen mass transfer coefficient (h -]) as a function of compressed air flow and air diffusers efficiency. As stated above, the control applied to maintain the DO level is a simple ON/OFF air injection strategy that increases of DO during air ON periods and reduces of DO during air OFF periods after the set-point has been reached. Thus, according to equation 1, it was possible to measure the OUR each time the valve was closed by acquiring DO values over time and adjusting them to a linear regression obtaining the slope of the curve. It must be taken into account the dynamic of the sensor and so the first measurements (50 seconds) after deactivating the aeration system were not used. Next DO values were acquired until the valve was opened again, and finally the linear regression was obtained (Corominas et al., 2004).

3. R e s e a r c h R e s u l t s The Pilot Plant SBR was set up at Cassfi Wastewater Treatment Plant, treating fresh wastewater from the sewers arriving at the facility. The Pilot Plant SBR operated with the 8-hour cycle for more than six months with a high organic matter and nitrogen removal efficiencies (Puig et al, 2004). To improve the SBR's performance, a new tool based on on-line calculated OUR was implemented in order to know the state of the plant and to control the aerobic phases length of each cycle. Figure 3 presents the calculated OUR, according to equation 1, during a typical aerobic phase of a SBR cycle. In addition, on-line monitoring of the pH is shown in this figure. Different stages related to the biological reactions could be identified in the OUR evolution. In the first stage, the OUR values decrease, from 110 to 95 mg O2.L -~ .h -~, for the degradation of rapidly biodegradable organic matter in the SBR. in the next stage, B, the calculated OUR values stabilize because of the oxidation of ammonia and the degradation of the biodegradable organic matter. After the 13 th

1294 minute, stage C, a huge decrease in the OUR values, around 50% of the initial OUR value, can be observed due to ammonia depletion. We call this OUR decrease ~ZOUR. (Puig et al., 2005). At the same time, a decrease and then increase tendency in the pH profile is observed. The resulting minimum pH point is called Ammonia Valley, and indicates, as well as aOUR, the end of the nitrification process (Plisson-Saune et al., 1996). Finally, in the last stage the OUR decrease slowly, the tail shape, when the slowly biodegradable organic matter is removed until it stabilizes at the 24 th minute when endogenous respiration is achieved, in this moment, the oxygen consumption is used only for biomass maintenance and the organic matter and ammonia are completely removed. 140

..

.

:ii!ii~?i!i::~i!i~!!ii:i:i!~!iA~ ,~, "

120

.

.

~i!i!i!i;ii~:!!~!~i~!i!ii~ii!i,~i!iiii~ii!i~

.

. °

.

6.835

~i:i!iiil;L~i~'~!iU~''C: ~,

'i!i!iiil;i!i~:i::!~i~:,!U:!i • ~i!iiiii''i) 6.830

"7

,,-

1 O0

0

80

E

60

6.825

i ,~J '~ fi;~,,,s. J~.~.....A

:

-¢, e~

~,i~JW'' ~

:'~ ~

6.820

40 0

6.815

/

20

6.810 0

5

10

15

20

25

30

Time (min.)

Figure 3. Identifying the state of the pilot plant SBR using the calculated OUR and on-line pH during a typical aerobic phase of the 8-hour cycle•

In order to design a real-time control system to optimize the aerobic phases length for ammonia and organic matter depletion, we analysed the on-line calculated OUR during the last aerobic phase of several SBR cycles with high nitrogen and carbon efficiencies (Figure 4). Until the 5th minute, which we define tM,N, the OUR values increase due to the activation of microorganisms, which is caused by the changing conditions (from the anoxic to aerobic phase). This transient response of the activate sludge most likely from the sequence of intracellular reactions involved in substrate degradation by the activated sludge (Vanrolleghem et al., 2004). In the Figure 3 after the tM,N and in the stage C there is a decrease in the calculated OUR values. Then, the OUR values stabilize to an OUR of 35 mg O2.L-l'h -1 for any aerobic phase. For this reason, a minimum OUR value, called OURM~N, was defined which corresponds with the complete removal of ammonia and biodegradable organic matter. From the OUR evolution analysis (Figure 4), we can see that the OURM,N is easily reached before the fixed time (TMAx) of the aerobic phase. So that, it is possible to adjust the aerobic phase using the OURMIN as an endpoint for the aerobic phases. Normally, this optimization is based on the Ammonia Valley as a control parameter of the length of aerobic phases (Kishida et al., 2003; Yu et al., 2001), but because of its oscillations due to the ON/OFF oxygen control, the OURM~N value has been used as the control parameter of the aerobic phase.

1295 :i ::v~i ~i:!~ i¸=:II

120 "-

100

._! 54

80

o

60

o')

E o

40

~:iii/

. . . . . . . . . . .

._

20 .

0

5

.

.

10

.

.

15

20

25

30

Time (min.)

Figm'e 4[. OUR pro./iles o/the last aerobic phase o.f several cycles (Puig et al., 2005).

Figure 5 presents the real-time control strategy diagram for the aerobic phases for treating urban wastewater in the Pilot Plant SBR. First, the control system calculates the OUR value. Then, it waits a certain delay time (tMjN) before starting to check the signal. It then compares the calculated OUR value with the OURM~N. If the value is lower than the OURM~y the endpoint will have been detected. Then, a safety time is applied (twA~T) before changing to the next phase. There is also a maximum time (tMAX) for the phase, which is checked at each time interval once the tM~N has been exceeded and which corresponds with the aerobic time in the 8-hours cycle. Calculated OUR

No

-,I

I No

No Yes; CHANGE TO NEXT PHASE

•

Figure 5. Real-time control strate~'.flow diagram in the aerobic phase.

On-line OUR control was applied in the Pilot Plant SBR during three months, treating urban wastewater. The control system acted in the aerobic phase using the OUR minimum value as a condition to adjust the aerobic time length and the effluent ammonia concentration. The ammonia and organic matter concentrations achieved, 1.6 mg.L -J N-NH4 ~ and 51 mg.L -j COD on average, respectively, at the end of the SBR

1296 cycle proved that the OUR minimum value was enough to achieve the complete ammonia (97%, on average) and organic matter removal (90 %, on average). These values were lower than the European Directive 91/217/CEE that regulates organic matter and nitrogen discharge into the rivers. Furthermore, the aerobic phase adjustment optimize the air supply and reduced management costs associated with aeration costs by around 11% on average.

4. Conclusions In a predefined 8-hour cycle, the state of the plant during the aerobic phases of the SBR was identified by means of a simple on-line OUR calculation. OUR analysis of the aerobic phases allowed us to achieve an OUR minimum value (OURM~N) and, an initial aerobic activation time of the aerobic microorganisms (tMIN). OURM~N and tM~N are control parameters of the designed control algorithm that can optimise the aerobic phases of the SBR cycle. The final implementation during three months in the SBR proved to be useful for treating real urban wastewater with high organic matter and ammonia removal efficiencies. The aerobic phase were reduced by 11%, twenty minutes on average, is associated to a significant operational cost reduction.

References Brouwer H., A. Klapwijk and K.J. Keesman, 1998, Wat. Res. 32(4), 1240-1254. Corominas LI., M. Rubio, S. Puig, J. Melendez, J. Colomer, M.D Balaguer and J. Colprim, 2004. Proceedings of 6th Specialist Conference on Small Water & Wastewater Systems. Gutierrez O., 2003, PhD. Thesis. Girona University. Spain (in Catalan). Irvine R.L. and A.W. Busch, 1979, Journal WPCF 51 (2), 235-243. Kishida N., J.H. Kim, M. Chem, H. Sasaki and R. Sudo, 2003, J. Biosci. Bioeng. 96 (3), 285-290. Mace S. and J.R. Mata-Alvarez, 2002, Ind.. Eng. Chem. Res., 41(23), 5539-5553. Plisson-Saune S., B. Capdeville, M. Mauret, A. Deguin and P. Baptiste, 1996, War. Sci. & Tech., 33(1), 275-280. Puig S., M.T. Vives, L1. Corominas, M.D. Balaguer and J. Colprim, 2004, Wat. Sci. & Yech. 50(10), 89-96. Puig S., LI. Corominas, M.T. Vives, J. Colomer, M.D. Balaguer and J. Colprim, 2005, Ind.. Eng. Chem. Res., submitted. Spanjers H. and P.A. Vanrolleghem, 1995, Wat. Sci. & Tech. 31(2), 105-114. Vanrolleghem P.A., G. Sin and K.V. Gernaey, 2004, Biotechnol. Bioeng., 88(3), 277-290. Vives, M.T., 2004, PhD. Thesis. Girona University. Spain. Yu, R..F., S.L. Liaw, B.C. Cho and S.J. Yang, 2001, War. Sci. & Tech., 43(3), 107-114.

Acknowledgements The authors would like to thanks INIMA-Servicios del Medio Ambiente (Grupo OHL), the Government of Catalonia, the Spanish Government (MCYT-DPI-2002-04579-C0202) and the University of Girona for their financial support in this study.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1297

On-Line Dynamic Monitoring of the S H A R O N Process for sustainable nitrogen removal from wastewater Kris Villez a*, Christian Rosen b, Stijn Van Hulle a, ChangKyoo Yoo a and Peter A. Vanrolleghem a a BIOMATH, Ghent University Coupure Links 653, B-9000 Gent, Belgium

b IEA, Lund University Box 118, SE-221 00 Lund, Sweden

Abstract The goal of this work is the development of a suitable monitoring module, which is to be the first module of an integrated fault detection and control system for the SHARON process. To model the process properly, different PCA models are tested. As a first step, PCA is used in an iterative manner to exclude data not considered to represent normal operational conditions and process behaviour from the original data set. To improve the performance of the identified model, it is decided to account for dynamics in the SHARON process by means of auto-regressive exogenous (ARX) structuring of data before the identification. A fruitful replacement of missing values for this purpose is done by means of a static PCA model. It is shown that the different criteria used in model selection lead to the same DPCA model. In this paper all steps of the monitoring module design are explained and the performance of different models is analyzed.

Keywords: environmental biotechnology, wastewater treatment, statistical monitoring, fault detection, Dynamic PC A

1. Introduction In the SHARON process (Single Reactor High Activity Ammonia Removal Over Nitrite) the oxidation of ammonia to nitrite is achieved. The conversion of nitrite to nitrate is avoided by applying a high temperature (above 25°C) and an appropriate hydraulic residence time. When half of the ammonia is converted, coupling with an Anammox unit becomes economically interesting, as in the Anammox process equilnolar amounts of ammonia and nitrite are removed (van Dongen et al., 2001). The concept's success relies however on the control of the SHARON process since the requirements for equimolar concentrations of ammonia and nitrite and absence of nitrite inhibition in the Anammox reactor have to be fulfilled (van Dongen et al., 2001). To control highly dynamic processes as the SHARON process, a supervisory control system is developed. Monitoring, fault detection and diagnosis and the actual supervisory control are part of this system. A PCA-based monitoring module is created first. Applications /'or industrial process monitoring have been established in the past

1298 decade (MacGregor and Kourti, 1995, Kourti and MacGregor 1995, Wise and Gallagher, 1996). Applications to wastewater treatment plants have emerged as well in more recent research (Ros6n and Lennox, 2001, Yoo et al., 2003, Lee et al., 2004). In this study the development of a dynamic PCA (DPCA) model for monitoring is described. Simple static PCA modeling and data selection is discussed firstly. Secondly, the replacement of missing data is explained. Afterwards, different DPCA models are constructed and compared to eachother. Finally, a monitoring model is selected.

2. Materials and m e t h o d s For a detailed description of the data set the reader is referred to Van Hulle et al. (2003). The data set contains 503 data samples of 10 variables: (1) hydraulic residence time (HRT), (2) ammonia load, (3) the influent ratio of total inorganic carbon to total ammonia nitrogen (TIC:TAN), (4) daily mean dissolved oxygen (DO), (5) daily mean pH, (6) daily mean acid addition, (7) daily mean base addition, (8) effluent ammonia, (9) effluent nitrite and (10) effluent nitrate concentrations. Ku et al. (1995) developed a procedure for dynamic PCA (DPCA) modeling, which is adapted in this work. The procedure uses the calculation of the newly found inner relations in the data set by a step-wise increase in the window length of the ARX structure. As long as the number of new relations is more than zero, the window length is increased. Ultimately, the last model which still reveals new relations is selected.

3. Results and discussion 3.1. Simple static model In the model for "normal data" selection, two principal components (PC's) were retained as a compromise between guaranteed detection of abnormal data samples and an acceptable number of false alarms. Despite its simplicity, a two-component PCA model allows to discern the following states: (1) low ammonia load and high nitrate values, (2) moderate ammonia load and low nitrate values and (3) high ammonia load and low nitrate values. 3.2. "Normal data" selection A proper selection of the data used for modelling the normal behaviour is imperative in statistical modeling. Data which caused Hotelling's T 2 or SPE to be violated at 95% confidence levels were investigated in detail. Data that did not represent normal behaviour were omitted. In the next iteration, only the data samples that caused either the 99% -limit for SPE or Hotelling's T 2 to be violated were investigated. As only 10 further data samples were removed in this iteration, no further iteration was performed. The number of samples was cut from 440 to 378 (14% reduction). 3.3. Completion of incomplete samples by PCA projection method To base the dynamic models on continuous series which extend as long as possible, missing values for off-line measurements were estimated. The missing values were estimated by backward calculation from the scores (inverse PCA), which were estimated by the single component-projection method (Nelson et al., 1996). Negative estimates for concentrations were set to zero and remaining missing variables were

1299 estimated again by the same method. Afterwards, samples with estimates which caused H o t e l l i n g ' s T 2 and/or SPE to rise above the 95% level were omitted.

3.4. Construction of models and comparison In Table 1, the calculated inferences from Ku et al. (1995) are listed along with the percentage of captured variance, the false alarm ratio and the undetected failure ratio. The approach of Ku et al. (1995) leads to a model with ARX window length equal to two because this model is the last one by which new relations are found. Typically, the captured variance is important for prediction purposes. In this case, all featured models are considered to satisfy (all captured variances are 70% or higher). Table 1. S;mm;a;3' o.['model characteristics

w (window length)

1

2

3

4

m (variables)

10

20

30

40

c (principal components)

4

4

6

6

r=m

c (inner relations found)

6

16

24

34

6

4

-2

-

captured variance (%)

74.7

70.0

77.9

75.7

false alarm ratio (%)

2.5

4.8

6.4

8.2

undetected failure ratio (%)

76.7

23.9

28.4

27.8

rn~,, (new inner relations found)

A third and key criterion is the success in discerning abnormal from normal behaviour. The ratio of false alarms to normal samples (false alarm ratio) and the ratio of undetected abnormal samples to total abnormal samples (undetected failure ratio) relate to this performance. An alarm was induced when either the 95%-level of Hotelling's T 2 or SPE was violated. The false alarm ratio rises with increasing window lengths, but is acceptable for all models (see Table 1). A minimal undetected failure ratio is found for a window of two. The undetected failure ratio is 76.7% in the static PCA model, while it is lower than 30% for all DPCA models. Accounting for the dynamics is thus essential. Based on the used criteria, the window length of the ARX structure should either be two or three. Therefore, the relations that were observed between the model and the mechanistic knowledge of the real system are summarised only for these two models. 3.4.1 Model with window length = 2 (one time delay) a n d J b u r P C ' s HRT, acid addition and DO values are affecting the 3 rd score the most (not shown). Also, the effect of a temporary low value of HRT was noticed very clearly in this score. pH (variable 5), nitrate (variable 10) and base addition (variable 7) are the dominating variables of the tburth PC (see Figure 4, left). A remarkable distinction of two periods is observed: (1) rather unstable pH values and a rather high base addition (days 99 to 400)

and (2) more stable pH values and lower base addition. Discussion with the operator of the labscale SHARON setup reveals that these differences in pH dynamics had not been detected before. Even though the cause could not be determined, the most sensible hypothesis is that the ingrowth of second step nitrifiers resulted in the conversion of nitrite to nitrate, which in turn reduced the toxic effects of nitrite on the first step nitrifiers. Since this was not observed before the PCA modeling, it shows that PCA modeling can be helpful in understanding the characteristics of biological processes.

1300

0,6

loading .............................................i....................................:~

Bj

$cor~ ...............................................................................................................................

04

0.2

~, oL0i, :i

-0.21

"

"

1

2

_0,41

.............................. 3

4

5 6 variable

7

8

9

~1.....k..]

-2 !1i!wl -4 -,61 .....

10

IO0

200

300 day

400

50:0

600

Figure I" Loading plot and score plot of component 4 in the model with ARX window equal to 2. Red bars show the loadings of the delayed variables (time instant-1) while the yellow bars show the actual variables (time instant 0). 3.4.2 Model with window length = 3 (two time delays) and six components To a large extent, the PC3 and PC4 captured the same effects as in the former model. Acid effects are not captured in the third but in the fourth PC. Base addition is only influential in PC5. Nitrate build-up is reflected in this score as well. However, the latter effects appear yet in the fourth PC of the previous model. PC6 is dominated by the DO and effluent nitrate. The resulting trends are however observed yet in the first score. As the last two PC's seem only to capture information which is captured in the four PC' s of the 1st model, they lead only to a larger captured variance, which is not of prime interest.

3.5. Selection In the final selection step, the false alarm ratio was omitted as a criterion as the values are comparable for both models. In Table 2, the relevant results are summarized. In three out of four criteria, the model of window length of two is performing the best. Thus, a window length of two is selected, which leads to a four-component DPCA model (see Table 1). Table 2: Summary of selection procedure: for each of the criteria, the preferenced model is marked by "+"

w

2

3

rncw

captured variance undetected failure ratio model description

3.6. Application of the model Figure 4 shows the SPE and Hotelling's T 2 values. The following list of errors or abnormal situations that are detected by the model confirms that PCA monitoring is a valid approach in monitoring of biological processes : - startup phenomena (73-94) - sensor failures: DO sensor (188-190, 431), pH sensor (121-125, 193-195,386, 431)

1301 actuator failures: acid addition (138-140, 241-243), base addition (178, 181,209-214), oxygen supply (251-256, 466), influent supply (278-281, 292-293), effluent withdrawal (171-174) - operational changes: change of HRT (449), change of TIC:TAN ratio (541) - abnormal conversion rates: high (206), low (333,395) - addition of biomass (168-170) - excessive water evaporation due to supply of dry rather then moist air supply (220222) - running of fast-dynamic kinetic experiments (308)

-

e~o

I

"

:

'

:g %

~0 ~

L. 0

~,00

~00

@

IO0

2 O0

SO{?:

4<j:O

5900

600

4.00

5<10

600

I5

£_

~a y

Figure 2. Hotelling's T; and DmodX (distance to the model plane) control charts based on the selected model I 3.7.

Effect

of

data

estimation

Since considerable effort is put into the estimation of missing data it is interesting to know what effect it has on the model performance. The results for the selected model structure with and without estimates are summarised in Table 3. Captured variances are comparable and the false alarm ratio is equal for both models. The undetected failure ratio seems to be influenced largely by the effect of gaps in the data, as this ratio is almost doubled when no estimates are used. Table 3." E/feet of the use of estimation data on model petjbrmance

inference captured variance (%) false alarm ratio (%) undetected failure ratio (%)

4. Conclusions

with estimated data 70.0 4.8 23.9

without estimated data 70.7 4.8 46.0

1302 This paper describes the development of a module for PCA based monitoring of the SHARON process. A dynamic PCA (DPCA) model is selected from several DPCA models, with different window lengths. For monitoring model selection, the criteria include captured variance, added new relations (Ku et al., 1995), false alarm ratio, undetected failure ratio and mechanistic relations between the components and the process characteristics. It is shown that ARX structuring of data clearly improves the monitoring performance compared to a static PCA model. Furthermore, estimation of missing data concerning the nitrogen species improves the performance of a DPCA models. In the selection, loss of captured variance is traded for an improved undetected failure ratio and a smaller span of the PCA space. The method of Ku et al. (1995) for DPCA model selection lead to the same model, which approves their procedure as a relative fast and good-quality method for DPCA model selection.

Acknowledgements This work was supported by the Institute for Encouragement of Innovation by means of Science and Technology in Flanders (IWT), the Visiting Postdoctoral Fellowship of the Fund for Scientific Research-Flanders (FWO) and the ICON Project No. EVK1CT2000-054.

References Kourti, T. and J.F. MacGregor, 1995, Process analysis, monitoring and diagnosis, using multivariate projection methods, Chem. Intell. Lab. Syst. 28, 3. Ku, W., R.H. Storer and C. Georgakis, 1995, Disturbance detection and isolation by dynamical principal component analysis, Chem. Intell. Lab. Syst. 30, 179. Lee, D.S. and P.A. Vanrolleghem, 2004, Adaptive consensus principal componenent analysis for on-line batch process monitoring, Environmental Monitoring and Assessment 93(1-3), 119. MacGregor, J.F. and T. Kourti, 1995, Statistical process contol of multivariate processes, Control Eng. Practive 3(3), 403. Nelson, P.R.C, P.A. Taylor and J.F. MacGregor, 1996, Missing methods in PCA and PLS: Score calculations with incomplete observations, Chem. Intell. Lab. Syst. 35, 45. Rosen, C. and J.A. Lennox, 2001, Multivariate and multiscale monitoring of wastewater treatment operation, Wat. Res. 35(14), 3402. van Dongen, L.G.J.M., M.S.M. Jetten and van Loosdrecht M.C.M., 2001, The Combined Sharon/Anammox Process, A Sustainable Method for N-removal from Sludge Water. IWA Publishing, Water and Wastewater Practicioner Series: Stowa Report, pp 64. Van Hulle, S., S. Van Den Broeck, J. Maertens, K. Villez, G. Schelstraete, E. Volcke and P.A. Vanrolleghem, 2003, Practical experiences with start-up and operation of a continuously aerated lab-scale SHARON reactor, Proceedings 16th Forum Applied Biotechnology, Comm. Agri. Appl. Biol. Sci. 68/2(a), 77-84. Wise, B.M. and N.B. Gallagher, 1996, The process chemometrics approach to process monitoring and fault detection, J. Proc. Contr. 6 (6), 329. Yoo, C.K, P.A. Vanrolleghem and I. Lee, 2003, Nonlinear modeling and adaptive monitoring with fuzzy and multivariate statistical method in biological WWTP, J. of Biotechnology, 105(12), 135.

European Symposiumon ComputerAided Process Engineering- 15 L. Pui~janer and A. Espufia(Editors.) ~"~2005 Elsevier B.V. All rights reserved.

1303

Robust Controller Design for a Chemical Reactor Monika Bako~ov~, Dalibor Puna and Alojz M6sz~,ros Department of Inlbrmation Engineering and Process Control, Faculty of Chemical and Food Technology, Slovak University of Technology Radlinsk6ho 9, 812 37 Bratislava, Slovakia

Abstract In this paper, the design of a robust static output feedback controller is presented. This problem is transformed to solving of linear matrix inequality (LMI) problems. A computationally simple LMI based non-iterative algorithm is used. The design procedure guarantees with sufficient conditions the robust quadratic stability and guaranteed cost. The presented approach is applied for robust controller design for an exothermic continuous-time stirred tank reactor (CSTR). The designed robust controller is able to stabilize the CSTR with four uncertain parameters in the entire operating area.

Keywords: robust control, static output feedback, LMI, chemical reactor 1. Introduction Chemical reactors are the ones of most important plants in chemical industry. But their processing is connected with many different uncertainties. Some of them arise from varying or not exactly known parameters, as e.g. chemical kinetics or reaction activity. In other cases operating points change. Chemical reactors are also affecting by various types of perturbations. All these uncertainties can cause poor performance or even instability of closed-loop control system. Application of robust control approach can be one of the possibilities how to overcome all these problems (Alvarez-Ramirez and Fermat, 1999). Robustness has been recognized as a key issue in the analysis and design of control systems for the last two decades. One of the up to now opened problems is also the problem of a robust static output feedback (Syrmos et al., 1997). Various approaches have been used to study the two aspects of the robust stabilization problem. The first aspect is related to conditions under which the linear system described in the state space can be stabilized via output feedback. The necessary and sufficient conditions can be found e.g. in Ku6era and DeSouza (1995), Vesel~ (2004). The second aspect is related to finding a procedure for obtaining a stabilizing or robustly stabilizing control law. Recently, it has been shown that an extremely wide array of robust controller design problems can be reduced to the problem of finding a feasible solutions of LMIs, see e.g. Vesel~ (2002), Benton and Smith (1999), Yu and Chu (1999) and others. In this paper, conditions for robust stabilization of linear continuous-time variant (LTV) systems via static output feedback are presented. The problem of robust controller design with the output feedback is reduced to LMI problems (Boyd, S. et al., 1994). A computationally simple LMI based non-iterative algorithm is used for the design of

1304 robust static output feedback controller (Vesel~, 2002). The designed robust controller is used to robust stabilization of an exothermic CSTR.

2. Problem formulation Consider the LTV system in the form of a polytopic linear differential inclusion (PLDI) (Boyd et al., 1994)

5c(t) = A(t)x(t) + B(t)u(t),

X(to) = x o

(1)

y(t) = C(t)x(t) whose system matrix S ( t ) - I A(t)

/ c(t)

S(t) E Co{S1,...,S n }'-

¢:ziS i

B(t)l varies within a fixed polytope of matrices" o I O~i -- 1

"o~ i _> 0,

(2)

i=1

where Co{S1,...,S ,} is the convex envelope of a set of linear time invariant (LTI) models S i -

[t/8/] Ci

0

'

i - 1,... n, representing vertex systems.

The static output feedback problem can be formulated as follows. For the system (1) find a static output feedback u(t) = Fy(t) such that the closed loop system (3) is stable.

5c(t) - (A(t) + B(t)FC(t))x(t) = ACE (t)x(t)

(3)

3. Robust output feedback controller design Consider the uncertain closed-loop system (3) with

A sufficient condition for the asymptotic stability of the system (3) is feasibility, e. a. the existence of a quadratic Ljapunov function V(x)= x(t) r P x( t) ,

P > 0 such that

dV(x(t))

< 0 along all state trajectories. If a P > 0 exists, system (3) is quadratically dt stable and following statement holds: system (3) is quadratically stable if and only if there exists a positive definite matrix P>0 such that following inequalities are satisfied

A & i P + PA~L i < O, e > O, i - 1,...,n

(5)

Consider the polytopic closed-loop system (3). Then the following two statements are equivalent (Vesel2~, 2002): 1. The system (3) is robust static output feedback quadratically stabilizable. 2. There exist a positive definite matrix P = p r > 0 and a matrix F satisfying the following matrix inequality

(A i + B i F C i)T p + P(Ai + B i F C i)< 0, P > 0, i - 1 , . . . , n

(6)

1305 Consider the polytopic closed-loop system (3). Then the following three statements are equivalent (Vesel3), 2002)" 1. The system (3) is simultaneously static output feedback stabilizable with guaranteed cost oo

~(x~,~ Qx~,~ + .~,~

~.~,~)~, ~_xo~,~ ~ ~xo ~,~-

~

~ *, ~ >o

0 2. There exist matrices P > 0, Q > 0, R > 0 and a matrix F such that the following inequalities hold

(A i + BiFC i )r p + P(Ai + BiFC i )+ Q + Cri F T R F C i < O, i - 1,...,n

(8)

3. There exist matrices P > 0, Q > 0, R > 0 and a matrix F such that the following inequalities hold

Ai TP + PA i - PBiR-1Bri P + Q <_o, i - 1.... ,n

(9)

(BTiP+ RFCi)~il(BTi P-k- g f c i ~ - g~ O where

(10)

@i--(mi TP + Pmi-PBiR-1BTi P--I-Q), i-I,...,H

(11)

The design procedure for simultaneous static output feedback stabilization of the system (3) with guaranteed cost is based on statements formulated above. 1. Compute S - S r > 0 from the following inequality

S(Q

< O, yI < S , i - 1,...,n

(12)

when 7" > 0 is any non-negative constant and S = P I. 2. Compute F from the following inequality

+

+•

1 °, i =',---,

If the solutions of (12), (13) are not feasible, either the system (3) is not stabilizable with a prescribed guaranteed cost, or it is necessary to change Q, R and 7" in order to find a feasible solution.

4. Simulation results Consider a continuous-time stirred tank reactor (CSTR) with the first order irreversible parallel exothermic reactions according to the scheme A

k, >B, A

~2 >C, where B

is the main product and C is the side product. Under the condition of perfect mixing, the dynamic mathematical model of the controlled system has been obtained by mass balances of reactants, energy balance of the reactant mixture and energy balance of the coolant. Using usual simplifications, the model of the CSTR can be described by four nonlinear differential equations

1306

dCAdt - -

Vr

/

qr + k 1 + k 2 CA + Vr CA f

(14)

dCB - _ q___LCB+ klCA + q__L d----~-

Vr

dTr --=

hlkl + h2k2

dt

IOr Cpr

dTc

_

(15)

Vr cBf

qc (Tcf

cA +

qr -~r

AhU

(Trf- Tr) + - - ( T c

AhU _Tc)+__(Tr_Tc

Vr Pr Cpr

- T~)

(16)

)

(17)

with initial conditions CA(0), cB(0), Tr(0) and Tc(0). Here, t is time, c are concentrations, T are temperatures, V are volumes, p are densities, Cp are specific heat capacities, q are volumetric flow rates, h are reaction enthalpies, Ah is the heat transfer area and U is the heat transfer coefficient. The subscripts denote .r the reactant mixture, .c the coolant, .f feed values and the superscript .s the steady-state values. The reaction rates k~, k2 are expressed as

kj =k0jex p

RTr

,j-1,2

(18)

where k0 are pre-exponential factors, E are activation energies, R is the gas constant. The values of all parameters and feed values are in Table 1.

Table 1. Parameters and inputs of the chemical reactor Vr = 0.23 m 3 V~= 0.21 m 3 qrs = 0.015 m 3 m i n 1 qc~= 0.004 m 3 m i n -1

,Or= 1020 kg m -3 Ah = 1.51 m 2 CAC= 4.22 kmol m -3 Pc = 998 kg m -3 U = 42.8 kJ m-2 min -1K-1 CBr = 0 kmol m -3 cp~ = 4.02 kJ kg-1K-I gl =El~ R = 9850 K T~f= 310 K Cpc = 4.182 kJ kg-1K-j gz=E2 / R = 22019 K T~f= 288 K

Model uncertainties of the over described reactor follows from the fact that there are four only approximately known physical parameters in this reactor:

1.6 0,1] k20 ~ [4.95 x 1026", 12.15 x 1026 ] . The nominal values of these parameters are mean values of intervals. The steady state behavior of the chemical reactor with nominal values and also with all 16 combinations of minimal and maximal values of 4 uncertain parameters was studied at first. It can be stated the reactor has always three steady states, two of them are stable and one is unstable. The maximal concentration of the product B is obtained in the unstable steady state. So, the main operating point is described by unstable steady-state values of state variables. The situation for the nominal model is shown in Figure 1, where Q~EN is the heat generated by chemical reactions and Qouf is the heat removed by the jacket and the product stream. The main operating point for the nominal model is

[c,A,CB,Tr s , ,T c,] -[1.8614kmol.m -3 1 0113kmol.m -3 338.41K,

328.06K]

1307 CB (kmol m -3 1,25

QGEN' QOUT (kJ min" ) 5000 4000

)

1,00

3000 0,75 t

2000

0,50

1000

{

0,25

0 -1000 300

310

320

330 340 mr(K)

350

360

370

0,00 300

310

320

330

340

350

360

370

T r (K)

Figure 1. Stead), state behavior of the chemical reactor for nominal values of uncertain parameters

Design of a robust stabilizing controller is based on having a linear state space model (1) of the controlled system. Linearized mathematical model has been derived under the assumption that the control inputs are the reactant flow rate qr and the coolant flow rate qc and the controlled output is the temperature of reaction mixture Tr. The other input variables are considered to be constant. The matrices of the nominal linearized model in the main operating are

A0 -

C0 -(0

-0.1479

0

-0.0226

0.0354

-0.0652

0.0057

1.3763

0

0.2118

0.0685

0

0

0.0737

-0.0928)

0

~

(10.2546 1-4.3968 Bo - 1 ' ,-123.5131 (

O

0 0 0

,

-190.7612

1 0). This model is unstable, the eigenvalues of A0 are-0.0652, 0.1195,

-0.0741+0.0310i,-0.0741-0.0310i. For 4 uncertain parameters, we have obtained 24 =16 linearized mathematical models, which differ in coefficients of Ai, Bi. These systems represent vertices of the uncertain polytopic system and they all are unstable. It was further important to find a robust static output feedback, which would be able to stabilize the whole uncertain system with the guaranteed cost expressed by (7), where Q - q~o,,,.t.diag(1, 1, 1 × 10 5, 1 × 10 5),

R - rco,,.,,t.diag(1 x 103, 1 × 103) . The parameters

of matrices Q, R have been chosen according to the values of state variables and control inputs. For finding a stabilizing output feedback controller it is necessary to solve two sets of LMIs (12), (13), each set consisting of 16 LMIs. The feasibility of the solution of (12) assures that the reactor is robust static output feedback quadratically stabilizable and the feasibility of the solution of (13) gives robust static output stabilizing controller with guaranteed cost for the whole uncertain system. For solving the LMIs, the LMI MATLAB toolbox was used. There are three parameters, which

influence

solution

and can be changed:

qco,st,rco,st,y.

In

dependence on the choice of these parameters, it was possible to find several stabilizing controllers, which stabilize the polytopic system with 16 vertices and also stabilize the reactor. For all stabilizing controllers all closed loop systems obtained for the nominal system and also for all vertices of the polytopic system are stable, e. a. all eigenvalues of all state matrices (4) of all 17 closed loop systems have negative real parts.

1308 c B (kmol m -3 )

T r (K)

339

1,04

J

1,00

338

0.96 337

0.92 336

3~

0.88

0

.

. ~'0

.

4o

.

.

t (min)

6'0

~'0

~00

084

0

.

.

~0

.

.0

.

.

6'0

8'0

~00

t (min)

Figure 2. Closed-loop response of the CSTR with robust output feedback controller

Some of the simulation results obtained with the robust static feedback controller F = [0.0023

0.0186] v are shown in Figure 2 for the nominal values of uncertain

parameters.

Conclusions

In this paper, the possibility to stabilize an exothermic chemical reactor with uncertainties working in the unstable operating point via static output feedback controller is studied. The robust controller design is converted to solving of LMI problems. A computationally simple LMI based non-iterative algorithm is used for the design of robust static output feedback controller. This algorithm is based on linear state-space representation of a controlled system. The design procedure guarantees with sufficient conditions the robust quadratic stability and guaranteed cost. The designed robust controller is able to stabilize the exothermic CSTR for the entire operating area not only for a single operating point.

References Alvarez-Ramirez, J. and R. Fermat, 1999, Robust PI stabilization of a class of chemical reactors. Systems Control Lett. 38, 219-225. Benton, I.E. and D. Smith, 1999, A non iterative LMI based algorithm for robust static output feedback stabilization, Int. J. Contr. 72, 1322-1330. Boyd, S., L. E1 Ghaoui, E. Feron and V. Blakrishnan, 1994, Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia. Ku6era, V. and C.E. de Souza, 1995, A necessary and sufficient conditions for output feedback stability, Automatica 31, 1357-1359. Syrmos, V.L., C.T.Abdallah, P.Dorato and K. Grigoriadis, 1997, Static output feedback. A survey, Automatica 33,203-210. Vesel~, V., 2004, Design of robust output affine quadratic controller, Kybernetika 40, 221-232. Vesel~, V., 2002, Robust output feedback controller design for linear parametric uncertain systems, Journal of Electrical Engineering, 53, 117-125. Yu, L. and J. Chu, 1999, An LMI approach to guaranteed cost control of linear uncertain timedelay systems, Automatica 35, 1155-1159.

Acknowledgements The authors are pleased to acknowledge the financial support of the Scientific Grant Agency of the Slovak Republic under grants No. 1/0135/03 and 1/1046/04.

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1309

A MINLP/RCPSP decomposition approach for the shortterm planning of batch production N orbert Trautmann a and Christoph Schwindt b aInstitute for Economic Theory and Operations Research University of Karlsruhe, 76128 Karlsruhe, Germany blnstitute for Business Administration and Economics Technical University of Clausthal, 38678 Clausthal-Zellerfeld, Germany

Abstract We present a new solution approach for short-term planning of batch production, which decomposes the problem into batching and batch scheduling. Batching converts the primary requirements for products into individual batches. We formulate the batching problem as a mixed-integer nonlinear program, which can be solved by standard software. Batch scheduling allocates the batches to scarce resources such as processing units and intermediate storage facilities. The batch scheduling problem is modelled as a resource-constrained project scheduling problem, which is solved by a novel priorityrule based method.

Keywords: Batch production; Scheduling; Decomposition; Mixed-integer nonlinear programming; Resource-constrained project scheduling

1. Introduction This paper deals with short-term planning of batch production in the process industries. In batch production mode, the total requirements of intermediate and final products are partitioned into batches. To produce a batch, at first the inputs are loaded into a processing unit. Then a transformation process is performed, and finally the batch is unloaded from the processing unit. We consider the case of multi-purpose processing units, which can operate different processes. The duration of a process depends on the processing unit used. The minimum and maximum filling levels of a processing unit give rise to lower and upper bounds on the respective batch size. Between consecutive executions of different processes in a processing unit, a changeover with sequence-dependent duration is necessary. Moreover, to avoid ongoing reactions of residuals, a processing unit needs to be cleaned before an idle time. In general, storage facilities of limited capacity are available for stocking raw materials, intermediates, and final products. Some products are perishable and must be consumed immediately after production. The product structure may be linear, divergent, convergent, or general. In the latter case, the product structure may also contain cycles. The input or output proportions are either fixed or can be chosen within prescribed bounds. For a practical example of a batch production, we refer to the case study presented in Kallrath (2002).

1310 A plant is operated in batch production mode when a large number of different products are processed on multi-purpose equipment. In this case, the plant is configured according to (a subset of) the required final products. Before processing the next set of final products, the plant has to be reconfigured, which requires the completion of all operations. In order to ensure high resource utilization and short customer lead times, the objective of makespan minimization is particularly important. That is why we consider the short-term planning problem which for given primary requirements consists in computing a feasible schedule with minimum makespan. Various solution methods for short-term planning of batch production are known from literature. Most of them follow a monolithic approach, which tackles the problem as a whole starting from a mixed-integer linear programming formulation of the problem. In those models, the period length is either fixed (time-indexed formulations, cf. e.g., Kondili et al., 1993) or variable (continuous-time formulations, see e.g., Ierapetritou and Floudas, 1998, or Castro et al., 2001). A disadvantage of the monolithic approaches is that the CPU time requirements for solving real-world problems tend to be prohibitively high (cf. Maravelias and Grossmann, 2004). To overcome this difficulty, heuristics reducing the number of variables have been developed (cf. e.g., B16mer and Gtinther, 1998). A promising alternative approach is based on a decomposition of the problem into interdependent sub-problems, as it has been proposed e.g. by Brucker and Hurink (2000), Neumann et al. (2002), and Maravelias and Grossmann (2004). The solution approach developed in what follows decomposes the short-term production planning problem into a batching and a batch-scheduling problem. Batching provides a set of batches for the intermediate and final products needed to satisfy the primary requirements. Batch scheduling allocates the processing units, intermediates, and storage facilities over time to the processing of all batches. In this paper, we use a new formulation of the batching problem as a mixed-integer nonlinear program that, in contrast to the model discussed in Neumann et al. (2002), allows for taking into account alternative processing units of different size. Moreover, we present a novel priority-rule based method for batch scheduling which is able to cope with large problem instances. The remainder of this paper is organized as follows. In Section 2 we formulate the batching problem as a mixed-integer nonlinear program. In Section 3 we show how to model the batch-scheduling problem as a resource-constrained project scheduling problem, and we sketch an appropriate priority-rule based solution method. Results of an experimental performance analysis of the new approach are discussed in Section 4. Section 5 is devoted to concluding remarks.

2. The batching problem In what follows, the combination of a transformation process and a processing unit is referred to as a task. For example, if there are three alternative processing units for the execution of a transformation process, we define three tasks for this process. Let T be the set of all tasks and let 13~ and e~ be the batch size and number of batches for task e T. By 1-I~ and 1-I+ we denote the set of input and output products, respectively, of task "c. I-I~ "-1-I~-~[1 +~ is the set of all input and output products of task i: , and

1311 FI := UFI: is the set of all products considered. In addition to 13~ and ~ , the proporc¢T

tions c ~ < 0 of all input products rce H7 and the proportions c ~ > 0 of all output products rc e 17I+ have to be determined for all tasks 1: e T such that ~{~=-

Zc~=I

rcclq +

(T~T)

(1)

rccl-I r

Batch sizes 13~ and proportions (~:~ have to be chosen within prescribed intervals [ ~ r , ~ ] and [ _ ~ , ~ ] , ot~_
i.e.,

{ ' c ~ T , rcEH~)

(2)

B

_~ <13~<13 ~ ( T ~ T )

(3)

Let T~ and T+ be the sets of all tasks consuming and producing, respectively, product n E H and let H P ~_ H be the set of perishable products. Then equations c~3~ - -{~,;D~

( 7: E H " , (~, r')~ T~+ × T~ )

(4)

ensure that the amount of a perishable product rc produced by one batch of some task +

1: E T~ can immediately be consumed by any task 1: E Tn consuming re. By p~ we denote the primary requirements less the initial stock of re. For recycled products x ~ H , p~ is augmented by an unavoidable residual stock after the completion of all batches. The final inventory of product rc then equals ~ot~13~e~ . This amount :cT must be sufficiently large to match the requirements P~ for re. On the other hand, the final stock ~c~,~13~e:-p~ of product n must not exceed the given storage capacity coT

c~ for re. Both necessary conditions can be formulated as p~-< Z o ~ 1 3 ~ 8 ~ - - - p ~ + ~

(rccl-I)

(5)

rcT

in addition, the number of batches e~ must be integral, i.e., e~eZ_0

('c~T)

(6)

To formulate the objective function, we divide the processing units into a set F of groups 7 in such a way that first, each processing unit belongs to exactly one group and second, each transformation process can only be executed on processing units of one and the same group. Let Yy be the set of processing units in group 7 E F . By T,) we denote the set of tasks that can be executed on processing unit u. We refer to the processing unit t)e Y~, with maximum potential workload

~p~

T

as the bottleneck of

C TL,

group 7, where p~ stands for the processing time of task "c. The objective function to

1312 be minimized is chosen to be the sum ~ max ~ p~e~ of all bottleneck workloads. In

7cFUCYr~cT~,

this way we ensure that the total bottleneck workload is kept as small as possible while the actual workload to be processed is equally balanced among the alternative processing units of a group.

3. The batch-scheduling p r o b l e m 3.1 Modelling as a resource-constrained project scheduling problem Suppose that n batches numbered from 1 to n have to be scheduled. We model the processing of the batches as a project (cf. Brucker et al., 1999) that consists of a set V - { 0,1,... n, n + 1} of activities, which require resources and time for their execution and which are linked by prescribed time lags between their starts. The processing of a batch is identified with exactly one activity i ~ {1,...,n} of the project. Dummy activity 0 represents the production start and dummy activity n + 1 corresponds to the production end. Let S i > 0 be the start time sought of activity i. Then Sn+ 1 coincides with the production makespan. Vector S = (S i)i~v with S o - 0 is called a schedule. Each processing unit can be viewed as a unit-capacity renewable resource. Let R ~' be the set of all renewable resources and let k i ~ R ° be the resource processing real activity i. By

Pi

and c i we denote the processing and cleaning times of activity i, where

we suppose that Pi = ci = 0 for i = 0, n + 1. The need for cleaning a processing unit generally depends on the sequence in which the activities are executed on this unit. Let P~. ~ V x V be the set of activity pairs (i, j ) for which passing from i to j requires a cleaning of processing unit k. Given a schedule S , let Ok (S) designate the set of all pairs (i, j ) such that i :/: j ,

S i ~

S j , and

ki -

kj.

O k (S) can be partitioned into the set C k (S) containing all pairs (i, j ) for which k has to be cleaned between the completion of i and the start of j (because (i, j ) s Pk or Sj > S i + Pi ) and the set Ck of pairs for which j must be started immediately after the

completion of activity i. A schedule S is called process-feasible if Sj

>_- S i nt-

Sj-S

Pi + ci, if (i, j ) ~ C k (S)}

i+pi,

if(i,j)~Ck(S)

_

R° (k~

)

(7)

Now we turn to the intermediates and storage facilities, which are both represented by so-called cumulative resources (cf. Neumann and Schwindt, 2002). For each nonperishable product, there is one cumulative resource keeping its inventory. Let R r be the set of all cumulative resources. For each k ~ R r , a minimum inventory R__k (safety stock) and a maximum inventory R~- (storage capacity) are given. Each activity i s V has a demand r/k for resource k ~ R v . If r/k > 0, the inventory of resource k is replenished by r/k units at time S i + P i . If rik < 0, the inventory is depleted by -r/k units at

1313 time

S i . FOk

represents the initial stock level of resource k. Let V~+ "- {i ~ V r/k > 0}

and V~; "-{i ~ V r/~ < 0} be the sets of activities replenishing and depleting, respectively, the inventory of k ~ R Y . Schedule S is said to be storage-feasible if

Rk <

~l~

+

ic~"~+. 'Si +Pi
~rik
(k~RV,t>O)

(8)

icI"~.- :S i
To avoid waiting times between activities respectively producing and consuming perishable intermediates, temporal constraints of the type S/

>_ S i -+- 6(/

((i,j)e E)

(9)

with E c_ V x V have to be taken into account as well. 6ii is a minimum time lag between the start of activities i and j . If ;5ij < 0, then -60 can be interpreted as a maximum time lag between the start of activities j and i. In case of 6 ! / - P i , the corresponding temporal constraint is referred to as a precedence constraint. A schedule S satisfying Sj _>S; + 6!/ for all (i,./)e E is called time-feasible. A schedule which is time-, process-, and storage-feasible is called feasible. The batch scheduling problem consists in finding a feasible schedule S with minimum makespan S,+I •

3.2 Solution procedure The priority-rule based scheduling method consists of two phases. During the first phase, we relax the storage-capacity constraints. Using a serial schedule-generation scheme, the activities are iteratively scheduled on the processing units in such a way that the inventory does not fall below the safety stock at any point in time. Deadlocks are avoided by means of a specific unscheduling technique. Based on the resulting schedule, precedence constraints between replenishing and depleting operations are introduced according to a FIFO strategy. Those precedence constraints ensure that the material-availability constraints are always satisfied. In the second phase, which again applies the serial schedule-generation scheme, the activities are scheduled subject to the storage-capacity and the precedence constraints introduced. Details of this procedure can be found in Schwindt and Trautmann (2004).

4. Computational results We have compared our decomposition approach to the time-grid heuristic by B16mer and Gfinther (1998) and to the decomposition method by Maravelias and Grossmann (2004). As a test bed we have used the 22 instances introduced by B16mer and Gt~nther, which have been constructed by varying the primary requirements for final products in the case study presented by Kallrath (2002). In addition, we have solved Example 2 discussed in Maravelias and Grossmann (2004). For solving the batching problem, we have used the Solver package by Frontline Systems. For batch scheduling, we have implemented a randomized multi-pass version of the priority-rule based solution procedure in ANSI C. All computations have been performed on an 800 MHz Pentium III personal computer.

1314 It turns out that for each of the 23 instances in the test set, the batching problem could be solved within less than 8 seconds. In each case, the optimality of the solution found could be verified by using an alternative MILP-formulation of the problem. The sizes of the resulting batch scheduling instances range from 24 to 100 operations. For all instances, within less than four minutes the priority-rule based method has either provided an optimal solution or the best solution known thus far could be improved. The results obtained for the large instances with more than 50 operations indicate that our decomposition approach scales quite well. The mean relative improvement achieved for those instances with respect to the time grid heuristic amounts to more than 35%. Moreover, the CPU time requirements have been decreased significantly compared to the time-grid heuristic and have been comparable to those reported by Maravelias and Grossmann.

5. C o n c l u s i o n s In this paper we have presented an efficient heuristic method for the short-term planning of batch production, which is based on a decomposition of the problem into a batching and a batch scheduling problem. Whereas the batching problem is formulated as a MINLP of moderate size, the batch scheduling problem is solved by a novel two-phase priority-rule based method for resource-constrained project scheduling. The decomposition heuristic is able to approximately solve problem instances of practical size in the space of a few minutes. An important area of future research will be the development of efficient online-scheduling procedures that are based on the priority-rule based method. Such an online-scheduling algorithm could be used in the Available-to-Promise module of Advanced Planning Systems for Supply Chain Management.

References B16mer, F. and H.O. Giinther, 1998, Scheduling of a multi-product batch process in the chemical industry, Comp. Ind. 36, 245. Brucker, P. and J. Hurink, 2000, Solving a chemical batch scheduling problem by local search, Annals Oper. Res. 96, 17. Brucker, P., A. Drexl, R. M6hring, K. Neumann, and E. Pesch, 1999, Resource-constrained project scheduling: notation, classification, models, and methods. Eur. J. Oper. Res. 112, 3. Castro, P., A.P. Barbosa-Pdvoa, and H. Matos, 2001, An improved RTN continuous-time formulation for the short-term scheduling of multipurpose batch plants, Ind. Eng. Chem. Res. 40, 2059. Ierapetritou, M.G. and C.A. Floudas, 1998, Effective continuous-time formulation for short-term scheduling. 1. Multipurpose batch processes, Ind. Eng. Chem. Res. 37, 4341. Kallrath, J., 2002, Planning and scheduling in the process industry, OR Spectrum 24, 219. Kondili, E., C.C. Pantelides, and R.W.H. Sargent, 1993, A general algorithm for short-term scheduling of batch operations- I. MILP formulation, Comput. Chem. Eng. 17, 211. Maravelias, C.T. and I.E. Grossmann, 2004, A hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants, Comput. Chem. Eng. 28, 1921. Neumann, K. and C. Schwindt, 2002, Project scheduling with inventory constraints, Math. Meth. Oper. Res. 56, 513. Neumann, K., C. Schwindt, and N. Trautmann, 2002, Advanced production scheduling for batch plants in process industries, OR Spectrum 24, 251. Schwindt, C. and N. Trautmann, 2004, A priority-rule based method for batch production scheduling in the process industries. In: Ahr, D., R. Fahrion, M. Oswald, and G. Reinelt, Eds., Operations Research Proceedings 2003. Springer, Berlin, 111.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) ¢¢)2005 Elsevier B.V. All rights reserved.

1315

A F r a m e w o r k for On-line Full Optimising Control of Chemical Processes P. A. Rolandi*, J. A. Romagnoli

Centre for Process Systems Engineering Department of Chemical Engineering The University of Sydney Sydney, NSW, 2006, Australia

Abstract An increasing demand for improved productivity and better quality control has shifted the interest of the research community to nonlinear model-based control, which has a better chance to meet these requirements due to the intrinsic nonlinear nature of chemical and physical processes. Recent progress in modelling, simulation and optimisation environments (MSOEs) and open software architectures (OSAs) have created the conditions to conceive novel paradigms for advanced process control (APC) of large-scale complex process systems. However, large-scale mechanistic models have scarcely been used in control algorithms and, therefore, issues arising from embedding these process models in APC applications have not been addressed satisfactorily. In this manuscript we propose a novel framework Ibr advanced nonlinear model-based control of process systems which aspires to bring the latest advances in model-based technology closer to the Process Industries.

1. Introduction Nowadays, not only state-of-the-art MSOEs support efficiently most stages of the modelling process, but also allow the creation of large-scale mechanistic models and solution of advanced model-based activities that were impossible to engage in one decade ago (Pantelides, 2001). Additionally, as rigorous process models conforming to the CAPE-OPEN (CO) standards proliferate in the public domain of the PSE and CAPE communities, the time and eflbrt to develop large-scale mechanistic models is reduced considerably. Even though these mathematical models could be used as precursors of advanced model-based control algorithms, the research community has failed to provide a framework to use rigorous mechanistic models in APC applications. Undoubtedly, MSOEs and OSAs have driven major changes in model-based technology and will continue to promote further transformations. However, how to benefit from MSOEs and OSAs to conceive new visions and establish novel paradigms in the area of APC is still an unresolved question. In this work, we present to the research community and industry the most important aspects of the framework tbrfidl optimising control of process systems (FOCoPS) proposed by Rolandi (2004).

Author to whom correspondence should be addressed: [email protected]

1316

2. F r a m e w o r k Definition 2.1. Control algorithm and general philosophy The framework is centred on hierarchical control architecture where multivariable constrained control and process optimisation (which were traditionally segregated into distinct layers (e.g. Qin and Badgwell, 1996)) are combined into a single hierarchical level. A rigorous mechanistic dynamic model of the process is used for this purpose. The core of the proposed control algorithm is based on the on-line iterative solution at time t = t o - A of a finite horizon open-loop optimal control problem (FHP) of the form: min ~o(t0 + P-A) ~(,).,~[,0.,0+cA]

(1)

F(2(t),x(t),y(t),u(t))- O, t ~ [t0,t 0 + P. A]

(2)

~(~(,0 ). x(,0 ). y(,0 ).. (,0))= 0

(3)

~ ( t ) - ~(t 0 + C. A), t e (to + C. A,t 0 + P. A]

(4)

~(,) ~ v ,

(5)

, ~ [,0,,0 + e A]

y(,)~ ~, , ~ [,o,,o + v . d

(6)

x(,) ~ x . , ~ [,0.,0 + P A]

(7)

The nomenclature conventions adopted in the equations above are straightforward. The symbols P , C and A denote the prediction horizon, the control horizon and the control window, respectively. Additionally, h~(t) indicates the subset of controlled input variables. In the proposed architecture, these decision variables correspond to the setpoints of the regulatory (PID) control layer. The FHP is solved via a control vector parameterisation approach, or sequential solution method, with piecewise-constant controls h-A e U . Details on feedback mechanisms and other features of the control algorithm can be found in Rolandi (2004). In the proposed framework for FOCoPS, we suggest to differentiate the objective function (i.e. Eq. (1), a primary and direct performance measure) from the series of process constraints on state and output variables that define the admissible set of trajectories (i.e. Eqs. (6) and (7), secondary and indirect measures of performance). In effect, objective functions such as productivity or overall profitability are more intuitive and natural performance measures for the purpose of simultaneous process optimisation and control than the multivariable objective function typically encountered in linear model-predictive control (LMPC) applications. However, translating the constraints arising from a control problem into equivalent terminal and path constraints of the corresponding NLP problem formulation and simultaneously guarantying the existence of a non-empty feasible region is a non-trivial problem. We will address this issue in subsequent sections of this paper. The reader may feel persuaded to think that the rupture with the multivariable constraint dynamic control (or quadratic cost) objective function and consequent reduction of the

1317 number of algorithmic parameters (i.e. elimination of weighting matrices intrinsic to any multivariable objective function) is a drawback of the proposed framework. On the contrary, in the author's opinion, it represents a paradigm shift that holds the potential for significant boost of the process systems performance due to a more realistic treatment of process constraints given by the specification of the control problem. Effectively, Prett and Garcia (1988) recognised that performance requirements cannot be appropriately reflected by the combination of multiple objectives into a single objective function. For instance, not only should control requirements be translated into appropriate relative weights, but care should also be exercised to avoid scaling problems and ill-conditioned solutions (Qin and Badgwell, 1996). Ultimately, the weights are used as tuning parameters of the control algorithm balancing the relative enforcement of admissible input and output trajectories. On the contrary, in the proposed framework, the performance of the controller is intimately associated with the structure of the control problem, that is, the characteristics of the objective function, and number and nature of the control variables and constraints. Since these reflect true specifications of the required process operation, better control performance can be expected from the proposed framework. 2.2. On-line formulation of the control problem

The framework for FOCoPS has been centred on the initiative of translating a process control problem into an equivalent NLP jbrmulation, and then converting this problem into a high-level declarative definition consistent with the native language of state-ofthe-art MSOEs. Even though this is an important conceptual breakthrough, several complications arise since the control problem is likely to be stated by the user (e.g. an operator) in a very straightforward way, with little resemblance with the conventions of modern modelling languages. In order to fulfil this vision, the FOC/APC application currently supports the following mechanisms: a) the user has the ability to communicate with the application kernel by posting a series of elementaw events describing the structure of the control problem at discrete points in time; b) concurrently, the application kernel has the capacity to translate this series of future events posted by the user into an equivalent NLP problem. The elementary event data model (EVNdm) has been suggested as an abstraction of all relevant information that should be contained in an event to make it useful for the purpose described above (Rolandi, 2004). Additionally, a dynamic optimisation object data model (DOOdm) was created to represent the high-level declaration of the NLP/FHP within the FOC/APC application. Since the conventions of gPROMS' highlevel declarative language were used to describe the mathematical form of the NLP problem, the generation of the gPROMS language input file describing a dynamic optimisation problem given by the DOOdm was straightforward. The control problem de[in#ion and solution supervisor (CPDaSS) is the software component of the FOC/APC application in charge of manipulating instances of the EVNdm and transforming them into a DOOdm. The algorithmic nature of this component is fairly involved and research is still being conducted in this area. In spite of this, a general discussion of the issues involved during such translation and associated software implementation aspects can be found in Rolandi (2004).

1318 2.3. Advanced features of the framework In industrial processing plants, input process variables may be "lost" due to hardware or software signal failure or unavailable due to direct intervention from the operator or the supervisory control system. Concurrently, constraints on output process variables may be modified due to alterations on process operation specifications. On the other hand, solution ill-conditioning may result from poor control problem definition or abnormal process performance, and an adequate modification of configuration (input and/or output variables, Eqs. (5) and/or (6)) could be used to recover from this situation. All of these circumstances cause the structure of the control problem to change dynamically. In the proposed framework for FOCoPS, changing the structure of the control problem is possible via the introduction of a series of mechanisms which allow a flexible definition of the associated on-line NLP/FHP. These mechanisms respond to the type of elementary event. At the moment ten different types are supported. PH C h a n g e ,

CH_Change and CW_Change keywords trigger changes in the prediction horizon, control horizon and control window respectively, thus affecting the nature of the multistage dynamic optimisation problem. PC C r e a t e and PC D e l e t e are used to modify the structure of piecewise-constant decision variables of the NLP problem. For instance, PC C r e a t e adds an additional control variable and/or modifies the magnitude of upper and lower bounds and initial guesses of an already-existent control variable. In addition, PC D e l e t e removes a piecewise-constant control variable from the list of decision variables. FR C r e a t e and FR D e l e t e are used for similar purposes for the case of process constraints, while FR C r e a t e F i x e d E n d P o i n g and FR D e l e t e F i x e d E n d P o i n g are special cases of the latter and are needed when the occurrence time of the elementary event is always coincident with the end of the prediction horizon. Finally, OV C h a n g e allows the user to change the process variable reflecting the objective function. At the moment, the user is the driving force in the definition of the control structure because the elementary events can only be posted by a restricted set of mechanisms. It is important to highlight, though, that such elementary events could be initiated by internal and/or other external agents to the FOC/APC application. The opportunity to modify the NLP formulation on-line by posting elementary events gives good flexibility and generality to the framework. In spite of this, it also gives rise to several non-trivial issues such as guarantying the validity and feasibility of the newly created NLP problem. Effectively, problem infeasibility or ill-conditioning may occur as a result of abnormal process operation and/or an intrinsically badly-posed control problem. In the FOC/APC application, constraint ranking and elimination was exploited as a mechanism for recuperation form infeasible solutions. In other words, when the solution of the NLP problem becomes infeasible, constraints below a priority level are eliminated from the formulation and the calculation is repeated. The NLP is considered infeasible for the purposes of implementation only when constraints above a certain priority level cannot be enforced. In addition, constraint identification and relaxation has been proposed as a complementary approach to infeasibility recuperation (Rolandi, 2004), although the lack of standard methods for communication with numerical solvers halts the implementation of this idea for the moment. Infeasibility recuperation is handled by the control problem definition and solution supervisor (CPDaSS), since the

1319 function of this component is to respond to control problem formulations that change dynamically according to endogenous or exogenous reasons.

3. Implementation State-of-the-art MSOEs such as gPROMS provide standard mechanisms to interact with the modelling and solution engine at a lower level than the conventional model development and activity execution environment. This is accomplished via the gPROMS Server (gSERVER), which allows any application to construct process models in gPROMS' native language, perform all supported model-based activities, and have full access to the mathematical description of the corresponding models and activities as specified by the GCO standard. The FOC/APC application has been implemented in C÷+ object-oriented programming language, although some components will support XML soon.

4. Results and Discussion In this manuscript, the framework is presented and exemplified through a case study. The process under consideration is a continuous cooking digester and auxiliary units. A large-scale model consisting of approximately 14000 algebraic and 1000 ordinary differential equations (DAEs) and 100 statuses within the state transition network (STNs) is the process model used by the FOC/APC algorithm. This model has been implemented in gPROMS modelling language. The communication between the virtual (simulated) process system (VPS) and the FOC/APC application is accomplished via Honeywell Experion PKS T M by means of the network application programming interface (NAPI) protocol. The viability and performance of the FOC/APC application is assessed by the following illustrative case-study. Let us assume that the results of an off-line study seeking to find the optimal transition management procedure for slowing down the production from 650.0 to 600.0 ad.ton/day is available to mill personnel. In this study, pulp yield was maximised while keeping the deviation of pulp selectivity fi'om its target operating value below a given threshold for quality control. Typically, these transition planning case-studies would be obtained under the assumption that the process system was initially operating at steady-state. Let us assume, instead, that a production rate change from 600.0 to 650.0 ad.ton/day had taken place five hours before the new transition (following similar optimality criteria, though). By doing this, we would like to support the thesis that results from off-line process optimisation and transition planning studies are useful to indicate the direction for enhancement of the process operation but are not directly applicable as control recipes unless process performance is sacrificed. The transition is accomplished by manipulating the set-point of three controllers: the chip meter speed (feed rate of wood chips), and the temperature of the lower and wash circulation heaters (.indirect column heating). Path (interior-point) and terminal (endpoint) constraints were imposed on the trajectories and final magnitude of blow-line kappa number and blow-line pulp production rate. Two additional (en-point) constraints were added for the deviation and violation of soft-control bounds of the kappa number. The prediction and control horizons were 7hr and 5hr, and the control window was l hr.

1320 Figures 1 and 2 compare the trajectories of key process variables for the transition based on process knowledge derived off-line (OFL) and that driven by the on-line FOC/APC control algorithm (ONL). It is clear that the FOC/APC application was able to manage the transition more efficiently than what operators could have done on the basis of previous process knowledge.

I ..................... oF,

............ oN,

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[hr]

Figure 1" Kappa number trajectory.

I

5; !

0

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2

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4

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6

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Figure 2." Lower heater set-point trajectory.

5. Conclusions This work presented a novel framework (FOCoPS) for on-line optimising control of large-scale processes. The emphasis was centred on creating a paradigm which would support the definition of a control problem in a way consistent with the structure and formalisms of high-level declarative languages and the framework imposed by the CO standards. The innovative elementary event data model was presented as a means to change the structure of the control problem dynamically due to the interaction of the APC application with the operators and the process system. A large-scale mechanistic process model of an industrial continuous pulping area was used to illustrate the framework. In this work, only key issues of the novel framework have been addressed, and no attempt has been made to compare the proposed algorithm with other standard model-based control technologies such as LMPC. However, the framework is expected to bring improved process profitability and quality control because optimisation and control occur simultaneously in the proposed architecture for FOCoPS and the FOC/APC application is centred on mechanistic process models. Overall, this paper has provided a framework for advanced process control (APC) compatible with the paradigm for open software architectures (OSA) given by the Global CAPE-OPEN (GCO) project. Naturally, the PSE, CAPE and APC community will greatly benefit from further research in the path delineated by this manuscript.

6. References Pantelides, C.C., 2001, New challenges and opportunities for process modelling, ESCAPE-11, Kolding, Denmark. Prett, D.M., Garcia, C.E., 1988, Fundamental Process Control, Butterworths, Boston. Qin, S.J., Badgwell, T.A., An overview of industrial model predictive control technology, Chemical Process Control- CPC V, CACHE, Tahoe City, California. Rolandi, P.A., 2004, PhD Thesis, University of Sydney, Australia.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1321

Wavelet-Based Nonlinear Multivariate Statistical Process Control Abd Halim S. Maulud*, Dawei Wang and Jose A. Romagnoli Process System Engineering Laboratory, Department of Chemical Engineering, University of Sydney, NSW 2006, Australia

Abstract In this paper, an approach of wavelet-based nonlinear PCA for statistical process monitoring is presented. The strategy utilizes the optimal wavelet decomposition in such a way that only approximation and the highest detail functions are used thus simplifying the overall structure and making the interpretation at each scale more meaningful. An orthogonal nonlinear PCA procedure is incorporated to capture the nonlinearity characteristic with minimum number of principal components. The proposed nonlinear strategy also eliminates the requirement of nonlinear functions relating the nonlinear principal scores to process measurements for Q-statistics as in other nonlinear PCA process monitoring approaches.

Keywords: Fault detection, Orthogonal Nonlinear PCA, Optimal multivariate wavelet decomposition

1. Introduction Principal component analysis (PCA) has been widely applied in multivariate statistical process monitoring due to its capability to extract information in multivariate environment. In practice, many processes do exhibit significant nonlinearity correlation and in these cases a linear PCA mapping results in substantial loss of information or large numbers of linear components are required to obtain the required accuracy. Several nonlinear PCA have been proposed in the literature to improve the data extraction when the nonlinear correlations among the variables exist. Wavelets have also become a promising tool in many applications due to its property of time-frequency localization. However, up to date few combinations of PCA and wavelets have been reported for process monitoring. A multi-scale-PCA strategy (Bakshi 1998; Misra et al. 2002) has been proposed to capture information in both time and frequency domains and in addition, some wavelet nonlinear PCA combination have been reported (Shao et al. 1999; Palazoglu et al. 2001) Despite these developments there are still some issues remaining on the development and implementation of wavelet based nonlinear PCA approaches. Orthogonality is a problem when dealing with nonlinear extensions of PCA strategies. In a conventional nonlinear PCA (NLPCA), the data information tends to be evenly distributed among the

Author/s to whom correspondence should be addressed: [email protected]

1322 principal components or bottleneck layer (Chessari et al. 1995). Thus, loosing the orthogonally characteristics inherent of linear PCA. On the other hand, when wavelet decomposition is applied in process measurements, the signals are projected onto the approximation and detail coefficients. As the signals are decomposed by using discrete wavelet transform to multi-level decompositions, more information is being transferred from approximation function to detail functions. If the signal is overly decomposed, it will eventually smoothing out the underlying features in the approximation function. In this paper, an approach of wavelet-based nonlinear PCA for statistical process monitoring is presented. A significant contribution of the proposed strategy is the identification/definition of the optimal level of decomposition making possible to use only the approximation reconstruction and the highest level detail (the lowest frequency) reconstruction for process monitoring. This strategy improves the fault interpretation by separating the deterministic features and localized events. A modified Kramer's NLPCA (Kramer 1991) called orthogonal non-linear PCA (O-NLPCA) is incorporated into the strategy to improve the explained variance by maximizing the data variability in the first few principal. In addition, the number of principal components specified can be relaxed while in NLPCA the number of principal components must be optimally specified in advance. The proposed nonlinear strategy structure also eliminates a requirement of nonlinear functions relating the nonlinear principal scores to process measurements for Q-statistics monitoring as in other nonlinear PCA approaches.

2. Orthogonal Nonlinear PCA Let X be a data matrix with n number of observations and m number of dimensions. In PCA, the X matrix can be decomposed into two matrices as follows:

(1)

X = TP ~ - ~ t , p ~ i=1

where T and P are called scores and loadings matrix, respectively. If the variables in X are collinear, the first f principal components can sufficiently explain the variability in data X. Thus, the data X can be written in term of a residual, E, as; f

X-

TrPrr + E - ~

t,p~ + E

(2)

i=1

In order to improve the orthogonality property in NLPCA, the Gram-Schmidt training algorithm is applied in NLPCA in such that the nonlinear score produced are orthogonal at the end of training session (Chessari et al. 1995). A major disadvantage of this scheme is it may suffer a constraint of trade-off between the main objective (overall convergence) and the secondary objective (orthogonal principal components). In addition, the network training is quite complex as it involves iterative procedure. In this paper, a simpler alternative approach to orthogonal NLPCA is proposed. This approach utilizes the Hammerstein model concept by incorporating linear PCA into the NLPCA. In Hammerstein model, the nonlinear and linear parts are separated into two blocks as shown in figure 1. In this case, the bottleneck layer nodes are called non-orthogonal nonlinear principal components and their outputs are called non-orthogonal scores.

1323 When linear PCA is applied on non-orthogonal score, it will produce orthogonal nonlinear principal components as shown in figure 2.

X

J

Nonlinear Block

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Linear I ¥

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Figm'e l

The ttammerstein Model

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PrincipalComponents

Figm'e 2 • Orthogonal Nonlinear PCA

Let T is the non-orthogonal nonlinear scores matrix generated at the output of bottleneck layer. Thus, the non-orthogonal matrix T can be transformed to orthogonal matrix U; T - UP r

(3)

where P is the eigenvector matrix. Another advantage of this approach compared to conventional NLPCA is a number of bottleneck layer neurons can be relaxed as long as the number is reasonably selected.

3. Optimal Wavelet Decomposition In multi-resolution analysis theory (Mallat 1989), any signal can be approximated by successively projecting it down onto scaling function and wavelet function. The projections onto the scaling functions are known as scaling or approximation coefficients. The projection onto the wavelet functions are known as the wavelet or detail coefficients which capture the details of the signal lost when moving from an approximation at one scale to the next coarser scale. Let us define the optimal decomposition level as the highest decomposition level in which the approximation function is adequately representing the actual deterministic signal with a minimum noise for given wavelet type. In a multivariate case, each variable may have a different optimal decomposition level. In most practical application, only a single decomposition level will be applied on all variables for computational simplification. Thus, the decomposition level selected must be appropriate or optimal to ensure that the underlying features of each variable are adequately preserved in approximation function with minimum noises. In this paper, a graphical method based on PC A concept is presented to determine the optimal decomposition level for multivariate system. It is assumed that the deterministic features of the process data are continuous smooth functions. Let a PCA is being applied on the approximation reconstruction function with single-level wavelet decomposition. Recall equation (2), the E matrix consist mainly of noises. As the wavelet decomposition is recursively applied, the magnitude of matrix E is reduced as more noises have been captured by the detail fimctions. However, the compositions of thefprincipal components remain more or a less constant as the underlying features are still adequately preserved. As the decomposition level increases, at the l level some of the underlying features of the signals in the approximation function start to be lost to the

1324 detail function and the composition of the f principal components start to change significantly. This change can be detected by plotting the explained variance of the first principal component of the approximation reconstruction function for different decomposition level. An example plot is shown in figure 4. The explained variance is calculated based on the eigenvalue of the approximation reconstruction covariance matrix. The optimal decomposition level is given as (/-1) which is can be determined from the plot.

4. Wavelet-Based Nonlinear Statistical Process Control Wavelet-based nonlinear statistical process control (WNSPC) combines the optimal wavelet decomposition ability to extract the deterministic features of the process variables in the approximation reconstruction with the ability of orthogonal nonlinear PCA to extract the correlation among the variables. The proposed monitoring strategy is shown in figure 3. Orthogonal Nonlinear PCA Approximation function A I Nonlinear , ~ PCA Optimal Wavelet Decomposition & Reconstruction I Linear I D PCA Highest level v"I detail function

Y ~"

ii Linear PCA

Z

.I

"1

E

Figure 3. Wavelet Based Nonlinear Statistical Process Control

The measurement data matrix, X, is decomposed and reconstructed by using orthonormal wavelet at optimal decomposition level. Most of the noises will be filtered in this process. Only the approximation function and the lowest frequency detail function (the highest level) are retained for process monitoring. The advantage of this strategy is that the interpretation of a fault detected is more meaningful and simpler since only bi-scale is utilized. The approximation function represents the cleaned process deterministic features while the detail function represents the localized activities or stochastic features. In the multi-scale strategy, the process deterministic features are decomposed onto multi-scale which makes it difficult for interpretation. In addition, cleaned measurement data in the approximation function improves the data analysis. The orthogonal nonlinear PCA is applied onto the approximation reconstruction function as the nonlinearity characteristics are exhibited in the deterministic features. For the detail reconstruction function, a linear PCA is utilized as mostly noise is expected to be present. It is assumed that Y adequately represents the measurement data X in a compact form. Thus, the multivariate statistical process monitoring can be performed in Y instead of X. As a result, this strategy reduces the overall monitoring system to a conventional linear PCA system. The Q-statistic can be computed as in a conventional linear PCA manner between Y and Z. For the detail function, it is not necessary to apply Q-statistic because it mainly contains noises.

1325 5. S i m u l a t i o n C a s e S t u d y An irreversible exothermic reaction of A--) B is conducted in an ideal CSTR. There are 9 variables monitored and 1000 data points are generated from the simulation and are corrupted with random noise with zero mean. The Daubechies-4 wavelet is utilized in this application. Figure 4 shows the explained variance for the first principal component of approximation reconstruction at different decomposition level. Level 8 is selected as the optimal decomposition level based on normal operating data. Two types of fault have been introduced. The first fault is a step mean shift in the inlet concentration of component A, between samples 200 and 399. The second fault is a drift deterioration of the overall heat transfer coefficient of the cooling system starting from a sample 601 onward. 95% and 99% significance points are considered as warning and action limits, which are indicated by dotted and solid lines, respectively. The WNSPC utilizes three control charts (T&approximation, Q-approximation and 74-detail) compare to two control charts in conventional PCA (7': and Q). 70

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Figure 6b. Q-PCA

From figure 5 through 6, the mean shift can be easily detected by both WNSPC and PCA methods. This can be seen in Q-statistic plots which indicate a sharp increase that goes beyond the 99% limit at sample 200. For the T:-plots, both methods cross the 95% limit, but the WNSPC response is faster. A sudden change in mean is also warned by the T:-detail at sample 200 and 400. An advantage of O-NLPCA is being applied in the WNSPC approach can be clearly seen in the second fault. The fault is quickly detected by Q-approximation as it occurred by crossing the 95% and 99% limits at sample 515 and 539, respectively. While Q-PCA is only crossing the 95% and 99% limits at 628 and 668 respectively. This indicates that WNSPC approach is much faster compared to PCA in detecting a gradual process of characteristic change. A utilization of T:-detail plot gives some advantages. In addition its ability to warn any sudden or sharp changes (as illustrated in figure 5c), it has a potential to warn some localized events. A simulation of sensor stalled of outlet A concentration is performed

1326

from point 201 to 400 as shown in figure 7. Dotted line indicates the actual deterministic path. Both T:-approximation and Q-approximation (figure 8a-b) do not indicate any warning regarding this fault as it does not involve the mean shift or process characteristic change. However, the T:-detail (figure 8c) quickly warns that there is some localized event taking place. For PCA, the Q-PCA does indicate some warning since some points are crossing 95% limit from points 201 to 400. However, an interpretation of fault type can not be quickly addressed. This illustrates an additional advantage of this strategy as it is able to provide an initial guess of the fault types. 2-

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6. C o n c l u s i o n Wavelet-based Nonlinear Statistical Process Control strategy has been presented which utilizes optimal wavelet decomposition and orthogonal NLPCA. The strategy provides an alternative approach to uncover the nonlinear characteristic and simultaneously provide an initial fault interpretation platform.

References Bakshi, B. R., 1998, AIChE Journal 44(7), 1596-1610. Chessari, C. J., G. W. Barton and P. Watson, 1995, IEEE International Conference on Neural Networks 1, 183-188. Kramer, M. A., 1991, AIChE Journal 37(2), 233-243. Mallat, S. G., 1989, IEEE Transactions on Pattern Analysis and Machine Intelligence 11(7), 674-693.

Misra, M., H. H. Yue, S. J. Qin and C. Ling, 2002, Computers & Chemical Engineering 26(9), 1281-1293. Palazoglu, A., F. Doymaz, W. Sun, A. Bakhtazad and J. Romagnoli, 2001, ESCAPE-11 supplementary, 115-120. Shao, R., F. Jia, E.B. Martin and A.J. Morris, 1999, Control Engineering Practice 7(7), 865-879.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) ::c)2005 Elsevier B.V. All rights reserved.

1327

Anaerobic digestion process parameter identification and marginal confidence intervals by multivariate steady state analysis and bootstrap. G. Ruiz ~*, M. Castellano b, W. Gonzfilez t~, E. Rocd' and J.M. Lema ~ ~' Department of Chemical Engineering. Institute of Technology. b Department of Statistics and Operation Research. University of Santiago de Compostela. E- 15782, Spain

Abstract There are a few works related to on line steady state detection algorithms and less with parameter estimation. This work used Principal Component Analysis (PCA) for reduction of the dimension of the data space and producing independent variables, allowing the application of the multivariate Cad and Rhinehart algorithm in steady state detection. Once steady states were detected, model parameters can be calculated by steady state mass balance equations and non linear fit of data. Bootstrap method was used in order to approximate the parameters estimators distribution and confidence boundaries fbr the kinetic model. These methodologies were applied to a case of anaerobic wastewater digestion process where four different organic loading rates (OLR) were applied.

Keywords: PCA, steady state, parameter estimation, bootstrap.

1. Introduction Parameter identification l-br wastewater treatment process is usually determined by model fit to dynamical data both, in batch and continuous operation (Batstone, 1999; Markel et al, 1996: Lokshina, 1999). These methods have the disadvantage of not consider time delay in dynamic data due to unknown time dependence of data, especially due to non-ideal liquid flow pattern. Usually steady state identification is analysed by an expert or an operator, In many cases, it is not possible to count with the expert advice. Furthermore, experts are always subjected to human error in recognition of steady state, especially when measurements are noisy and process changes are slow (Szela and Rhinheart, 2002). Consequently, it is important to define an algorithm tbr steady state detection, specially an algorithm for on line steady state detection. Ruiz et al (2004) have developed a multivariate extension of the Cad and Rhinehart (1995) methodology giving good results. Because of the reduced number of steady states available from process data and because the use of mean data of steady state data sets, usually high estimation errors can arise

Author to whom correspondence should be addressed: [email protected]

1328 from parameter identification, so it is necessary to increase as much as possible the accuracy of the identification procedure. Re-sampling of data by means of bootstrap, a technique invented by Bradley Efron (Efron, 1979; Efron and Tibshirani, 1993) with inferential purposes, will give more accuracy to parameter identification. Furthermore, it would be possible to obtain marginal intervals at a desired confidence. Statistical Inference studies how to use the information of a parameter estimator for obtaining probabilistic results about the real and unknown parameter. The bootstrap method rise from the analogy between a population and a sample from it. In the bootstrap word the sample is the population. In the present work, a steady state detection algorithm for multivariate process was used to generate a data base of steady states data set. Bootstrap was used for re-sampling the data set and to generate a parameter distribution in order to obtain a marginal interval for each variable. This approach will improve the common methodology of model (Haldane Kinetic Model) fit to average data and will give marginal intervals for identified parameters. All these methodologies are applied to an anaerobic digestion process for wastewater treatment, as an example, but it is extensible to any other kind of chemical and biochemical process.

2. M a t e r i a l s and M e t h o d s 2.1 Experimental setup The anaerobic wastewater treatment pilot plant is composed of a hybrid UASB-UAF reactor of 1 m 3. The measurement devices were: feed and recycling flow meters, pH meter; inflow and reactor Pt100, gas flow meter, infrared gas analyser (CH4 and CO), gas hydrogen analyser and TOC/TIC combustion analyser. The sensors gave a signal every 5 seconds and every 15 minutes a moving average window was saved in the data base. Other parameters were calculated using the measured variables: methane flow rate (Q CH4), hydrogen flow rate (QH2) and organic loading rate (OLR).

2.2 Experimental conditions The reactor was operated at stable conditions for more than a month at an OLR of 5 kg COD/m3.d. Three consecutive increases of the OLR were performed in order to obtain three different steady states (plus the initial steady state). Table 1 present the different conditions for each organic load. The duration of each state was around 5 days, considered enough to achieve steady state because the HRT was around of 0.6 to 1.5 d. For all the calculations, the first period (day 0 to 4) was considered as a normal operation state.

2.3 Multivariate steady state detection algorithm The steady state detection algorithm used was previously presented by Ruiz et al (2004). Principal component analysis (PCA) was applied for reducing the N-dimension space of the multivariate data to two dimensions. By using PCA it is possible to retain the maximum variability (information) of the process with just a few new variables (principal components). Two PCs are usually enough and represent a high level of the total variability of the process. Steady state then is identified using Cao and Rhinehart

1329 (1997) methodology. When both the first and second principal components (PC1 and PC2) are in steady state, the process will be considered at steady state.

Table 1. Experimental conditions applied to the reactor for thejour states State

Duration OLR Feed flowrate (d) (kg COD/m3"d) (Qinf) (L/h)

1: (N.O.)

0-4

5

22

TOC influent (mgC/L) 3000

2: H.O.

4-9

15

66

3000

3: H. O+O. O

9-14

28

66

4500

4: H.O+O.O

14-15.5

32

66

6000

5: (N.O)

15.5-17

5

22

3000

N.O.: Normal operation; H.O. Hydraulic overload; O.O. organic overload

2.4 Bootstrap A parametric bootstrap method is used to estimate the distribution of the kinetic parameters estimators. Lets be y the methane flow rate, x the sustrate concentration, and mo the Haldane kinetic model for methane production. The model can be written as:

y-mo(x)+g

(1)

Where ~ is the noise of the process. The N data are separated by groups and the mean of each group is calculated. Using the mean of each group and the minimun mean squared error criterium, the first estimation of the kinetic parameters is done using simplex algorithm. Each data y, can be expressed as follows. y: - m 0 ( x ) +

~";, 1 _< i _< N

(2)

The residual errors, ~,' will be used to generate the bootstrap samples. The bootstrap sample is obtained from the Haldane model with estimated parameters plus a residue with the same mean and variance of the original error. The expresion of the B bootstrap samples is

Y, */ - m o (x, ) + g ':. Z ,.i, I <. i <.N , I.< j <. B

(3)

Being Z~ a random variable with zero mean and unity standard deviation. Each bootstrap sample, using the agrupation criterium described above, will generate a parameters estimation. By this way B parameters estimation will be obtained, and used to estimate a confidence region for the Haldane curve and for the marginal parameters values.

3. Results 3.1 Anaerobic digestion process Figure 1 presents, as an example, some of the on line data obtained from the hybrid UASB-UF anaerobic reactor monitoring. The presented data are a four step increment in the organic loading rate (OLR), both by inflow and inlet concentration increase. The

1330 reactor supported the OLR increases but in the last increaset the process arose to a high destabilisation state. The process was followed by 26 variables. 70

....................................................................................................................... I

60

~50

:6000

~ 7000

800 700

5000

:i:::::

g 4o

083o >

~

3000 ~

12~ 400

A

20

i I

10

~: :,:~ ::~................::i:i

5oo6°°

4000

i:

2000 ~

::

1000

i ":i :

300

: :: ::

:

I~ 200 1 O0

....

................

i 0

o

~..................................................................................................... 0

5

10

15

20

0

5

10

tiempo (d) ,,

VCO . . . .

15

tiempo (d) TOCinf

Qa

QCH4

..... Qgas

100 ..................................................................................................................................................................... 90 I 2500 80

O2000

2000

70 Z O

•

"

...........

E

:

60 50

!

40

1500

1500

1ooo

ff

1000

30 20

500

10 0 ':

: ......

0

5

10

15

tiempo (d) %CH4

20

5

10

15

20

tie m po (d) H2

Figure 1" Multivariate on-line data for the four step organic loading rate increase of the hybrid UASB-UF anaerobic reactor up to a complete destabilization of the process. Nine variables are presented as an example.

3.2 Dimension reduction The normal operation state was used for PCA model building. Previously data were normalized. As it can be seen in Figure 2, the use of two PCs is enough to explain the process since it retained almost 80% of the total variability of the process. Subsequently data were normalized and decomposed to PC1 and PC2. Figure 3-A presents the value of the PC1 and PC2 over time. It can be clearly seen the 4 states of the experiments. These data were used for steady state detection, with the Cao and Rhinehart proposed methodology. 3.3 Steady state detection using modified Cao and Rhinehart methodology Once reduction of the process dimension was performed through PCA decomposition, Cao and Rhinehart (1997) multivariate methodology for steady state detection can be applied, because PC1 and PC2 are independent from each other. The used filter parameters were k~= 0.2 and k2 = k3=0.1. These values give a good balance between type I and type II error (Cao and Rhinehart, 1997). Data were manually labelled by an expert as steady state and non steady state. Resampling the data, the R-critic was computed in order to obtain a confidence level of %,ocess of 0.08 (92%), the R-critic was defined as 2.62 and 2.16, for the R-statistic for PC 1 and PC2, respectively. Figure 3-B presents the classification results.

1331 100%

. . . . . . . . . . . . . . . . . . . . . . . . . .

90% 80% ~>

70%

-~

60%

~

50%

o

40%

20% 10% 0%

{. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2: Cumulative explained ~'ariance by using more principal components (PC) 10

10

5

~ o

zii, iiiii!i

.....

...........

-5

-10 40

-5

5i!ili!:~: .....i¢iiili;~:

-~!iiii!~

10

. . . . . . . . . . . . . . . . . . . . . . . . .

0

2

4

6

8

10

12

14

16

18

-6

time(d)

PC1

PC1 ~ P C 2

::; N o n S S © S S

F ~ u r e 3. Steady states detected on process data. PC1 and PC2 over time (.4) and PC1 against PC2 (B), steady state data marked on the graph.

3.4 Steady state data obtained Figure 4-A presents, as an example, the steady state methane flow rate and the effluent DOC. These two variables can be fitted by a Haldane model, usually by obtain the mean of a group of data, as presented in figure 4-B. In this figure, the variance of the data is lost, loosing information and subtracting accuracy to the final identified parameters, even if the fit is quite good as can be seen in figure 4-B.

500

~"

3oo~ 2OO

,~

100 0

OOO0

0

. 0

~

qcH4~=_1324 (Lc~m3.h)

:i \ 4oo!

40O

500

1000

. . 1500

. . 2000

DOC (mgOL)

I~= 154rrgO'L _ _ 1

[

200 100 0

2500

30o0

0

1000

200O

~

3000

4O0O

(m~_)

Figure 4 Steady state data detected on process data /~n" methanejlow rate and dissolved organic carbon. All data sets (14) and mean data with model.fit.

3.5 Bootstrap confidence levels. Figure 5 shows, in summary, the model fit with maximum boundaries computed by 5000 bootstrap parameters estimation (A) and the relationship between the three estimated parameters (B). As it can be seen there is a high correlation between them. The relation between QCH4max and Ks seems to be linear (R2=0.9998), and a power

1332 relationship between KI and both, QCH4max and Ks. Figures 6C,D and E present the histograms of the parameters distribution obtained by bootstrap. Eslimated C . . . . . PARAMETRIC BOOTSTRAP 5000 resamples

d Confid . . . .

Boundaries

.....

]

....~ , \ \

1

..

K

0

QCH4

DOC

Histogram QCH4max 250

Histogram Ks

Histogram Ki 300 250 200

15@ I I_~ 0 50

O0

Figure 5 Haldane Estimated Curve, Confidence Boundaries and Parameter Estimation Histograms using Bootstrap

4. Conclusions A methodology for parameters estimation based on steady state data has been developed using Bootstrap in order to consider the variability of the original data instead of the data mean and an algorithm for multivariate steady state detection was applied. This methodology was applied to an anaerobic digestion waste water treatment process of pilot plant but their fundamentals are extensible to any other kind of processes. As an example methane production fitted to a Haldane model was considered. This methodology allows to obtain parameter estimations as well as marginal confidence boundaries for both, the Haldane curve and the parameters estimation.

References Batstone, D., 1999, High Rate Anaerobic Treatment of Complex Wastewater. PhD dissertation in Chemical Engineering at The University of Queensland Cao,S.L. and R.R. Rhinehart,1995, Journal of Process Control 5 (6), 363-374. Cao,S.L. and R.R. Rhinehart,1997, Journal of Process Control 7 (2), 149-152. Efron,B.,1979, The Annals of Statistics, 7, 1-26. Efron,B., and R.J. Tibshirani,1993, An introduction to the bootstrap. New York: Chapman-Hall. Lokshina, L.Ya. and V.A. Vavilin, 1999, Ecological modeling. 117, 285-303. Merkel, W., A. Schwarz., S. Fritz, M. Reuss and K. Krauth, 1996, Wat. Sci. and Tech. 34 (5-6), 393-401. Ruiz,G., M. Castellano, W. Gonzfilez, E. Roca and J.M. Lema, 2004,. Algorithm for steady state detection of multivariate process: Application to anaerobic wastewater digestion process. In: Proceedings of the 2nd International IWA Conference AutMoNet. Pp 181-188 Szela, J. and R.R. Rhinehart, 2002, Journal of Process Analytical Chemestry 8 (2), 1-4.

Acknowledgements This work has been carried out with the support provided by the MCyT (European FEDER support included) BFM 2002-032123 and ANACON Project (CICYT CTQ2004-07811-C02-01/PPQ).

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1333

An Efficient Real-Time Dynamic Optimization Architecture for the Control of Non-Isothermal Tubular Reactors. Miriam R. Garcia ~, Eva Balsa-Canto b, Carlos Vilas ~, Julio R. Banga a and Antonio A. Alonso a* aprocess Engineering Group, Instituto de Investigaciones Marinas-CSIC C/Eduardo Cabello, 6-36208 Vigo, Spain bDepartment of Applied Mathematics II University of Vigo 36280 Vigo, Spain

Abstract In this work we present the development of an efficient model-based real time dynamic optimization (DO) architecture for the control of distributed parameter systems (DPS). The approach takes advantage of the dissipative nature of this class of systems to obtain reduced order models (ROM) which are then used by the optimization modules to compute in real time the optimal operation policy. The DO module is based on the combination of the control vector parameterization (CVP) approach and a suitable NLP solver selected among several local and global possibilities.

Keywords" Real-Time Optimization, Distributed Process Systems and Low Order Models.

1. Introduction Model Predictive Control (MPC) emerged in process industry as a technology which simultaneously was able to provide optimal operation while offering a systematic way of handling constraints and solving the strong coupling between inputs and outputs. Essentially, a model predictive controller requires a reliable representation of the process (a model) to explore future scenarios plus an optimization algorithm to search over a given horizon the best possible applicable operation policy maximizing or minimizing a given objective function. Despite the success of this technology in process industry, a number of crucial issues related with the harmonious coordination of its different components (models, optimisers, observers etc) and efficient prediction models still remain (Cannon, 2004). In fact, the latter issue is particularly critical in DPS where descriptions are obtained from microscopic conservation laws for mass and energy balances, what results into highly coupled nonlinear sets of partial differential equations (PDEs). In this way, and despite some work done in MPC for distributed process systems (Chen, 2003 and

* Author/s to whom correspondence should be addressed: [email protected]

1334 Dufour, 2004), research efforts are needed to efficiently deal with the high dimensionality of the problem. In this paper, we take advantage of the dissipative nature of the process systems to obtain low order finite dimensional representations of the original set of PDEs, suitable for fast on line optimization. In particular, the Finite Element structure (FEM) is exploited to obtain ROMs of the systems based on the use of the Galerkin projection on a set of spectral eigenfunctions and proper orthogonal functions (PODs), already used by Bendersky and Christofides (2000) in optimal control, thus allowing the comparison of their predictive capabilities, simulation and re-calculation costs. This new methodology is evaluated in the control of a non-isothermal tubular reactor.

2. N o n l i n e a r M o d e l Predictive Control In general, the model predictive control problem is formulated so as to solve in real time a finite horizon open-loop optimal control problem subject to system dynamics and constraints involving states and controls.

2.1. Open loop optimal control problem. Mathematical formulation. The open loop optimal control problem can be formulated as the computation of time (and usually also spatial in DPS), varying control profiles in order to minimize a certain performance index:

J(v(t, ~), u(t, ~), t) - O(v(t f , ~)) + ~ L(v(t, ~), u(t, ~), t)dt

(1)

where L can arise from productivity, economical or ecological considerations. The objective function we will consider in this work fits into the standard MPC stability objective, of the form: L ( v , u ) : ( v - v ' ) r Q(v - v ' ) + (u - u ' ) r R(u - u ' ) (2) where v s and u s are setpoints, and Q and R positive definite symmetric weighting matrices. Equation (1) is subject to the system dynamics (PDEs) of the form:

(v(t, ~)), = g(v(t, ~)) + F ( v ( t , ~), u(t, ~:))

(3)

where ~(.) represents a linear parabolic operator defined on a given spatial domain D with smooth boundary. F(v(t, ~),u(t, ~)) is a nonlinear vector field depending on the state variables (v) and on the control variables (u). Initial and boundary conditions must be imposed on the system so as to guarantee that a unique solution exists. Other restrictions such as bounds for both the control variables and alternative process constraints (path, point and/or final time) can be included as well.

2.3. Solution approach: Control Vector Parameterization. The high dimensionality of DPS nonlinear systems makes the MPC problem particularly challenging. This issue was partially overcome, however, in the recent years by developments in efficient CVP methods adapted to distributed systems (Balsa-Canto et al. 2004a). The CVP approach transforms the original infinite dimensional problem in a nonlinear programming problem (NLP) by means of the discretization of the control variables into a number (p) of elements, and approximating the control values using low order polynomials (Vassiliadis, 1993).

1335 The solution of the resulting NLP problem can be obtained through standard, global or local, NLP solvers: local methods, although efficient, may converge to local solutions in the case of multimodal problems while global methods, although more robust, usually require large computational effort. In addition, it is worth mentioning that the evaluation of the objective function demands the solution of a set of PDEs (Eqn. 3) that the traditional techniques transform into a large scale set of ordinary differential equations (ODEs) unsuitable for MPC. Therefore ROM models described in section 3 arise as the alternative.

2.4. Feedback implementation in D PS. Real time implementation of the optimal control policy needs to consider the effect of unmeasured disturbances not being part of the prediction model. To that purpose, feedback is implemented by regularly measuring the current state of the process. In our case and to overcome the considerable computational delays in the optimization step, the following feed-back logic is proposed: First the open-loop optimal control problem is solved off" line and the result (1./,*) is applied to the real system. The measurement obtained at each sampling time t~ is fed to the ROM to estimate the initial conditions at t~+t,, (where t, is the computational delay). These conditions are the ones employed by the optimizer to compute the new control profile to be implemented in the real plant This profile will initialize the next optimization.

3. L o w order finite d i m e n s i o n a l r e p r e s e n t a t i o n The conventional approach (e.g. FEM and finite differences) to simulate DPS is based on spatial discretization schemes which approximate the original PDEs (Eq. 3) by a large set of algebraic equations and ODEs. However, the solution of the resulting system is computationally involved thus conditioning the efficiency of dynamic optimization algorithms. Alternatively, one can make use of the dissipative nature of DPS (Courant and Hilbert, 1937) to represent the solution as an infinite series expansion of the form:

v(t, g) - ~ c,(t)~, (~)

(4)

i--I

where each element of the set of basis functions {~o;(~)}~j is calculated as the solution of the following integral equation: ~R~,d~ - 2~o • Depending on the nature of the kernel R, two different methods are considered: 1.- Spectral decomposition where R is the Green function associated with the spatial operator and 2.- Proper orthogonal decomposition (POD) where R is a two point correlation matrix constructed form empirical data (Alonso el al., 2004). A key feature of dissipative systems is that any point of the system domain will evolve to a low dimensional hyperplane where it will remain (Alonso and Ydstie, 2001) what allows the extraction of a low dimensional dynamic manifold capturing the relevant dynamic behaviour of the system. In this way, the solution can be approximated as a truncated series expansion of the form:

1336 k

,(t, ~') ~ fi(t, ~') = ~ c, (t)(p, (~'). The projection of the original PDE, on the basis i=1

functions, results into the following set of ODEs" c, - A c +

f(c);

u - [(Pl ,-.-, (Pk ] c

(5)

where A and f(c) are the projections of the linear and nonlinear parts of the PDE system on the basis functions. In this work, a methodology which efficiently exploits the underlying algebraic FEM structure is used to implement the previous projections (Vilas et al., 2004). If the PDE is highly nonlinear, state transformations as those proposed by Balsa-Canto et. al. (2004b) would reduce the class of nonlinearities to polynomial type thus facilitating the projection. In addition, the number of decision variables can be drastically reduced by expanding the control in terms of the ROM basis functions, this being especially attractive in dealing with 2D or 3D problems. Finally, it must be noted that the although the selection of the basis function class is problem dependent, spectral projection methods are more systematic than PODs. In fact, POD's accuracy depends at a high extent on the number and quality of the experimental data used, what calls for recursive POD update algorithms to preserve prediction accuracy (Annaswamy et al., 2002).

4. Case study: Tubular Chemical Reactor The methodology proposed is applied to a nonlinear distributed chemical reactor which consists of two highly nonlinear coupled PDEs describing temperature (v2) and concentration (v~) (the detailed mathematical problem may be found in Padhy and Balakrishnan, 2003). The control variable u(t,~) is the cooling water temperature and it has been assumed that actuators and sensors are on the entire domain. 4.1. P r o c e s s s i m u l a t i o n . F E M vs ROM. FEM has been used to simulate the reactor dynamics (122 ODEs) and results obtained where compared with ROMs predictions. Figures 1 and 2 illustrate the comparisons between FEM and ROMs based on the spectral decomposition (8 ODEs) and PODs (8 ODEs), respectively. LSODE was used to solve the ODE systems. l 1.8 I.

/

1.6 .~1.4

~

i

u

V, E,IdiRes|mode) ! ~; v i ~eld (ROMmodel) !

!--,,i~ ~,,d ~,R,o=mo'~°'~ i

1.2

i ~, v.: f~Id (ROM model)

e) 1

V ~ n~e, ld (ROMmodel) v..,~ld (ReaJmodsl) vl f~Id (ROM model) !

l~ ~"~

~ ; 1.2 1

0.8

0

o,~

o.4 oo ~pace

olo

~i

Figure 1. Comparison between real and spectral basis models

o

o.2

o.4 ot~ ,~p=ce

~8

Figure 2. Comparison between real and POD models

From the figures it becomes clear that both low order models present good predictive

1337 capabilities. However, because the computational effort is larger for the POD model, spectral decomposition was the choice selected for the on line optimization. 4.1. NMPC implementation and results. The main objective, stated as in Eqns. (1)-(2), is to reach the reference (set point) trajectories for the state variables in an optimal way. The references used in this case (v~~; and v2~) correspond to the open-loop stationary state. Details on the reference states, weighting matrices in the objective function, reactor residence time, can be found in Padhy and Balakrishnan (2003). The control variable was approximated using 4 eigenfunctions, and each of the four time dependent coefficients was approximated using 15 steps along the residence time (large enough to maintain the close-loop stability). Thus resulting into a NLP problem with 60 decision variables. Regarding the NLP solver, several alternatives were evaluated: two global stochastic/hybrid methods and a collection of local methods where the SOLNP (SQP method, by Ye, 1989) was finally selected due to its ability to reach the optimal solutions with reasonable computational effort. The behaviour of the real plant is reproduced through FEM simulation on a second computer communicated with the MPC controller through data files. Each five minutes (30 minutes is the reactor residence time) new measurements are introduced in the optimizer (with a previously ROM simulation). Simultaneously, the new optimal control is implemented on the FEM simulation.

~

~!!!~'i~'~¸''~i¸'............... ~¸~

....

~:~,4 ~ ~ ~

Time

:~

~

Spruce

......

T{m~.

Figure 3. Concentration deviations with MPC

•............

i

,~i~¸ iii !~

........ iI

::

~

1

,~l::~c:e

Figure 4. Temperature deviations with MPC

......

~iiiiii i ! ii i! ~ !i i!~

i iiiiii!i

.....~::::.~:~ : ~ -

,

........~_. . . . . . . . . . . . . . . . . . . . . . 5

Time

i-"]

Space

Figure 5. Control with MPC

-

Ii

~,~ Time

::

~

Space

Figure 6. Temperature deviations without MPC

The performance of the open and closed loop plant under perturbations of temperature and concentration in the inlet stream is illustrated through Figures 3-6. As compared

1338 with Figure 6 (open loop response), the proposed real-time optimization scheme is able to efficiently reject disturbances and to enforce fast convergence of the reactor temperature and concentration to the desired set points.

5. Conclusions In this work, ROMs have been proposed as an alternative to standard discretization methods for the online dynamic optimization of DPS, without any linearization around the reference trajectory and, thus, allowing changes in the operations conditions. The methodology was evaluated for the control of a tubular chemical reactor, simulated using FEM approach. The control expansion combined with the CVP method, resulted in a nonlinear optimization problem efficiently solved with an SQP based optimizer (SOLNL).

Acknowledgements The authors acknowledge financial support received from the Spanish Government (MCyT Projects PPQ2001-3643) and Xunta de Galicia (PGIDIT02-PXIC40209PN).

References Alonso, A.A.. and B.E. Ydstie, 2001, Stabilization of distributed systems using irreversible thermodynamics. Automatica, 37, 1739. Alonso, A.A., C.E. Frouzakis and I.G. Kevrekidis, 2004, Optimal Sensor Placement for State Reconstruction of Distributed Process Systems. AIChE Journal, 50, 7. Annaswamy, A., J.J. Choi and D Sahoo, 2002, Active Close-loop Control of Supersonic Impinging Jet Flows Using POD models, Proceeding of the IEEE CDC, Las Vegas, NV. Balsa-Canto,E., J.R. Banga, A.A. Alonso and V.S. Vassiliadis, 2004a, Dynamic Optimization of Distributed Parameter Systems Using Second-Order Directional Derivatives. Industrial & Engineering Chemistry Research, 43, 6756. Balsa-Canto, E., A.A. Alonso and J.R. Banga, 2004b, Reduced-Order Models for Nonlinear Distributed Process Systems and Their Application in Dynamic Optimization. Industrial & Engineering Chemistry Research, 43, 3353. Bendersky, E. and P.D. Christofides, 2000, Optimization of transport-reaction processes using nonlinear model reduction. Chemical Engineering Science, 55, 4349. Cannon, M., 2004, Efficient nonlinear model predictive control algorithms. Annual Reviews in Control, In Press. Chen, W., D. J. Balance and P.J. Gawthrop, 2003, Optimal control of nonlinear systems: a predictive control approach. Automatica, 39, 633. Courant, R. and D. Hilbert, 1989, Methods of Mathematical Physics. Wiley, New York. Dufour, P., D.J. Michaud, Y. Your6 and P.S. Dhurjati, 2004, A partial differential equation model predictive control strategy: application to autoclave composite processing. Computers & Chemical Engineering, 28, 545. Padhy, R. and S.N. Balakrishnan, 2003, Proper orthogonal decomposition based optimal neurocontrol synthesis of a chemical reactor process using approximate dynamic programming, Neural Networks, 16, 719. Ye, Y, 1989, SOLNP users' guide. University of Iowa. Vassiliadis, V. S., 1993, Computational Solution of Dynamic Optimization Problems with General Differential-Algebraic Constraints. PhD, Imperial College, Londres. Vilas, C., M.R. Garcia, M.R. Femfindez, E. Balsa-Canto, J.R. Banga and A.A. Alonso, 2004, On Systematic Model Reduction Techniques for Dynamic Optimization and Robust Control of Distributed Process Systems.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1339

M o d e l B a s e d C o n t r o l of Solidification B. Furenes a and B. Lie a* aTelemark University College Department of Electrical Engineering, IT, and Cybernetics P.O. Box 203, N-3901 Porsgrunn, Norway

Abstract In this paper, model based control of solidification is studied. A one-dimensional model that describes the dynamic response of the solidification rate for a pure substance is developed. The solidification of a metal column is controlled in order to solidify at a desired rate. The manipulated variable is the power to the heater at the top of the casting. A linear PI-controller is implemented and yields acceptable performance for the simulated case. Keywords: Phase transition, solidification, numerical methods, model based control

1. Introduction Phase transition in processes is an area of great technological importance in many fields, such as materials science, geology, energy processes, environmental sciences, food processing, and cryobiology. The characteristic feature of these processes is the presence of time evolving unknown boundaries separating the phases. Consequently, they belong to the class of moving boundary problems. The prototype of such problems is the Stefan problem, named after the early work of J. Stefan, who studied the melting of the polar ice cap around 1890. In metal casting, two important characteristics that determine the quality of the finished material are the growth velocity and the local thermal conditions at the solidification front. Figure 1 shows an example of the morphology of the solid/liquid interface as a function of the growth velocity. At high growth velocities, the interface between the solid and liquid phase becomes dendritic. The dendritic morphology at the interface may cause heavy segregation of impurities between the dendrite arms during solidification (Kou 1996), and thus the concentration of impurities in the solidified metal may be dependent of the solidification velocity. Hence, it may be desirable to control the rate of solidification to a predefined value in order to make the solidified metal as pure as possible. In this work, a one-dimensional numerical model for controlling the solidification rate in a pure substance is developed. Solidification modeling is reported in numerous papers and books. Since the advent of computers, many studies have been carried out in

Author to whom correspondence should be addressed: [email protected]

1340 order to describe phenomena at meso- or microscale levels. Nevertheless, according to Zabaras (1999), little research has been carried out on solidification modeling for real time control purposes. Modeling for control purposes requires a simplified description of the complex processes, in order to achieve acceptable computation time. Yet, the model must be able to predict the behaviour of the system reasonably well. References to related previous work in the field of phase transition modeling will be given in the next section. Control of solidification processes is reported in Zabaras (1990) and Zabaras et al. (1988). In these works, the control problem is adressed as an inverse problem, and a perfect model is assumed. No corrections are made due to model error and disturbances. The presence of model and parameter uncertainties are taken into account in Franke et al. (1996) where strategies to minimize a deviation error is calculated online, and action is taken by the furnace control system. Inverse Stefan problems are reported in several papers and books. Detailed information about this subject is found in Gol'dman (1997). Other works treating the inverse Stefan problem are Hoffmann and Sprekels (1982), Sagues (1982), and Jochum (1980). This paper is organized as follows: First a brief overview of modeling strategies for two-phase transitions is presented. Then the case study process is described. After that, simulation and control of the solidification rate are discussed. Finally some conclusions are drawn.

,,~

a) l~..... 0~2 Bm/s

b) Iv ~ 1,0 gm/s

-~:~"

c) V = 3.0 pmls

d) V = 7.0 t~.m/s

Figure 1. Example of morphology of the solid~liquid interface at different growth velocities in a transparent organic system. Takenfrom Stefanescu (2002).

2. Modeling strategies for two-phase transitions Two different approaches are used in the modeling of phase transitions in a spatial domain. In the most common approach, a sharp interface between the phases is considered, defined by the phase change temperature. The total domain ~ of the substance is then divided into two separate subdomains (one for each phase), ~x and ~::~ in figure 2, and the heat and mass balance equations are formulated for each subdomain. This approach leads to one partial differential equation (PDE) for each subdomain (phase), with one boundary condition and one interface condition. The interface, or moving boundary, yields an ODE for the position of the interface. The one-dimensional classical Stefan problem is given by (Crank 1984):

1341 aT,. a2T, =a i c~t c~z2

(1)

for z c f2;(t), i= 1,2

where a~- k/(,od,) is the thermal diffusivity,

T is the temperature,

k

is thermal

conductivity, p is the density, and Of, is the specific heat capacity. At the interphase between the phases, the energy balance and Fourier's law of conduction yields

pAf[ r dh dt - q2 ...., _ q, : ,, - _k2 ( V ~ )+ k, (VT~ ) '

(2)

where A/~/ is the latent heat, and h is the position of the interface front. The boundary condition at the interface is"

r,(t,~ - h ) - r~(t,z - h ) - ~h, where Tch is the phase-change temperature.

Z

Heating

A

= ~1

(t)

U ~2(t)

Phase 2

f~2 (t) t/

.........

h(t) = af21 (t) A c3~2(t)

n~ (t) Phase 1 !

.... Cooling

Figure 2. Simploqed sketch o f the two-phase transition problem, v=dh/dt is the interface velocity and n is the normal vector o f the interface. In the two-domain approach, the domain is divided into two subdomains (phase 1 and 2), and the balance equations are formulated on each subdomain. In the one-domain approach, the balance equations are formulated on the whole o f the domain.

Numerical methods for solution of the sharp interface approach are e.g. the level set method, fixed grid, and variable grid methods. The level set method is implemented for solidification processes in Gibou et al. (2003), whereas the method in general is described in Osher and Fedkiw (2003). Front tracking and front fixing methods are described thoroughly in Crank (1984). in the second approach, the domain is considered as a whole, f2 in figure 2. The balance equations are then formulated on the whole of the domain; thus one PDE with

1342 two boundary conditions are valid for the whole domain (total volume). In this approach, the phase interface position must be calculated from the solution of the PDE. Some methods mentioned in the review of Hu and Argyropoulos (1996) are the methods of latent-heat evolution, the apparent heat capacity methods, the effective capasity method, and the enthalpy method.

3. The solidification model We consider a metal column of height L, originally in liquid form. The metal column is assumed to be fully insulated on the vertical surface. The enthalpy method is employed. In the enthalpy method, equations (1) and (2) reduce to the single equation •2T P~/40t = k~.~2

(3)

where H is specific enthalpy, and it is assumed that k and 9 are independent of the temperature. The temperature and enthalpy are related by the function

Jq(r) = ~

4;(T- V~k),

Le '~( r -

rc ~ ) + ~ q :

r < rc~ r > Tc ~

(4)

and the temperature is found from the enthalpy found by inverting equation enthalpysemperature. The model is discretized in space (fixed and uniform grid) by the method of lines, yielding a system of ODEs. The discretized system is implemented in MATLAB (2004). A drawback of the enthalpy method is that the temperature and phase boundary dynamics become oscillatory, especially for isothermal phase changes. This is because the phase front is represented by a control volume rather than a surface (Chun and Park 2000). Works employing the enthalpy methods are found in Voller and Cross (1981) and Voller et al. (1990). In these works, the front position is located by introducing a variable called local solid fraction, which locates the discretizing element containing the front position. Voller and Cross (1983) assumed that the fraction of solid may be linearly interpolated during latent heat release for the discretizing element containing the phase front. The amplitude of the oscillations in the phase front was reduced, but the fluctuations in the temperature were not influenced. Tacke (1985) suggested an improved discretization of the enthalpy method to obtain an oscillation-free solution. In that method, however, equal material properties for both phases are assumed. In this work, the method of is extended to be valid for materials having different material properties in the two phases. This is done by using the mixture theory (Stefanescu 2002) for the grid cell containing the phase front

k =Lk, + (1 -L)k~, where k is the conductivity, fs is the value of the improved estimate of the fraction of solid calculated by Tacke's method. The online estimate of the position is h(t) = ( i - 1)Az + LAz,

(S)

where i is the index of the grid cell containing the phase front, and Az is the grid size.

1343

4. S i m u l a t i o n

and control

of the solidification

rate

We now write the model as x - f(x,u)

a n d f' - g ( x , u ) ,

where the states are the enthalpies in the grid cells ...

-

and .j? - g ( x , u ) -

(x,

...

h(t)

is the estimate in equation (5).

The manipulated value is heating at the top of the casting (assuming constant cooling conditions): u -

QL - u ~ .

if we want to control the velocity, the position must track a ramp. in continuous processes, an integrator is included in the controller to achieve zero error at steady state. Even though the solidification process is a batch-process, and hence never reaches steady state, it may be advantageous to include an integrator in order to decrease the controller deviation as the time elapses. The linear PI controller is given by tfi -

Kee

where

+ Ktcr

,

e- S.:r- 2 ,

s,.~j.(t)

v,.el, t

-

and c r -

fedt

The result of the closed loop

.

simulation is shown in figure 3. From the figure, the system appears to track the reference well. Interface

Position

Temperature

100

Distribution

A

,

..... / / , I , ,~,

¢'

,

1.1---,~:~:- . . . . . ;- . . . . . . . . . .

! ..........

i ..........

: .........

..~, ._ o

•"G

40

ca

20

.................

-

,~-.s-

:.

.

.

.

00

i 0.'2

'

0.'4

i

0.6

018

6O

";i """'%

o8 • 0

1

:,

0.2

Position Deviation

E

3k~ 'i 2

-:'~'::-"'~i

-~ 0.9 ........... '.~.......... :;->-,~.z:-:; -'I:::, ..........

.

..f

:,

0.4

Manipulated

:,

0.6

"

"%-0.8 ............ .............. !1

Variable

0.8

:

:

i

. . . .

\ / ........ "7":>->_~. ......... :........... :. . . . . . .

~

]

0.6

0.4

g

i ,

0.2

,

~

I

i

.1

,

0

0.2

0.4

0.6

Scaled Time [-]

0.8

1

0.2

0.4 0.6 Scaled Time [-]

0.8

Fi~m'e 3. Control of the solidi ficatiot7 ratejbr u constant reference.

1344

5. Conclusions The intention of this paper is to develop a fast and simple mechanistic model for the position of the solidification interface. The model is simplified to make it suitable for control purposes, and is used to develop a linear PI-controller in order to control the solidification velocity. For the cases simulated above, the position tracks the reference well. It may be possible to extend the model and control strategy to a gas-liquid transition. Further research will include validation with experimental plant data and comparison with other modeling methods (e.g. the level set method). References

Chun, C.K and Park, S.O., 2000, A Fixed-Grid Finite-Difference Method for Phase-Change Problems, Numerical Heat Transfer Part B 38, 59. Crank, J., 1984, Free and Moving Boundary Problems, Oxford University Press, Walton Street, Oxford OX2 6DP. Franke, D., Steinbach, I., Krumbe, W., Liebermann, J. and Koch, W., 1996, Concept for an Online Material Quality Control by Numerical Simulation of a Silicon Ingot Solidification Process, Proc. 25th IEEE Photovoltaic Specialist Conference, 545. Gibou, F., Fedkiw, R., Caflisch, R. and Osher, S., 2003, A Level Set Approach for the Numerical Simulation of Dendritic Growth, Journal of Scientific Computing 19, 183. Gol'dman, N.L., 1997, Inverse Stefan Problems, Kluwer Academic Publishers, P.O. Box 3300 AA Dordrecht, The Netherlands. Hoffmann, K.H. and Sprekels, J., 1982, Real-Time Control of the Free Boundary in a Two-Phase Stefan Problem, Numerical Functional Analysis and Optimization 5, 47. Hu, H. and Argyropoulos, S.A., 1996, Mathematical modelling of solidification and melting: A review, Modelling Simul. Mater. Sci. Eng. 4, 371. Kou, S., 1996, Transport Phenomena and Materials Processing, John wiley and Sons, Inc. MATLAB, 2004, MATLAB 7, The MathWorks Inc., Natick, MA, USA. Osher, S. and Fedkiw, R., 2003, Level Set Methods and Dynamic Implicit Surfaces, SpringerVerlag New York. Sagues, C., 1982, Simulation and Optimal Control of Free-Boundary Problems, in Workshop on Numerical Treatment on Free Boundary Value Problems 58 Birkhauser, 270. Stefanescu, D.M., 2002, Science and Engineering of Casting Solidification, Kluwer Academic/Plenum Publishers, 233 Spring Street New York NY 10013. Tacke, K.H., 1985, Discretization of the explicit enthalpy method for planar phase change, Int. J. Numer. Meth. Eng. 21,543. Voller, V. and Cross, M., 1981, Accurate Solutions of Moving Boundary Problems Using the Enthalpy Method, Int. J. Heat. Mass Transfer 24, 545. Voller, V. and Cross, M., 1983, An explicit numerical method to track a moving phase front, Int. J. Heat. Mass Transfer 26, 147. Voller, V.R., Swaminatham, C.R. and Thomas, B.G., 1990, Fixed Grid Techniques for Phase Change Problems: A Review, Int. J. Num. Meth. Eng. 30, 875. Zabaras, N., 1990, Inverse Finite Element Techniques for the Analysis of Solidification Processes, Int. J. Num. Meth. Eng. 29, 1569. Zabaras, N., 1999, Inverse Techniques for the Design and Control of Solidification and Forming Processes, Proceedings of the Integration of Material, Process and Product Design, 249. Zabaras, N., Mukherjee, S., and Richmond, O., 1988, An Analysis of Inverse Heat Transfer Problems with Phase Changes Using an Integral Method, Journal of Heat Transfer 110, 554.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1345

h-Techsight: a Knowledge Management Platform for Technology Intensive Industries •

a*

A. Kokossls , R. Bafiares-Alcfintara b, L. Jimdnez c and P. Linke a aDepartment of Chemical and Process Engineering, University of Surrey Guildford, Surrey GU2 7XH, UK bDepartment of Engineering Science, Oxford University Parks Roads, Oxford OX1 3PJ, UK CDepartment of Chemical Engineering and Metallurgy, University of Barcelona Marti i Franqubs 1, Barcelona 08028, Spain

Abstract In knowledge-intensive industries it is of crucial importance to keep an up-to-date knowledge map of their domain in order to take the most appropriate strategic decisions. The main objective of the knowledge management platform (KMP) is to improve the capabilities of chemical process industries to monitor, predict and respond to technological trends and changes. The search, retrieval, analysis, filtering, rating and presentation of information retrieved from the web (or any other type of document) are elucidated through the use of multi-agent systems, dynamic ontologies and learning techniques (conceptually similar documents are clustered and natural language processing techniques are used to retrieve new terms). Discovery of new knowledge leads to recommendations of modifications in the ontology (either classes or instances) by pruning irrelevant sections, refining its granularity and/or testing its consistency. The KMP works using an intelligent, asynchronous and concurrent process to achieve high quality results.

Keywords: knowledge management; knowledge retrieval; web search; ontology. 1. Introduction Decision making in technology intensive industries has to be made based on information that is constantly evolving. New technologies, markets and products emerge and change, and relevant information can be found only if one knows exactly where to look for it. Unfortunately, the amount of information and the various ways in which it can be presented, makes the retrieval of useful information an increasing more difficult and work intensive task. A KMP to monitor, predict and respond to technological, product and market trends has been developed (h-Techsight, 2001; Stollberg et al., 2001), which innovative points are:

Author/s to whom correspondence should be addressed: [email protected]

1346

•

h-TechSight performs the search based on an initial ontology supplied by the user. An ontology is a conceptualisation of a domain. Ontology-based search is more accurate and complete than traditional keyword-based search (Fensel, 2001). • h-TechSight has the capability to suggest desirable modifications to the initial ontology based on the information retrieved (in the web or the databases). We refer to this capability as dynamic ontologies because it provides a mechanism to update the understanding of a domain with the available, ever-evolving, information. h-TechSight KMP can operate in two different modes: as a generic search or as an application search tool. In the generic search mode the system uses the whole web (or a selected domain in the web) as an information source. Search is performed by a multiagent system and the links retrieved are analysed using text analysis techniques and clustered into new categories. In the application search mode the system searches in domains where the information, while unstructured can be found in documents of similar patterns The smaller number of records and their similar format permit the application of powerful analysis tools (GATE and WebQL). 2. G e n e r i c Search M o d e The generic search mode architecture (Figure 1) is based in four different modules: the ontology editor, the multi-agent search system, the clustering search system and the dynamic ontology update.

2.1. Ontology editor Under the generic search mode, a ontology editor has been integrated in the KMP to facilitate the creation, customisation, browsing and modification of ontologies. Each user of the KMP has a personalised area in which his/her ontologies are stored, thus versions of the same ontology are stored to further analyse their dynamics. Uploading and downloading of ontologies are always performed in RDF format.

2.2. Multi-agent search system This module receives as an input the ontology and uses search engines to perform semantic based search, according to a predefined set of searching parameters. In this way, the Multi Agent Search System (MASH) finds web pages that contain relevant information to each concept in the domain of interest (described by the class path, as each class inherits all instances defined in their ancestors). The retrieval, rating and filtering processes are performed asynchronously, concurrently and in a distributed fashion by the agents with different roles. MASH is described in detail elsewhere (Banares-Alcfintara et al., 2005).

2.3. Clustering search module It is used to perform analysis on the results received from the MASH to propose new categories. For each URL provided by the MASH system, this module finds the URLs that point to it. Let A, B and C be three incoming links of URL D (Figure 2). The module extracts keywords from the incoming links, processes their contents and extracts terms from their hyperlinks to D. Each set of terms that corresponds to a URL D is mapped to a set of concepts of the ontology. WordNet (Wordnet, 2004), an online lexical reference system, in which English nouns, verbs, adjectives and adverbs are

1347

organised into synonym sets, is used for this purpose, and thus, the system is able to process html, pdf, doc or xls documents. The procedure is as follows: • For each term (t~) in the set, a clustering mechanism finds the closest ontology concept (c,i) in WordNet. • Extracted terms are mapped to WordNet (t) is mapped to nodes t~,~, t~,2 and t~,3). • Ontology concepts are mapped to WordNet (c~ is mapped to nodes c~.~ and c~.2). • The distance between every node of t~ and c~ is computed using the Wu and Palmer distance (1994). • The closest pair of nodes (t~,x,c~.>,) defines the distance between term t~ and concept C1.

After this process, each URL is described by a set of terms and a set of ontology concepts. Clustering is performed using the set of concepts of each URL using the D B S C A N (Density Based Spatial Clustering of Applications with Noise) and a similarity measure between URLs (Ester et al, 1996). • For each document D of a cluster the neighbourhood of D has to contain at least a minimum number of documents (MinDoc).

I

~

!

On~otogy e d i t o F (Java iippiet)

f

<.....i::i....

/

f ~

~1

i

.......::::t:n~.erne~ search e~gi~w~-;......... ~:i ......... ((;ooete, A.RaVis~a) ......

<,earct~ system

i v<e.~>s~Trrice>

%,,,

¢

J

-~i

°(

K M P data~ase ::

~Set Vie~ )

recommel~da~ions

J

addi~io~Jdele~iof~

Figm'e 1. Generic search mode architecture. / J ...............\

t2, t 3

~

t3. t4

(

)

Figure 2. (a ) URL relationships, (h) where A, B, C and D are URLs, ti and ti,i are terms and ci and ci,/ are concepts.

:.:

1348 • • •

The neighbours of D are defined to be all the documents whose similarity to D is higher than, or equal to, a minimum similarity threshold (MinSim). DBSCAN is able to detect clusters with strange geometries. The number of clusters is not predefined. The algorithm is repeated for different values of MinDoc and MinSim and the scheme that provides the most compact and discrete clusters is selected.2.4.

Dynamic ontology update Based on the clustering results, the user has the ability to extend/modify the ontology with the newly discovered keywords. In both search modes the systems presents a table to the user where she/he can choose which items should be added to the ontology, and if the recommendation is to add the new terms as new classes or as instances of existing classes. Each time the user saves an ontology, a new version is created and stored in the database. Therefore, a user is able to return to a previous version of the ontology at any point in time. The versioning mechanism allows the user to keep track of the modifications applied to an ontology (as stated in section 2.1).

2.5. Scheduler mechanism The scheduling sub-system of the KMP gives the ability to the users to schedule both search modes of the platform and view the results at a later stage. The scheduled searches are fully configurable (e. g. search parameters of the MASH/Toolbox). This facility opens up the possibility to apply the KMP functionalities not only to snapshots of the web but as it evolves in time.

3. Application Search Mode In the application model the user defines a set of URL sites or database of documents that contain relevant information. The user may wish to automatically extract information, classify documents according to the ontology, assess the "dynamics" of the domain (e.g. site), and monitor changes. The application search mode is illustrated in Figure 3. A number of dedicated Natural Language Processing (NLP) tools are employed. 3.1. GATE GATE is an architecture for NLP, that enables an automatic semantic annotation of web mined documents using the terms of the ontology (entities or relationships). The KMP uses GATE to support the evolution of instances. The findings are stored to perform statistical analysis in order to monitor trends over time. GATE is described in detail elsewhere (Maynard et al., 2004). 3.2. Toolbox This module applyes NLP techniques to assess and validate ontologies. The latter are usually developed in an ad-hoc fashion or are recycled without a prior assessment for relevance and quality. Modules in the toolbox can be applied to enhance ontology relationships, discover new terms, and adjust ontology components according to the application context.

1349

| I

"-. N \ \

I

~i! .....~........... *N~a~bti~°~ ............... ....................... ~::}-~-

\

%.....

\

:;~ta~vgis

.i<~.,~i,:-,..,:-

::::::~'*

S,.."}'c-h.~{i ~5.

%

\ l

\

\'~

Too|box

:~i:

+ '!<%%:~dem{~ f .i.................... b s ,:,'¢: /:

•............;b,.:~:,:~i ....

Web servh'e

~

--{

(Web

{

T

~ <:,...{~ i { -:

f.

i

service}

.,,.:.~,~,.......( ...........................................i....................

.#:............... #............................................ ..~:~............. .,% .....

......( R e h~ ~i{m s 5 et wee~:?%..

Figure 3. Application search mode description. 3.3. WebQL WebQL (WebQL, 2005) is a commercial web mining tool used to collect unstructured data and prepare them for analysis. WebQL has been selected out of several packages. 3.4. Contextual ontologies Contextual ontologies are developed "on-the-fly" out of an ontology superset and a knowledge domain of preference. Contextual ontologies are descendants of the parent ontologies and combine concepts, relationships and properties of each parent. A contextual ontology in "Patenting catalysts" can be thus developed out of a "Chemical Engineering" ontology, a "Materials" ontology, and a "Patent Office" ontology.

4. Knowledge Management Platforms Developed A number of case studies have been developed in diverse areas (e.g. technologies, employment, health services), as shown in Kokossis and Bafiares-Alcantara (2003). These include process engineering applications (mostly with h-TechSight partners), chemical engineering employment applications (in collaboration with IChemE), and biomedical applications (in collaboration with the Parkinson's Disease Society).

4.1. Employment markets The KMP prototype was used to create a portal for employment markets, as this tool is useful to help individuals or organisations to monitor trends in demands for a particular areas of expertise to enable a systematic continuing professional development. The portal (http : / / p r i s e - s e r v . cpe. surrey, ac. u k / h T e c h S i g h t / )

aims to

support engineers with a wish to understand the job market and search for a job, companies and SMEs to subcontract/undertake projects, academic institutions preparing students for the job market, and professional institutions. The dynamic change identified in employment markets is continuously incorporated in revised ontology versions that reflect up-to-date knowledge in the field.

1350

4.2. Parkinson portal The portal makes use of an extensive knowledge model for Parkinson's Disease. The model is an extensive ontology modelled in DAML+OIL and developed at the University of Surrey with the collaboration of medical doctors, practitioners, communities and local hospitals. The portal site can be found in h t t p : / / p r i s e s e r v . c p e . s u r r e y , ac. uk: 8 0 8 0 / .

5. C o n c l u s i o n s This paper describes the results obtained with the prototype of the KMP. The main objective of the platform is to improve the capabilities of chemical process industries to monitor, predict and respond to technological, product and market trends and changes. The analysis, modification and presentation of information retrieved from the web (or any other type of resource) are achieved through the use of multi-agent systems, data mining, natural language processing and clustering analysis. Ontologies are used to specify and represent the knowledge, and the KMP proposes a set of terms to be introduced as new classes or as instances of existing classes. Preliminary user evaluation and feedback (IChemE and Bayer AG) are positive, but more improvements are needed to improve the usability of some aspects, to clarify terminology and to remove false positives.

References Bafiares-Alcfintara, R., L. Jim6nez and A. Aldea, 2005, Multi-Agent Systems for Ontology-Based Information Retrieval, European Symposium on Computer Aided Process Engineering , Barcelona, Spain. Ester, M., H.-P. Kriegel, J. Sander and X., 1996, A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise, 2nd International Conference on Knowledge Discovery and Data Mining (KDD-96). Fensel, D., 2001, Ontologies: A Silver Bullet for Knowledge Management and Electronic Commerce, Heidelberg, Germany. h-TechSight, 2001, IST Project (IST-2001-33174). Available at http://priseserv.cpe.surrey.ac.uk/techsight (Access: January 2005). Kokossis, A. and R. Bafiares-Alcantara, 2003, Dynamic Information Management for Webenabled Environments in the Chemical Process Industries, FOCAPO, USA. Maynard, D., M. Yankova, N. Aswani and H. Cunningham, 2004, Automatic Creation and Monitoring of Semantic Metadata in a Dynamic Knowledge Portal, 1l th Int. Conf. on AI Methodology, Systems, Applications-Semantic Web Challenges. Stollberg, M., A. Zhdanova and D. Fensel, 2001, H-TechSight: a Next Generation Knowledge Management Platform, J. Inf. and Knowledge Manag., 3 (1): 47-66, 2004. WebQL, 2005, Available at http://www.ig.com.au/WebQL.htm (accessed January 2005). Wu, Z. and M. Palmer, 1994, Verb Semantics and Lexical Selection. 32nd Annual Meeting of the Associations for Computational Linguistics, 133-138, Las Cruces, New Mexico. http://citeseer.ist.psu.edu/wu94verb.html (accessed January 2005). WordNet, A Lexical Database for the English Language. Available at http://www.cogsci.princeton.edu/-wn/(accessed January 2005).

Acknowledgements

h-TechSight is a Framework

V EU funded project (IST-2001-33174).

European Symposium on Computer Aided Process Engineering- 15 !,. Puigianer and A. Espufia (Editors) C>2005 Elsevier B.V. All rights reserved.

1351

Modelling for Control of Industrial Fermentation Jan Kamyno Rasmussen ~, Henrik Madsen b and Sten Bay Jorgensen ~ ~CAPEC, Department of Chemical engineering, Technical University of Denmark, Building 229, DK-2800 Lyngby, Denmark blnfbrmatics and Mathematical Modelling, Technical University of Denmark, Building 321, DK-2800 Lyngby, Denmark

Abstract This paper presents application of a grey-box stochastic modelling framework for developing continuous time models for dynamic systems based on experimental data. The framework will be used to develop predictive models suited for control purposes. The main idea behind the framework is to combine stochastic modelling with data to obtain information on parameter values and model (in-)validity. In case the initial model is falsified the method can point out specific deficiencies which facilitates further model development. The industrial fermentation case is production of an amylase enzyme by a filamentous fungus.

Keywords: Parameter estimation, industrial fermentation, modelling for control, greybox modelling 1. Introduction Fed-batch processes play a very important role in chemical and biochemical industry. Fermentations are widely used in biochemical industry and are most often carried out as ted-batch processes. Present control schemes do not utilise the full potential of the production facilities and may often fail to achieve uniform product quality and optimal productivity. Application of advanced multivariable control schemes can help solve this problem. The introduction of model based control strategies is considered difficult because suitable models are not readily available and require a significant investment in experimental work tbr their development. First principles engineering models can be used in the controller assuming that they possess satisfactory predictive capabilities. Parameter estimation in a first principles engineering model can be very time consuming and can cause problems when scaling up from laboratory to industrial fermentors. Especially parameters for mass and heat transfer models may change when the volume of the fermentor is changed. These phenomena can not be investigated in laboratory scale equipment which therefore makes large scale experiments necessary. The approach taken in this paper is to combine first principle engineering models with operational data to produce predictive models suited for control purposes. The method described in this paper is grey-box stochastic modelling which consists of a set of stochastic differential equations describing the dynamics of the system in continuous

1352 time and a set of discrete time measurements. An important advantage using this approach compared to using ordinary differential equations type model is that they can account for random variations in data. A framework for this kind of model development has already been developed (Kristensen et al., 2004) and is described in figure 1.

LNonparamet modeling ~~ric Firstprinmodel cipless

engineering

Stati testsstical II

IU/~dr'at~I nen

(re)'oM°du//tioJ\~ /-~~Ex t(? I ara eter J estimation ~

/-~~ ~u nM~sde2 ~ Yes,St°phaS tiCodlale

esidua, I a n a l y s i s ~

Figure 1. Grey-box modelling cycle. One of the key ideas behind the grey-box stochastic modelling framework is to use all prior information for formulation of an initial first principles engineering model. Unknown parameters of the initial model are then estimated from experimental data and a residual analysis is carried out to evaluate the quality of the resulting model. The next step in the modelling cycle is the model falsification or unfalsification which determines if the model is sufficiently accurate to serve its intended purpose. If the model is unfalsified the model development is completed. In case of falsification the modelling cycle must repeated by reformulating the initial model. In this case statistical tests can be used to provide indications of which parts of the model that are deficient. Nonparametric modelling can be applied to estimate which functional relationships are needed to improve the model.

2. Process description The process studied is fermentation of the filamentous fungi Aspergillus oryzae for production of the enzyme amylase. The fermentation is initiated by transferring the contents of a seed tank to the main fermentation tank when a certain transfer criterion has been satisfied. The main fermentation tank contains an initial amount of substrate and the main fermentation process starts immediately after inoculation. The main fermentation is carried out in a batch and fedbatch phase. When the initial substrate has been consumed by the microorganisms the fedbatch phase is initiated. Feed dosing is started at a low level and increased to its final value within a certain time span. The fedbatch phase continues for the rest of the fermentation process. The fermentors are equipped with sensors for online measurements of different variables but some values are only available as offline measurements which makes closed loop control more difficult and requires a more accurate model for predicting the variable values.

1353 The first principles engineering model to be studied here is proposed by Agger et al .(Agger et al., 1998). The model is based on the assumption that the total filamentous biomass can be divided into three distinct regions: • Active region (Xa): Responsible for uptake of substrate and growth of the hyphal element, a-Amylase synthesis occurs in this region. • Extension zone (xe): Building of new cell wall. • Hyphal region (Xh): Contains the degenerated part of the hyphal elements and can be considered as an inactive region. The original model contains 5 states, (The 3 morphological states, substrate concentration (s) and product concentration (p)). During the development of the model Agger et al. has assumed that no oxygen limitation is present. In order to be able to model the behaviour at low dissolved oxygen values and relate the morphological states to off-gas measurements the model has been extended (see Zangirolami, 1998). The oxygen concentration has been introduced as an extra state and as the volume is changing this constitutes an additional state of the system. The formation rate of the three regions is given in equation (1)-(3). C

= q~ - Dx~

(1)

dt (_/

dt ~h

- -

&

= q3 -

q~ -

=

Dx/,

q2

-

q2

-

(2)

Dx

(3)

Substrate, product and oxygen concentration are described by (4)-(6)

dt-

--

dt

q 3 + r , , , - - x +m (xc+x +%) +D s / , - s gv, tl

=

5,x

dco

Dp

(.1

,

(4)

(5)

(6)

dt D -

-

,~'

F

(7)

V The three kinetic expressions are given in equation (8) and (9). It is assumed that the concentration of hyphal elements is above the critical value at all times, meaning that only the second inequality in (8) needs to be considered.

1354

0;

a < Cn

qlk~s

.x

0

>Ix)

,)' q2 -

k2x~ ;

q3 =

(8)

o

k3s

x / c,

axa

S + Ks3 xa / c,, + K 3

Co: ko~ + C~

(9)

In order to account for the decrease of growth rate for the active region under oxygen limiting conditions the last Monod term in equation (9) has been introduced. The specific growth rate and rate of product formation and carbon dioxide and rate of uptake of oxygen is given in equations (9)-(11). ¢t -

q3

(10)

xe + x a + x h kpls

ps

(s+/£,4 )(1+ exp (kp2 (s--S,.ep )))

FC02 ~ Yxc

kl - Y~c

q3 + m~ X e -t-X a nt-x h

;

+k~

ro2 _ Y °

(11)

q3 +m o X e nt-x a -Jr'Xh

(12)

kbran "104

(13)

4 (d. 10-4)2 (1- w ) f p ~-(d. 10- 4 )2 (1- w ) f p

k 3 - ktip,ma x • 10 -4 ~

d - 11.25./~+1.1

;

1

(14)

0_ 4

4~ (l_w)p

(15)

The relations to the off-gas measurements are given in (16). OgR-ro2

(Xe nLXa nt-Xh) ; C E R - r c o

2 (Xe nt-Xa nt-Xh) ; D O T - - -

Zt,

C 02

For more intbrmation on the details of the model please refer to Agger et al., 1998.

(16)

1355

3. Simulation Simulations have been performed to compare the predictions of the model with actual data from an industrial fermentation. The industrial data has been supplied by Novozymes A/S. The parameters for the simulation are provided in table 1. The only input used in the simulation is the feed profile (figure 2) which has been applied to one of the batches from the industrial data set. The figures in the following show characteristic results obtained in the simulation and experiments.

Table 1. Parameters used for the model simulation.

Parameter kbran Ktip...... ke K~I K~3 ins P W f Ysp k~ kpj kp2 Srcp Ks4 Vxc Vxo mc 1110 kLa ko2

Value 1.7"104 49 0.08 3"10 4 6" 10-3 0.01 0.57 1

0.67 0.8 5316 8 32 5000 9.5* 104 6,10 -4 0.01786 0.01563 6.3"10 .5 5.6* 10.7 79 2.25,104

Unit Tip*~am-J*h-1 gin*tip -1. h-I h-I g*L -1 g* L-1 g glucose*g DW-l*h -1 g active DW*g glucose -I kg/L g/g DW FAU*g glucose -1 FAU*g active DW*h -~ FAU*g active DW*h -1 L*g-~ g*L -1 g,L -1 tool CO:*g DW -1 tool O2*g DW -I tool CO2*g DW-l*h -1 mol O2*g DW-l*h -x h-1 mol*L -l

Source Agger et al. Agger et al. Agger et al. Agger et al. Agger et al. Agger et al. Agger et al. Agger et al. Agger et al Agger et al Agger et al Agger et al Agger et al Agger et al Agger et al Agger et al Carlsen et al. Carlsen et al. Carlsen et al. Carlsen et al. Zangirolami Fitted

Figure 3 shows that to some extent the model is able to predict the behaviour of the OUR. During the batch phase the OUR predicted by the model is somewhat lower than actually measured. As the feed dosing is initiated at t=25h a large drop in OUR occurs which is captured by the model. The prediction for the fed-batch phase is somewhat higher than the experimentally observed. Figure 4 shows the evolution of the biomass concentrations with time. It is seen that the concentration of active region and extension zone decreases during the fermentation and the concentration of the hyphal region increases. This behaviour can be explained by the decrease in substrate and oxygen availability occurring after the batch phase. The low concentrations decrease q3 (eq. 9) which reduces the rate of formation of active cells.

1356

0[

0.045[

0,o4[ fi

0.03[ i ii

~ ,150

6O

:.,

',.,.

....

".....,:

iJ

f t..,.( k;"

-i

0'02 t ,i

~100

O 0015~/i

--

101[/i

30

100 Time, h

150

Figure 2:Feedfiow rate used in the simulation.

200

o!

I

_

//

/

I .................

4o

x "1000 I i

:i I

/"

Total

I /;

5'o

....

Simulated

0.005t! 50

-

Time, h

4o

Figure 3:Oxygen Uptake Rate (OUR). Simulated values (dashed line). Experimental values (Continuous line).

0

................................

140 Time, h

150

Figure 4:Extension zone*1000 (dotted line).Active region (dash dotted line). Hyphal region (dashed line). Total biomass (continuous line).

4. Discussion The morphologically structured model presented is able to predict a large part of the behaviour of the industrial fermentation. The model has been developed in laboratory scale equipment where no oxygen limitation has occurred in the experiments. In order to be able to simulate an industrial scale fermentor some of the model parameters need to be reestimated and new functional relationships have to be introduced. It has been shown that the morphology changes drastically under oxygen limitation (Zangirolami, 1998). This runaway phenomenon will also be modelled. During low dissolved oxygen concentration the filamentous fungus changes its filaments which increases viscosity and impairs oxygen transfer. Hence the oxygen concentration becomes even lower. Parameter (re-) estimation and investigation of new functional relationships in the model based on experimental data are carried out in the software program CTSM (Continuous Time Stochastic Modelling) (Kristensen et al., 2004). CTSM provides a graphical user interface which allows the user to specify how the model parameter should be estimated. After specifying which experimental data sets to use, the program determines the parameter estimates and evaluates statistical tests.

References Agger,T., A. B. Spohr, M. Carlsen and J. Nielsen, 1998, Growth and Product Formation of Aspergillus oryzae during Submerged Cultivations: Verification of a Morphologically Structured Model Using Fluorescent Probes, Biotechnol. Bioeng., 57, 321-329. Carlsen, M., Nielsen, J., Villadsen, J., 1996, Growth and Gt-amylase production of by Aspergillus oryzae during continuous cultivations., J. Biotechnol., 45, 81-93. Kristensen, N. R., H. Madsen and S.B. Jorgensen, 2004, A Method for Systematic Improvement of Stochastic Grey-Box Models, Comp. & Chem. Eng., 28/8, 1431-1449 Zangirolami, T. C., 1998 Modeling of Growth and Products Formation in Submerged Cultures of Filamentous Fungi, Ph.D. thesis, Technical University of Denmark, Denmark.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1357

System-Dynamics modelling to improve complex inventory management in a batch-wise plant Zofia Verwater-Lukszo and Tri Susilowati Christina Delft University of Technology, Faculty of Technology, Policy and Management 2600 GA Delft, the Netherlands

Abstract The process industry has to cope with a rigorous competition caused by more short-term dynamics in supply, more unpredictable and turbulent demand patterns, stronger requirements on product variety, delivery lead-time and quality of product. It forces company to spend efforts at improving its competitiveness and productivity. Appropriate strategies or action in the area of inventory management can contribute to survive in these conditions. This paper describes a novel modelling approach aimed at improving complex inventory management of many product grades in a multi-product batch-wise industrial plant. The simulation model of the internal supply-chain addressing the order acceptance and processing constraints- the cornerstone of the proposed approach - is developed according the System Dynamics methodology. The proposed model implemented in a decision support tool assists the decision maker(s) by providing a systematic structure to arrive at potential improvement options for inventory management. The approach is applied in a chemical lnulti-product plant producing a number of grades of resins with different priorities.

Keywords: System Dynamics, internal supply chain, decision support 1. Introduction Inventory holds a crucial but double-sided role in a manufacturing plant. In "rough" situations such as when a plant cannot produce at the desired rate or in moments where suppliers are not reliable, inventory is seen as a saviour, as a survival tool. However, mostly, when everything goes smoothly, inventory is seen as a waste of money, a standing still investment that yields nothing. Inventory management is necessary to create a balance between these two sides. How to manage the inventory to find the right trade-off between both objectives is the basic question addressed in Christina (2004). Inventory decisions are high-risk and high-impact from the perspective of operations. Commitments on inventory and subsequent shipment to a market in anticipation of future sales determine a number of logistics activities. Without the proper inventory, marketing may find that sales are lost and customer satisfaction will decline. Likewise, inventory planning is critical to manufacturing. Raw material shortages can shut down a manufacturing line, which, in turn, introduces goods shortages. Just as shortages can

1358 disrupt planned manufacturing operations, overstocked inventories also create problems. Overstocks increase cost and reduce profitability through added warehousing, working capital requirements, deterioration, taxes, and obsolescence (Bowersox, 1996).

START

1

--)

Investigate the inventory system

Develop an influence diagram

Derive evaluation parameters

I Develop the simulation model to asses evaluations parameters

,

,

Determine plausible tactics and strategies

Choose the most preferred options

,

Deal with uncertainty

ssop -') Figure 1. The framework of the decision support system

Designing an effective inventory policy turns out to be a hard task. In order to properly evaluate the different alternatives, which potentially are intended to improve the inventory management, it is necessary to study the impact of the proposed options on the important performance indicators related to the enterprise goals. Two objectives are considered as the most important indicators: the minimization of the inventory costs and the maximization of the customer satisfaction. Therefore, the problem, which arises here, consists of finding the solution that is the appropriate compromise between expected inventory costs and the customer satisfaction level. By searching for the solutions the uncertainty related to strategies, should be taken into account, too (Verwater-Lukszo, 2004).

2. Decision support: Performance measurement system The approach adopted to attain the goal formulated as improvement of the inventory management of the WIP (Work In Progress) materials was aimed at developing a

1359 decision support tool that is expected to assist decision maker(s) in revealing the performance parameters (inventory level/costs and service level) behaviour under potential tactics and strategies concerning inventory with regards to uncertainties of the system. The approach is decomposed into four phases, as presented in Figure 1. The first phase is to get insights of the inventory conditions in the company and to identify the evaluation parameters, which could measure the influence of potential improvement options on inventory management to the achievement of the company's objectives. This is a creative process supported by an influence diagram representing relations between variables in the internal supply chain with regard to customer orders, materials and production resources; see Figure 2. :< ......

.-

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?:', \ t' ~--.~. ~ ,'i' .i :

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' ~';::t I'1 _P. ['1 l'f'l I"~1.1I-:tj. I"11"i S el .P-c:t.i oli

s e,::t,_-~-

Figm'e 2. The overall invento,y system it?/Tuence-diagram

Having insight into the inventory, the second step is to construct the model that can be used to simulate the behaviour of performance parameters tinder the implementation of the decisions (improvement options). A System Dynamics (Sterman, 2000) approach is used to capture the dynamic relationships and feedback structures, as presented in Figure 3. In the developed model the internal supply chain is divided here into three sectors: production and inventory sector; customer service sector (including shipment) and grade production sector. These sectors are related to each other as visualized in the influence diagram presented in Figure 2.

1360

I

X(t) dX Y(t)

= IdX.dt +X(0) =j(Y(t)) = g(X(t))

¥ Figure 3. Basic buildings blocks for System Dynamics diagram X(O) means the initial state of the stock value. The stock level X(t) accumulates by integrating the flow rate (dX). Auxiliary variables (Y) control or convert other entities (g(X(t))).

It should be mentioned here, that production and inventory sector as well as customer service sector and apply similarly for all grades in their own 'private' model. However, these 'private' models don't work independently of each other. They interact through the grade production selection. Grade production selection is a very important decision moment in a batch-wise multi-product plant: very often one grade may be produced in different types of equipment, the importance of grades for business values may be different and the (expected) frequency the grades have to be produced can be very diverse. Basically, a grade needs to be produced if its inventory level is not sufficient to fulfil the demand. Therefore, less inventory and higher demand increases its chance to be produced. Importance of the grade symbolizes a need for priority rule in determining which grade should be produced. This happens in the grade selection sector. As already mentioned, the influence diagrams as presented in Figure 2 and their decomposition into the interconnected sub-models are translated into quantitative relations and implemented in a System Dynamics simulation model using the software tool Powersim Studio. The idea was to develop a general model, which can be easily adapted to specific industrial situations. The developed model is capable to simulate physical and informational aspects of the inventory-management in real batch plants and to predict the behaviour of the system if influenced by new decisions. After satisfactory model is available, the determination of the plausible tactics and strategies (improvement options), can be performed in the third phase. The model is used then to analyse which options are promising to be further studied to improve the system's behaviour. These options are then utilized as tactics, e.g. eliminating safety stock for shutdown, and strategies, which are a combination of tactics. The fourth step is to treat the uncertainty in one of the three types: external uncertainty, system response uncertainty and value uncertainty (Walker, 2000). External uncertainties, e.g. the expected orders, are inputs that are beyond the control of decision maker. System response uncertainty is related to the system responses to the external uncertainties. Finally, value uncertainty is related to the uncertainty about the valuation of system outcomes e.g. due to changes of decision makers' preferences. In this study, employing scenario analysis treats external uncertainty. Scenarios related to the market growth and plant disruption are investigated. Then, robustness of strategies is evaluated under the proposed scenarios by judging the impact of scenarios to performance parameters. This concludes the analysis, so that the most robust options for inventory improvement, e.g. reducing safety stock level by x%, can be recommended.

1361

3. Case study in a c h e m i c a l plant The presented approach is applied in a chemical plant producing 7 grades of resins, whereby two grades, say X 1 and X5 may be produced in two production lines, but the other grades may be only produced in the dedicated line. Each line has its own speed, which can be different for each grade. Currently, resin production is determined by the silo level and demand. Operator looks at the silo level and if it reaches minimum level, the particular resin will be produced. The most common grade produced in line 1 is grade X1, and X3 for line 2. Production is also adjusted to the current situation, i.e. demand and line condition. For example, if there is an urgent need (i.e. rush demand) for grade X7, then X7 will be produced in line 1, and line 2 will produce other grade depending on the priority settings. Moreover, every grade change in the production line generates transition (twilight) material, which should be minimized. Furthermore, there is only limited amount of silos available on-site, and not each silo has blending capability, which is needed when twilight material is produced.

3.1 Simulation model Having the necessary assumptions about the plant situation and data, the general model, as presented in Figure 4, is adapted to simulate the real condition of the plant.

~

m

e

n

\ o r drati fulfillr~nt eor

t

/

backlogdemand ~

-"? h

plantre~liabili l

\

1

\

/

desiredservice

/

smoothe~demand / smootheddemand rate

"+"

C u s t o m e r service

grade priority setting

productionrule of other grades

P r o d u c t i o n selection

Figure 4. Overall picture of the model

3.1 Tactics and strategies as improvement options Tactics analysed in this study are derived from discussion with the company and from the results of the sensitivity analysis of the simulation model. These are: (1) increasing plant reliability, (2) eliminating safety stock for shutdown, (3) reducing safety stock, and (4) reducing desired service level. Performance of each of these tactics is appraised through their capability to influence the performance indicators of inventory management of the company, which are inventory level, which has to be minimized and

1362 order fulfilment ratio (service level), which has to be maximized. Next, the tactics are combined to two strategies: "change safety stock policy" (tactics 2,3,4) and "entitlement strategy" (all tactics). A qualitative result of each strategy can be seen in Table 1, which pictures the result compared with base case. Table 1. Result of strategies. Effects are calculated based on average value relative to the average value of the base case simulation

Performance indicator

Change effect to base case Strategy 1 I Strategy 2

Inventory level X 1 inventory

-54%

-60%

X7 inventory Total inventory Order fulfillment ratio (OFR)

-53% -54%

-57% -59%

-3% -9%

-4% -8%

. o .

X60FR X70FR

Taking into account the model assumptions, we can conclude that the first strategy developed could lower inventory by 54% with 9% decrease in service level. Second strategy reduces 59% lower average inventory with less than 8% decrease in the service level.

4. F i n a l r e m a r k s Multipurpose batch plants often operate in a very dynamic environment with a high variability of demand. Determination of appropriate safety stock levels and possible options for the improvement of inventory management are difficult tasks. Capturing the complexity of inventory management through an aggregate model, which can accurately simulate the effects of improvement options and take into account the production and capacity constraints helps to find a trade-off between inventory costs and customer satisfaction level. This creates conditions for the coming order acceptance and scheduling as well as processing tasks.

References Bowersox, D.J., David J. Closs, 1996, Logistical Management: The Integrated supply chain process, McGraw-Hill Companies, Inc. Christina T.S., 2004, System Dynamics Model as a Decision Support Tool for Inventory Management Improvement, Master Thesis, Faculty of Technology, Policy and Management, TU Delft Sterman. J.D.,2000, Business Dynamics: Systems thinking and modeling for a complex world, Irwin McGraw Hill, Boston "Verwater-Lukszo Z., H. Roeterink, 2004, Decision Support System for Planning and Scheduling in Batch-wise Plants, IEEE International Conference SMC 2004, the Netherlands Walker, W.E., .2000, A systematic approach to supporting policy making in the public sector, Journal of Multicriteria Decision analysis, Vol. 9(1).

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1363

Dynamic Modeling and Nonlinear Model Predictive Control of a Fluid Catalytic Cracking Unit Raluca Roman a, Zoltfin K. Nagy a'b'*, Frank Allg6wer b and Serban P. Agachi a aDepartment of Chemical Engineering, "Babes-Bolyai" University, 11 Arany Janos, Cluj-Napoca, 3400, Romania blnstitute for Systems Theory in Engineering, University of Stuttgart, Pfaffenwaldring 9, 70550, Stuttgart, Germany

Abstract The paper presents the application of nonlinear model predictive control (NMPC) to a simulated industrial fluid catalytic cracking unit (FCCU). A complex dynamic model of the reactor-regenerator-fractionator system is developed and used in the controller. The novelty of the model consists in that besides the complex dynamics of the reactorregenerator system it also includes the dynamic model of the fractionator, as well as a new five lumped kinetic model for the riser, and hence it is able to predict the final production rate of the main products (gasoline and diesel). Simulation results presented in this paper demonstrate that a numerically efficient, inferential NMPC approach that regulates easily measurable variables in the reactor and regenerator is able to provide good control of the product composition for certain disturbance scenarios.

Keywords: catalytic cracking, nonlinear model predictive control, dynamic modeling.

1. Introduction Fluid Catalytic Cracking Unit (FCCU) is one of the most important processes in a refinery, because its product is high quality gasoline. Due to its complexity, the modeling and control of FCCU poses important challenges (McFarlane et al., 1993). This chemical process has been traditionally controlled by using linear model predictive control approaches, which have proved their benefits in the petrochemical industries in the past two decades. Nonlinear model predictive control (NMPC) has the potential to achieve higher productivity by exploiting the advantages of taking process nonlinearities explicitly into account (Qin and Badgewell, 2003). However, the application of NMPC requires models with good prediction quality. In this paper simulation results obtained with a complex dynamic model of the FCCU are presented. The developed model simulates the dynamic behavior of the reactor-regeneratorfractionator system and predicts the composition of the main products (gasoline and diesel), which are then controlled in an inferential NMPC scheme, based on the complex high-order nonlinear model. The advantages of a modern NMPC approach, the so-called quasi-infinite-horizon nonlinear model predictive control (QIHNMPC) are

Author to whom correspondence should be addressed: [email protected]

1364 illustrated to achieve better control performance, however with increased computational burden. Efficient solution of the on-line optimization is achieved even in the case of the very high dimensional model, based on a multiple shooting technique. The paper is structured as follows: Section 2 presents the description of the plant and simulation results obtained with the model. Before conclusions, section 3 describes the NMPC approaches and optimization technique, with the simulation results.

2. Dynamic Modeling of the FCCU The schematic diagram of the FCCU, for which the mathematical model was developed and the assessment of the NMPC has been performed is presented on Figure 1. In the FCCU raw material is mixed with the regenerated catalyst in the reactor riser. The cracking reactions and coke formation occur in the riser and the products (gasoline, diesel, slurry) are separated in a fractionator. The deactivated catalyst due to coke deposition is regenerated in the regenerator. The developed dynamic simulator consists of detailed models of: the feed and preheat system, reactor stripper, riser, regenerator, air blower, wet gas compressor, catalyst circulation lines and main fractionator. Based on the assumption given in Dupain at al. (2003) a five lump kinetic model (schematically shown on Figure 2) that predicts the yields of valuable products is proposed and included in the simulator. The resulted global model of the FCCU is described by a complex system of partial-differential-equations, which was solved by discretizing the kinetic models in the riser and regenerator on a fixed grid along the height of the units, using finite differences. The resulted model is a very high order DAE, with 2143 ODEs (143 from material and energy balances and 2000 resulted from the discretization of the kinetic models). The model was implemented in C programming language for efficient solution and was used first to study the dynamics of the process and then in the NMPC controller. Figure 3 shows that the catalyst-oil ratio (CTO) has a small influence on the gasoline composition at the outlet from the riser, however it has an important influence on the composition in diesel of the product resulted in the riser. Therefore controlling the CTO is important in the plant. The model was also used to study the open-loop dynamic behavior of the system in the case of different disturbance scenarios. Figure 4, for example, illustrates the simulation results in the case of disturbance in the pressure drop between main the fractionator and the reactor.

React°r[~ n Stack gas

~~..Regenerator

I~1 [ ~

~

I

Steam ~ ~ ~=~ .... Atm.

~

air Air Blower

Fractionator [~]i

~-] [--) ._.....~ [ !1 If..--- ~ 4, l| nstea m or, Wet gas compressor II

Furnace ,,]"~. ~ Fresh feed

Coke

7 Gasoline

~-~Diesel Gas

Slurry Fuelgas Diesel Washoil

Figure 1. FCCUplant

Figure 2. Five lump modelfor the catalytic cracking

1365

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.

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01.

............................................................. + 2 4 6 8 10 riser station~ry time (s)

0

2

4

6

8

riser s t a h o n a r y t i m e (s)

10

Figure 3. Composition prol?les of the main products in riser at d(fferent catalyst-oil ratio (CTO) O 95 ...................................... C.O...mJ~o.z.lt!.(P.l)....!.:O...~f.[acl~!o.!).a.to[.~.top) .....................006 ~

:

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o

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time (m+n) Figure

I

"~' 130 ...................................................................................................................................................................

.+-.. 665

+- ~5:,

4o+

4. F C C U

simtdation

200

400

600

800

time (rain)

results

in t h e p r e s e n c e

o/pressure

drop disturbance

(10%

increase)

When the pressure drop increases with 10% at t = 500 rain, the temperature in the reactor (T,.) and in the regenerator (T,.cxD decrease (I°C for T,. and 8°C for T,.c~). This disturbance has a significant influence on the catalyst inventory: 6% increase in the amount in the reactor (W,) and 2 % decrease in the regenerator (W,.cg), respectively. The influence of this disturbance for the gasoline and diesel composition in the fractionator is below 1%, however considering the throughput of a typical FCCU this can lead to important economical consequences. The system is very stiff (there are large differences in the time constants of different process variables). In addition significant delays and complex dynamic behavior can be observed (e.g., higher order with zeros for the/+,.and non-minimum phase behavior for the gasoline composition in the bottom of the column), suggesting the use of NMPC, which is a control strategy that simultaneously can cope with complex nonlinearities, delays, and constraints, whereas optimizing economic control objectives. 3. N o n l i n e a r M o d e l P r e d i c t i v e C o n t r o l o f t h e F C C U Nonlinear model predictive control is an optimization-based multivariable constrained control technique that uses a nonlinear dynamic process model for the prediction of the process outputs. Different NMPC approaches have been proposed that guarantee stability of the closed-loop system even under finite prediction horizon (Allgoewer et al., 1999). The approach used in this paper is the so-called quasi-infinite horizon

1366

nonlinear MPC (QIHNMPC) proposed by Chen and Allgoewer (1998). The basic idea of this approach consists of the approximation of the infinite horizon prediction to achieve closed-loop stability, whereas the input function to be determined on-line is of finite horizon only. The terminal penalty term is determined off-line. Using a local linear feedback low and a quadratic objective function, the terminal penalty term can be chosen to be quadratic. The basic formulation of the on-line control problem in the QIHNMPC can be expressed as below: t+r~,

min{ f u(.)

(]x(T;x(t)

~

t)ll2

+

,

+ [p(t +

~

tll;}

(1)

t

subject to:

dx

- - -- f(x, u) ,

dt

x(t; x(t), t) - £c(t)

(2)

• (~-,4t)) c x , ~(~-)c u

(3)

x(t + T~;x(t), t)E f~

(4)

where u(T) c/// is the input vector, x(7-,x(t)) ~ X is the state vector, ~- c (t, t + Tp)is the time, Q c R ..... and R E R ........ denote weighting matrices, Tp is the finite prediction horizon, x(.,z(t),t) is the trajectory given by the integration of the equation (4) driven by u(.)'[t, Tp] ELt, Ilxll~- xTQx is the weighted 2-norm of x, and 2(t)is the measured or estimated initial states. The terminal inequality constraint (4) with the last penalty term from (1) will force the states at the end of the finite prediction horizon to be in some neighborhood ~ of the origin called terminal region, which can be obtained by the iterative solution of a complex nonlinear optimization problem. In the case of the very complex FCCU, the determination of f2 is a nontrivial task, but since computation is performed off-line, it does not affect the real-time feasibility of the approach. A very efficient solution technique for the problem (1)-(4) is based on the multiple shooting approach (Diehl, 2001). This procedure consists of dividing up the time interval r C [ t , t + T ~ , ] into a series of grid points [t0,tl,t2,...,ts] with t 0 = t and tf = t + T . Using a local control parameterizations a shooting method is performed between successive grid points. The differential equations and cost on these intervals are integrated independently during each optimization iteration, based on the current guess of the control. The continuity/consistency of the final state trajectory at the end of the optimization is enforced by adding consistency constraints to the resulted nonlinear programming problem (NLP). A set of starting values for the state and adjoint vectors is required at each grid point in time, and continuity conditions for the solution trajectory introduce additional interior boundary conditions, which are incorporated into one large zero-finding problem to be solved. The solution of control problem is performed using an NMPC tool (Nagy et al., 2004) based on the sequential-quadraticprogramming (SQP) type optimizer HQP, which is used in conjunction with the implicit differential-algebraic-equation (DAE) solver, DASPK, for robust and fast solution of the model equations. Using this implementation, the computational time for the solution of one open-loop optimization is obtained below 2 min (the considered sampling time) even in the case of 2124 th order FCCU model. The complex first-principles dynamic model was used in the NMPC algorithm. First the nominal NMPC is considered without the penalty term and terminal constraints, to test

1367 Compozition in fractionator (Dp)

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different control structures tinder different disturbance scenarios. From the simulations performed the best control structure resulted with the three controlled variables: reactor temperature (T,.), regenerator temperature (Treg) and catalyst amount in the reactor (W,.), and three manipulated inputs: openings of the spent and regenerated catalyst circulation pipes between the reactor and regenerator (svsc and svrgc, respectively) and the flow rate of the raw material (/7). This inferential control scheme is able to provide good control performance for the composition in the fractionator (see Figure 5). Figure 6 illustrates the performance of the QIHNMPC for different off-nominal initial conditions. It can be shown that asymptotic stability is achieved in all cases. The very small terminal region (projections of the hyper-ellipsoid on the shown state space) is caused by the strong nonlinearity of the system. Figure 7 illustrates that QIHNMPC achieve better control performance than NMPC. Using QIHNMP the system is stabilized faster.

1368

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4. Conclusions The paper presents dynamic simulations for the FCCU aggregate system that includes the main fractionator and a kinetic model for the riser leading to a 2144 th order ODE model. Based on this model an inferential control scheme is proposed that is able to control the product distribution resulted from the fractionator based on easily measurable variables in the regenerator-reactor system. The model was used to simulate the performance of the theoretically founded quasi-infinite-horizon NMPC (QINMPC), to achieve fast stabilization of the closed-loop system. It is shown that using state-ofthe-art optimization approaches based on modern multiple shooting algorithm real-time feasibility can be achieved even in the case of the very high order FCCU model. The results demonstrate that industrial applications of modern NMPC approaches to complex chemical processes can be brought in the realm of possibility.

Aeknowledgelnent This work was supported by the Marie Curie fellowship HPMT-CT-2001-00278.

References Allgoewer F., T.A. Badgwell, J.S. Quin, J.B. Rawlings, and S.J. Wright, 1999, Nonlinear predictive control and moving horizon estimation-An introductory overview, In P.M. Frank (editor), Advances in Control, 391. Chen H and F. Allgoewer, 1998, A Quasy-Infinite Horizon Nonlinear model Predictive Control Scheme with Guaranteed Stability, Automatica, 34, 1205. Diehl M., Real-Time Optimization for Large Scale Nonlinear Processes, 2001, PhD Thesis, University of Heidelberg. Dupain X, E. D. Gamas, R. Madon, C.P. Kelkar, M. Makkee, J.A. Moulijin, 2003, Aromatic gas oil cracking under realistic FCC conditions in a microriser reactor, Fuel, 82, 1559. Qin, S.J., and T. Badgewell, 2003, A Survey of Industrial Model Predictive Control Technology, Control Engineering Practice, 11,733. McFarlane R.C., R.C. Rieneman, J.F. Bartee and C. Georgakis, 1993, Dynamic simulator for a model IV Fluid Catalytic Cracking Unit, Computers Chem. Engng, 17, 275. Nagy Z. K., F. Allgower, R. Franke, A. Frick, B. Mahn, 2004, Efficient tool for nonlinear model predictive control of batch processes, in Proc. of the 12th Mediterranean Conference on Control and Automation (MED'04), Kusadasi, Turkey, on CD.

European Symposium on Computer Aided Process Engineering - 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1369

Improving of Wavelets Filtering Approaches Rodollb V. Tona. Antonio Espufia, Lluis Puigjaner Universitat Polit6cnica de Catalunya, Chemical Engineering Department. E.T.S.E.I.B.. Diagonal 647, 08028-Barcelona, Spain.

Abstract In this work, some simple strategies for signals filtering and estimation with wavelets are presented. Firstly, it is studied the adequacy of some type of wavelet for filtering. Then, it is proposed a strategy to determine the best decomposition level and, then, to improve wavelet filtering accuracy. Some known benchmark signals are used to validate the performance of the proposed methods and their comparison with some existing approaches. The results obtained expand the applicability and reliability of existing filtering schemes with wavelets and propose some useful alternative to do it.

Keywords: Data rectification, Wavelets, Depth of Decomposition. 1. Introduction Measured process signals are very important to support a wide number of engineering tasks with a critical impact on the global operation of the plant. Otherwise, these measurements inherently contain noise originating from different sources. Hence, data filtering is a critical step in the operation and control of any chemical plant. Over the last decades, numerous techniques have been proposed for filtering or data rectification. If a process model is available, data reconciliation may be used. If it is not the case, but measurements are redundant, rectification based on an empirical process model derived from data may be proved. However for cases without model or redundancy in measurements the option is the use of univariate filters. These methods are the most widely used in the chemical and process industry (Bakshi, 1997) and include EWMA, median filters and so on. Most recently, because the multiscale nature of process data, wavelets have been proposed for data rectification. In this work, we are focusing on developments for this category of data filtering. Wavelets are families of mathematical functions which are capable of decomposing any signal, y(t), into its contributions in different regions of the time-scale space such as: L

y(') - E uEZ

L

(,) + Z E

(,)

(,

1=1 ueZ

Each term at right of the equation represent a decompose part of the original signal. ¢z,o are the approximation coefficients, d/,o are the detail or wavelets coefficients, ~,~, represents scale [unctions, ~, ,, represents wavelet [unctions, I is the scale [actor, o is the translation [actor and L is the coarsest scale, normally called the decomposition level.

1370 The above decomposition has been shown as very useful for filtering and signal trend estimation (Donoho et al, 1995, Bakhtazad et al, 1999). In these applications, any measured variable signal, y(t), is assumed to be the result of:

y ( t ) = x(t) + e(t)

(2)

Where x(t) is the vector of true process variables and e(t) is the associated measurement error (noise). Then, the basic idea to estimate x(t) (filtering of y(t) and extracting the true trend) with wavelets is as follows (1) Decompose the raw signal by using wavelets (equation 1); (2) Remove wavelets coefficient below a certain threshold value fl (thresholding step); (3) Reconstruct the processed signal using the inverse of the wavelet used. The above procedure (Waveshrink method) was the first method proposed for filtering with wavelets (Donoho and Johnston, 1995). Other methods have also been proposed. In all cases, they are variations or extensions of the Waveshrink method and it remains as the more popular strategy for filtering. A practical difficulty encountered in the application of Waveshrink, consists on how to select the decomposition level L. As it is highlighted by Nounou (1999), thresholding of dl.o under high values of L may result in the elimination of important features of the signal, whereas thresholding under low values of L may not eliminate enough noise. Additionally, wavelets Daubechies (dbN) are commonly adopted for different filtering schemes (Doymaz et al, 2001; Addison, 2002) because their very good capabilities at representing polynomial behaviours within a signal. However, the choice of different dbN can slowly affect the quality of filtering (Nounou, 1999). In general, the choice dbN vary between authors and no rules of what to select exists. In this work, an empirical study of filtering with wavelets is presented. Firstly, it is explored the ability of some popular wavelets for filtering. Then, it is proposed a strategy to determine the best decomposition level. 2. A n a l y s i n g

the performance

of wavelets

for filtering

It was conducted an experiment based on using different dbN and different L values within the Waveshrink scheme. The experiments were organised as follows: - Typical signals from literature were used (Doymaz et al, 2001). They originally contain 1024 observations. In the experiments, they were used in the following intervals: (1) Blocks signal or S1 from 451 to 627; (2) Blocks signal or $2 from 620 to 965; (3) HeaviSine Signal or $3 from 251 to 820; Doppler signal or $4 from 35 to 550. - All signals were contaminated with random errors of N(0,0.5) (see figure 2). - Daubechies from db 1 to db9 were applied for each signal. - Constant L values (from 2 to 9) were used for each dbN and for each Signal. - Each combination (Signal-dbN-L) was applied on-line and according to the On Line rectification (OLMS) and Boundary Corrected Translation Invariant (BCTI) schemes (Nounou et al, 1999) - For the waveshrink, soft thresholding was used and the threshold, fl, was determined by the visushrink rule (Nounou et al, 1999).

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Mean Square Error (rose) between the filtered signal and the original signal (without noise) is computed on windows of 32 observations length and each time after 16 observations are filtered. This results in 8 consecutive intervals with rose computed for signal S 1, 18 consecutive intervals for signal $2, 32 consecutive intervals for signal $3 and 29 consecutive intervals for signal $4. Then, the frequency of each L value that leads to the low rose in each interval is computed. Similarly, the frequency of each dbN filter that leads to the low rose in each interval is computed. These frequencies are shown in table 1. Table/. Frequency of L values and dbN filters as leadings to the best estimation of different signals. Frequencies for L OLMS L=2 L=3 L=4 L-N L=6 L=7 L=8 L=9

Sl 0 0 1 1 5 0 0 1

$2 5 0 6 0 3 2 0 2

$3 2 2 15 I0 3 0 0 0

Frequencies for dbN

values BCT!

$4 4 10 II 3 0 1 0 0

Si 0 0 1 7 0 0 0 0

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dbl d b2 d b3 d b4 db5 db6 db7 db8 db9

$1 6 0 0 0 0 1 1 0 0

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$3 13 1 1 6 1 0 5 1 4

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S1 8 0 0 0 0 0 0 0 0

$2 11 I 0 1 2 2 1 0 0

$3 20 3 0 3 2 2 1 1 0

Sa 2 6 1 4 0 3 4 7 2

Analysing the frequency for dbN it can be noted that dbl is particularly appropriate for signals like S1 in both OLMS and BCTI applications. For signals S2 and S3 dbl is also useful for BCTI. In the OLMS case some other filters are also frequents for $2 (db2) and $3 (db4-db 7). It is noted that these lasts occurrences corresponds to intervals where abrupt changes are at the end of the data window in case of $2 and for intervals with slow trends in case of $3. So, db 1 may be more appropriate for stationary patterns (as in S l) or for dealing with abrupt changes (see discontinuities in signals $2 and $3). In case

1372 of $4 the pattern of the curve is continuously changing through fast and smooth patterns and many filters occurs at different intervals. Only is noted a slow tendency of more occurrences of dbN with even values of N (particularly db2 and db8). So, slow and changing patterns as in $4 may be best treated with db2 or db8 filters. Now, for the frequencies of L values it is shown that every signal tends to be handled around bands of L values (L=2-L-4 for $2, L=4-L-5 for $3 and L=3-L-4 for $4) but a pattern is more difficult to establish than in the case of dbN.

3. Optimal Depth of Wavelet's Decomposition Here, it is explored a simple strategy to deal with L. To do this, consider the curve, y(t), that is shown in figure 3 (labelled as measured). Several approximations, AL, ofy(t) are calculated through equation 3 and varying the scale L from 1 to nL. Then, several powers Pz., between y(t) and each one of the AL are calculated. Also, variations of power, APL, from one scale to another, are computed. Now, by plotting the successive values of APz., one or more minima will be detected (see figure 4). The first minimum is identified and the associated L is labelled as Lm. It is observed that at Lm, the associated AL shows the closest behaviour to the original signal (see figure 3). Therefore, an optimal L can be set as the one corresponding to the first minimum reached in APL. Filtering 69.5

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Figure 3. Decomposition of the Jumps signal wit db8. From L--1 to L=4. Mathematically, the different steps required for this optimal depth determination can be set as follows: 1- The, cLo and d/,o at various scales I are obtained with wavelets as in equation (1). 2- The approximations AL, at each scale L is reconstructed through: L

1=1 3 - The power PL, at each scale L (daL), is computed as follows:

(3)

1373 [,

],

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(4)

4. The variation of PA is computed as follows:

A P - P/ ( d a ) - P/_, ( d a )

(5)

The optimal scale L,,, that corresponds to the first minimum of JPL is identified. 5. At L,,, a first thresholding, based on setting to zero all the dAo in scales greater than L,,,, is performed. Then, a second thresholding over remaining coefficients is performed through WaveShrink. The first thresholding gives the appropriate L and the second thresholding eliminates coefficients related to noise in scales less or equal than L,,,. 6. The de-noised signal is obtained by taking the inverse of the wavelets used.

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In the above procedure, computing approximations until nL with values between [10, 12] is sufficient to identify L,,,. The signals used in section 2 are used for testing the above proposed approach. The experiments were organised as follows: - The proposed strategy is applied on-line and for both OLMS and BCTI schemes. MSE between the filtered and the true signal are computed locally (on data windows as in section 2) and globally (over the entire set of each processed signal). Figures 5 shows the best fifteen estimations (expressed as global MSE values) that were obtained with the proposed approach (labelled as LevaShrink) and for the WaveShrink strategy. It is shown that, in general, the proposed approach can compete in estimation accuracy with WaveShrink for both OLMS and BCTI schemes. Only the signal S1 presents considerable differences with traditional WaveShrink but for the first estimation it is comparable in accuracy with WaveShrink. It is also shown some cases where LevaShrink gives best accuracy (lower mse in some plots of figure 5). This is possible because at each time the level tuned is adapted to the current pattern of the trend which is more appropriate than setting a same L tbr all times as it is the case for WaveShrink. Then, the LevaShrink method can be an advantageous alternative use for -

1374 filtering with wavelets. The advantage of use LevaShrink is to avoid the offline analysis of each signal for setting of appropriate values of L. C o m p a r i s o n on S i g n a l S 1

Comparison

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4. Conclusions Wavelet filtering schemes have been studied. By the way of experiments it has been show the adequacy of dbl for signals with stationary and/or abrupt change patterns, particularly under BCTI schemes. By other hand, wavelets like db2-db8 may be more appropriate for dealing with signals with smooth changing patterns. It has also been show that appropriate level values can be very variables from one type of signal pattern to another. Then, the proposed approach can deal with this issue by identifying at each time the required level. Finally, further improvements and extended comparisons with other existing approaches and for different case studies will be made in future works.

References Addison, P. S., 2002, The Illustrated Wavelet Transform Handbook: Applications in Science, Engineering, Medicine and Finance. Institute of Physics Publishing, Bristol. Donoho, D.L., and I.M. Johnstone, 1995, J. Am. Star. Assoc., 90, 1200. Doymaz, F., A. Bakhtazad, J. Romagnoli, and A. Palazoglu, 2001, Comp. Chem. Eng., 25, 1549. Nounou, M. N., B. R. Bakshi, 1999, AIChE J., 45(5), 1041. Bakshi, B. R., P., Bansal, M.N. Nounou, 1997, Comp. Chem. Eng., 21(Supplement), s1167. Bakhtazad, A., and A. Palazoglu, J.A. Romagnoli, 1999, Intelligent Data Analysis, 3,267.

Acknowledgements Financial support received from the "Generalitat de Catalunya" (a FI research grant to Tona, R. V.), from "Ministerio de Ciencia y Tecnologia" (project DPI2002-00856), and from the European Community (projects GIRD-CT-2000-00318) are fully appreciated.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) (¢2,)2005 Elsevier B.V. All rights reserved.

1375

Supply chain monitoring" a statistical approach Fernando D. Mele, Estanislao Musulin and Luis Puigjaner* Chemical Engineering Department, ETSEIB, Universitat Politbcnica de Catalunya Av. Diagonal 647, E-08028, Barcelona, Spain

Abstract Although the nodes of a supply chain (SC) network generate a huge amount of data along their operation, extracting useful information from them is not straightforward. Within the Supply Chain Management (SCM) scope, monitoring reveals as a key task that is currently waiting for further study. It is necessary to minimize risks of undesired situations and administrative efforts to manage material flows. Supply Chain Monitoring (SCMo) techniques should support manager decisions warning of the abnormal situation telling what have gone wrong and suggesting solutions. Additionally, they should be able to store the causes and consequences in order to help in the decision making onto future similar situations. This work presents an extension of multivariate statistical methods to SCMo that consists in a wavelet based multi-scale Principal Component Analysis (PCA) technique accounting for time delays. The proposed approach has been tested using data generated through an event discrete simulation model running in several scenarios. Results have revealed that statistical multivariate techniques are very useful for SCMo.

Keywords: SCM, SCMo, PCA.

1. Introduction A company's supply chain (SC) comprises both geographically dispersed facilities where raw materials, intermediate products, or finished products are acquired, transformed, stored, or sold, and transportation links that connect these facilities among them (Simchi-kevi et al. 2000). Within a SC there is an actual agreement among the different partners so as to award the general coordination task to a central entity. The central entity has a global view and tries to equilibrate the stresses that each SC nodes creates. In this point, Supply Chain Monitoring (SCMo) plays its essential role offering the information in a suitable way to the central entity's disposal. It is as the halfway between the transactional and analytical tools on which Supply Chain Management (SCM) is often supported. In recent years, astonishing gains in personal computer speed, e-commerce, and the power and flexibility of data management software have promoted a range of applications. Widespread implementation of transactional tools or backend-systems as Enterprise Resource Planning (ERP), Material Requirement Planning (MRP) or Distribution Resource Planning (DRP) systems offer the promise of homogeneous, Author/s to whom correspondence should be addressed: [email protected].

1376 transactional databases that will facilitate integration of SC activities. In many companies, however, the scope and flexibility of these systems have been less than expected or desired, and their contribution to integrated SCM has yet to be fully realised. Moreover, competitive advantage in SCM is not gained simply through faster and cheaper communication of data. Companies are seeking to utilise systems that automatically analyse their corporate databases to identify plans for redesigning their SCs and operating them more efficiently. Nevertheless, extracting useful information from data is not straightforward. These data are disparate in nature and, additionally they are collected at different frequency and even saved occasionally. Thus, within the SCM scope, monitoring reveals as a key task that has received little attention up to now and it is currently waiting for further study. In this work, monitoring is proposed as an intermediate technique that provides an initial analysis over the large amount of data saved in the aforementioned databases, which enables to characterise the normal operation of the system. This is very useful in order to visualise the operation of the SC to control whether it is kept between the normality boundaries. Otherwise the traditional fault detection for chemical processes, in SCM it is not necessary to detect the occurrence of a fault but to obtain a pattern indicating how this event, whose occurrence is known, affects the value of the measured variables in the system, e.g. inventory levels. The idea is to store in a database a model that could give notion about the variations or changes in the variables when the event is repeated in such a way to be able to study and anticipate corrective actions. This work is based on multivariate statistical methods usually applied to process monitoring.

2. Monitoring Methodology 2.1 Principal components analysis PCA (MacGregor et al. 1995) is a statistical method for process monitoring based on data correlation. Consider a matrix X (of dimension m x n) containing data corresponding to m samples of n variables. Each column of X is supposed to follow a normal probability distribution and is normalized with zero mean and unit variance. Let R be its corresponding correlation matrix. Then, performing singular value decomposition on R, a diagonal matrix D~ = diag()~l, )L2,..., ~n) where ~i are the eigenvalues of R sorted in decreasing order )~1 > )g2 > . . . > )gn, is obtained. The corresponding eigenvectors Pi are the principal components (PCs) and form an orthonormal base in R n. It is possible to divide the PCs in two orthogonal sets, P = [Pl, Pz,..., PA] and P = [PA+I, PA+~,..., P.]. The first containing most of the common cause variation and the second describing the variation due to the noise (called the residual subspace). A reduction of dimensionality is made by projecting every normalized sample vector x' in the subspace generated by P, obtaining t = PVx', which is called the principal score vector. Then, the state of the process can be monitored using two statistics, the Hotelling's statistic (7 e) and the Squared Prediction Error statistic (SPE). The first describing common cause deviations and the second describing deviations in the residual subspace.

2.2 Genetic algorithm-based delay adjusted PCA (DAPCA)

1377 One main drawback of PCA is that it does not account for time-delays present in data. Those delays can cause that the percentage of variance contained in the first few PCs is low and the difference between the variance contained in the last significant PC ()~A) and the next one ()~A+,) is not accentuated. Therefore, there exists a trade-off between the number of linear relations considered (A) and the embedded errors that is introduced in the model, causing an inefficient reduction of dimension and a bad performance to filter the noise and to detect disturbances and changes in the process correlation (faults). If one want to deal with all the complete adjustment problem, without additional assumptions, (dmax)n singular value decompositions have to be evaluated (Wachs and Lewin, 1999), where d,,,ax is the maximum delay considered. In this work, a Genetic Algorithm (GA) has been developed to solve this high combinatorial optimization problem. In this approach, each chromosome represents a backward shift vector (DV = [d~, d2.... , dn_~], with dj in the range 0 < dj < dma~ for j = 1, 2,..., n - 1) and contains the delays present in the process signals with respect to a reference signal. This reference signal can be in general any input. The optimization is performed in two loops. The first one, find DV that minimize the number of PCs that are selected by a parallel analysis (Himes et al. 1994). The fitness function is simply (I)~ = -A. The second loop searches DV that maximize the variance contained in the first A PCs (selected in the loop 1) (i.e. @~:~i' 2 ), which is considered as the true system variation. As a consequence, )~A results greater than )~A+,, making easier the distinction between spurious and system variance. Additionally, the model explains the most of the true process variance in the smallest number of PCs.

2.3. Multiscale DAPCA (MS-DAPCA): The capacity of PCA to eliminate the noise heavily relies on the assumption of the normality of data. Therefore, sometimes measurement and process noise can difficult the detection of small faults and disturbances. MS-DAPCA aims to join the properties of DAPCA to those of Multi-scale PCA (MSPCA, Bakshi, 1998). MSPCA is an approach that handles multi-scale data by using wavelets. PCA is then applied to generate independent latent variables at each scale. In addition, wavelets act as a multiscale filter by thresholding the coefficient of the more detailed scales. MSDAPCA performs similar to MSPCA, but DAPCA is applied instead of PCA, at each scale of the wavelet decomposition. One main advantage of this method is that two stages of dimension reduction are performed. First the MSPCA decomposition reduce the length of the coefficient matrixes from tn to m/(21), and the maximum delay considered results d,naxl : dmax/(2l) were l is the decomposition level. This situation reduces the computation time of DAPCA several times, especially in the approximation scale, sometimes allowing the use of exhaustive delay adjustment. Finally, delays can be estimated and compensated independently at different scales. The Matlab® genetic algorithm Toolbox developed by the University of Sheffield has been used in the following case study, which has been solved using an AMD XP2500 processor with 512MB RAM.

4. Case Study

1378 An event-driven simulation model has been constructed using two toolboxes of Matlab®: Stateflow and Simulink. The case study is a SC network involving six entities: one raw material supplier (S), a manufacturing plant (P), two distribution centres (DA, DB), and two retailers (RA, RB) (Figure 1). The row material that enters P is designed by W and the products manufactured by the plant are A and B. In this case, customer orders for A and B arrive to RA and RB, respectively, which, in turns, send orders to DA and De. The plant P supplies the distribution centres whilst S provides the raw material to the plant. Furthermore, the study is addressed to variables belonging to the operational and tactical level.

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Figure 1" Supply Chain case study.

The nineteen monitored variables are of two kinds: flows that involve material (inputs and outputs of materials at each node) and information (inputs and outputs of orders at each node), and cumulated variables that also involve material (inventory level at each location) and information (cumulated orders level at each node). Two different abnormal situations have been programmed. The first one is related to a machine breakdown in the production line of product B at the factory P. This causes a delay in the production response. The second one is due to a transport fault between P and DB. Then, during a certain time period De cannot replenish its inventory.

5. Results Firstly, a standard PCA model has been built using simulated data from normal operation condition. Seven PCs has been selected using parallel analysis (A - 7). The variance contained in each PC is presented in Table 1. Note that X7 ~ Xs, making difficult the distinction between the common cause and residual subspaces. 500

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With this model, Event II is easily detected. However, Event I cannot be detected (see Fig 2). In addition several false alarms (3 consecutive points out of limit) occur.

1379

Table 1 Variance percentage contained in the.first ten PC dimensions. Gray cells correspond to lhe selected PCs in each case. kl

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Therefore, DAPCA has been implemented to reduce the model dimension and to look for a better detection of Event I. In this case only three PCs has been selected (A = 3) and XA results significantly greater than XA.~(see Table 1). However, the detection performance has not improved (Fig. 3a). Then, to improve the monitoring performance the MSPCA has been applied. Five PCs are chosen. Results corresponding to the approximation scale of MSPCA are presented in Figure 3. The Event i is clearly detected without false alarms. 5O0

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Applying MS-DAPCA similar results are obtained, but using only three PCs (Figure 3c). Finally, MS-DAPCA has been applied but only on the six inventory signals because they are variables that are registered in an almost continuous manner. Then, data processing is easier than in case that the register is eventual, such as material flows transported by the lorries or the orders sent out by the customers. Now, only one PC is enough to describe the system variance contained in data. Figure 3d shows that the detection limit can be placed lower leading to a faster and more reliable detection. Once the deviation is detected, the causes and consequences of the abnormal events can be investigated. Figure 4 shows the statistics conesponding to Event I using the last implemented DA-MSPCA model. One can observe that the SPE is first deviated,

1380 showing a broke in the system correlation, and then the T2 statistic. Figure 5a shows that the D B is the inventories that cause the deviation in SPE, and then the disturbance in P due to accumulation of orders (Figure 5b). 15

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5 Conclusions Several statistical techniques usually applied in Chemical Engineering for process monitoring has been tested in a new environment, the SCM network. Results so far obtained are very promising. This study reveals that the standard PCA algorithm is not able to deal with the noise and non-gaussianity featuring of this kind of signals. Nevertheless, multiscale and the novel delay adjusted techniques can strongly improve the monitoring performance. Research tasks in this direction will continue.

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Acknowledgements

Financial support received from the Generalitat de Catalunya (FI programs) and from GICASA-D (I0353) project is fully appreciated. References

(1) Simchi-Levi, D., P. Kamisky and E. Simchi-Levi., 2000, Designing and managing the Supply Chain. Concepts, strategies and case studies. (2) Himes, D. M.; Storer, R H.; Georgakis, C. Determination of the number of principal components for disturbance detection and isolation. In Proc. of the ACC; IEEE Press: NJ, 1994. (3) MacGregor, J. F.; Kourti, T. Statistical process control of multivariate processes. Control Eng. Practice 1995, 3,403-414. (4) Wachs,A., Lewin, R. 1999, Improved PCA methods for process disturbance and failure identification. AIChE J. 1999,45 (8), 1688-1700Copyright © 1999 (5) Bakshi, B. Multi scale PCA with application to multivariate statistical process monitoring. AIChE Journal 1998, 44, 1596-1610.

European Symposiumon ComputerAided Process Engineering- 15 L. PuigAanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1381

Closing the Information Loop in Recipe-Based Batch Production Estanislao Musulin, Maria J. Arbiza, Anna Bonfill, and Luis Puigjaner 1 Chemical Engineering Department, Universitat Polit&nica de Catalunya, Av. Diagonal 67, 08028-Barcelona, Spain. Rasmus Olsson and Karl-Erik Arz6n Department of Automatic Control, Lund University, Box 118, SE-221 00 Lund, Sweden.

Abstract In addition to the basic regulatory functions, a batch control system must support production planning and scheduling, recipe management, resource allocation, batch report generation, unit supervision and exception handling. A closed-loop framework is presented in this work that integrates decision support tools required at the different levels of a decision-making hierarchical batch control system. Specifically, the proposed framework consists of a reactive batch scheduler (MOPP) and a fault diagnosis system (ExSit-M) developed by the Universitat Politacnica de Catalunya, and a S88-recipe-based coordinator (JGrafchart) developed by the Lund University. These tools need to exchange information to obtain optimal utilization of the production plant. The complete integrated system is built using a general recipe description and other guidelines from ISA $88 standard (ANSI/ISA 1995).

Keywords" Batch, Integration, Reactive Scheduling, Fault Diagnosis, Recipe

1. Introduction in a production plant environment the presence of unpredictable events not only related to external market factors but also to the operational level, e.g., equipment breakdowns and variable operation times, is usually unavoidable. Despite the uncertainty in the production scenario, the scheduler has to make some decisions both to start production and to face abnormal events. The need to increase the reliability of any decision-making process, thus reducing the gap between theory and practice, makes necessary to take this uncertainty into account. Research in scheduling under uncertainty has mostly been focused either on rescheduling algorithms, which are implemented once the uncertainty is disclosed, or stochastic approaches that incorporate the uncertain information at the decision level prior to scheduling. On one hand, the execution of deterministic optimal schedules based on nominal parameter values and the implementation of rescheduling strategies to tackle the problem once the uncertainty is revealed can result cumbersome or unrealistic without previous consideration of the uncertainty. If the uncertainty can be characterised at the time of scheduling, it should be advantageous to take possible future events into consideration before they happen in order to minimise the negative i Author to whom correspondence should be addressed: [email protected]

1382 outcomes. On the other hand, the future cannot be perfectly forecasted so, despite considering the uncertainty a priori, deviations from the predicted schedule can always occur once the uncertainty is realised. Therefore, it is required to adapt the schedule to the new scenario if a good performance of the system is pursued. The integration of a Fault Diagnosis System (FDS) aims to timely provide the process state information to the different levels in the decision-making hierarchical structure, thus reducing the risk of accidents and improving the efficiency of the reactive scheduling in the most effective way. To handle unit supervision, exception handling, and recipe execution a coordinator is implemented in JGrafchart. The unit supervision is based on modelling the state of each equipment object and procedural element using finite state machines. A closed-loop framework for on-line scheduling of batch chemical plants integrating, robustness considerations, fault diagnosis, recipe coordination, and exception handling is proposed in this work. This on-line integration leads to a fast execution of the recovery procedures and the rescheduling.

2. Scheduling and reactive scheduling The developed scheduler uses the Event Operation Network (Cant6n 2003) to model the system and has a library of different dispatching rules to determine a feasible schedule. The dispatching rules available can be classified into three sets: priority rules that determine a list of recipes to be sequenced and assigned to specific units, assignment rules that determine which equipment should be used for each stage of each batch, and sequencing rules that determine the sequence of batches and the sequence of operations for each unit. It also has a library containing a variety of heuristic and rigorous optimization algorithms to determine an initial optimum schedule. Furthermore, the objective function used by the optimization algorithms can be customized to optimize the use of resources, cost of changeovers, profit, makespan, etc. Once generated, the optimum schedule is sent to the coordinator to be executed in the process. Unexpected events or disruptions can change the system status and affect its performance. Therefore, during the on-line execution the scheduler receives from the process coordinator information about the actual executed schedule. Deviations from the original schedule and information about equipment breakdowns coming from the FDS will trigger a rescheduling (Arbiza et al. 2003 and Bonfill et al. 2004). The new generated schedule will be optimum according to the new plant situation. If some modification is made, the new schedule is sent to the process coordinator. The rescheduling algorithm (Arbiza et al. 2003b) is presented in Table 1. Table 1" Rescheduling algorithm 1 2 3 4 5

-

C r e a t e a master schedule. Send schedule to the process coordinator. Receives the actual executed schedule f r o m the process coordinator. Generate new optimal schedule. I f the new schedule differs f r o m the implemented one go to 2, else go to 3.

The rescheduling system is completely configurable and customizable considering the manager objectives. It allows selecting different dispatching rules, optimizers and objective functions according to the process knowledge. The alternative rescheduling

1383 techniques (recalculate a new robust schedule, recalculate considerations, actualize operation times, reassignment, system selects the best suited ones according to the Optimization algorithms may be included depending on maker and the required reaction time.

schedule without robustness etc.) are evaluated and the objective function adopted. the interest of the decision

3. Fault Diagnosis The FDS is designed based on artificial neural networks (ANN) and fuzzy logic, with a modular structure based on process decomposition following the ISA $88 standard. It was developed using G2 ...., and operates in collaboration with the coordinator and the scheduler sending complete information with regard to the process state (equipment breakdowns, lime of unavailability, etc.). Furthermore, it incorporates a complete decision-support system for the process operator based on the information obtained from a HAZOP analysis and a user friendly graphical interface. Normal operation conditions modelling is a central issue in batch process monitoring. To improve and simplify the modelling a step-wise model of the process is built. Each unit is represented by a set of ANN models that model the behaviour of each unit during a specific operation. In processes with complex dynamics this step-wise modelling can be extended to model the equipment at the phase level. Then, during the on-line operation, a model-manager activates and deactivates the models depending on the active process operations that are being executed into the process; information that c o m e s f r o m the coordinator. Phase/Operation residuals alarms

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The model predictions are compared with historical data to obtain limits for the normal operation conditions. Residuals corresponding to one variable from 20 operation runs are presented in Figure 4a. The area between the inner limits is considered as the normal behaviour region. Outer limits are calculated by multiplying the inner bounds by a factor. The factor depends on the trade-off between incipient fault diagnosis and robustness (no false alarm generation). Note that the limits depend on the process variability along the operation/phase time, and using the phase-time instead of the operation-time the limits can be set tighter especially around the change of phases. Finally, the methodology presented in (Ruiz et al. 2001) has been extended to obtain rules from a HAZOP analysis. Rules are introduced into a fuzzy system to relate the deviated residuals with taults. The membership functions change during the operation in such a way that residual values in the inner limits are considered normal, values located between the two limits lie in two fuzzy sets (High and Normal or Low and Normal), and finally, values located outside the external limits are considered to lie either in the Low or High set (Figure 4a). For each control operation the system shown in Figure 4b is applied.

1384

4. Coordinator The coordinator is implemented in JGrafchart, a Java implementation of Grafchart (A~rz6n 1994). The coordination involves management of scheduled batches, recipe execution, unit supervision, alarm propagation, and exception handling. The plant is divided into units according to $88. Each unit consists of equipment and control modules such as agitators, valves, and pumps. The units also contain the equipment control. The recipe/equipment control separation is on the operation level in $88, i.e., the recipe makes a procedure call from a procedure step representing a recipe operation to a procedure representing the corresponding equipment operation. Within the coordinator each batch is represented by a control recipe expressed using Sequential Function Chart (SFC) formalisms. Since the control recipe is carrying all the information about the development of the batch a report can be sent back to the scheduler every time a new phase is started. If an exception occurs and a batch has to be aborted this information is also sent back to the scheduler. The unit supervision is based on finite state machine models of the state of each equipment object and procedural element (Olsson 2002). The equipment state machine serves two purposes. The first is to be able to check that all the equipment objects are in a consistent state when an operation is invoked. The second purpose is to provide a structure for organizing the safety and supervision logic at the equipment control level. if a fault occurs, the safety logic causes a state transition from a normal state to a fault state. The state of an equipment/control module will propagate up to the unit level. Most of the functionality is associated with equipment operations. Each equipment operation object contains a procedure (i.e. the sequential control) and a state machine monitoring the state of the procedure. The procedure of an equipment operation holds not only the equipment sequential control, but also contains several checks, which need to be performed when a procedure is called from a recipe. It checks if the procedure itself is in the Idle state and, if so, changes the state to Running. The check if the unit is in a consistent state at the start of the operation is also checked using state machines. The separation between the normal recipe execution and the exception handling can be made in different ways. In Procel most of the exception handling is operation specific. When a procedure containing the operation is called the associated exception handling is enabled. The exception handling logic of an operation involves both the recipe level and the equipment level. Exception handling logic that must be active also for an idle equipment unit is contained in the unit exception handling object. Exception handling is also needed at the recipe level. For example, an exception that has occurred must be fed back to the control recipe, recorded in the batch report and sent to the scheduler, and appropriate actions must be taken to deal with the exception. An important consideration is how to separate the recipe information from the exception handling logic and operations. The actions that are taken in the recipe depend on the type of exception. In a few special cases it might be possible to "undo" an operation and rollback the execution of the recipe to a safe execution point, and from there continue the execution using, e.g., a new unit. However, due to the nature of chemical batch processes a rollback is in most cases not a viable alternative. Also in the more common case where the batch cannot be produced as intended there are several alternatives. In certain situations it might be possible to still make use of the batch to produce a product of a different quality. In other situations it is possible to recirculate the batch ingredients for later reuse.

1385

5. Integration Methodology and Technology The proposed integrated framework along with the flow of information through the different modules is depicted in Figure 1. There exists a central agent (DTM) that manages the information flows. ~

1.sched__J_"~ ~rS..executed I 12.scheduleschedule alarms 2.schedul.e [- ~ 7.8~'$c°u~tj21::ht,)dnu~eI [ 8...... 2ed,schedale 11.SChl~U21earalm~i/ msDTM I 6.pro~:s~lasr~2t'----~ ' 6"Pr°c5e:rSo::tsas data~~n trolactions

Figure 1. hTtegration diagram The scheduler generates an initial schedule that is then translated into control actions and executed into the process by the Process Coordinator. When an abnormal event is detected by the fault diagnosis system (FDS), it sends an alarm to the scheduler through the Process Coordinator, which executes some pre-specified recovery procedure, depending on the alarm. The scheduler receives the alarm and generates a new optimum schedule. All the information is stored in an ISA $88 compliant database. The developed software toolboxes have been integrated in a common infrastructure, named the CHEM Communications Manager (CCOM) (CHEM 2003) that allows communication through the exchange of XML messages. It is based on public domain Message Oriented Middleware (MOM) software that provides Publish/Subscribe and Point to Point message communication. CCOM acts as a server that clients can connect to. Moreover, a client API has been developed on top of the MOM interface to provide additional functionality and hide the aspects of transport protocols to the clients.

6. Case study The proposed integration architecture has been successfully tested on PROCEL, a pilot plant located at UPC (Fig. 5a). It consists of three tank reactors, three heat exchangers, sensors, and the necessary pumps and valves to connect the equipment. Tests of the performance of the FDS, and the reaction of both the coordinator and the scheduler in case of abnormal events have been performed. A test starts with the generation of an initial schedule and its execution into the plant. During the execution of the schedule a fault is introduced. The FDS isolates the fault and informs the coordinator about the equipment unavailability. The coordinator starts an exceptionhandling procedure to abort the batch and sends a schedule alarm to the scheduler. A new schedule considering the actual plant situation is generated and sent to the coordinator for its execution. Once the fault is corrected, the loop is repeated to find a new optimum schedule considering the repaired equipment. In Figure 5b, the main GUI interface of the scheduling package is presented. It summarizes the execution of the test. The upper left of the screen shows a Gantt-chart of the initial schedule. The down left part shows the actual executed schedule. There is a dotted batch that represents a faulty batch. Finally, at the upper right is presented the new schedule.

1386

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7. Conclusions The applicability and effectiveness of the proposed on-line integrated framework is illustrated with its implementation into a batch chemical plant. The integrated system has shown the ability of detecting and reacting to abnormal process events under uncertainty. A structured FDS approach has been presented that leads to simpler, robust and faster to train models, which allow tighter detection limits leading to an incipient and robust detection of faults. Knowledge from a HAZOP analysis is introduced as rules to isolate the faults and to support operator decisions. The simplicity and adaptability of the FDS for its application in complex plants is presented. An open and flexible system for rescheduling has also been presented which takes advantage of user's process knowledge. The efficiency of the rescheduling system to adapt the schedule to the current situation in the plant has been successfully tested.

Acknowledgement Financial support from the E.C, (Project G 1RD-CT-2001-00466) is gratefully appreciated. References

ANSI/ISA, 88.01 Batch Control, Part 1: Models and Terminology, 1995. Arbiza M.J, Cant6n J., Espufia A., Puigjaner, L. Flexible rescheduling tool for short-term plan updating, AIChE 03', San Francisco, USA, 16-21 November 2003. Arbiza, M.J., Cant6n, J. Espufia, A. and Puigjaner, L. Objective based schedule selector: a rescheduling toolfor short-term plan updating, [CD-ROM]. ESCAPE 14, Lisboa, 2003b ]krzdn, K.E. Grafcet for intelligent supervisory control applications. Automatica, Volume 30, Issue 10, October 1994, Pages 1513-1525. Bonfill A., Arbiza M.J., Musulin E., Espufia A., Puigjaner, L. Integrating robustness and fault diagnosis in on-line scheduling of batch chemical plants. In: Proceedings of IMS International Forum 2004, Milano, Italy, pp. 515 - 522. Cant6n J., 2003, Integrated support system for planning and scheduling of batch chemical plants, PhD Thesis, Universitat Polit6cnica de Catalunya, Espafia. CHEM, Advanced Decision Support System for Chemical~Petrochemical Manufacturing Processes. fOrt-line][Accessed 2003] Available on: < http://www.chem-dss.org/>. Olsson, R. Exception handling in recipe-based batch control, Licentiate thesis, Department of Automatic Control, Lund Institute of Technology, 2002, Sweden. Ruiz, D., Nouguds, J.M., Puigjaner, L. Fault diagnosis support system for complex chemical plants. Computers & Chemical Engineering, 25, pp. 151-160 (2001).

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1387

Agent-based intelligent system development for decision support in chemical process industry Ying Gao, Antonis C. Kokossis* Chemical Process Engineering, University of Surrey Guildford, Surrey, GU2 7XH UK

Abstract This paper experiments with an agent-based system designed to support decisions in chemical process industry. Chemical engineering technology, artificial intelligent and information technology are integrated to automate decisions on-line. A multi-agent system is employed to coordinate tasks and information stored in heterogeneous resources. The system architecture is first discussed in this paper. The implementation of the system provides an environment to coordinate manufacturing and integrate rules, optimization and simulation models.

Keywords: Multi-agent system, artificial intelligence, coordinate manufacturing and decision support.

information

integration,

1. Introduction Data and information resources are important assets of the chemical process industry. Their effective management and sharing are vital to maintain sustainable operations. Available assets include several software applications, models, reports (text, design results, software solutions etc) that are largely unstructured making it difficult for search, management procedures and computer environments to register and support management. The development of agent-based tools enables flexible infrastructures that support integration, manufacturing management, information sharing, and decisionsupport. In contrast to traditional software programs, software agents facilitate collaboration and integration of software as well as access to in-hourse resources (Bradshaw, et al., 1997). Agent-based systems have capabilities to function in networked distributed environment and cope with system changes (Nwana, 1996). Agents can further incorporate legacy programs by building wrappers around the program that manage interactions with other systems (Genesereth and Ketchpel, 1994, p. 48) and require only minor modification as programs change or replaced. *To whom the correspondence should be addressed: [email protected]

1388 In this paper, we explain the prototype of an agent-based system with a focus on on-line operations and negotiations. The paper is organized as the follows. Its first section, introduces basic concept. The system architecture is described next with an emphasis on the decision-support tools to use in the chemical process industry. Implementation issues are last discussed with an example of an operational scenario.

2. Multi-agent system and agent communication

2.1 Multi-agent system Multi-agent systems (MAS) have their origin in distributed artificial intelligence and object-oriented distributed systems. An agent is a computational process that implements the autonomous, communicating functionality of an application (FIPA00023, 2000). The intelligent agents have capabilities to acquire information from its environment and make decisions. Agents are relatively independent pieces of software interacting with each other through a message-based communication. Two or more agents acting together form a multi-agent system. Unlike those stand-alone agents, agents in a multi-agent system collaborate with each other to achieve common goals. These agents share information, knowledge, and tasks among themselves. Cooperation and coordination between agents is the most important feature of a multi-agent system. Major advantages in utilizing agent-based techniques are that: •

• •

Multi-agent systems have capabilities to incorporate legacy programs using wrappers that one could build around them so that the legacy programs can be accessed and exploited. Systems can be incorporated into wider cooperating agent systems and rewriting of application programs can be avoided. Multi-agent system can provide efficient solutions when information sources and expertise is distributed in the chemical manufacturing process. Application of agent-based systems help to enhance system performance in the aspects of computational efficiency, reliability, extensibility, maintainability, flexibility and reusability (Sycara, 1998). System development, integration and maintenance are easier and less costly. It is easy to add new agents into the multiagent system, and the modification can be done without much change in the system structure.

2.2 Agent communication Cooperation and coordination of agents in a multi-agent system requires that the agents be able to understand each other and communicate effectively. The infrastructure that supports the agent cooperation includes the following key components: a common agent communication language (ACL), and a shared ontology (Wooldridge, 2002).

1389

Agents typically communicate by exchanging messages represented in a standard format and using a standard agent communication language (ACL). A number of ACLs have been proposed, in which Knowledge Query and Manipulation Language (KQML) (Finin, et al., 1997, p. 291) and FIPA's agent communication language (FIPA ACL) (FIPA00023, 2000) are used most frequently. If two agents are to communicate about a specific domain, then it is necessary for them to agree on the terminology that they use to describe the domain. In the terminology of the agent community, agents must share a common ontology. Ontology is defined as specification schemes for describing concepts and their relationships in a domain (Gruber, 1993, p. 199). Once interacting agents have committed to a common ontology, it is expected that they will use this ontology to interpret communication interactions, thereby leading to mutual understanding and predictable behaviors. With a common communication language, and a shared ontology, agents can communicate with each other in the same manner, in the same syntax, and with the same understanding of the domain.

3. Agent-based information system architecture for decision support in chemical process industry Figure 1 presents the system architecture. The integrated components include process simulation, rules that comprise a decision support system, and black box regression tools in the form of artificial intelligent components and neural network (ANNs) for process analysis, data processing, process monitoring and diagnosis, process performance prediction and operation suggestion. The system comprises a knowledge base with access to software agents, and a user interface. A system knowledge base comprises process models, heuristics, as well as process data. Process models may include models for process simulation, optimization, scheduling, forecasting, and manufacturing planning and can be developed utilizing different computing languages and software. Forecasting applies to the history data and real-time data of plant operation and management. Heuristic rules provide for on-line decisions that may or may not use optimization models. Information on expert knowledge and technical resources related to the chemical manufacturing process are also provided in the knowledge base. The agents can be specialized around specific expertise and tasks to assemble and process relevant intbrmation and knowledge utilizing the available resources in the knowledge base. They could also negotiate and cooperate with each other to achieve timely decisions in dealing with different operational scenarios. Scenarios can involve negotiations with trading points and other agents. Agents are organized in a layered, distributed system, which comprises user agents, a coordinator and task agents. User agents process jobs triggered by users and managed by the coordinator that ushers jobs and regulates communication. The task agents are

1390

UserAgents

Taskagents Process P monitoring& I Optimization I Dataanalysis ati°Kng Production process

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Utility system

~

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Figure 1. Agent-based information system architecture assigned to different processes that monitor performance, forecast trends, apply optimization, support scheduling and planning decisions and develop scenarios for negotiation. Monitoring agents review performance and may release warnings about abnormal operations. Forecasting agents develop trends applying artificial neural network. Data management agents collect data, and apply mining and clustering. A separate set of agents is devoted to analyze text from documents following h-techsight technology (Banares et al., 2003). These agents employ Natural Language Processing analysis to retrieve text from reports, populate ontologies with relevant resources, correlate resources and update ontologies, and apply background search. The system infrastructure supports communication between previously established application software and programs for process simulation, optimization, scheduling and forecasting. Agents can run on the same or different computers, and information sources can be stored in distributed locations. This enables applications in networks of CPU's as these exist in industrial R&D environments. The cooperation and coordination is exemplified in negotiation examples of open markets, as this can be the case of utility networks that can trade steam and power in changeful environments. Utility systems have to compete with main grids, mini-grids, and local suppliers and service regular (process operations) and unplanned customers, as they become available during peak demand periods.

1391

4. System implementation JADE (Java Agent DEvelopment Framework) is used as a standard to develop the different agents described above. A user interface is constructed to account for a functional access to tasks, services and data. The agents communicate in FIPA, use ACL for security and control in the communication, and employ machine interpretable ontologies in RDFS. With the common communication language and shared ontologies, agents can launch experiments in negotiation, and integrate decision stages with models, rules and operational data. A simple illustration case is next presented to demonstrate the application of agents on a process operation case. Benzene-toluene separation process is selected as a process with an objective to monitor process operation condition and adjust process operation parameters in the case of abnormal situation. Agents are used to: (i) monitor operational data and compare data with acceptable profiles (ii) calculate the abnormal error and optimize the maintenance schedule (iii) warn and alarm about operational failures and under-performance (iv) communicate with users for authorization and decisions (v) forecast operational changes and economic impact Figure 2 illustrates the user interface of the agent-based system for process performance prediction. A simple ontology is developed to model the basic knowledge behind the process and allocate the different agents and models employed in the experiment. -

-

Agents in (i) apply a rule based system that calculates deviations from design profiles. Flags for acceptable or unacceptable performance are set by the agent to the user. Agents in (ii) and (v) apply models that make use of artificial neural networks trained from history data of 30,000 points that represent operation of a past year. ANN's apply back-propagation to tune parameters.

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1392 Agents in (iii) apply simple rules with the flags noted earlier. Agents in (iv) launch communication windows such as the ones shown in Figure 2. Forecasting models are programmed in C and wrapped by JAVA Native Interface (JNI). The coordination of monitoring agent and prediction agents operate at regular time intervals.

5. Conclusion and future work In this paper we presented an agent-based system capable of supporting information integration and decision-making for the chemical process industries. The system architecture is discussed first. Knowledge management is applied with the use of ontologies to integrate regression, simulation and optimization models, heuristic rules, and data management tools. The Java Agent Development Framework (JADE) has been deployed as the basis. With a common communication language and shared ontologies, agents cooperate to exchange and share information, and achieve timely decisions in dealing with various enterprise scenarios. The system has also been tested in a variety of negotiation problems that involve utility networks and trade energy and power. Agents take up negotiations, trigger optimization studies and determine prices dynamically. The paper illustrates a maintenance problem that requires the monitoring of data, comparisons with design solutions, and optimization. Agents manage information on-line, process tasks and communicate recommendations to users who authorize decisions. The work illustrates the potential of the technology to change the shape of process engineering practices and upgrade the quality of the environments currently in use. References

Bradshaw, J. M., Dutfield, S., Benoit, P., Woolley, J.D., 1997, Software Agent, MIT Press. Finin,T., Labrou, Y., Mayfield, J., 1997, Software agents, MIT Press. FIPA00023, 2000, FIPA agent management specification, Foundation for Intelligent Physical Agents, http://www.fipa.org/specs/fipa00023/ Genesereth, M.R., Ketchpel, S.P., 1994, Communications of the ACM 37, 7. Gruber, T. R., 1993, Knowledge Acquisition, 5. Nwana, H., 1996, The Knowledge Engineering Review 11, 3. Sycara, K. P., 1998, Artificial Intelligence Magazine 19, 2. Wooldridge, M., 2002, An Introduction to Multi-agent Systems, John Wiley and Sons Limited. Bafiares-Alcfintara, R., AC Kokossis and P. Linke, 2003, Applications: Building the Knowledge Economy: Issues, Applications, Case Studies, P. Cunningham, M. Cunningham, P. Fatelnig (Editors), pp 892-897

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1393

Enhanced Modeling of an Industrial Fermentation Process through Data Fusion Techniques Sophia Triadaphillou, Elaine Martin, Gary Montague l, Paul Jeffkins ~, Sarah Stimpson ~, Alison Nordon 2 Centre for Process Analytics and Control Technology University of Newcastle, Newcastle upon Tyne, NE 1 7RU, England ~GlaxoSmithKline, Worthing, England 2~Centre for Process Analytics and Control Technology University of Strathclyde, Glasgow, G1 1XN Scotland

Abstract A novel strategy for the analysis and interpretation of spectral data from a fermentation process is considered. The interpretation is challenging as a consequence of the large number of correlated spectral measurements recorded from the process in which a complex series of biochemical reactions occur. A full spectral analysis using PLS is the standard interpretation strategy. However, within this paper an alternative method, Spectral Window Selection (SWS), is proposed, and compared with that of genetic algorithms. SWS is shown to provide a more robust calibration model. Furthermore its performance is hypothesised to be enhanced by multiple model bagging. This claim is investigated and proven. Finally an overall calibration model is compared with a local modelling approach. The methodologies are applied and compared on an industrial NIR data-set from an antibiotic production process.

Keywords: Data Fusion; Modelling; Fermentation Process; Industrial Application

1. Introduction The large scale manufacture of pharmaceutical products is a highly competitive industry in which technological improvements can maintain fine business margins in the face of competition from those with lower manufacturing overheads. Processes in which pharmaceuticals are produced are particularly susceptible to large variability due to limited monitoring and control options. Previous research has demonstrated that the infrared spectral analysis of fermentation broth can provide on-line measurements of key concentrations throughout the duration of a batch but signal interpretation remains a challenge. Relating the spectra to the analyte of interest requires the construction of a robust calibration model. The traditional strategy is to apply projection to latent structures, PLS (Tosi et. al., 2003) utilising the full spectrum or else implement wavelength selection through genetic algorithms, GAs (Abrahamsson et. al., 2003) for example. An alternative approach is reported in this paper where a search strategy identifies a limited number of spectral windows (SWS) that are most descriptive of the concentrations of interest. The methodology is demonstrated by application to NIR spectral data generated from the routine operation of an industrial antibiotic production process. NIR spectroscopy was used as a result of recent successes in the determination of individual component concentrations in fermentation broth (Tamburini, et. al., 2003). J Author to whom correspondence should be addressed:[email protected]

1394

2. Wavelength Selection and Model Bagging When developing a linear model for quantitative analysis of spectral data, prediction results can be affected by wavelengths that do not offer predictive information about the analyte of interest. Also absorbance ranges of different functional groups may overlap and many substances contained in the complex samples may contribute to signals across the complete spectral wavelength range. Wavelength selection is one approach to eliminating wavelengths where descriptive information is not present. Typical wavelength-selection approaches have focused on selecting individual wavelengths using methods such as genetic algorithms. GAs' are a global search method that mimic biological evolution. GA's apply the principle of survival of the fittest to produce better approximations to the solution. Each member of the population is made up of a binary string which in this case serves to indicate whether a wavelength is selected or not. It is an iterative procedure and at each generation a portion of the population of solutions are selected with consideration of their fitness. The fitness is assessed through an objective function that characterises the performance of an individual member of the population. Once the individuals are chosen from the population, genetic operators are applied and the population is updated to produce the next generation. Further details of the GA methodology can be found in Goldberg (1989). Many significant drawbacks have been reported in the literature (McShane et al 1999): GAs tend to be slow to converge, they present a configuration challenge because of the adjustable factors (e.g. initial population, number of generations) that influence their outcome, and finally they can be biased by including wavelengths with a spurious correlation to the prediction property and the chosen wavelength subset may therefore not be appropriate for predicting future samples. In this paper, a spectral window selection (SWS) algorithm is proposed where windows of wavelengths are chosen. The algorithm is based on that described in Hinchliffe et al. (2003). By constraining the spectra selection to a limited number of windows rather than allowing multiple individual wavelengths to be selected potentially improves the calibration model performance by preventing it becoming too specific to the training information. The steps in the algorithm are summarised in Figure 1. 'Bagging' has been proposed in the literature to improve the accuracy of models. It has proven to be successful mainly in classification and pattern recognition problems. It was originally introduced by Breiman (1996). The bagged prediction is generated as a weighted combination of the predictions from n individual models. Two methods were investigated for the calculation of the weights, mean and PLS for both the results from the GAs and SWS. For average bagging, each individual model is equally weighted and the mean of the predictions for each time point is calculated. For PLS bagging, linear PLS is used to attain a weighted average.

3. Data and Spectral Measurements The data considered is from an industrial pilot-plant scale fermentation process, which involves two stages, the seed and final stage. Biomass is grown in the seed stage and is then transferred to the final stage for the production of the desired product. The final stage is a fed batch process and lasts approximately 140 hours. Seven fermentations were carried out and NIR measurements were collected on-line from the final stage of the process. Product concentration in the broth was considered to be critical to the monitoring of the batch and in this paper is the analyte of interest. A further approach investigated to improve model robustness was local modelling as suggested by Arnold et. al (2001) to achieve an improvement in overall performance compared with a global

1395 model. The local modelling approach was considered for this data set, with three regions of operation identified using mechanistic process knowledge. Algorithm initialization r-

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4.

Application of the Methodology

Calibration model training was carried out utilising two thirds of the data with the remaining one-third being used to test the models. Several pre-treatments steps were required. The raw spectroscopic data for a batch can be seen in Figure 2. For this application, first derivatives were taken (Figure 3). The derivatives were calculated using Savitsky-Golay smoothing (Gory, 1990) for l l points and a second order polynomial. For the fitness function of the GA algorithm, the RMS prediction error was used in order to be consistent with the SWS method. The reproduction was performed with a single point crossover with probability 0.7 followed by mutation. A population of 100 individuals was used. 100 generations were performed with a generation gap of 0.5.

1396

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5. Results and Discussion The results from the various approaches for the prediction of the product concentration are summarised in Table 1 and Table 2. Table 1 summarises the RMS errors for global modelling both without SWS, i.e. applying PLS to the complete spectra, and through the application of SWS and Average and PLS bagging. The results indicate that if a global modelling approach is implemented there are some benefits to be gained from the wavelength selection algorithm when average bagging is applied. PLS bagging tends to produce better fits to the training data but the models become too specific and consequently does not perform as well on the test data set. Table 1. Results for global modelling of the product concentration

Without SWS

With SWS Average Bag

PLS Bag

Linear PLS for Training

0.056

0.068

0.045

Linear PLS for Testing

0.092

0.059

0.096

Table 2 reports the performance of the local models constructed following the application of SWS and GAs to the test data set The training data results are not presented due to space limitation. The enhanced performance of the local model approach in terms of the RMS error is a consequence of limiting the range over which the calibration model is constructed. The local model strategy (SWS with average bagging) outperforms both global modelling and strategy involving GAs followed by PLS in all but the first time interval where the results are comparable. Table 2. RMS for the quality variable from the NIR spectra for the testing data set Time Interval 1 Time Interval 2 Time Interval 3

PLS Bag Average Bag PLS Bag Average Bag PLS Bag AverageBag SWS with Linear PLS 0.045 0.049 0.059 0.048 0.095 0.058 GAs with Linear PLS PLS (without wavelength selection)

0.045

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0.067

0.069 0.059

0.177

0.139 0.084

The importance of bagging can be observed in Figure 4 where the results of the thirty individual model errors are presented. Most notably, the RMS error for the bagged model (presented in Table 1) is lower than that for the individual model errors justifying the bagging strategy.

1397

Figure 4. Errors /br the 30 models.for the first time interva/.[br the standard batches for the ¢:rperimental and the testing &ira set, ..... RMS error qflter PLS Bagging 'r

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As an example of typical model behaviour in Table 2, Figure 5 shows the results from Time Interval I from a SWS PLS bagged model. Thirty models were used to generate the final model. Multiple batches are concatenated and the large falls in product concentrations are the breaks between batches. It can be observed that an off-set exists which is most significant for the second validation batch. The issue of offset removal is discussed in the conclusions. Figure 6 shows the frequency distribution of the wavelengths selected by the SWS algorithm and the GA. The wavelengths in the region 30 to 40 were selected the most frequently. This range aligns closely with those identified by analytical chemistry specialists. The GA did not indicate any special critical regions and the important wavelengths were not selected preferentially.

6.

Conclusions and Future W o r k

NIR spectroscopic techniques can potentially be used to measure and predict within a few minutes a number of critical components concentrations in an unprocessed

1398 fermentation broth sample. This paper has demonstrated that the selection of informative spectral regions can improve the results by reducing the contribution of overall noise from those regions not containing relevant information on the analyte concentrations. In this paper a new method, SWS, in combination with bagging has been developed and compared with the traditional approach of GAs. A local modelling strategy was used to improve the accuracy of the prediction. Offsets in predictions based solely on spectral analysis still occur, particularly if the calibration region is large. The inclusion of other process measurements in a hybrid calibration model structure can potentially deliver more robust models and reduce the offsets. For example, the residuals of the calibration model can be related to other process information to 'explain' the model deviations and 'corrections' to spectral prediction can be made. This is an ongoing area of research (Triadaphillou et al., 2004).

References Abrahamsson C., Johansson, J, Spardn A. and Lindgren, F. 2003. Comparison of different variable selection methods conducted on NIR transmission measurements on intact tablets, Chemometrics and Intelligent Laboratory Systems, 69, 1-2, 28: 3. Arnold, A.S., Matheson, L, Harvey, L M., McNeil, B. 2001. Temporally segmented modelling: a route to improved bioprocess monitoring Using near infrared spectroscopy?, Biotechnology Letters, 23:143. Breiman L. 1996. Bagging Predictors. Machine Learning Journal. 24(2): 123-140. Goldberg D.E. 1989. Genetic algorithms in search, optimization and machine learning, Addison Wesley. Gory, P.A. 1990. General least-squares smoothing and differentiation by the convolution (Savitzky-Golay) method. Anal. Chem. 62:570. Hinchliffe M, Montague GA, Willis M, Burke A. 2003. Correlating polymer resin and end-use properties to molecular-weight distribution. AIChE Journal. 49:2609. Kornmann, H, Rhiel, M, Cannizzaro, C, Marison, I, von Stockar, U. 2003. Methodology for realtime, multianalyte monitoring of fermentations using an in-situ mid-infrared sensor. Biotechnology and Bioengineering, 82 (6): 702. McShane M.J., Cameron, B.D., Cote, G.L., Motamedi, M., Spiegelman, C.H. 1999. A novel peakhopping stepwise feature selection method with application to Raman spectroscopy. Analytica Chimica Acta 388:$251. Tamburini E, Vaccari G, Tosi S, Trilli A. 2003. Near-Infrared Spectroscopy: A tool for monitoring submerged fermentation processes using an immersion optical-fiber probe. Applied Spectroscopy. 57(2). Tosi, S., Rossi, M., Tamburini, E., Vaccari, G., Amaretti, A., Matteuzzi, D. 2003. Assessment of In-Line Near-Infrared Spectroscopy for Continuous Monitoring of Fermentation Processes', Biotechnology Progress, 19(6):1816. Triadaphillou, S., Martin, E., Montague, G., Jeffkins, P., Stimpson, S., Nordon, A. 2004. Monitoring of a fermentation process through on-line spectroscopic data and the conjunction of spectroscopic and process data. Presented in BatchPro Symposium, Poros, Greece.

Acknowledgements ST would like to acknowledge the EPSRC award, KNOWHOW and the EU project BATCHPRO for financial support. CPACT acknowledges the vendor company Clairet Scientific for the loan of spectroscopic instrumentation.

European Symposium on Computer Aided Process Engineering- 15 I,. Puigjaner and A. Espufia(Editors) <, 2005 Elsevier B.V. All rights reserved.

1399

Implementation of Multi-Kalman Filter to detect Runaway Situations and Recover Control R. Nomen*, J. Sempere, E. Serra, and J. Cano Institut Quimic de Sarrih. Universitat Ramon Llull Via Augusta, 390, 08017 Barcelona (Spain)

Abstract This work should concentrate on developing a tool able to detect runaway conditions in a batch reactor and act on the reactor to recover a safer condition. Parallel Kalman filters are implemented, corresponding to some possible models that potentially can describe the system (i.e. parallel or consecutive reactions). Acting over each one of the filters, the Bayes' theorem allows determining the probability of success of each filter and, finally, estimating the divergence of the system. If the divergence were positive, a runaway situation is detected and prevention and protection procedures should be activated dangerous situations. Using the divergence criterion, a runaway situation is detected at very early stages, giving time enough to decide and apply the most convenient actions.

Keywords: Kalman filter, divergence, runaway, control, batch reactor 1.

Introduction

Calculation of the divergence of the trajectory of a chemical reaction carried out in an industrial reactor has demonstrated [2] to be an excellent method to early detecting runaway situations. However, noise on the measures and a lack of knowledge of a suitable kinetic and transport model of the system make the task of calculating the divergence some more difficult. Kalman filters are able to be used both to reduce the level of noise of a signal and to adjust a model. A Kalman filter is essentially a set of mathematical equations that implement a predictor-corrector type estimator that is optimal in the sense that it minimises the estimated erlvr covariance when some presumed conditions are met (scheme show in Figure 1) [I]. This occurs in large part to advances in digital computing that makes the filter useful, but also to the relative simplicity and robust nature of the filter by itself. Rarely do the conditions necessary for the optimal application of the filter, however, the filter works well for many applications. However, the model-based Kalman filter is only possible thanks to a great deal of a prior information about the process put together in a mathematical model. This is the

*Author to whom correspondence should be addressed: [email protected]

1400 most time consuming step in the application of the model single Kalman filter. Equations necessary to compute the filter are indicated in Figure 2.

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E,).P(Ej}

j=l

When a particular event Ei occurs on condition of the event A, the posterior probability P(Ei A) of the event Ei is actualised, in order to judge the state of the objective system by Bayes' theorem combined with Kalman filter, "the system in observation is considered to correspond to a model Mi" is associated with event El. Likewise "the hypothesis is assumed to be correct" is associated with the A. Also the posterior probability in a prior step is to be a priori probability of the new step. Furthermore if the actual system corresponds to a certain model, with respect to the residual from Kalman filter, the output is to be followed with the normal distribution of the average 0 and variance (det(Vi(k)) °5. e

N(¢)

0.5.~. T (k).Vi(k) 1.~(k)

= 2 . rc ~.........-~'. (det

V~(k)) °5

(9)

Therefore, regarding ~ (the difference between measure and prediction, z(k)-h(x(k)), which represents the residual obtained from the Kalman filter of model Mi, its probability density function is provided as N (Equation 9). From equations 8 and 9 the probability P~(t) corresponding to a specific model Mi is obtained from the recursion Equation 10. P~(k) -

(10)

~~Ni .Pi(k-1) i=1

1402 If the probability concerning the model Mi exceeds the probability of the other models, it can be concluded that model Mi is the better description of the system.

Divergence. Divergence establishes a universal criterion to detect unsafe situations in chemical reactors. The divergence in a reactor is defined as the trace of Jacobian that is the sum of he partial derivatives of the difference equations 1, 2 and 3 (consecutive reactions) or 4, 5 and 6 (parallel reactions). If the divergence is positive, a runaway situation is detected [2].

2. Results and discussion Figure 3 exposes the decision structure used to maintain the reactor within safer limits.

it y(t) IKalmanfilter-1I IKalmanfilter-ij [Kalman_filter-nl y(t)-9o(tl [Changeconditions]

lBiyes~e°iem-~ Pl(t)

Pi(t)

P.(t)

Yes N Figure 2. Structure of Multi-Kalman filters It is assumed that the parameters of the systems are invariant during the reaction, so the transition matrix A of the Kalman filters is set as the identity matrix. The measurement matrix is the Jacobian of the set of equations 1 to 3 or 4 to 6. Those systems do not have analytical solution, so the matrix H is calculated numerically. Y1

~'2

~'3

9

;L

e

ot

13

nl

n2

n3

30

40

25

0.5

0.3

0.7

0.53

30

1

1

1

Table 1. Condition of simulation Figure 4-1. Table 1 shows the parameter set used to simulate the system of parallel reactions. A stochastic noise with variance of 0.01 was added to the simulated profiles. When the two parallel filters were applied to the simulated measured profiles, the filter with a parallel reaction model produces the best estimation of composition. On the other hand, the filter with equilibrium model produces wrong predictions. Temperature estimates by both filters are quite similar to the real (Figure 4). The probability of each filter using the Bayes' theorem is shown in Figure 5. When the adimensional time reaches a value

1403 of 0.03, the probability of the parallel model is about 76% and at a time of 0.05, the probability is near to 100%. This filter is able to differentiate both mechanisms after short intervals of time. In addition, the multi-Kalman filter is very efficient reducing the measured variables. Concentration measured

Temperature measured

1.5 c.O

1.04

1 ~-,................."~"~'~"~~..,,~

p ........

05

i

cC~ C c

..................... "....................

I1

.

E

O

() 0

0.05

0.1

0.15

0.2

0.9

0.25

0

0.05

0.1

Time

0.'15

,

0.2

0.25

Time

Figure 4. Temperature and composition measured. //] --7

0.9

S /

0.8

Paralell Equilibrium

/

l

0.7 ....J

0.6 s

g

g

J

0.5 . . . . . . >,

~- 0.4

\

:.

0.3 o.2 0.1

005

0

0.01

0.02

0.03

0.04

0.05

0.06

rJl

n15

02

025

03

U35

04

,b45

Time

0.07

Time

Figure 5. Probability of each reaction using Multi-Kalman filter

Figure 6. Divergence along the time.

At an adimensional time of 0.05 the divergence of the system (Figure 6) takes a positive value so the control system acts over the jacked temperature to recover the control. The reduced temperature changes only from 300K to 298K (Figure 7), but the divergence of the system becomes negative, indicating a very high sensitivity of the system. Concentration measured

Temperature measured

1 0.8

(1,) 1.04 ......................................................................

0.6

0

" c') 1.02

0.4 (,~

0.2

0

........

"

0

0.1

02

' 0.3

' 0.4

'-

0.5

1

//"i

t/'

\

I/ /' y

",,, -............................................. .......................;................

0

0.1

""

0.2

0.3

0.4

0.5

Time Time Figure 7. Composition and temperature profiles.

4. Conclusions. The Kalman filter using temperature measures, composition measures or both of them reduces meaningfully the noise and avoids all false positive values of the divergence criterion for early warning runaway.

1404 Kalman filters have demonstrated to be a robust and powerful tool for fitting kinetic parameters of a reaction, and to calculate the divergence of the system. In addition, Multi-Kalman filters help to select the most convenient model to describe a system. The Multi-Kalman filter combined with the adjusted parameters solves the problem of the great amount of initial information needed to implement traditional Kalman filters, making efficient predictions in a wide range of possible cases. The combination of different Kalman filters using the Bayes' theorem and the divergence runaway criterion provide a tool to detect unsafe reaction conditions at a very early stages, providing time enough to decide actions to prevent the final runaway.

5. Symbols Cp E n

Tw U AHi

Heat capacity. activation energy. reaction order Jacket temperature, K overall heat transfer coefficient, W/mZK heat of the i-th reaction, J/mol 1

Damk6hler number, 13- - ( v A)'CB0 "k. e v • t ref dimensionless adiabatic temperature parameter, ot -

( - A I - I , ) • Uao

9f .Cp • T w dimensionless activation energy,

Yi --

Ei

R.~

dimensionless temperature 0-T/Tw dimensionless time, r =

tref X Z

~k

reaction rate state estimate measured state a posteriori state estimate

^ _

Xk

K

P; Pk

a priori state estimate Kalman gain

a priori estimate error covariance a posteriori estimate error covariance

6. References [ 1] Gelb, A., Applied Optimal Estimation. Cambridge, MA:MIT Press., 1974 [2] J.M. Zaldivar, J. Cano, M.A: A16s, J. Sempere, R. Nomen, Journal of Loss Prevention, 2003, 187-200.

European Symposiumon ComputerAided Process Engineering- 15 I,. PuiNaner and A. Espufia(Editors) (C~2005 . Elsevier B.V. All rights reserved.

1405

Supply Chain Management through a combined simulation-optimisation approach Fernando D. Mele a, Antonio Espufia a, and Luis Puigjaner a* a

Chemical Engineering Department, ETSEIB, Universitat Polit6cnica de Catalunya Av. Diagonal 647, E-08028, Barcelona, Spain

Abstract Supply Chain Management (SCM) involves the decision-making related to resources management through the entire Supply Chain (SC), from the initial suppliers to the final customers (Shapiro, 2001). Many of present SCM approaches consider operations research optimisation models, which often assume centralised management and are inadequate to efficiently undertake SC dynamics and uncertainty. On the contrary, simulation-based approaches are able to deal with these two issues but they are not appropriate to optimise the SC operation. In this work, a combined framework, which offers the advantages of simulation and optimisation, is proposed and a methodology is presented in order to explicitly include not only the traditional economic criteria, but also the other concerns: environment, safety, flexibility, customer satisfaction, etc. In this way, the simultaneous consideration of multiple criteria provides a way to further explore the necessary trade-offs upon which decision-making should be based. The results so far obtained are very promising.

Keywords: LCA, multiobjective optimisation, SCM.

1. Introduction Within the Supply Chain Management (SCM) scope, it is possible to identify two kinds of managing modes: push systems or planning-based approaches, which are centralised approaches with global information sharing, and pull systems or demand-driven approaches that can be either centralised or decentralised with a variable degree of information sharing. Many of present SCM approaches belong to the first group, considering operations research optimisation models and solving them through mathematical programming methods. Usually, these models assume centralised management and they are not able to efficiently deal with SC dynamics and uncertainty. Otherwise, within the second group, simulation-based approaches do recognise the role of uncertainties in SCM, but lack of optimisation aptitudes is their major shortcoming (Wan et al., 2003). in this work, a combined framework, which offers the advantages of simulation and optimisation, is proposed. The simulation-optimisation procedure is aimed to support the decision-making process at a tactical level determining the policies to implement Author/s to whom correspondence should be addressed: [email protected]

1406 along the simulation time horizon. Additionally, the methodology presented is able to explicitly include not only the traditional economic criteria, but also other concerns such as environment, quality, customer service, demand satisfaction, etc. Particular emphasis has been placed on environmental considerations on the basis of Life-Cycle Assessment (LCA) principles, which consider environmental issues as an integral part of the SCM problem. On the contrary, most of environmental developments tend to reduce waste generation, without explicitly accounting for wastes associated with inputs to the process and emissions that occur during acquisition of natural resources, raw material production, and use and final disposal of the product. Under these circumstances, the simultaneous consideration of multiple criteria provides a way to further explore the necessary trade-offs upon which decision-making should be based (Hugo and Pistikopoulos, 2003). Validation of the proposed approach methodology has been done through a case study and results obtained are discussed.

2. Methodology As it can be seen in Figure 1, in the core of the methodology there is an agent-based simulator module that acts as an execution system responding to uncertainties through local dispatching rules, invoking when necessary local optimisation modules, and solving conflicts through message exchange. front between : ~ j ~ t i v ~ •

[

decision

Impro v e d

variables values

I I

' no

L J ' ~

r

Settings for

o...,o°.

I

I

" ', Multio~ec:tive I met~heu~i~icol~m~n

,_

.....!

:

I ~- . . . . .

.

~

Optimality/

/

.o

"~

o0,:o::.oo

".........................

! -7................ I

"

Ooma.nd ~atisP~ction

I I,

---I

.

~V~ronrnontindex

/ i

A

!

~r-,l,. I,.,~, t.....i~,H,,,,,, .....i,,i~,.pl,o-

.......... II

[I

I1

Figure 1. GA-based strategy

The simulator receives a set of input values (decision variables) and then, by emulating the system dynamics, provides valuable information (performance measures) to an external optimisation module. The optimisation, which in our case has been implemented based on genetic algorithms (GA), utilises the information from the simulator and proposes new trial solutions for the decision variables trying to improve the performance of the entire supply chain (SC). This loop goes on until the optimality/convergence criteria are reached. As a result, an approximation of the set of trade-off solutions, commonly referred to as the efficient, non-inferior or Pareto set of solutions, is obtained. A given value of the decision variables is Pareto optimal if and

1407 only if there exist no other feasible solution that yields better in all the objectives simultaneously. Therefore, the decision maker obtains not only one solution, but a set of alternatives from which he/she can then further explore interesting trade-offs. There are two reasons for using metaheuristics (GA in this work) in the optimisation tasks. Firstly, this class of methods clearly shows that they are appropriate to address a problem of such combinatorial complexity in which the model is very difficult to be described through explicit differential or algebraic equations. Secondly, metaheuristic multiobjective algorithms have the advantage that they can potentially obtain Pareto optimal solutions also from the non-concave parts of the Pareto front in one single run, most of times clearly outperforming the strategies using mathematical programming techniques. In the specific case to be presented in this paper, the multiobjective GA works as follows. An initial population consisting of a number of chromosomes or individuals is created and evaluated in all the objectives through the corresponding simulation runs. Each individual encodes all the decisions variables for the problem. From the initial population, the initial Pareto-optimal set of solutions is isolated. Then a fitness value is assigned to each solution in the current population on the basis of its non-dominance level. Pairs of solutions are selected according their fitness value and then recombined and mutated. New individuals are inserted in the old population and the Pareto-optimal set is updated. The procedure is repeated until the maximum number of generations is reached. The GA strategy has been considerably improved on the basis of elitism mechanisms and the utilisation of neural networks metamodels which discard the lowperformance individuals avoiding unnecessary simulation runs. The performance measures include a traditional economic indicator, the total profit, and a set of environmental impact indicators calculated according to the LCA principles. The total profit measures the operational profit of the SC over the simulation time horizon. It basically considers revenues, and storage, manufacturing and transport costs. With regard to the environmental impact indexes, they are based on the third phase of the LCA methodology, Life-Cycle Impact Assessment, as defined in the ISO 14042. Taken from Heijungs (1992), the indicators incorporated in the model are: enhancement of the greenhouse effect (GHE), acidification (Ac) and biochemical demand of oxygen (BDO). In general, the methodology enables to deal with many objective functions, then, the multiobjective problem can be posed as: li (x) - - p . o f i t ./'2 (x) - e n v i r o n m e n t a l index

min U .I) (x) : .

.

.

where U is the set of objective functions and f(x) is the i-th objective function depending on the vector of decision variables x.

3. Case study

1408

3.1. Scenario description Let us consider the SC system consisting of nine interconnected entities shown in Figure 2. There are two plants (F1 and F2), two distribution centres (D1 and D2) and five retailers (R1 to R5). Raw materials enter the plants and the three different products elaborated (A, B and C) are distributed through the rest of the chain. Therefore, the material flow will move from the plants to the customers and the ordering flow will do in the opposite direction. Production and transportation times are defined as random parameters. Details about the operational scheduling at plants are not considered because it is accepted that in practice these decisions are local and belong to a more detailed level of analysis. ,~_~.,~. F1

Manufacturing Plar"ts "

D!

'.-, ./ ~':'~-~"

~.,

J "

.

.

.

.

Distr~blltir)r~; ,....er,tres

~

,_._~ ~ ' R 1

....

ua4

F2

-i__._-41r~

.......

..

~ ~'R5 Figure 2.SC motivating case study.

The demand has been modelled as a set of events distributed over the time horizon of the study, each of these events having an associated amount of material and time of occurrence. Both parameters, the amounts and the inter-arrival intervals between events, are time-variant. For this example, the material quantity of each demand event has been selected according to a normal distribution law. Instead, a Poisson process has been used to emulate the inter-arrival times between orders, as it is usually accepted (Law and Kelton, 1991). An important issue that determines the system behaviour is the implemented inventory control law. In this case, a periodic revision strategy has been implemented at the factories and distribution centres, being R the time period between two consecutive inventory reviews. Every R time units, the inventory position I n v is checked. If I n v is below the reorder point s, a replenishment quantity u = S - I n v is ordered to raise the stock level to S. If the position is above s, nothing is done until the next review. Thus, the strategy has three parameters whose values have to be determined: R, S and s. For the retailers, a similar but continuous revision strategy has been adapted. A number of input parameters have been also set to apply the economic and environmental model. For instance, for profit calculation, unit product prices as well as unit costs for raw materials, utilities, production, storage and transportation, have been defined. Regarding the environmental indexes calculations, utilities and raw material consumption and emissions for each process and product have been used. After setting the value of all the input parameters for the multi-agent simulator, the GAbased strategy properly designed and tuned has been applied to find those decision variables values that optimise simultaneously all the objectives posed. The planning

1409 horizon has been set to one week with precision of 1/2 hour for each simulation run. In this work, the GA handles 22 decision variables that characterise the inventory replenishment strategy: the s, S and R inventory parameters at the factories and distribution centres (12 variables), and the s and S parameters at the retailers (10 variables). Real-valued encoding for the variables and maximum number of generations as termination criterion have been used.

3.2. Results

i

Figure 3.Pareto front for two objectives In Figure 3, an approximation of the Pareto-front involving the total profit and the GHE environmental index is depicted. Figure 4 shows the inventory level evolution at distribution centre D 1 for two different points on the Pareto front, as it appears in the graphical user interface of the multi-agent system. The CPU time required for the algorithm execution varies from 20 minutes to 2 hours in the cases tested. Although the quality of the solutions may be improved by increasing the iterations number, the algorithms are able to give a feasible and acceptable solution set in a fair period of time. It is important to notice that this time depends on the number of simulation runs to be made during each algorithm execution, and then on the tuning parameters of the GA-based strategy. The multi-agent system has been developed in C# language and operates in an AMDK6 computer, 2.16 GHz, 512 MB, and the GA has been coded using MATLAB®.

4. C o n c l u s i o n s The SC operational behaviour has been simulated by using a dynamic multi-agent model. Some of the parameters that feature this behaviour have been obtained by using a GA-based method as improving/optimisation technique. The most relevant contribution of this study is the methodology employed. The GA application coupled with the use of metamodels clearly shows that other optimisation techniques would be difficult to use in solving a problem of such combinatorial

1410 complexity. Moreover, the proposed approach obtains high quality solutions with reasonable computation effort even if optimality can not be guaranteed. Perhaps the main drawback on using GAs is the need of a sensitivity analysis to study the influence of the tuning parameters.

6000

.

.

.

.

.

.

:

~

300

,-

2~n~O

.-~..............................................................................................~ .................~ ..........................................

0

............................

i .................................

~ ......

:

~50

~o0

. . . .

~ ..........................

.....................

..........~

~

:::i

.................

..............

. . . . .

............. :: ..............:i~ .....

~

-

'

,

~ ....... i i .............. ; ......

'

........ 2;

..............

~:... ...........................................................................................................................................................................................................................

Figure 4. Inventory level at D1 for one point on the Pareto front.

! ...........................................................................................................................................................................................................................

Figure 5. Inventory level at D1 for another point on the Pareto front..

On the other hand, the methodology provides a good platform for exploring the inherent conflicts between the traditional economics objectives and other important socioeconomic factors. The consideration of environmental issues into the optimisationsimulation framework at a tactical level is a novel and promising contribution to the SCM state-of-the-art. References Heijungs, R. (final editor), 1992, Environmental life cycle assessment of products- Backgrounds. National Reuse of Waste Research Programme (NOH). Hugo, A., and E. N. Pistikopoulos, 2003, Environmentally conscious planning and design of SC networks. In Proceedings of PSE 2003 (B. Chen and A. Westerberg, eds.), Elsevier: Amsterdam, 214-219. ISO 14042 (1999) Environmental Management. Life Cycle Assessment. Life Cycle Impact Assessment ISO/FDIS. Law, A. M. and W. D. Kelton, 1991, Simulation Modeling & Analysis. McGraw-Hill International Editions. Shapiro, J. F., 2001, Modeling the Supply Chain; Duxbury. Wan, X., S. Orgun, J.F. Pekny and G. V. Reklaitis, 2003, A simulation based optimization framework to analyze and investigate complex supply chains. In Proceedings of PSE 2003 (B. Chen and A. Westerberg, eds.), Elsevier: Amsterdam, 630-635. Acknowledgements Financial support received from the "Generalitat de Catalunya" (FI programs) is fully appreciated. Besides, financial support from GICASA-D 00353) and OCCASION (DPI2002-00856) projects is gratefully acknowledged.

European Symposiumon Computer Aided Process Engineering- 15 L. PuiNaner and A. Espufia(Editors) ~) 2005 Elsevier B.V. All rights reserved.

1411

Data-Based Internal Model Controller Design For A Class of Nonlinear Systems Ankush Ganeshreddy Kalmukale and Min-Sen Chiu* Department of Chemical and Biomolecular Engineering National University of Singapore, 119260, Singapore

Abstract An Internal Model Control (IMC) design strategy is proposed for a class of nonlinear systems that can be described by data-based modeling technique called Just-in-Time Learning (JITL). The proposed controller consists of a conventional linear controller augmented by a series of correction terms to account for nonlinearities in the system. The resulting controller is shown to have superior performance when compared with a linear IMC controller. This is evaluated by a case study of a polymerization reactor.

Keywords" Nonlinear systems; Just-in-time-learning; Internal model control 1. I n t r o d u c t i o n Although many processes exhibit significant nonlinear behavior, most controller design techniques are based on linear models. The prevalence of linear control strategies is primarily due to two reasons. First, there are well-established methods for the development of linear models from input-output data while practical identification techniques for nonlinear models are still being developed. Furthermore, controller design for nonlinear models is considerably more difficult than for linear models (Nahas et al., 1992). In available linear control strategies, linear IMC is a convenient and powerful controller design strategy for the open-loop stable dynamic systems (Morari and Zafiriou, 1989). This is mainly due to two reasons. First, integral action is included implicitly in the controller. Moreover, plant/model mismatch can be addressed via the design of a robustness filter. IMC design is expected to perform satisfactorily as long as the plant is operated in the vicinity of the point where the process model is obtained. However, many chemical processes exhibit a certain degree of nonlinearity. Furthermore, different operating conditions are usually necessitated by the external factors such as the persistent load disturbances or the increasingly demand of product diversification and cost reduction, e.g. grade changeover in a polymerization reactor. Under this situation, the process dynamics is forced away from its nominal design condition, which exacerbates the effect of the inherent nonlinear nature of the process. As a result, the performance of linear IMC controller will degrade or even become unstable. The extension of linear IMC strategy to nonlinear systems has been popular model-based control approach. Several nonlinear IMC schemes have been proposed in

Author/s to whom correspondence should be addressed: checms(/tmus.edu.sg

1412 literature. Among these results, Doyle et al. (1995) has proposed a partitioned model inverse controller synthesis scheme based on Volterra model that retains the original spirit and characteristics of conventional (linear) IMC while extending its capabilities to nonlinear systems. When implemented as part of the control law, the nonlinear controller consists of a standard linear controller augmented by a nonlinear correction term. Furthermore, the nonlinear correction term can be "turned off" on-line, with the control law reverting to the chosen linear control scheme. It is this flexibility that gives partitioned model inverses great promise in nonlinear control schemes. However, Volterra model derived using local expansion results such as Carleman linearization is accurate for capturing local nonlinearities around an operating point, but may be erroneous in describing global nonlinear behavior (Doyle et al., 1995). Another drawback is that second-order Volterra models require many parameters to describe nonlinearities. Harris and Palazoglu (1998) has proposed similar control scheme as Doyle et al. (1995) by using functional expansion (FEx) models instead of Volterra model. However, these models are limited to fading memory systems and the radius of convergence is not guaranteed for all input magnitudes. Maksumov et al. (2002) used neural network (NN) as a nonlinear model and a linear ARX model in partitioned model inverse controller design in an experimental study of a pit neutralization process. Inspired by the previous work, a nonlinear IMC design strategy is proposed for a class of nonlinear systems that can be modelled by data-based modeling technique called Just-In-Time Learning (JITL). JITL has been shown to have better modeling accuracy over the traditional black-box modeling technique like NN (Bontempi et al., 2001). In section 2, the proposed control strategy is discussed in detail and a polymerization reactor example is used to illustrate the proposed controller design method in section 3.

2. Proposed Control Strategy 2.1 Just-in-Time Learning (JITL) There are three main steps in JITL to predict the model output corresponding to the query data: (1) relevant data samples in the database are searched to match the query data by some nearest neighborhood criterion; (2) a local model is built based on the relevant data; (3) model output is calculated based on the local model and the current query data. The local model is then discarded right after the answer is obtained. When the next query data comes, a new local model will be built based on the aforementioned procedure (Bontempi et al., 2001). In the literature, distance measures are overwhelmingly used in the JITL to evaluate similarity between two data samples. Recently, Cheng and Chiu (2004) developed an enhanced JITL methodology by exploring both distance measure and the complementary information available from the angular relationship. In this work, we have incorporated this enhanced JITL methodology as a modeling tool in the proposed control structure. The detail algorithm is referred to Cheng and Chiu (2004).

2.2 Nonlinear IMC strategy The IMC structure (Morari and Zafiriou, 1989) has enjoyed considerable success for linear control system design and analysis. The general IMC structure is illustrated in

1413

Fig. l, where P is the process to be controlled, M represents the model of the process, and Q is the IMC controller. r

+

u

,.I o

,-I

P

Y

M

Figure l. General IMC structure

This structure is sufficiently general to allow the use of variety of process models, such as fundamental nonlinear models, as well as NN and black-box-type models. The difficulty in the use of these models in the IMC strategy arises in the design of IMC controller. Because the controller is based on the inverse of the model M, a reliable and efficient method is required to achieve this inversion (Maksumov et al., 2002). In literature, numerical and analytical inversion techniques have been employed; however these approaches can be COlnputationally demanding. +

N-L Figure 2. Partitioned model inverse

In this work, we utilize a partitioned model to yield a flexible nonlinear model inversion (Maksumov et al., 2002). Considering a process for which a linear (L) and a nonlinear (N) model are available, the models can be combined into a composite model M as

M-L+(X-L)

(1)

The inverse can then be determined as

M-' - [ Z + t 1 ( N - L ) ] - I L

I

(2)

Z,,-,,

[

-y

,

.lpI

7V

I

+

J l-Figure 3. IMC structure with partitioned controller

1414 Note that only the inverse of the linear model is required. Additionally, this inverse can be computed on-line using the feedback loop illustrated in Fig. 2. Here, we use this partitioned model inverse structure in IMC control scheme, with linear model L obtained around an operating point and nonlinear model obtained by JITL algorithm. The resulting IMC controller, referred to as nonlinear IMC (NLIMC) henceforth, has the structure illustrated in Fig. 3, where Q is the standard IMC controller (3)

Q : L-_' F L

where L is the minimum phase of linear model and F L is a low-pass filter. Typically, this filter is given by

1 FL (s) = (as + 1),.

(4)

where r is the relative degree of the system and a acts as a tuning parameter. The second filter F N is used to provide robustness for the nonlinear IMC. F N would ideally be chosen as the inverse of F L ; however, this choice for second filter amplifies noise in the controller's feedback loop. A more practical choice for this filter is given by (Harris and Palazoglu, 1998) (5)

F[~(s) F x ( s ) - (fls + 1)'

where fl is a tuning parameter and typically fl < a .

3. Case Study In this section we consider the application of NLIMC to a polymerization reaction taking place in a jacketed CSTR. The reaction involves free-radical polymerization of methyl methacrylate (MMA) with azo-bis-isobutyronitrile (AIBN) as initiator and toluene as solvent. The model is represented by the following equations (Doyle et al., 1995): dCm

: - [ k{p"

dt dC

+ k~ ~TmPo + ....

' :-k,C,

+

FI C lin - F C I

dt

V

(6)

'

(7)

,

V

{

dD o

+ k,,

-

dt

"

[

dD______L_, dt

F( Cmi. - f r o )

+ k, ,Cme,-

'

\

= M (kp + kl;')C m Po -

where Po -

m

FD_______L_~ V

ii/2 I 2f*klC I kT:, + kf,

'

FD___~o V

'

(8) (9)

1415 Owing to the space constraint, the physical parameters of this reactor are not included and readers can refer to Doyle et al. (1995) for the details. The control problem focuses on manipulating the volumetric flowrate of the initiator ( u = F / ) in order to regulate the number-average molecular weight ( ) , = D ~ / D o ) . chosen for this study is zt¢, :0.016783

The nominal operating condition

and 3',, = 25000.5. From the first-principles

reactor model, a linear model was obtained around this operating point by Taylor series approximation. The inverse of this linear model is augmented by a linear filter to obtain the linear IMC controller ( Q ) with tuning parameters r = 2, ~z = 0.5. NLIMC consists of the identical Q and the second filter F , is designed with /Y = 0.1. Fig. 4 shows the response of two controllers for +50% step changes in setpoint, it can be seen that NLIMC tracks reference trajectory much better than linear IMC. Reference trajectory is the linear filter response, which represents ideal system response in case of IMC structure when the process model is perfect. To evaluate disturbance rejection capability of the proposed control strategy, unmeasured +25% step disturbances in inlet initiator concentration are assurned and the simulation results are displayed in Fig. 5. It is evident that control performance using NLIMC scheme is better than linear IMC. In both cases considered above, NLIMC scheme has reduced the integral square tracking error, relative to linear IMC scheme, by a margin of approximately 80-95%. xlO 4 4

0.018 t

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.

.

.

.

.

.

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2

3

4

0

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2

Time (h)

3

4

Time (h)

xlO 4 0.08

.,,

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0

3

6

9

Time (h)

Figure 4. Closed- loop re,v~onses for +50% step changes in the setpoint. Dotted. rqference. dash. lineaF IMC. solid. NLIMC.

1416

xl0 4 2.55 ~

-

!

2.5

0.017 -

-!

-~',,

0.016

2.45 Y

.''"""

2.4

~

~

2.35i

' '

,,

2.3

' 3.3

xl04

"

0.013 L 0 0.024

2.8 2.7

~",

0.014

111 212 Time (h)

0

'",

~ /

u0"015

111 212 Time (h)

3.3

i

0.022

, ',

. ..- ....__

, , ...... r a

u 0.02 Y 2"6 1 ~ ~ _ ' . 0.018 2.5 ! 0

-'i

2

4 Time (h)

6

0.016

0

2

4

6

Time (h)

Figure 5. Closed-loop responses for +25% step disturbances in inlet initiator concentration ( CI," ).Dotted: reference; dash: linear IMC; solid: NLIMC.

4. Conclusion An internal model control strategy utilizing a partitioned model is proposed for nonlinear systems using JITL as an estimator of process dynamics. The fact that only a linear inversion is required in the synthesis of this controller is an attractive feature of this control scheme. Simulation results for a case study of polymerization reactor indicate that the proposed control scheme is able to provide better performance over a large range of operation as compare to a linear IMC. References Bontempi, G., H. Bersini and M. Birattari, 2001, The local paradigm for modeling and control: from neuro-fuzzy to lazy learning. Fuzzy Sets and Systems 121, 59-72. Cheng, C. and M.S. Chiu, 2004, A new data-based rnethodology for nonlinear process modeling. Chemical Engineering Science 59, 2801-2810. Doyle, F.J., B.A. Ogunnaike and R.K. Pearson, 1995, Nonlinear model-based control using second-order Volterra models. Automatica 31,697-714. Harris, K.R. and A. Palazoglu, 1998, Studies on the analysis of nonlinear process via functional expansions-III: Controller design. Chemical Engineering Science 53, 4005-4022. Maksumov, A., D.J. Mulder, K.R. Harris and A. Palazoglu, 2002, Experimental application of partitioned model-based control to pH neutralization. Ind. Eng. Chem. Res. 41,744-750. Morari, M. and E. Zafiriou, 1989, Robust Process Control. Prentice-Hall, Englewood Cliffs, NJ. Nahas, E.P., M.A. Henson and D.E. Seborg, 1992, Nonlinear internal model control strategy for neural network models. Computers Chem. Engng. 16, 1039-1057.

European Symposiumon ComputerAided Process Engineering- 15 L. Pui&janerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1417

M e a s u r e m e n t - b a s e d Run-to-run Optimization of a Batch Reaction-distillation System A. Marchetti a, B. Srinivasan a, D. Bonvin a*, S. Elgue b, L. Prat b and M. Cabassud b aLaboratoire d'Automatique Ecole Polytechnique Fdddrale de Lausanne, CH-1015 Lausanne, Switzerland bLaboratoire de Gdnie Chimique Institut National Polytechnique de Toulouse, F-31106 Toulouse, France

Abstract Measurement-based optimization schemes have been developed to deal with uncertainty and process variations. One of the methods therein, labeled NCO tracking, relies on appropriate parameterization of the input profiles and adjusts the corresponding input parameters using measurements so as to satisfy the necessary conditions of optimality (NCO). The applicability of NCO-tracking schemes has been demonstrated on several academic-size examples. The goal of this paper is to show that it can be applied with similar ease to more complex real-life systems. Run-to-run optimization of a batch reaction-separation system with propylene glycol is used for illustration.

Keywords: Dynamic optimization, Reaction-distillation system, Batch processes, Measurement-based optimization, Run-to-run optimization.

1. Introduction The sequence of reaction and separation steps represents a process configuration that is frequently encountered in batch chemical processing (Schenk et al., 1999). Optimization of such processes falls under dynamic optimization, where a given performance index is minimized while satisfying path and terminal constraints. In the presence of uncertainty (modeling errors, disturbances), the constraints are typically satisfied by applying a conservative policy that is non-optimal in most cases (Terwiesch et al., 1994). One possibility of reducing this conservatism consists of using measurements to improve the performance of the real process. This can be accomplished via model refinement and re-optimization (explicit optimization) (Eaton et al., 1990) or by adapting the inputs directly (implicit optimization) (Srinivasan et al., 2003). This paper considers thc use of measurements for optimization via the tracking of the necessary conditions of optimality (NCO) (Srinivasan ct al., 2003). NCO tracking attempts to meet the NCO by adjusting the parameters of a solution model that is typically generated from numerical optimization of a nominal (tendency) model. The optimal inputs are typically discontinuous, but are continuous and differentiable within each arc. These inputs arc dissected into various parts and appropriately parameterized. The Author to whom correspondence should be addressed: [email protected]

1418 resulting free variables are then linked to the various elements of the NCO, and appropriate adaptation laws are provided. So far, NCO tracking has been investigated via simulation of academic-size problems involving relatively low-order single-input systems (Frangois et al., 2002, Srinivasan et al., 2003). However, the scheme should also be applicable to more complex systems since the ease with which it is implemented does not depend on the complexity of the system (in terms of the number of states or equations), but rather on the possibility of approximating the optimal solution with a solution model. Along these lines, this paper investigates a realistic two-input batch reaction-separation system for which a largescale rigorous model is available (337 states and about 2000 algebraic equations). The paper is organized as follows. Section 2 describes the NCO-tracking scheme for run-to-run optimization. The problem of optimizing the production of propylene glycol is formulated in Section 3, while Section 4 generates the corresponding solution model. The optimization results via run-to--run adaptation are presented in Section 5, and Section 6 concludes the paper.

2. Measurement-based Run-to-run Optimization The following terminal-cost dynamic optimization problem is considered: min

(1)

cp(x(tf),tf)

u(t),t I

s.t.

)? = F ( x , u )

x(O) = x o

S ( x , u ) <_0

T ( x ( t f )) <_0

where q~is the scalar cost function, x the n-dimensional states with the initial conditions Xo, u the m-dimensional inputs, and tr the final time. F are the equations describing the system dynamics, S the ~-dimensional path constraints, and T the T-dimensional terminal constraints. Without loss of generality, all terminal constraints are assumed to be active in the optimal solution, the non-active ones being simply discarded. Since optimality requires meeting the NCO, the optimization problem can be treated as a control problem via NCO tracking. The NCO consist of several parts that deal with both constraints and sensitivities. One way of enforcing the NCO is to parameterize the inputs using time functions and scalars and assign them to the various NCO parts. This assignment corresponds to choosing the solution m o d e l (Srinivasan et al., 2004). In this work, the inputs are parameterized using the n~-dimensional parameter vector st. Note that n~ _> r so as to be able to meet all terminal constraints. Also, the path constraints are assumed to be implicitly satisfied with the chosen parameterization. Then, using the fact that x(tr) = X(70, the dynamic optimization problem can be recast as the following static optimization problem. min

~(~r)

s.t.

T (~) = 0

(2)

For the above static optimization problem, the constraint and the sensitivity parts of the NCO are given by (Srinivasan et al., 2003): T =0,

~oN) +v

T ~0T =0

where v are the r-dimensional Lagrange multipliers for the terminal constraints.

(3)

1419

Since batch processes are intended to be run repeatedly, it is natural to exploit this feature for process optimization. This way, optimal operation can be found iteratively over several runs. Furthermore, since there is often more to gain by keeping the constraints active compared to pushing the sensitivities to zero, this study will focus on a run-to-run controller to keep the terminal constraints T=O active. A gain matrix relating the input parameters to the terminal constraints (local sensitivities) is used for this purpose. Consider the r × n~ gain matrix G -c~T/OJ with n~ _> r and rank(G) = r. The pseudo-inverse of this matrix can be used for decoupling (Franqois et al., 2002): ~(k + 1)= : r ( k ) - G + K

T(k)

(4)

where k is the batch index and K a diagonal gain matrix of dimension r x r, and the superscript + is used for the pseudo-inverse.

3. B a t c h P r o d u c t i o n o f P r o p y l e n e G l y c o l 3.1 Reaction-distillation System The production of propylene glycol (PG) by acid-catalyzed hydration of propylene oxide (PO) is considered. In addition to the monoglycol, dipropylene glycol (DPG) and tripropylene glycol (TPG) are obtained in smaller amounts as by-products, according to the following reaction scheme: PO + H~O ~ PG,

P O + P G --~ D P G ,

P O + D P G --~ T P G

(5)

The three reactions are highly exothermic. A high H20/PO initial molar ratio favors the production of PG. Methanol is used as a solvent to break the partial solubility between water and PO. The initial conditions described by Furusawa et al. (1969) are used. The larger activation energies of the higher-order glycol reactions indicate that higher temperatures will favor the production of DPG and TPG over PG. The reaction is carried out in a jacketed stirred tank reactor. The reactor temperature is controlled by a PID controller that adjusts the jacket inlet temperature. After the reaction stage, water and methanol are removed from the glycol mixture by distillation. The column is represented by six theoretical stages with constant volume hold up. Thermodynamic properties and liquid-vapor equilibrium are rigorously calculated using the software BibPhy32 of Prosim. The integration of the set of nonlinear differential equations is carried out by DISCo (Sargousse et al., 1999), which can handle discontinuities in the differential equations. A rigorous mathematical model of order 337 is used (see Elgue (2002) for detailed description).

3.2 Optimization Problem Two manipulated variables are considered, the reactor temperature 7',., and the internal reflux ratio r. The objective is to minimize the operation time tr while meeting terminal constraints on the reaction selectivity, and the yield and final mole fraction of PG: rain

(6)

J = tS

T, ( t ).r( t ),t t

s.t.

DAE system

0 <_r(t) <_ 1

T i,i,, (t) <_ 170 °C

y e c , ( t f ) >_0.89

w/~p ( t s ) <_0.04

X p G ( t f ) >_0.8

1420 YPc -

n pG

o

W DPG + WTp G

Whp =

n po

W p G + W D p G .k- W T p G

where Xpc, is the molar fraction of PG in the reactor, ypG the PG yield, npc. the number of moles of PG in the reactor, n~.o the initial number of moles of PO in the reactor, wi the mass fraction of glycol i in the reactor and Tj,~.the jacket inlet temperature.

4. Formulation of the Solution Model Generating the solution model consists of (i) identifying the input arcs and choosing an appropriate parameterization, and (ii) linking the input parameters to the NCO (in this case the active terminal constraints). It can be seen from the numerical solution presented in Elgue (2002) that the optimal solution consists of three arcs: (A) the reaction phase, (B) the start up phase of the distillation, and (C) the distillation phase. All terminal constraints are active at the optimum. The reactor temperature exhibits a sensitivity-seeking arc during phase (A), which expresses the compromise between speeding up the main reaction and producing side products. In the other two phases, the reactor temperature is determined from the maximum jacket inlet temperature. As far as the internal reflux ratio is concerned, there is full reflux during phases (A) and (B) and a sensitivity-seeking arc during the distillation phase, which represents a compromise between quality and quantity in distillation. Though different parameterizations are possible, the two sensitivity-seeking arcs are approximated by exponential functions with two parameters: I a l + e a2t

T r (t) =

0 <_ t <_ t h

LU(Tj,,. max)

[ 1 r(t) = l [31 + e~2(t_tp )

t h < t <- t f

0 <_ t <_ tp tp < t <- t f

(7)

where the operator 7-~Tj,~) represents the reactor temperature that results from a given choice of Tj,~,. The optimal solution, computed numerically, is presented in Fig. 1. 180 ~---i ............ t I ,

t60

T,. l.Jn

,---, t40

L)

0.8 ._0

120

T

100

!

#

~

:1

~

r

0.6 X

2 L.

~L 60 E 40 ::

° k/IA~ o

,..," ,-" -'~"

t

(D ~0.4 I ~

I

ft~

~B> .... th t

cc)

loo 16o P Time [rain]

[o 2oo

tf

Figure 1. Optimal profiles: Reactor temperature T,. (solid), jacket inlet temperature Tj, i, (dashed) and internal reflux ratio r (dot-dashed) Table 1. Optimal input parameters, switching times and constraints. a2 fil fi2 tz[min] tp[min] ~min] Xpc YPc wbp al 32.4 1.04x10-3 -0.92 3.78x10 -5 49.25 73.0 247.1 0.8043 0.890 0.040

1421 The duration of the start-up phase can be fixed a priori. Furthermore, the final time b can be determined on-line by stopping the distillation at a pre-determined reactor temperature that is related to the desired final concentration of PG. This way, the constraint regarding the final mole fraction of PG in the reactor is kept active in every batch. The distillation is stopped when the boiling mixture in the reactor reaches 128°C. Finally, if all PO has reacted when time th is reached, any further increase of th has no effect on the reactor concentrations. Hence, instead of adapting g, the reaction phase is stopped when the reactor temperature reaches some heuristically-determined value. This temperature can be chosen within a wide range with little effect on tt. Here, it is chosen as 54°C. With these simplifications, the only parameters that need to be adapted are at, a,, IJ~ and fi:. The numerical optimal solution is presented in Table 1. Had the switching times th, t~,, and t / b e e n included in the parameterization, the gain in performance (reduction of b) would have been of only 0.5 rain, i.e. 0.2%.

5. Optimization via Run-to-run Adaptation 5.1 Conservative Starting Points The numerical optimization presented in the previous section uses a model, labeled "simulated reality", that is normally unknown. Thus, one has to have initial guesses for the parameters. Two starting points are considered to evaluate the run-to-run adaptation. The first point (Case I) comes from the numerical optimization of a conservative mechanistic model. In this model, conservatism with respect to the rate of reaction, the heat transfer efficiency and the separation efficiency of the distillation column is introduced. The second starting point (Case If) considers a guess that can be considered as an industrially-relevant solution due to low temperatures in the reaction phase and high reflux during the distillation phase. The choices are summed up in Table 2. Tuble 2. Initial input paranTeter.s', initial ./inn/ times and adaptation re.s'ults. /mprovemenl is computed with respect to the initial gttess and loss with t'especl to the ideal optimal solution.

Starting conditions at

CaseI Case II

32.95 27.0

#[rain] 9.4x10 -4 -0.70 2.11x10 -5 298.5 8.6x10 -4 -0.85 3.9x10 -5 311.3 ~_,

fil

[~2

Adaptation results #[min] 255.0 250.6

hnprovement 14.6% 19.5%

Loss 3.2% 1.4%

5.2 Adaptation Results The measurements of the final mole fractions are considered to exhibit 0.5% zero-mean Gaussian noise. The calculation of n pc; at final time requires the measurement of the final product density, which is considered to have 0.2% zero-mean Gaussian noise. The gain matrix G is determined at the starting point I and the adaptation law is deterlnined t?om (4). Fig. 2 shows the cost thnction obtained for 10 runs tbr Cases I and II. In order not to violate the constraints, the margins of 0.2 and 0.01 were used for the PG yield and the fraction of higher glycols, respectively. The region where the adaptation is within the noise level is reached after 2-4 batches and the adaptation may be stopped at

1422 this point. The column "improvement" is computed with respect to the initial guess and the "loss" with respect to the ideal optimal solution. The adaptation starting from the second point (Case II) performs better since the directions that are not adapted are closer to the optimal ones in Case II than in Case I. 320~

....

,

.

.

.

.

.

.E 31oi

!\

E

- - ' 3ook~

0

.~

i

.... -"----"-- . . . .

250! |

..---t

. . . . ~" . . . . . . . . . . . . . . . 2

3

4

5

Batch

6

7

8

g

0

number

Figure 2. Evolution of final batch time. Case I: solid, Case H." dashed.

6. Conclusion This work has considered a fairly complex reaction-separation process and showed that a simple solution model with a few adjustable parameters can be used efficiently for optimization purposes. The input parameters are adjusted using on-line and off-line measurements to compensate uncertainty and process variations. Most performance improvement can be done simply by keeping certain constraints active, in this case the terminal constraints, using run-to-run adaptation. Also, the improvement in cost was obtained in 2-4 batches, showing that the success of the method depends on a welldesigned adaptation law. References Eaton, J. W. and J. B. Rawlings, 1990, Feedback control of nonlinear processes using on-line optimization techniques, Comp. Chem. Eng., 14, 469-479. Elgue, S., 2002, Optimisation de syntheses pharmaceutiques globales intdgrant les aspects environnementaux et de securit6. PhD thesis, INP Toulouse. Fran9ois, G., B. Srinivasan and D. Bonvin, 2002, Run-to-run optimization of batch emulsion polymerization. In 15th IFAC World Congress, 1258, Barcelona, Spain. Furusawa, T., H. Nishiura, and T. Miyauchi, 1969, Experimental study of a bistable continuous stirred-tank reactor, Journal Chem. Engng. Japan, 2, 95-100. Sargousse, A., J. M. Le Lann, X. Joulia, and L. Jourda, 1999, Disco, un nouvel environnement de simulation orientde objet, In MOSIM'99, Moddlisation et simulation des flux physiques et informationnels, 2~m°Conference Francophone de Moddlisation et Simulation, Annecy. Schenk, M., R. Gani, I. D. L. Bogle, and E. N. Pistikopoulos, 1999, A hybrid approach for reactive separation systems, Comp. Chem. Eng., 23, Suppl., $419-$422. Srinivasan, B., and D. Bonvin, 2004, Dynamic optimization under uncertainty via NCO tracking: A solution model approach, In BatchPro, 17-35, Poros, Greece. Srinivasan, B., D. Bonvin, E. Visser, and S. Palanki, 2003, Dynamic optimization of batch processes: II. Role of measurements in handling uncertainty, Comp. Chem. Eng., 27, 27-44. Terwiesch, P., M. Agarwal, and D. W. T. Rippin, 1994, Batch unit optimization with imperfect modeling - A survey, J. Process Contr., 4, 238-258.

European Symposiumon Computer Aided Process Engineering- 15 I,. Puigjaner and A. Espufia (Editors) :©2005 Elsevier B.V. All rights reserved.

1423

Nonlinear Behaviour of a Low-Density Polyethylene Tubular Reactor-Separator-Recycle System M. Hfifele ~', I. Disli-Uslu b*, A. Kienle a'b, V. M. Krishna c, S. Pushpavanaln ~ and C.-U. Schmidt d aMax-Planck-Institute for Dynamics of Complex Technical Systems 39106 Magdeburg, Germany bInstitut ftir Automatisierungstechnik, Otto-von-Guericke Universitfit 39106 Magdeburg, Germany CDepartment of Chemical Engineering, Indian Institute of Technology Madras, 600036, India dBasell, Polyolefine GmbH 50387, Wesseling, Germany

Abstract The aim of this work is to analyse the nonlinear behaviour of a low-density polyethylene reactor-separator-recycle system. A simplified dynamic model is derived based on the detailed model presented in Hfifele (2004). A numerical bifurcation and stability analysis is performed to predict the region of stable operation. As a result multiple steady states and oscillatory behaviour were found. The implications of these findings for practical process operation are discussed.

Keywords: polymerisation, tubular reactor, low-density polyethylene(LDPE), nonlinear dynamic model, nonlinear analysis

1. Introduction A distributed parameter dynamic model of an industrial scale low-density polyethylene process was developed by Hfifele (2004). The resulting set of partial differential and algebraic equations were transformed into a DAE system with order of 30000 using an adaptive method of line approach (H~ifele et al., 2004). Dynamic simulations demonstrated that the mass recycle has strong influence on the process dynamics such that it increases the time constant of the overall process significantly and gives rise to intricate nonlinear behaviour including thermal runaway phenomena. In practice the reactor is stabilized under this condition using suitable lmans of control. Since open loop operation is also of major practical interest, a further investigation of the nonlinear dynamic behaviour is presented in this study.

Author/s to whom correspondence should be addressed: [email protected]

1424

Recent studies on the nonlinear behaviour of coupled reactor-separator-recycle networks have shown that multiple steady states and instabilities have their origins in mass recycles alone where energy feedback was excluded by means of heat exchangers (Pushpavanam and Kienle (2001); Kiss et al. (2003)). Pushpavanam and Kienle (2001) studied a first order exothermic reaction in a CSTR-separator network with mass recycle. It was found that the behaviour of such a system strongly depends on the mode of operation whether the feed flow rate or recycle flow rate is controlled. Severe operational problems including monotonic and oscillatory unstable steady states were found for fixed feed flow rates. It was concluded that fixed recycle flow rates should be preferred for feasible steady state plant operation. Nonlinearity analysis for a plug flow reactor-separator-recycle polymerisation system with a fixed feed flow rate was presented by Kiss et al. (2003). They found that state multiplicity is a common feature of consecutive-autocatalytic reactions. In an application study considering a low density polyethylene process, they predicted the existence of rmltiple steady states and that a large range of conversion corresponded to an unstable point. However, their analysis was based on a steady state model. Hence, the stability and dynamic behaviour in the Jegion of multiple steady states was not studied. In the present study, first a simplified model is presented and compared to the detailed dynamic model of H~ifele (2004). A numerical bifurcation and stability analysis is performed to predict the region of stable operation. As a result multiple steady states and oscillatory behaviour were found. The implications of these findings for practical reactor operation are discussed.

2. Process description A simplified flow diagram of the low-density polyethylene plant is shown in Figure 1. It consists of a tubular reactor, a flash unit and a recycle stream. A detailed flow sheet of the LDPE plant is given in H~ifele (2004).

I nit)a to)

I niti

C;O01 i I'I~

atol

I nlti

•: : : : ~ :: : : :. : :~

ato)

I n)tl a t o I

C~ooh)~

C~o

h )%)

i i i--

r

......~,.

Ethy~n

Figure l. Simpl!l~edflow sheet of the LDPE plant

F~oly~thyl~ n

1425 The polymerization process is carried out at pressures up to 3000 bar. The tubular reactor considered in this study has a length of 1000 m Despite the length of the reactor, conversion is kept low, about 20-30% due to the high exothermic reaction of the polymerisation. Unreacted monomer is separated from the product in the flash unit and recycled to the inlet of the reactor. The reaction is started by the addition of different initiators, which selectively decompose into radicals at different temperatures. The radicals start the chain growth by forming longer radicals. The excess heat is removed by means of cooling jackets around the reactor. Moreover a distributed injection of the initiator distributes the reaction along the tube.

3. M a t h e m a t i c a l M o d e l The reactor model takes account of the main reactions which are common for free radical polymerisation as shown in Table 1. These are decomposition of the initiator, initiation of the chain growth, chain growth reaction and termination by either combination or disproportion. In Table 1, ! represents the initiator, I* is the initiator radical, M is the monomer, R is the growing or live polymer radical, P is the dead polymer, n and m denote the degree of polymerization. Kinetic rate expressions in Table 1 are taken from the literature.

Table

1.

Reaction

mechanism

k/l~ = 1.35xl013cxp{-I 17476- 10.2805x 0 R . ~ , 5p ]a

Initiator decomposition

I /~,; >2•*

k;;; =2.89x10~cxp - 138237-1.012x R T 10-SP ]a ) k~ = k;,

(l/s)

(l/s)

.v

Initiation

/*+ M

~' >R,

Propagation Termination by combination

k,,=5.88xlO~exp(-29704+2325xlO-SP] b r:.. R R,,+R,,,

"" >P. ....

Termination by R,, + R,,, ~ ' >P,, + P,,, disproportionation a reference: Kim and Iedema (2004) b reference: Lee and Marano (1979)

k,, =1.075x10~ cxp[ - 1247+ 1"422xlORT5p)b

(m3/gmol s)

(m3/gmOl s)

k,, t = k

The dynamic model of the LDPE process is based on the mass and energy balances. The following assumptions hold : one phase flow (supercritical); no axial dispersion; constant pressure drop; constant coolant temperature; constant physical properties: negligible time delay and constant temperature in the recycle;negligible energy balance on the coolant medium and the reactor wall: ideal separation in the flash unit. Two types of initiators are used by employing the low temperature initiator at the first injection point and the high temperature initiator at later injection points.

1426 The dynamic model of the tubular reactor is developed for one section of the reactor which comprises one coolant cycle; hence the whole reactor consists of four sections. The general structure of the model equations as follows"

Ox

Ox

Ot

Oz

- + v

- - S[x_] + U [ x ] ,

x(O, t) - x , , ( O ;

0 < z < L

(1)

i C . x ( z , O ) - Xo ( z )

Where I.) is the axial velocity of flow; z is the axial coordinate; L is the total length of a reactor section and t is the time. The state vector x_ consists of the temperature and concentrations of monomer, initiators, initiator radicals, moments of living and dead polymer chains. ()x/Ol is the rate of accumulation, ( ) x / ~ z m

is the rate of convection.

S[x] represents sources and sinks due to chemical reactions. U[x__]is the heat transfer term. J

S[x] =~_,vor j ' i=l,..., NC

(for the mass balances)

(2)

j=l J

Six] = AH,. ~., rj ( for the energy balance )

(3)

j=l

U[x] - u(T - Tc )

(4)

Where v is the stochiometric coefficient,j is the index for reaction, u is the heat transfer coefficient, A[/,., is the heat of reaction. In Equation (3) equal heat of reaction for propagation, initiation and termination reactions is assumed. Furthermore the method of moments is used to represent the progress of the reaction in terms of the leading moments of the chain length distribution of the "live" and "dead" polymer chains. These morrents are defined by the following equations"

i~i - Eki[Rk] k =1

where ~ a n d l / i a r e

and

~i -- E ki[Pk ] k=2

(5)

the [h moment of the living polymer and the dead polymer

respectively. The moments will close for the considered reaction mechanism. For the purpose of stability analysis only zeroth moments are employed in the model. Mass and energy balances for both flash and mixer are assumed to be quasi-stationary. Hence the simplified model results in a system of partial differential and algebraic equations (PDAE) with 24 PDE. Subsequently it is transformed into a DAE system (with the order of 1200) by using a finite difference approximation on equidistant grid. Then it is solved within the simulation environment DIVA which also provides continuation methods for the numerical bifurcation analysis as explained in Mangold et al. (2000). 4. Results

In this section, the results of the steady state and dynamic simulations and numerical bifurcation analysis are presented. First of all the simplified model is validated by

1427 comparing to the detailed model. In Figure 2 it is shown that the temperature profile of the simple model agrees reasonably well with the detailed model. A constant heat transfer coefficient used in the simple tmdel is the main reason for the large deviation through the end of reactor. The agreement between two models can be improved by correlating the heat transfer coefficient to the polymer concentration along the reactor in order to take account decreasing heat transfer due to increasing polymer chain lengths. Dynamic simulations of the detailed model demonstrated that the mass recycle has strong influence on the process dynamics such that it gives rise to intricate nonlinear behaviour including thermal runaway phenomena (H~ifele, 2004), which can be prevented by proper control actions in practice. Transient behaviour of the simple model also agrees with this result. Figure 3 shows the response of the reactor temperature to a 10 % and 20 % decrease in the fresh feed flow-rate, indicated with the dashed and continuous lines respectively. For the later case the system temperature runs away. This phenomenon may be explained by means of stability analysis in the following paragraph.

0_9, -

-

- --

aetaiied mode: s:;r-qpte rq,;,cel 11[

0.85~

i

~®i

08

~o_7si

,

' J

",

",

,' t

",

-~i.o~;

",

-

lo2i

~0.65

0_6 0

20 e.¢ de:.:~ease :;F ~

0 9 8 '~

0_2

0a 0_6 D~:wers ,:7<ess reactc, r lengtq

0.8

Figure2. Steady stale temperature profile

~

0 96

0

02

014

0.6

0.8 ! ;i

1

1.2

l _4

~.6

Figure3. Dynamic temperature response

Next, the stability analysis is carried out to predict the multiple steady states, unstable or oscillation regions of operation. The important parameters that influence the stability are the feed flow-rate (residence time), heat transfer coefficient and initiator concentrations. In this study we present the results that were obtained if the residence time is considered as a continuation parameter. As shown in Figure 4a the simplified model predicts typical S-shaped wultiplicities. The branches of stable and unstable solutions are represented by the solid and dashed lines respectively. The current nominal operating point is illustrated as a circle on the lower stable branch. The bifurcation diagram shows five fold points corresponding to three nested hysteresis loop. It is worth noting that no steady state solution exists for very low residence times, which is in agreement with the results of Kiss et al. (2003). Stable branches above the conversion level of 0.26 are not feasible because of corresponding high temperature

1428

05 g .............................................

~ ...........................................................................................................................................................................................

7

t:

~i °°I

~' i,,, ~~., I 03

0 ~i

...................

' OI

0

02

0.4 0.6 Normalizecl ~es~der~ce t!,m,e

Figure4a. Bifurcation diagram

08

02 0.2

/ 0.3 04 Normailzed re~icte~ce ~ime

05

Figur4b.Bifurcation diagram

values. The highest conversion achievable for economically reasonable operation is found to be 0.26 whereas in commercial plants it is more than 0.30. However, at this operating point a small increase of the residence time may drive the reactor to the upper stable branch where the temperature is far above its upper limit for a safe operation. This behaviour is also demonstrated in the dynamic simulation results in Figure 3. At the hopf bifurcation point (shown as a filled square in Figure 40 one gets large amplitude oscillations of temperature and concentrations but because of very high temperatures this branch is not feasible as mentioned above. Furthermore multiplicity regions in a two dimensional cross-section of the parameter space can be mapped out by the two parameter continuation of the limit points of Figure 4 by using DIVA.

5. Conclusions In this study the nonlinear behaviour of the tubular reactor-separator-recycle system was investigated. The simplified model takes account only the main features of the detailed model. Nevertheless it was shown that the simple model agrees at least qualitatively well with the detailed model. As a result of stability analysis multiple steady states and oscillatory behaviour vere found. The implications of these findings for practical reactor operation were discussed. In the future the influence of the other important parameters such as overall heat transfer coefficient and initiator feed concentration will be studied. References

H~ifele, M., 2004, Thesis in preparation. H~ifele, M., A. Kienle, M. Boll, C.-U. Schmidt and M. Schwibach, 2004, Accepted for publication in J. Comp. Appl. Math. Kim, D.-M. and P. D. Iedema, 2004, Chem. Engng. Sci. 59, 2039-2052 Kiss, A.A., C.S. Bildea, A.C. Dimian and P.D. Iedema, 2003, Chem. Engng. Sci. 58, 337-347. Lee, K.H. and J.P. Marano, 1979, ACS Symp. Ser. 104, 221. Mangold, M., A. Kienle, K.D. Mohl and E.D. Gilles, 2000, Chem. Engng. Sci. 55, 441-454. Pushpavanam, S. and A. Kienle, 2001, Chem. Engng. Sci. 56, 2837-2849.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) ~') 2005 Elsevier B.V. All rights reserved.

1429

Control and optimal operation of simple heat pump cycles Jorgen B. Jensen and Sigurd Skogestad* Department of Chemical Engineering, NTNU N-7491 Trondheim, Norway

Abstract Cycles for heating and cooling have traditionally been studied in detail when it comes to thermodynamics and design. However, there are few publications on their optimal operation which is the theme of this paper. One important issue is which variable to control, for example, degree of super-heating, pressure, liquid level or valve opening. Also, unlike open systems, the initial charge to the cycle may have a steady state effect, and it is discussed how different designs are affected by this factor. Numerical results are provided for an ammonia cycle. Keywords" Operation, heat pump cycle, cyclic process, charge, self-optimizing control

1. Introduction Cyclic processes for heating and cooling are widely used in many applications and their power ranges from less than 1 kW to above 100 MW. All of these applications use the vapor compression cycle to "pump" energy from a low to a high temperature level. A schematic drawing of a simple cycle is shown in figure 1 together with a typical pressure-enthalpy diagram for a sub-critical cycle. The way the cycle works" The low pressure vapor (4) is compressed by supplying work W, to give a high pressure vapor with high temperatttre (1). This stream is cooled to the saturation temperatttre in the first part o f the condenser, condensed in the middle part and possibly sub-cooled in the last part to give the liquid (2). In the expansion choke, the pressure is lowered to its original value, tvsttlting in a two-phase m ixtulv (3). This mixture is vaporized and heated through the evaporator gi~'ing a super-heated vapor (4) closing the cycle. The coefficients of performance for a heating cycle (heat pump) and a cooling cycle (refrigerator, A/C) are defined as Q/, hl - h, COPh = W~ = hl - h4-

and

Q,. COP,. - W~

h4 - h3 h I - h4

(1)

respectively. Heat pumps typically have a COP of around 3 which indicates that 33% of the gained heat is adder as work (eg. electric power). In industrial processes, especially in cryogenic processes such as air separation and liquefaction of natural gas (LNG process), more complex cycles are used in order to improve the thermodynamic efficiencies. These modifications lower the temperature differences in the heat exchangers and include cycles with mixed refrigerants, several pressure levels and cascaded cycles. The Mixed Fluid Cascade process developed by the Statoil Linde :Author to whom correspondence should be addressed skoge(3!chemeng.ntnu.no

1430

z~ 3

WS

>k,J

i

er-heating- ~

"

Figure 1. Schematics of a simple vapor compression cycle with ~pical pressure-enthalpy diagram Table 1. Specifications in design and operation

Design Operation

Given Load (e.g. Qh), Pl, Ph, A~.up and AT~,t, W, (load), choke valve opening (z) and UA in two heat exchangers

5 4

Technology Alliance is being built at the LNG plant in northern Norway and incorporates all of the above modifications. The resulting plant has three cycles, all with mixed refrigerant and the first with two pressure levels. Our long term objective is to study the operation of such processes. However, as a start we need to understand the simple cycle in figure 1.

2. Operation of simple vapor compression cycles 2.1. Design versus operation Table 1 shows typical specifications for simple cycles in design (find equipment) and in operation (given equipment). Note that the five design specifications results in only four equipment parameters; compressor work W,, valve opening z and UA for the two heat exchangers. As a consequence, with the four equipment parameters specified, there is not a unique solution in terms of the operation. The "un-controlled" mode is related to the pressure level, which is indirectly set by the charge of the system. This is unique for closed systems since there is no boundary condition for pressure. In practice, the "pressure level" is adjusted directly or indirectly, depending on the design, especially of the evaporator. This is considered in more detail below. --

I)

Figure 2. Four different evaporator designs; I.a D ~ evaporator, 1.b with TEV, H.a Flooded evaporator, lI.b with level control

1431

2.2. Operational (control) degrees of freedom During operation the equipment is given. Nevertheless, we have some operational or control degrees of freedom. These include the compressor power (Ws), the charge (amount of vapor and liquid in the closed system), and the valve openings. The following valves may be adjusted on-line: • Adjustable choke valve (z); see figure 1 (not available in some simple cycles) • Adjustable valve between condenser and storage tank (for designs with a separate liquid storage tank before the choke; see design IIl.a in figure 3) In addition, we might install bypass valves on the condenser and evaporator to effectively reduce UA, but this is not normally used because use of bypass gives suboptimal operation. Some remarks: • The compression power W, sets the "load"/br the cycle, but it is otherwise not used for optimization, so in the following we do not consider it as an operational degree of freedom. • The charge has a steady-state effect for some designs because the pressure level in the system depends on the charge. A typical example is household refrigeration systems. However, such designs are generally undesirable. First, the charge can usually not be adjusted continuously. Second, the operation is sensitive to the initial charge and later to leaks. • The overall charge has no steady-state effect for some designs. This is when we have a storage tank where the liquid level has no steady-state effect. This includes designs with a liquid storage tank after the condenser (Ill.a, figure 3), as well as flooded evaporators with variable liquid level (If.a, figure 2). For such designs the charge only effects the level in the storage tank. Note that it may be possible to control (adjust) the liquid level for these designs (If.a, figure 2), and this may then be viewed as a way of continuously adjusting the charge to the rest of the system (condenser and evaporator). • There are two main evaporator designs; the dry evaporator (I) and the flooded evaporator (II) shown in figure 2. In a dry evaporator, we generally get some superheating, whereas there is no (or little) super-heating in a flooded evaporator. The latter design is better thermodynamically, because super-heating is undesirable from an efficiency (COP) point of view. In a dry evaporator one would like to control the super-heating, but this is not needed in a flooded evaporator. In addition, as ,just mentioned, a flooded evaporator with variable liquid level is insensitive to the charge. • It is also possible to have flooded condensers, and thereby no sub-cooling, but this is not desirable from a thermodynamic point of view.

2.3. Use of the control degrees of freedom In summary, we are during operation left with the valves as degrees of freedom. These valves should generally be used to optimize the operation, In most cases "optimal operation" is defined as maximizing the efficiency factor, COP. We could then envisage an

1432 on-line optimization scheme where one continuously optimizes the operation (maximizes COP) by adjusting the valves. However, such schemes are quite complex and sensitive to uncertainty, so in practice one uses simpler schemes where the valves are used to control some other variable. Such variables could be: • Valve position setpoint z,,, (that is, the valve is left in a constant position) • High pressure (Ph) • Low pressure (P1) • Temperature out of condenser (T2) or degree of sub-cooling (AT~,,b = T2 - T '~"t(Ph)) • Temperature out of evaporator (T4) or degree of super-heating (A~up = T4 - T "~at(P1)) • Liquid level in storage tank (to adjust charge to rest of system) The objective is to achieve "self-optimizing" control where a constant setpoint for the selected variable indirectly leads to near-optimal operation (Skogestad, 2000). Control (or rather minimization) of the degree of super-heating is useful for dry evaporators (with TEV, design I.b). However, it consumes a degree of freedom. In order to retain the degree of freedom, we need to add a liquid storage tank after the condenser (design III.a). In a flooded evaporator, the super-heating is minimized by design so no control is needed. With the degree of super-heating fixed (by control III.a or design II.a), there is only one degree of freedom left that needs to be controlled in order to optimize COR To see this, recall that there are 5 design specifications, so optimizing these give an optimal design. During operation, we assume the load is given (W~), and that the maximum areas are used in the two heat exchangers (this is optimal). This sets 3 parameters, so with the super-heating controlled, we have one parameter left that effects COR In conclusion, we need to set one variable, in addition to A~up, in order to completely specify (and optimize) the operation. This variable could be selected from the above list, but there are also other possibilities. Some common control schemes are discussed in the following. 2.4. Some alternative designs and control schemes Some designs are here presented and the pro's and con's are summarized in table 2.

2.4.1. Dry evaporator (I) For this design there is generally some super-heating. l.a In residential refrigerators it is common to replace the valve by a capillary tube, which is a small diameter tube designed to give a certain pressure drop. On-off control of the compressor is also common, but we will consider capacity control to get comparable results. l.b Larger systems usually have a thermostatic expansion valve (TEV), (Dossat, 2002) and (Langley, 2002), that controls the temperature and avoids excessive super-heating. A typical super-heat value is 10 °C. 2.4.2. Flooded evaporator (II) A flooded evaporator differs from the dry evaporator in that it only provides vaporization and no super-heating.

1433

I.a I.b

lI.a

II.b lll.a

Table 2. Operation of alternative designs Con's Pro's Sensitive to charge Simple design No control of super-heating Super-heating Controlled super-heating Sensitive to charge No super-heating by design Not sensitive to charge How to use valve? Valve is free No super-heating by design Sensitive to charge Not sensitive to charge Complex design How to use valve?

ll.b In flooded evaporator systems the valve is used to control the level in either evaporator or condenser (figure 2 lI.b). II.a We propose a design where the volume of the flooded evaporator is so large that there is no need to control the level in one of the heat exchangers. This design retains the valve as a degree of freedom. 2.4.3. Other designs (II1) Ill.a To reduce the sensitivity to the charge in designs l.b and II.b it is possible to include a liquid receiver before the valve as shown in figure 3. To retain a degree of freedom a valve may be added before the receiver (shown with dashed lines). lll.b It is possible to add a internal heat exchanger as shown in figure 3. This will superheat the vapor entering the compressor and sub-cool the liquid before expansion. The latter is positive because of reduced expansion losses, whereas the first is undesirable because compressor power increases. < l_

III.a

III.b

Figure 3. Special design features: IlI.a Liquid receiver, Ill.b hTternal heat exchanger

3. A m m o n i a case study Figure 4 shows a pressure enthalpy diagram for the ammonia case study. The cycle operates between -10'C and 20+C taking out 20 kW of heat. The model and diagram is based on simplified thermodynamics with constant heat capacities. A detailed model description and more results are available from the internet (Jensen and Skogestad, 2005). In table 3 we show the effect of super-heating. Designs I.a and I.b (with TEV) require some superheating to assure vapor out of evaporator, whereas the flooded evaporator (II.a/b) has no super-heating. The result is an improvement in COPc from 4.56 (10 °C super-heating) to 5.39.

1434 Table 3. The influence of super-heating on performance for given equipment and load AT,.,,p [°C ] COP,: 10 4.56 0 5.39 The main disturbance for the cycle is the air temperature in the condenser (Tair) and we now consider a case where T.ir increases by 10 °C while the load (Q~.) remains constant. Table 4 shows for alternative controlled variables the losses in terms of increased work W~ compared with a re-optimized case. This is done for design II with no super-heating where there is one degree of freedom. Pressure control gives infeasible operation. Fixing the valve gives a loss of about 12 % and fixing the evaporator level (design iI.b) gives a loss 1.6 %. The best "self-optimizing" controlled variables are the condenser liquid level and the condenser sub-cooling (AT~,,,~) which have losses of only 0.02 %. A more detailed study reveals that constant condenser level is the best strategy (not considering implementation accuracy). Table 4. Loss for different control structures for lO °C increase in Tai r (design H with constant Qc Constant z Ph P/ Evaporator level Condenser level AT,.,,b AW~. [%] 11.8 Inf" Infb 1.6 0.02 0.02 Inf = Infeasible "Feasible only for small disturbances bNot possible to fix both evaporator-duty (Qc) and pressure (P/) since Qc - UA(T sa'(el) - T,i,)

soc

106

oc

250 c o

0.5

1.5 h [W/moll

2

2.5 x 1o 4

Figure 4. Pressure-enthalpy diagram for optimal design of the ammonia case study using design l.b References Dossat, R. J. (2002). Principles of refrigeration. Prentice Hall. Jensen, J. B. and Skogestad, S. (2005). Study of an Ammonia vapor compression cycle, Internal

report, http-//www.nt .ntnu.no/users/skoge/publications/2005/jensen internalreport/. Langley, B. C. (2002). Heat pump technology. PrenticeHall. Skogestad, S. (2000). Plantwide control" the search for the self-optimizing control structure. Journal of Process Control, 10(5):pp. 487-507.

Acknowledgments This work has been done as part of the The Gas Technology Center, NTNU-SINTEF. Funding from the Norwegian Research Council is gratefully acknowledged.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigianerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1435

Advanced process control of pantolactone synthesis using nonlinear model predictive control (NMPC) Calin Cormos , Serban Agachi "Babes - Bolyai" University, Faculty of Chemistry and Chemical Engineering, 11 Arany Janos Street, RO-400028, Cluj - Napoca, Romania, Tel: +40264593833, Fax: +40264590818, E-mail: [email protected], [email protected]

Abstract In this paper, the discontinuous synthesis of racemic pantolactone has been described. The chemical steps of the synthesis take place in two stirred tank reactors, operated batchwise. The chemical reactions are highly exothermic. For a good quality of the product, the reactor temperature must be maintained between 1 2 - 14°C. The control of the reactor temperature was studied in two different situations, first using Proportional- Integral - Derivative (PID) controllers and second using a Nonlinear Model Predictive Control (NMPC). The aim of this process control study was to reduce the cooling agent consumption and to improve the quality of the product by better reactor temperature control. The pantolactone synthesis process was modeled and simulated using MATLAB / SIMULINK software package. It was demonstrated that using PID controllers the cooling agent consumption can be reduced with 10 % (comparing to real plant operation), but the reactor temperature control could be improved. In case of using an advanced reactor temperature control (model predictive control), the cooling agent consumption can be further reduced with 8 % and the temperature of the reactor is very well controlled. The applications developed for racemic pantolactone synthesis were validated by comparison with data collected from real plant operation and can be used to improve real plant operation.

Keywords: Modeling, simulation, model predictive control, batch processes 1. Introduction Calcium pantothenate is one of the most used pro-vitamins in the therapy for the human beings and for the veterinary use. Pantothenic acid is a vitamin from the complex of vitamins B; it plays an important role in the metabolism, its biological active form is Coenzyme A (Neamtu, 1996). The chemical formula of calcium pantothenate is presented below: CH 3

O

O NH

OH

O]2Ca

1436 In the synthesis of calcium panthotenate, pantolactone (a-hydroxy-13,13dimethyl-y-butyrolactone) and beta-alanine are used as starting materials. In this paper the synthesis of racemic pantolactone has been described. The chemical steps of the synthesis take place in two stirred tank reactors operated batchwise (Distiler and Goetze, 1980). The first step of the synthesis consists in the reaction between formaldehyde and isobutyraldehyde, the reaction is catalyzed by sodium hydroxide. The reaction is highly exothermic (AH1 =-36.45 kJ/mole). For a good control of the temperature, the reactor is equipped with an external jacket and two internal coils. As cooling agent, a mixture of methanol and ethylene glycol, with a low temperature (-12°C), is used. The reactor temperature must be maintained under 14°C. The control of the reactor temperature is achieved both using the sodium hydroxide flow added into the reactor and the cooling agent flows (from the jacket and the coil of the reactor). The first reaction product is a,Gt-dimethyl-13-hydroxy-propionic aldehyde (oxymethyle). The second step of the synthesis consists in the reaction between a,Gtdimethyl-13-hydroxy-propionic aldehyde and a sodium cyanide solution. The reaction is highly exothermic (AH2 = -84.4 kJ/mole). The control of the reactor solution temperature ( 1 2 - 14°C) is achieved controlling sodium cyanide solution flow and cooling agent flows (from the jacket and the coil) as manipulated variables. The second reaction product is a,y-dihydroxy-13,13-dimethyl-butyronitrile (nitrile). The Gt,y-dihydroxy-13,13-dimethyl-butyronitrile solution is then transferred in a different stirred tank reactor (operated batchwise) and hydrolyzed in acidic condition in order to obtain an aqueous racemic pantolactone solution.

2. Modeling and simulation of the synthesis process The mathematical model of a,y-dihydroxy-13,13-dimethyl-butyronitrile synthesis uses mass and energy balances for the reactor. During the synthesis, the parameters analyzed are: reactor mass (M), reactor volume (V), temperatures for reaction mass (T), jacket-cooling agent (Tag) and coils-cooling agent (Tags) and molar concentrations of the different chemical species (Ci). The model of the pantolactone synthesis is nonlinear. Because the mathematical equations for the each step are similar, below are presented only the equations for the second reaction, between sodium cyanide solution and Gt,c~-dimethyl-13-hydroxy-propionaldehyde (Cormos and Agachi, 2000).

dM dt

-- FNaCNPNaCN

(1)

dV dt

= FNaCN

dT

1

dt

(M@)

(2) (FN~cN P N.CN Cp N.CN T°

-

FN.CN

P N~CNCp T

-

- K , A , (T - T~g ) - 2K,sA~. (T - T.g. ) -- A M 2 k 2 CNaCN Coxymethyle V -

A M 1 k 1 CNaOHCIBA V )

(3)

1437

KtAt

dTag - Fag ( T 0 ag - Tag) +

V,,

dt dT ,,~

_ -

dt

F

(T- Lg)

(4)

(T - T

(5)

I/m Pag O a g

,,~.,. ( T o

-

K,,,A,,

+

C,.,.

V,,,

d C IBA

FNaCN C IBA

dt

V

)

Cp,,

(6)

- k 1C NaOHCIBA

d C NaOH

FNaCN C NaOH

dt

V

dCN.cN

F x . c N (C o N.CN - C x . c N )

art

V Fx,,cx C o~,,,,,~,,,,lc

dt

V FNaCN Cnitrile

art

V

(8)

- k 2 CNaCN Coxymethyle

dCo.,,,,.~,h,./~

dCnitrile

(7)

+ k2 C NaCN Coxymethyle

-

k 2 CN,,('N

(9)

Coxr,,,erhv/{,+ k I Cx.o, CIBA

(10)

+ k 2 CNaCN Coxymethyle

Table 1. Parameters of pantolactone synthesis model (Cormos, 2004 and Frost, 1961) T °= o

T ag

288 K ___

260 K

T°ags = 260 K Kt = 443 W / m 2 K Kt~ = 817

W/m 2 K

At~ = 1 . 5 m 2

AH1 = - 3 6 4 5 0 0 0 0 J / k m o l e

0Na('N = 1150 k g / m 3

AH,-, = - 8 4 4 0 0 0 0 0 J / k m o l e

Pag = 9 6 5 . 6 4 kg/m 3

CONaCN=6.122 k m o l e / m 3

Cp = 2 9 0 0 J/kg K

CONaoH=7.5 k m o l e / m 3

CpNacN = 3414.01 J/kg K

Vrns = 0.1 m 3 Vm = 0.5 m 3

kl = Al e x p ( - E a l / R T )

Cpag = 2 2 3 1 . 1 3 J/kg K A l = 1011 m3/kmole s

k2 = A2 exp(-Ea2/RT)

A.-, = 2* 1011 mB/kmole s

At = 10 m 2

_

Eal = 73.24 k J / m o l e Ea2 = 75 k J / m o l e

The nonlinear model described above was simulated using MATLABSIMULINK software package (the model was implemented as an S-function). The control of the reactor temperature was studied in two different situations. The first study was made using Proportional- Integral- Derivative (PID) controllers to control the reactor temperature. For this purpose, three PID controllers were used (for sodium hydroxide solution flow, sodium cyanide solution flow and cooling agent flow). The second study was made using a MPC controller. The MPC controller was implemented from SIMULINK library (MPC Toolbox). In case of reactor temperature control using model predictive control, two disturbances of the process (one measured and one unmeasured) were simulated. The measured disturbances were variations, in ramp and sinusoidal modes, of sodium hydroxide and sodium cyanide inlet concentrations (feedforward compensation). The unmeasured disturbance was variation, in a ramp mode, of the cooling agent inlet temperature (feedback compensation).

1438 3. R e s u l t s a n d d i s c u s s i o n s In the figure 1 is presented the application for simulation of pantolactone synthesis using three PID controllers (Cormos, 2004).

......

I R

I

t

....

Figure 1. Simulation of pantolactone synthesis using PID controllers

In the figures 2 and 3 are presented the variations of chemical species concentrations and temperatures (reaction mass and cooling agent) during the synthesis. .

1

20

.........

j/

.

1 CH3OH 2 CH20 3 IBA 4 H20 5 NaOH 60xymethyle 7 NaCN 8 Nitrile

.

.

.

20

] / I / [ / I

I ~ 18[~ I [ 16 .[ ~ /

I I

1 Reactor temperature 2 Cooling agent temp. (jacket) [ 3 Cooling agent temp. (coil) I

4

g15

=~10

\

6

6

2

o 0

2

4

6 -time [h]

8

10

----

Figure 2. Concentrations variation

12

0

0

2

4

6 .time [h]

8

- - - -

10

Figure 3. Temperatures variation

The real plant has only two PID control systems for the reactor temperature using sodium hydroxide and sodium cyanide flows as manipulated variables. From the comparison of the simulation results (3 PID controllers) with real plant operation data, a close similarity can be observed. This fact validates the application developed for simulation of pantolactone synthesis (Cormos, 2004). Also, it was calculated that the introduction of one supplementary temperature control systems leads to a cooling agent economy with 10 %. The annual cooling agent economy, obtained by introduction of third PID, is $2,500 (Cormos and Agachi, 2003). In addition, the introduction of supplementary temperature control systems leads to a better reactor temperature control in comparison with the present situation used in practice, with benefic consequences on the quality of the product.

1439 In the figures 4 and 5 are presented the applications for simulation of pantolactone synthesis using a MPC controller. In these applications two disturbances of the process were implemented, one measured (sodium hydroxide and sodium cyanide inlet concentrations) and one unmeasured (cooling agent inlet temperature). The MPC applications use, for prediction of the system behaviour, a linearized model of the synthesis reactor. The sampling time was set to 1 rain., control horizon to 1 and prediction horizon to 10. The weights on manipulated variables rates were set to 0.2, weight on controlled output variable (reactor temperature) was set to 2 and the rest of output variables weights were set to 0 (no control). The reference temperature of the reaction mass was set to 13°C for the first reaction and to 12°C for the second reaction. File Edit View SimulationFormat Toots Help ............. C.7[[:[i [.......................................... *t ........'..

Temperature c ,-,nling Torr,p

....,:.mrr,~

i.................!;

..............

e2;; ~''........ ....... ~.....

Figure 4. MPC.I~r oxvmethvlation process

Figure 5. MPC for nitrilation process

The variations of chemical species concentrations, reaction mass and reaction volume in case of using a MPC controller are similar with the variations of these parameters in case of using PID controllers. In the figures 6 and 7 are presented the variations of temperatures (for reaction mass and cooling agent from jacket and coils) during the oxymethylation (figure 6) and nitrilation (figure 7) processes. j

16

I\

~

3

~

temperature (coil)

/

'

[ 5

~-

4 :~i .

.

.

.

.

2

2 ~

1 r~ 0 0

....... 2 3 - 0.5

Reactor t e m p e r a t u r e Cooling agent temperature (jacket) Coolig agent temperature (coil) 1

1.5

~~_~_~,~,~,~,~_,~,..~

3

0

2

2.5

Time [hi

Fit4ure 6. Temp. variation dm'ing oxvmethv/ation

0

0.5

1

1.5

2 -time [h]

2.5

3

3.5

Figure 7. Temp. variation during nitrilation

1440 Comparing the simulation results in case of using 3 PID controllers with simulation results in case of using a MPC controller it was calculated that the in the second case the cooling agent consumption is lower with 8 % comparing with the first case. The value of additional annual cooling agent economy is $2,000. Also, the reactor temperature is better controlled in case of a MPC controller even if the process disturbances are present. This fact has benefic consequences on the quality of the pantolactone and in the end on the quality of calcium pantothenate.

4. C o n c l u s i o n s In this paper the discontinuous synthesis of racemic pantolactone was presented. The mathematical model of the synthesis process was modeled and simulated using MATLAB / SIMULINK software package. The control of the reactor temperature was studied in two different situations. In the first case Proportional - Integral - Derivative (PID) controllers were used. The second case uses MPC controller implemented as a SIMULINK block (MPC Toolbox, version 2). The aim of this process control study was to reduce the cooling agent consumption, to study the disturbance rejection and to improve the quality of the product by better reactor temperature control. It was demonstrate that using PID controllers the cooling agent consumption can be reduced with 10 % comparing to the real plant operation, but the reactor temperature control stands for further improvement. In case of using an advanced temperature control (model predictive control), the cooling agent consumption can be further reduced with 8 % and the temperature of the reactor is very well controlled. The model proved to be a reliable tool for analyzing pantolactone synthesis process. Using the model of the synthesis process and the simulation results (for different operational conditions) very valuable information can be obtained for the real plant operation (temperature control improvement, reduction of cooling agent consumption, disturbance rejection, investigation of different control strategies etc.).

5. References Neamtu, G., 1996, Substante naturale biologic active, Editura Ceres, Bucuresti, page 329 - 346 Distiler H., Goetze W., 1980, Preparation of ot-hydroxy-J3,13-dimethyl-?-butyrolactone,BASF AG, US patent 4200582 Frost, A. A., Pearson, R. G., 1961, Kinetic and Mechanism- A Study of Homogenous Chemical Reactions, Wiley International, Second Edition, page 335- 351 Cormos, C., Agachi, S., 2000, Modeling and simulation the process of synthesis of D,L calcium pantothenate, International Conference on Automation, Control and Robotics Q&A-R 2000, Cluj -Napoca, vol. 2, page 7 - 12 Cormos, C., Agachi, S., 2003, Modeling and simulation of pantolactone synthesis using ChemCAD, 30-th International Conference of Slovak Society of Chemical Engineering, Tatranske Matliare, Slovakia Cormos, C., 2004, Mathematical modeling and simulation of racemic calcium pantothenate synthesis, Ph.D. thesis, Cluj -Napoca, page 119- 170 6. Acknowledgements The authors thank the World Bank for financial support through grant CNCSU/CNFIS, no. 46174, code BM70.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1441

Design and Analysis of a Classical Controller to the Residual Oil in a Small Scale Semibatch Extractor Aline F. Cust6dio, Daiton F. Rezende, M. R. Wolf Maciel and Rubens Maciel Filho Chemical Engineering School- Universidade Estadual de Campinas: UNICAMP Cidade Universitfiria Zeferino Vaz CEP. 13081970, CP. 6066, Campinas, S.P., Brasil. e-mail: alinefc@feq, unicamp.br

Abstract The main effects of the variables concerned with the isothermal and isobaric supercritical extraction of grape oil are determined using a two levels factorial design. It is verified that the solvent velocity can be manipulated to control the residual oil content in the solids. Disturbances in the mean diameter of the particles can not be controlled during the extraction process. Parameter sensitivity supported the design and the performance investigation of the classical controller to the residual oil in the solid material. The proposed procedure was able to control the extraction process under individual and simultaneous step disturbances in the initial content of oil in the solids and in the solvent inlet concentration.

Keywords: Supercritical Extraction, Semibatch Extractor, Classical Controller 1. Introduction The solvent extraction process for oilseeds has been considered the mo st efficient way for extracting vegetable oils from its solid matrixes. The success of this technology is due to its ability in reducing to a minimum the residual oil in the extracted solid material. The hexane has been the widest used solvent, but because of its toxicity and flammability there exist incentive to replace it. Supercritical carbon dioxide has been successfully experienced for extracting natural products, due to its atoxicity, chemical stability, availability and low costs. While too much attention has been directed to know the supercritical - CO2 performance for extracting a variety of oil-bearing materials, less effort has been dedicated to the optimization and to the control of this extractive process. Several approaches have been proposed and analysed for control of semibatch processes (Garcia-Munoz et. al 2004; Asteasuain et. al. 2004; Srinivasan et. al., 2003; Grau and Puigjaner, 2000; Flores-Cerrillo and MacGregor, 2004) and can be identified the benefits of such approaches to operate the systems at higher performance when compared to manual operation. However, the CO2 semibatch extractors have peculiar characteristics, specially in their quick dynamic and operating variable interactions, so that the results and conclusions of other types of system may not be directly used. It is important to consider that a good control strategy may lead the process to be operated at high performance, which has a direct impact on the process viability, specially for supercritical extraction, that is an expensive process. The present work intends to contribute to this unexplored field through parametric sensitivity analysis and

1442 investigation of the performance of a classical controller. The first requisite to accomplish this analysis is the availability of a mathematical model and, so, extensive simulation can be carried out.

2. Supercritical Extraction Model A review on the mechanisms of the solvent extraction process of oilseeds showed that there are at least four steps that can potentially dictate the rate at witch the oil is removed from its solid matrixes. They are: 1-solvent penetration in the intraparticle pores; 2-dissolution of the oil adhered to the solid particles by the solvent that fulfill the intraparticle pores; 3-diffusion of the dissolved oil through the solvent in the intraparticle pores until the particle surface; 4-convection of the oil from the surface of the solid particles to the bulk phase of the solvent. A mathematical extraction model that includes all the steps mentioned above requires a considerable number of parameters. A common procedure (Sovovfi ,1994 and Sovovfi et al. 1994), here also adopted, is to take in consideration only the two last steps. The following considerations, in addiction to the above mentioned, are made: the extraction occurs in a fixed bed of solid particles; the solvent flows continuously through the bed of solids; the oil is treated as a single specie and no axial dispersion and isothermal and isobaric operation are considered. The equations describing the model are composed by material balances of oil in the solid and in the fluid phases: ax - J(x, y) Solid Phase" Ps (1- e)-'~-

(1)

0y U 0h 0y = j ( x , y ) Fluid Phase: 9fe--~-+Pf

(2)

where: t-time of extraction ;9s-density of the solid particles; ~-bed porosity ; x-oil mass fraction in the solids in an oil free basis ; y-oil mass fraction of the solvent in an oil free basis; J(x,y)-rate of extraction; 9f-solvent density ; U-solvent velocity ; h -axial distance in the bed. J(x,y)depends on a critical residual oil concentration in the solid particles, ~i. This concentration makes the transition of a period of extraction dictated by convection in the film surrounding the solid particles to a period dictated by diffusion through the solvent inside the particles. The fast extraction rates, in the convection period, are described by:

J(x, y) = kfaop f ( y r - y)

(3)

when x >_ x k ; Yr- oil solubility in solvent; k f a 0 - mass transfer coefficient based on the solvent phase. The slow extraction rates, in the diffusion period, are described by:

J(x, y) = ksaoPsX(1- y/yr )

(4)

when x >_ x k ; ksa0: mass transfer coefficient based on the solid phase. Equations (1), (2), (3) and (4) are subjected to the following initial and boundary conditions" x(h, t - 0)= x 0 , y ( h - 0, t ) - Y0, y(h, t < t,im)- Yr

1443 where: :~ -initial oil content in the solids: Y0 -inlet solvent oil content; yr-equilibrium solubility of the oil in the solvent; tlim_minilnum time required to the no saturated solvent reach a point h of the bed. Equations (1) to (4) were solved numerically with the fourth order Runge-Kutta method in respect to time ( At = 0. 1 s) and finite differences were used for the spatial coordinate discretization ( Ah = 0.00005

m). Values for the mass

transfer parameters may be found in Sovova et al. (1994) for the supercritical extraction

of grape oil. The pressure is 280 bars and the temperature is 40°C. The laboratory scale extractor is 5.0 Cln of useful length.

3. S o l v e n t a n d S o l i d O i l C o n t e n t s at t h e E x t r a c t o r E x i t Important information for the equipment design as well as for the definition of the operating strategy is that related to the extraction time regarding to the residual oil contents, in both, solids and solvent. Figures 1 and 2 show, respectively, the residual oil in the solids and in the solvent at the extractor exit as a function of the extraction time. The magnitude of the numerical errors in presented in the right y-axis of Figure 1 (dashed line). In terms of extraction, it can be seen that in the initial phase of the convection period, the extraction is very slow, as consequence of the high solvent oil content. As soon as fresh solvent achieves the extractor exit, the extraction becomes faster. This zone, in the convection period, characterized by fast rates of extraction, is called extraction front region. When the residual oil critical concentration in the solids is attained, at the diffusion period of extraction, the extraction rate decreases, and the residual oil content in the solids changes very slowly. The design and performance evaluation of control strategies require the knowledge of the effects of the variables concerned with the extraction process. To ensure that the obtained effects are meaningful in a computational solution, it is important to know the magnitude of the numerical errors. As can be seen in Figure 1, the relative numerical errors in the of the residual oil in the solids is smaller than about 2.5%. c o m ~utation 016

3 £ 00E-O03

j' {

~= 012

600E-003 m

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Figure/.Solid residual oil at the extractor exit.

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1000 1500 EXTRACTION TIME (s)

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Figure ~..Solvent oil content at the extractor exit as a.function o f extraction time.

1444

4. Parameter Sensitivity Analysis The objective of this section is to understand how the variables affect the residual oil content in the solids (time dependent) at the extractor exit. The variables analyzed were" mean solvent velocity (U); oil mass fraction of the solid material (N); oil mass fraction of the solvent at the extractor entrance (Y0), and mean solid particle diameter (dp). The values of the variables related to the extraction process in a standard condition are" U=5.0E-4 m/s; ~= 0.144; Y0 = 0.0 and dp=2.7 E-4 m. Figure 3 shows the main effects as a function of the extraction time. It can be seen that, in the initial extraction time (limited by convection), only the effect of the initial oil content of the solid particles is not null. In the extraction front region, however, all the variables have significant effects. The effects of the solvent velocity and of the initial oil content in the solids have positive effects on the residual oil, while the solvent velocity has a negative effect. The mean solid particle diameter shows an inversion in the signal of the main effect, in the region of the front of extraction. Firstly, the signal is negative, indicating that the residual oil in the extractor exit is lower for greater particles. After, the signal becomes strongly positive, signifying that as bigger the particles, greater will be the residual oil content in the solids. In the period of extraction rates limited by diffusion inside the solid particles, the particle mean diameter is the unique variable with important effect on the residual oil in the solids. The analysis made above indicates that the solvent velocity may be manipulated to control the residual oil concentration at the extractor exit, after disturbances in the solid and inlet solvent initial oil contents. The analysis of the impact of changes in the particle mean diameter is also useful, since although it may not be controlled during the extraction, an appropriated treatment in the particles before the extraction will be an effective procedure for high performance process operation t 20,-T ...........................................................................................................................................................................................................................

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1000 1500 2~ EXTRACTION TIME (s)

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Figure 3." Effects o f variables on the residual oil in the solids at the extractor exit.

1445

5. Performance of a Classical Proportional F e e d b a c k Controller As the semi-batch extraction process is intrinsically transient, it was necessary to define a reference extraction curve as a guide for the controller. This extraction curve was adopted as the time dependent residual oil at the extractor exit, for the variable levels considered in Figure 3. The effect of the sampling period on controller's performance was observed in Rezende (1998). The larger sampling period that still leads to a good performance of the controller was 200 seconds. This was adopted in this work. It was, also, noted that the addition of the integral and derivative actions could not improve the classical controller performance. The controller is investigated for keeping a time dependent residual oil concentration at the level dictated by the reference extraction curve, after individual and simultaneous step disturbances (5 and 15 %) in the initial solid oil content and in the inlet solvent oil concentration. The effect of the proportional controller on a time dependent curve for the residual oil concentration at the extractor exit, after positive step disturbances (5 and 15 %) in the initial solid oil content is such that, after 1400 seconds, the profiles of the controlled extraction joins the reference extraction one. Concerned with the solvent velocity after disturbances in ~, it can be seen that as soon as the period of slow rates of extraction is reached, the velocity backs to its standard value although the error is essentially null, and this velocity is no more an efficient variable to control the extraction. The performance of the proportional controller after disturbances of 5 and 15 % in the solvent concentration, at the extractor entrance, is presented in Figure 4a. Curves representing the controlled extractions are seen to follow the reference extraction curve. The behavior of the manipulated variable (the solvent velocity) can be observed in Figure 4b. Again, when the final period of slow rates of extraction is reached, the standard value of the solvent velocity is recovered. The performance of the proportional controller is shown in Figure 5a. In spite of disturbances in these two variables, the controller is still able to guide the extraction to the neighborhood of the reference extraction curve. The behavior of the solvent velocity is shown in Figure 5b.

i Disturbance of 0 5 0 0 % in xo I

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I 400

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800 EXTRACTICN

I 1200 TIME (s)

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1600

Figure 4a. Pelformance oj'the proportional controller after disturbances o[5 and 15% in the entrance solvent oil c o n t e n t .

5.00E-004 "'t

i ~ 0

I 400

800 1200 E X T R A C T I O N TIME (s)

1600

2000

Figure 4b. Proportional controller in the solvent velociO~ qfter disturbances in the inlet solvent concentration.

1446 Reference Extraction Curve Open Loop Closed Loop

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0

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2500

3000

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I

500

'

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1000 1500 2000 EXTRACTION TIM E (s)

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Figure 5b. Proportional controller in the solvent velocity after simultaneous disturbances.

6. Conclusions The parameter sensitivity analysis required to the design of control systems showed important features for the period of extraction controlled by the oil convection at the vicinity of the solid particles. The proportional controller is able to drive the time dependent curve for the residual oil in the solids towards a predefined extraction pattern, during the period of extraction limited by the oil convection. This control action is made manipulating the solvent velocity after individual or simultaneous disturbances in the initial solid oil content and in the solvent inlet concentration. References Asteasuain M., Brandolin A., Sarmoria C., et al. Simultaneous Design and Control of a Semibatch Styrene Polymerization Reactor, Industrial & Engineering Chemistry Research, 2004, vol 43, No. 17, 5233-5247. Flores-Cerrillo J., MacGregor J.F. Control of Batch Product Quality by Trajectory Manipulation using Latent Variable Models, Journal of Process Control, 2004, vol 14, No. 5,539-553. Garcia-Munoz S., Kourti T., MacGregor JF. Model Predictive Monitoring for Batch Processes, Industrial & Engineering Chemistry Research, 2004, vol 43, No. 18, 5929-5941. Grau M.D., Puigjaner L. Batch and Semibatch Reactors Modelling and Validation Based on Online pH Measurement, Chemical Engineering Communications, 2000, vol 178, 49-65. Rezende, D.F. PhD Thesis (in pomlguese), LOPCA/FEQ/UNICAMP, S.P. Brasil, 174p., 1998. Sovovfi, H., Rate of Vegetable Oil Extraction with Supercritical CO2 - I. Modelling of Extraction Curves, Chemical Engineering Sciense, Feb. 1994, vol. 49, No. 3,409-414. Sovov/t, H., Kucera, J. & Jez, J. Rate of Vegetable Oil Extraction with Supercritical CO2 - II. Extraction of Grape Oil, Chemical Engineering Sciense, Feb. 1994, vol. 49, No. 3,415-420. Srinivasan B., Bonvin D., Visser E., et al. Dynamic Optimization of Batch Process - II. Role of Measurements in Handling Uncertainty, Computers & Chemical Engineering, 2003, vol 27, No. 1, 27-44.

European Symposiumon ComputerAided Process Engineering- 15 L. Pui~janerand A. Espufia([~ditors) (('~2005 Elsevier B.V. All rights reserved.

1447

Optimal Sensor Network Design and Upgrade using Tabu Search Mercedes C. Carnero a, Jose L,. Hernfindez a and Mabel C. Sfinchez b* ~Facultad de Ingenieria, Universidad Nacional de Rio Cuarto Campus Universitario, (5800), Rio Cuarto, ARGENTINA bplanta Piloto de lngenieria Quflnica (UNS-CONICET) Camino La Carrindanga Km 7, (8000) Bahia Blanca, ARGENTINA

Abstract In this work a Tabu Search heuristic is proposed to solve the optimal design and upgrade of sensor structures thai satisfy both economic criteria and specific requirements on key variable estimates. The heuristic is based on the Strategic Oscillation Technique around the feasibility boundary, a procedure that has good intensification and diversification capabilities. Comparative performance studies between stochastic solution strategies are performed for two industrial process networks.

Keywords: Sensor Network Design, Tabu Search, Meta-heuristics, Data Reconciliation 1. Introduction Basic and high-level plant activities, such as monitoring, regulatory and supervisory control, real-time optimisation, planning and scheduling, etc., provide valuable results only if a reliable and complete knowledge of current plant state is at hand. The quality and availability of variable estimates strongly depend on the structure of instruments installed in the process and the software tools applied to enhance its precision. The design and upgrade of sensor structures consists in selecting the type, number, accuracy, failure rate, and location of new sensors that provide the quantity and quality of information required from the process. To solve this combinatorial problem different deterministic and stochastic strategies have been presented. The existing deterministic algorithms are only efficient for solving specific problems of small to medium size (Bagajewicz and Cabrera, 2002). Consequently stochastic optimisation methods arise as an alternative to tackle the design of large-scale plant sectors subject to complex function constraints. There exist stochastic procedures based on Genetic Algorithms (GA) to design general sensor structures. Recently Chao-An el al. (2003) presented a methodology to maximize the network availability subject to cost and precision constraints on key variables, but they solve the problem for a small size network using the classical approach. In contrast, a hybrid novel procedure is developed by Carnero et. al (2004) to minimize the Author to whom correspondence should be addressed: [email protected]

1448 instrumentation network cost during its life cycle subject to precision and availability constraints. Furthermore parallel techniques based on GA are proposed by Gerkens and Heyen (2004). The Tabu Search (TS) is a memory-based stochastic optimisation strategy (Glover, 1986), that has shown to be effective for solving hard problems such as The Travelling Salesman Problem, the global optimisation of Artificial Neural Networks and telecommunication networks. Recently some applications to chemical engineering problems have appeared (Lin and Miller (2004a-b), Teh and Rangaiah (2003), Cavin et al. (2004)). It was reported that TS has a more flexible and effective search behaviour than other stochastic methods (Glover, 1986) as consequence of the use of adaptive memory. Thus it was investigated how TS could be used to solve the open sensor network design and upgrade problem. Within the framework of TS, the Strategic Oscillation Technique was applied to develop a solution procedure and its performance was compared with other existing techniques. This paper reports the results of this study and is structured as follows. In Section 2 the design problem is briefly introduced. The new strategy is described in Section 3. Application results are provided in Section 4 for two case studies and, conclusions are addressed in Section 5.

2. Sensor Network Design and Upgrade Problem The minimum cost sensor network design and upgrade problem that satisfies precision and estimability constraints for a set of key variable estimates is formulated as follows Min

cTq

s.t.

~ j ( q ) _
V j E Sj

E k (q) > 1

V k ~ Sx

qi =1

Viii

(1)

o

q ~ {0,1}n-I° where q is a (n- Io) dimensional vector of binary variables such that: qi = 1, if variable i is measured and q i - 0 otherwise; e T is the cost vector; ~'/ is the standard deviation of the j-th variable estimate after a data reconciliation procedure is applied and Ek stands for the degree of estimability of variable k (Bagajewicz and Sfinchez,1999). For this formulation E~ is set equal to one, consequently only a variable classification procedure run is needed to check its feasibility. Furthermore Sj and Sx are the set of key process variables with requirements in precision and estimability respectively, I0 is the initial set of instruments that is empty at the network design stage and, n is the total number of measurable variables. For large-scale processes, the dimension of the search-space for Problem (1) increases significantly; consequently the design turns out to be a huge combinatorial optimisation problem.

1449

3. A Tabu Search Heuristic based on Strategic Oscillations Tabu Search is a meta-heuristic optimisation technique, which makes use of historical information about the solution process to explore the entire solution space and escape from local optima. The historical information is maintained in the form of Tabu lists that record the recency and frequency of solutions. At each iteration a neighbourhood of possible solutions N(q) is defined by modifying the current solution q through a sequence of moves. The new neighbours are examined to determine the best one, q', which is absent from a Tabu list. This is selected as starting point for the new iteration even it is worse than q. Also the best solution ever found, q*, is saved. New solutions are incorporated to the Recency based Tabu list and maintained there, as forbidden moves, until the Tabu tenure (pt) period is elapsed. This prevents solution cycling and being entrapped in local optima. The tabu property can be invalidated, for example, if the best neighbour is in the tabu list but it its better than q*. Frequency based Tabu list records the solutions that have been found more often. This memory enables TS to examine regions that have not been previously explored and others that have historically given good solutions. In this work the Strategic Oscillation Technique around the feasibility boundary is used to solve Problem (1) with the framework of TS. This technique provides a good balance between intensification and diversification over the intermediate to long term (Glover and Laguna, 1997). it consists of a sequence of destructive and constructive phases. Given a feasible solution, the search is strategically driven to cross the feasibility boundary and to continue in the infeasible region (destructive phase) until certain depth is reached, then the search changes the direction towards the feasible region where it continues until the same depth (constructive phase). The process of repeatedly crossing the feasibility boundary from different directions originates an oscillatory behaviour. Standard TS mechanisms are applied to avoid going back over previous trajectories. For the sensor structure design problem the procedure progress as follows. Given a feasible set of instruments q the destructive phase consists in eliminating one measurement per iteration, consequently the quantity of null elements in the members of N(q) increases. The search crosses the feasibility boundary and proceeds in the infeasible region until the evaluation function reaches the bound Lo. Then it turns around and the constructive phase is initiated by incorporating measurements. In contrast to the previous phase, the quantity of null elements in the members of N(q) lowers and the search returns to the feasible region. The constructive phase finishes when the number of measurements is greater than the bound L1. In the rest of the section implementation details of the proposed strategy are provided.

3.1 Initial Solution The procedure used to generate the initial population in the GA based strategy developed by Carnero et al. (2004) is applied. It provides a set of solutions satisfying the condition that the variables in Sj and Sx are estimable (measured or unmeasured but observable). The best individual that satisfies precision constraints is selected as the initial solution for the TS procedure. This allows to compare the evolution of both strategies using the same base.

1450

3.2 Neighbourhood Search Given a solution q, its neighbourhood N(q) is defined as the set of solutions obtained by adding to (constructive phase) or eliminating from (destructive phase) q one measurement. The neighbourhood N(q) comprises a set of new solutions, qN, that are at a Hamming distance of one with respect to q, that is N(q) = {qN / qNi ~- qi and qNj = qj Vj ¢: i}

(2)

3.3 Evaluation Function As a move can originate an infeasible solution, a member of the neighbourhood is evaluated using a function, F, that takes into account constraint violations as follows: Ic X q

if q is feasible

F - ~ CTmax + Q(q)

(3)

if q is infeasible

where (CTma x

Q(q)

--CTq)/ncu/ \-~r j

if q not satisfy estimability constraints

:

(4)

c Tq

if q satisfy estimability but not precision constraints ~=

O" F

CTm~x is the cost of measuring all variables, nr is the number of variables in Sx and, R and ncu stand for the number of variables in Sj and SK whose constraints are unsatisfied respectively. 3.4 Short and Long Term Memories The Recency based Tabu list is a vector t of dimension (n-lo). A non-zero element of t indicates that this variable move is forbidden because it was performed to obtain a recent solution. Furthermore its value is the number of remaining iterations until the Tabu tenure period for this move is elapsed. The Frequency based Tabu list is represented by a vector h of dimension (n- Io). The ith component of h reports the number of moves of variable i used to generate the next solution during ph iterations. The evaluation function corresponding to the i-th allowable move is penalized in proportion to hi in order to direct the search to unvisited areas or regions visited less frequently. After ph iteration vector h is reset.

3.5 Aspiration and Termination Criterion If the best neighbour is in a tabu area but has a better evaluation function value than q* then its tabu property is invalidated. Termination on convergence criterion has been implemented. If the improvement after T iterations is no larger than a threshold, the search is stopped. 3.6 Bounds for the Strategic Oscillations The value for bound Lo is the instrumentation cost if all variables are measured plus the cost of the most expensive measurement. For bound L1, the 80% of the length of q is assumed.

1451

4. A p p l i c a t i o n E x a m p l e s The procedure described previously is applied to the instrumentation design of two process flowsheets. Design problems are selected as application examples because the search space for this type of problems is higher than for instrumentation upgrade. Three solution strategies are run to solve each case: l) Classic TS (CTS), 2) Strategic Oscillations (SO), 3) the procedure based on GA, developed by Carnero et al. (2004). The last one combines the benefits of a structured population in the form of neighbourhoods with a local search method, and takes advantage of process knowledge at different stages. The performance of the three methods is analysed in terms of the objective function value at the solution, that is the total cost CT, and the number of calls to the Evaluation Function (#FE).

4. 1 Case 1 The selection of flowmeters for the steam metering network (SMN) of a methanol production plant is performed. The process consists of 11 units interconnected by 28 streams. It is assumed there is no restriction for the location of sensors on any stream. Data of cost and standard deviation for measurement errors are obtained from Sen et al. (1998). The following constraints are imposed on the estimates of flowrates: o-,,=0.025, o-*6 =1.7851. Furthermore the flowrate of stream 1 should be measured or unmeasured but observable. Parameters pt and ph are set equal to 5 and 25 respectively. Table 1 shows SO solves efficiently the design. Although the three methods obtained the same solution, SO requires only 7% of the #FE of GA and 17% of the #FE of CTS.

4.1 Case 2 The flowmeter network design for a simplified ethylene plant (EP) is conducted. The process involves 82 streams and 47 units. It is assumed that the standard deviation of a flowmeter is 2.5% of the corresponding true flowrate. The following constraints are imposed on the precision of variable estimates: 0-~0 =1584.2, 0-~7 =1359.6, 0-35 =200.7, 0"39 -1580.6, 0-56=122.72,

0-69=1284.4.

The

lower bound for the flowrate degree of estimability of streams [5 12 14 35 37 44 62 70 77] is set equal to 1. Parameter pt is 9 and, ph=60 for TS and p h - 8 0 for SO. Table 2 shows the proposed strategy outperforms CTS and GA. It obtains the best solution using 41% of the #FE of GA and 50% of the #FE of CTS.

Table 1. Application Resultsjbr SMN Flowsheet Procedure CTS SO GA

Measurements 1 2 6 7 9 10 13 20 26 28 1 2 6 7 9 10 13 20 26 28 1 2 6 7 9 10 13 20 26 28

CT 533.56 533.56 533.56

# FE 4100 717 10000

1452 Table 2. Application Results for El:' Flowsheet

Procedure CTS SO GA

Measurements 1 2 5 l0 12 15 21 30 33-35 37 43 44 50 54-56 60 62 64-68 74-78 82 1 2 5 10 12 15 21 30 33-37 44 50 55 56 60 62 64-68 74-78 82 1 2 5 9 1 3 15 21 30 33-35 37 44 45 52 54-56 60 62 64-68 74-78 82

CT 50885.9

# FE 16400

50845.3

8298

50856.4

20000

5. C o n c l u s i o n s In this work a new strategy for the design and upgrade of sensor networks is presented. A Tabu Search heuristic based on the Strategic Oscillation Technique around the feasibility boundary is proposed, and its performance is compared to other existing procedures. Results indicate the strategy has good diversification capabilities because it obtains the best solution for the design problems analysed during our investigation. Furthermore, it efficiently searches the solution space, allowing to reduce significantly the number of required calls to the Evaluation Function. In future works alternative intensification and diversification techniques, such as path relinking, will be analysed.

References Bagajewicz, M. and M. Sfinchez, 1999, Cost Optimal Design and Upgrade of Non-Redundant and Redundant Linear Sensor Networks, AIChE J. 45, 1927. Bagajewicz, M. and E. Cabrera, 2002, New MILP Formulation for Instrumentation Network Design and Upgrade, AIChE J. 48,2271. Camero, M., J. Hemfindez and M. Sfinchez, 2004. Availability of Key Process Variable Estimates: An Evolutionary Approach, Proceedings of Escape 14 Congress, Lisboa, Portugal. Cavin, L., U. Fischer, F. Glover and K. Hungerbuhler, 2004, Multiobjective Process Design in Multi-purpose Batch Plants using a Tabu Search Optimization Algorithm, Comp. Chem. Eng. 28, 459. Chao-An, L., C. Chuei-Tin, K. Chin-Leng and C. Chen-Liang, 2003, Optimal Sensor Placement and Maintenance for Mass-Flow Networks, Ind. Eng. Chem. Res. 42, 4366. Gerkens, C. and G. Heyen, 2004, Use of Parallel Computers in Rational Design of Redundant Sensor Networks, Comp. Aided Chem. Eng., 18,667. Glover, F., 1986, Furore paths for integer programming and links to artificial Intelligence, Comp. Oper. Res. 1,533. Glover, F. and M. Laguna, 1997, Tabu Search. Kluwer Academic Publishers, M.A. Lin, B. and D. C. Miller, 2004a, Solving Heat Exchanger Network Synthesis Problems with Tabu Search., Comp. Chem. Eng. 28, 1451. Lin, B. and D. C. Miller, 2004b, Tabu Search Algorithm for Chemical Process Optimization, Comp. Chem. Eng. 28, 2287. Sen S., S. Narasimhan and K. Deb, 1998, Sensor Network Design of Linear Processes using Genetic Algorithms, Comp. Chem. Eng. 22, 385. Teh, Y. and G. Rangaiah, 2004, Tabu search for global optimization of continuous functions with application to phase equilibrium calculations, Comp. Chem. Eng. 28, 1665.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) c~2005 Elsevier B.V. All rights reserved.

1453

Multiperiod Planning of Multiproduct Pipelines Diego C. Cafaro and Jaime Cerdfi* INTEC (UNL - CONICET) Gtlemes 3 4 5 0 - 3000 Santa F e - ARGENTINA

Abstract Scheduling product batches in pipelines is a very complex task with many constraints to be considered. Several papers have been published on the subject during the last decade. Most of them are based on large-size MILP discrete time scheduling models whose computational efficiency greatly diminishes for rather long time horizons. By introducing an MILP continuous representation in both time and volume, Cafaro and Cerdfi (2004) recently developed a more rigorous problem description providing better schedules a! much lower computational cost. However, all model-based scheduling techniques were applied to examples featuring short time horizons and a unique duedate for all deliveries at the horizon end. Pipeline operators generally use a recurring monthly schedule involving several periods, with product demands to be satisfied at the end of each period. Because of the pipeline time delay, most of the market demands over short horizons are fulfilled through inventories already available at depot tanks or in pipeline transit. Therefore, the scheduled pumping runs have nothing to do with future product demands at distribution terminals and are aimed at simply moving product slugs along the duct. To overcome such drawbacks of current approaches, this work presents an efficient MILP continuous framework for the dynamic scheduling of pipelines over a multiperiod rolling horizon. At the completion of the current period, another one is added at the end of the rolling horizon and the re-scheduling process is triggered again over the new horizon. Pumping runs may extend for two or more periods. The approach successfully solved a real-world pipeline scheduling problem involving the transportation of four products to five destinations over a rolling horizon always comprising four one-week periods.

Keywords: multiproduct pipelines; multiperiod planning; MILP approach

1. Introduction The scheduling of multiproduct pipelines transporting refined petroleum products from a single origin to multiple destinations has attracted increasing attention among researchers in the last decade. Two different types of approaches have been proposed: knowledge-based search techniques (Sasikumar et al., 1997) and mixed-integer linear mathematical programming (MILP) formulations. Depending on whether or not the pipeline volume and the time horizon are both discretized, model-based methods can be grouped into two classes: discrete and continuous MILP approaches. Most of the Author to whom correspondence should be addressed: [email protected]

1454 proposed optimization models not only partitioned the horizon into time intervals of equal or unequal sizes but also the pipeline volume is divided into a number of singleproduct packs (Rejowski and Pinto, 2003; Magat~o, Arruda and Neves, 2004). In contrast, Cafaro and Cerdfi (2004) developed a novel MILP continuous formulation that requires neither time discretization nor pipeline division. In comparison with heuristic search techniques, one of the major drawbacks of the optimization approaches is the use of much shorter time horizons comprising just a few days. In this way, the model size remains reasonable and the optimal solution can be efficiently found. On the other hand, a common feature of all pipeline scheduling methodologies is the planning of pumping runs over a single-period time horizon and the specification of a unique due-date for every product demand just at the horizon end. However, pipeline operators generally use a recurring monthly schedule involving several periods, each one varying from 6 to 10 days. Moreover, multiple due-dates for the product deliveries to local markets are usually fixed at the period ends. One of the major challenges in the operation of pipelines is to meet just-in-time large product demands along the pipeline at different due-dates over a rather long multiperiod horizon. Since new transportation requests are placed by customers as time proceeds, the information on the problem is indeed time-dependent and the pumping run schedule should be periodically updated. But the dynamic nature of the problem forcing to periodically update the pipeline schedule has the delivery time delay as another major source. In fact, there usually is a time delay, as large as 3 to 10 days depending on the pipeline length and the depot location, between the batch injection into the pipeline and the actual delivery to its destination; i.e. the transportation lead-time. Over scheduling horizons shorter than the transportation lead-time, most of market demands are fulfilled through inventories already available at depot tanks or in pipeline transit. New pumping runs have just the purpose of moving product batches along the pipeline from their current locations to the nominated terminals. As a result, planned product injections have nothing to do neither with product demands to meet during the current horizon nor with still unknown future requirements. As time passes and new product needs at distribution terminals are considered, the update of the current pipeline schedule usually yields a completely different sequence of pumping runs. To overcome such limitations of the pipeline scheduling techniques proposed in the literature, it must be developed a new solution strategy for the dynamic pipeline scheduling problem (DPSP). In the DPSP, the information on new transportation requests becomes available as the time horizon rolls and a new period is incorporated at the horizon end to replace the first one already vanished. The DPSP is solved by tackling a sequence of static pipeline scheduling problems, a different one for every new time horizon. This work introduces an efficient multiperiod MILP continuous approach to the DPSP based on the formulation of Cafaro and Cerd/t (2004) for the static pipeline scheduling problem. The novel approach is capable of optimally updating the sequence of pipeline product injections over a rolling horizon.

2. Problem Definition Given: (a) the multiproduct pipeline structure; (b) the available tanks at every depot; (c) the product demands at every depot to meet at the end of each time period; (d) the

1455 sequence of slugs inside the pipeline at the starting time; (e) the scheduled product output at the refinery during the scheduling horizon; (f) initial inventory levels in refinery and depot tanks; (g) maximum injection rate in the pipeline, supply rate from the pipeline to depots and delivery rate from depots to local markets, (h) the number of periods involved in each time horizon and (i) the series of horizons to be considered for solving the DPSP. The problem goal is to dynamically establish/update the optimal sequence of pumping runs over a multiperiod time horizon in order to: (1) meet every product demand at each period in a timely fashion; (2) maintain the inventory level in refinery and depot tanks within the permissible range and (3) minimize the sum of pumping, transition and inventory carrying costs. 3. M a t h e m a t i c a l

Formulation

3.1 New problem variables The continuous mathematical model introduced by Cafaro and Cer&i (2004) for the static pipeline scheduling problem with a common due date for all product demands at the horizon end should be properly extended to tackle the DPSP. By considering a multiperiod planning horizon, the new formulation is capable of handling multiple duedates for the product deliveries to different distribution terminals which are supposed to occur at period ends. Let T be the ordered set of periods into which the planning horizon has been divided. The model parameters IP, and F P t represent the initial and final time of period t, respectively, while D e m / , . / ' ) stands tbr the demand of product p ~P at depot j 6J~, to be satisfied before the end of period t. The additional constraints to deal with the DPSP are given below. Other restrictions can be found in Cafaro and Cerdfi (2004). 3.2 The completion time period of a new pumping run i e l "e"'

Let us define a new binary variable w;, to denote that the pumping run i ~ I ''c~'~ is completed inside or at the end of period t (wi, - 1). The use of w;~ instead of the old variable wi prevent us from defining a different set of pumping run candidates for each period. By doing that, just a single set of new runs I ''~'~' is to be considered and consequently the increase in both the number of potential product injections and the problem size for multiperiod horizons remains quite reasonable. Every non-fictitious run i ~ i '~'~' featuring a finite length L; and containing a particular product p ~P (Zp y~.~, - 1) must be completed at some period of the planning horizon. wi,, t~T

~f'~Yi,v

(l)

V i ~ I ''~'"'

p~P

If run i ~ I ''~'~' is completed in period t, then the following conditions must be fulfilled:

Ci > IP, * w. C; < F P ,

+(1-w~.,)*MT

(2) Vi c 1,e,,, t ~ T

(3)

where MT is a sufficiently large number. Otherwise, constraints (2) and (3) both become redundant. Note that run i ~ i ''c'' can be started at some period t ' a n d finished at another period t > t' since nothing is said about the interval t ' a t which run i begins.

1456

3.3 Delivery due-date constraints In the formulation of Cafaro and Cerdfi (2004), the variable qmp,/i) denotes the amount of product p transferred from depot j to the local market during the injection of a new run i ~I "ew , i.e. over the interval [Ci-1, Ci]. If vmpj stands for the maximum discharge rate of product p at terminal j, then: q m (i)p,y <(Ci-Ci-

_ 1)*vrnpj,

Vi ~ I'e",p

~ P,j

~ Jp

(4)

Let us assume that the pumping run i e l "e'' is the last one completed in period t. The amount of product p transferred from depot j to the local market while injecting new pumping runs {1,2,3 ..... i-l, i} must be large enough to meet all pth-product demands at depotj from the initial time to the end of period t. But the last pumping run i completed at period t is not known beforehand. Consequently, the following conditional constraint must be incorporated in the problem formulation:

qm p(,~j ) > -e=l

D e m p, i

i,t

--

W i+l,t )

(5)

k=l

g ~ I new

Vp ~ P,j

~ Jp,t

~ T p j , i ~ I .....

where the set Tpj stands for the periods at which Demp,j a) takes a finite value. If run i ~/,ew is the last one completed in period t, then wi, = 1 and w(i+t), ,= 0. Therefore, the total amount of product p dispatched from terminal j to the local market will permit to meet the demand ofp from t-1 to t=t. Othewise, the constraint (5) becomes redundant.

4. Results and D i s c u s s i o n To illustrate the advantages of the proposed dynamic pipeline scheduling approach, the real-world example introduced by Rejowski and Pinto (2003) was solved but this time a much longer multiperiod horizon and multiple delivery due-dates were considered. The example involves the distribution of four refined petroleum products (P1-P4) through a single pipeline of 955 km to five terminals (D1-D5) over a planning horizon steadily comprising four weekly periods. Product demands at depots D 1 - D 5 to be satisfied at the end of periods tl-t4 are given in Table 1. Demand data for the subsequent time intervals t5-t7 still unknown at the time of developing the static pipeline schedule for the initial horizon {tl-t4} become available as the four-period horizon rolls. Let us assume a similar demand profile and refinery outputs for the next three time periods t5-t7 than the ones reported for tl-t3. The remaining data can be found in Rejowski and Pinto (2003). The pumping unit cost is assumed to be time-independent. The optimal static pipeline schedule for the initial horizon {tl-t4} is shown in Figure 1. Details on pumping runs and deliveries from the pipeline to distribution terminals are only given for period tl (Oh, 168h), i.e. for the "action" period of the initial horizon. The proposed pipeline schedule includes a sequence of five pumping runs involving the following products and volumes: p4425/P211J5/p 165°3/p3825/p 187°. Since the pipeline planning should be

1457

Table 1. Product demands at the.live distribution terminals for periods tl-t4 (Demr,/') Product demands D1 tl

D2

t2 t3 t4

tl

D3

t2 t3 t4

tl

D4

t2 t3 t4

tl

D5

t2 t3 t4

tl

t2 t3 t4

Pl

40 30 50 50

100 100 150 120 90 120 100110

140 180 170 150

P2

100120100120

100 100100110

70 80 70 60

200 200 200 220 220210250220

P3

30 40 30 20

0 0 0 0

20 30 20 30

50 60 50 40

30 20 20 40

P4

0 0 0 0

0 0 0 0

0 0 0 0

60 80 60 70

70 80 60 90

:.....

Run Time 0

Interval

i

[hi

'

~oo . . . . . . .

g

g .... ' ......

t

~o . . . .

=oo .....

19i ;,17o:1

/

i

188.7

i ~ ! ! i ~ i ~ f ~ ~ I I

192.75_261.081 '

..........650:3

I I

I I

,

,

i I

i

'"' .........

',

:~7° .......

t:" : " :

;

";. . . . .

I i

200

I

400

P1

600

~

P2

:

I

"

':: 1 I

1000

~

P4

765~:

1200

':

"

', I

800

~P3

',

', "

I

I I

~il ,,

'

"

I

672.o~

i ~ als I

i

i 1

0

I I

:

i 825 i

263.08_336.0~ ~4~.oo -

~!

,

~.oo_~~iiNi~iii~i~!!iii~

55.00

! .;o0

100 12090 100

1400

'

" I

:' :I ', I

1600

Volume [102m3]

Figure 1. Optimal static pipeline schedule for the time periods tl-t4 updated at the start of week t2 when demand data for period t5 become available, then the previous schedule is to be frozen just for the "action" period tl. As the fourperiod scheduling horizon has rolled from {tl-t4} to {t4-t7} and new demand data were considered, the sequence of pumping runs and the amounts of products delivered from the pipeline to terminals specified for the action period undergo significantly changes. Figure 2 shows the dynamic pipeline schedule finally proposed for periods tl-t4 at the start of the last horizon {t4-t7} through using the proposed DPS approach. It comprises a sequence of 9 pumping runs: p4425/p21115/PlI392/p336°/PlS/P21°65/p4('°°/P285°/p12814 including a P 1-plug to avoid the forbidden interface between products P3 and P2.

5. Conclusions A new MILP framework for the dynamic scheduling of products pipelines over a multiperiod horizon has been developed. The approach allows to consider multiple due-

1458 dates at period ends. Results show that the sequence of pumping runs finally executed over the horizon looks quite different from the one found through a static pipeline scheduling technique. Pumping runs become shorter and the number of them grows from 5 to 9, including a plug of P 1 to avoid the forbidden sequence P3-P2. Moreover, the scheduled pipeline idle time mostly vanishes and consequently the pipeline utilization is largely increased from 67.3% to 94.8% of the total available time.

Run Time 0 Interval

::::::: ::::::: :::..... ~200,. ~ ~ 2tqn

[h] 5.00_5

,.~.,

,

,

,

f

,,,

,

,,

,,;

;

l

I

I

l

',,

',

55.00_16

172.00 312.97~ 11691 324.00_336.0,~_~0

......................

:

....

,,

:

I~6:¢ ;TT,T~'~T;-

336.00 358.8(~

[ 26~

360.30 361

d"?¢ ~j

',

.3o,..18 12~41 ~ i ,~ ,[ 96 ! :::::~~:~: .....

'',

:

~: ....1~7ti~3 ~

...........~:i ~::~ii

,

: ~

64lI,961 :/ : 389i6

363.80_504.00m,

~

::::::/I j ,

509.00 55

i

83 672 00 : 128L_

.....

~

:~;:~:: :~:::..........

0

,

200

,

400

~P1

600 ~P2

,

800 ~P3

m~.~.~

~

~

.

~

~

........

~

m ~ ; : % ~ ; ~ .........~;~,~-;..,~,~;~;~#.~ , ,

1000 ~P4

1200

1400

1600

V o l u m e [lO~m ~]

Figure 2. Optimal dynamic pipeline schedule for the time periods tl-t4

References C a f a r o , D . C . , Cerdfi, J., 2 0 0 4 , Magat~o,

L., A r r u d a ,

Computers and Chemical Engineering, 28, 2 0 5 3 - 2 0 6 8 . Jr., F., 2 0 0 4 , Computers and Chemical Engineering, 28,

L. V . R . , N c v e s

171-185. Rejowski, R., Pinto, J.M., 2003, Sasikumar, 175.

Computers and Chemical Engineering, 27, 1 2 2 9 - 1 2 4 6 . S., 1 9 9 7 , Knowledge-Based Systems

M., Prakash, P.R., Patti S.M., Ramani,

10, 169-

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) (c:,2005 Elsevier B.V. All rights reserved.

1459

Statistical Performance Monitoring Using State Space Modelling and Wavelet Analysis A. Alawi, A. J. Morris and E. B. Martin ~ Centre for Process Analytics & Control Technology School of Chemical Engineering and Advanced Materials, Merz Court, University of Newcastle Newcastle Upon Tyne, NE1 7RU, UK

Abstract This paper describes the application of multiresolution analysis to the states and the model residuals calculated through the application of canonical variate analysis (CVA) for process performance monitoring. Applying Hotelling T: to the states and residuals and calculating the statistical limits will materialise in an excess of false alarms since the CVA model states and model residuals are observed to exhibit serial correlation. By applying wavelets to the states, the auto-correlation is removed and the standard monitoring metrics can then be applied. The performance and sensitivity of the proposed methodology was assessed for different monitoring indices using average run length (ARL) and false alarm rate as performance indicators. The basis of the study was a benchmark simulation of a continuous stirred tank reactor.

Keywords: Canonical variate analysis, Fault detection 1. Introduction In the chemical process industries, the on-line monitoring and diagnosis of process operating performance is extremely important in terms of the contribution it can make towards plant safety and the maintenance of process yield and high quality production. Where process monitoring and control schemes are implemented on the basis of empirical techniques, not only is it essential to ensure that the process variables reflect process behaviour and that the data is fit-for-purpose, but it is essential that the appropriate techniques are applied that capture the underlying characteristics of the process (e.g. linear, non-linear or dynamic behaviour). By implementing the appropriate techniques, thereby developing a robust monitoring scheme, the operator is empowered to discriminate between normal and abnormal operation. Under typical operating conditions, sensor measurements are highly correlated, consequently techniques such as principal component analysis (PCA), MacGregor and

i Author to whom correspondence should be addressed: [email protected]

1460 Kourti (1995), canonical variate analysis (CVA), Simoglou et al, (2002), have been applied to extract the information from the data. Although PCA has been widely applied, the most successful applications have theoretically been where the. methodology has been implemented for the analysis of steady state data that exhibits a linear relationship between the process variables. In industrial applications, the data generated does not necessarily satisfy such underlying assumptions, consequently where the process exhibits dynamic behaviour, techniques such as dynamic PCA (DPCA), Ku et al, (1996), and CVA, Simoglou et al, (2002), can be applied in the development of a monitoring scheme to capture the auto- and cross correlation present in the process data. Bakshi (1998)proposed multiscale PCA (MSPCA), which combines the ability of PCA to decorrelate the variables by extracting a linear relationship with the ability of wavelet analysis to extract the deterministic features and approximately decorrelate the autocorrelated measurements. An alternative approach proposed to capture the dynamics was proposed by Rosen and Lennox (2000) who combined adaptive PCA and multi-resolution analysis. More specifically, Simoglou et al, (2002) proposed a monitoring approach that utilizes a state space identification technique based on CVA to address the problem of process dynamics. This method takes the serial correlation into account during the dimension reduction step, as per DPCA, and then uses the state variables for computing the monitoring statistics. However, the states variables are autocorrelated, and thus neither Hotelling's 72 or the Squared Prediction Error (SPE) follow a F o r ~(2 distribution resulting in a higher than statistically desirable false alarm rate. Within this paper a methodology is proposed that utilises CVA for the resolution of the multivariate problem and then multiscale analysis is applied for enhanced fault detection. That is, a CVA model is developed to address the challenges of variable autocorrelation and cross-correlation and dimensionality reduction. Multiscale analysis is then applied to the state variables and the residuals to approximately decorrelate the state variables and the residuals. The performance and sensitivity of the proposed methodology was assessed using Average Run Length (ARL) and false alarm rates of different monitoring metrics. 2. Canonical Variate Analysis and Wavelets 2.1 Canonical Variate Analysis CVA is a multivariate statistical technique that is receiving increasing attention for the development of models for linear systems. In CVA, the orthogonal basis is selected as those linear combinations of a data set (the past inputs and outputs, p) that are most predictive of the future outputs of the process,j): p ( t ) = [y, (t - 1)...y, (t - k, )..y,, (t - 1)..y,, (t - k,,)

(1)

u , ( t - 1 ) . . . u ~ ( t - k ~ ) . . u , , ( t - 1 ) . . U m ( t - k .... ) ]r f (t) = [y~ (t)... y, (t + 1-- 1).. y,, (t).. y,, (t + 1-- 1)]r

With the state space model identified using'CVA taking the following form:

(2)

1461 X,+1 : ¢~Xt + GU, + W,

(3)

Y, - HX, + AU, + BW, + Vt

(4)

With knowledge of the canonical states and the plant data, the state space matrices • , G,H, A and B and the noise covariance matrix Q = E(w, kw,) and R = E(V,*V, ) can be computed using least-squares regression. In this representation, Xt denotes the states, Yt, the outputs, and Ut, the manipulated inputs. Wt describes the state or process noise, and BWt +Vt represents the measurement noise. Once the CVA model has been built, and the states identified, Simoglou et al. (2002) proposed the application of Hotelling's Te and SPE as the basis of the performance monitoring charts. The 7e statistic is developed from the k CVA retained latent variables: T2 -X,kSk-~X",.k

(5)

where Xt.k is the kTh retained state and Sk is the corresponding covariance matrix. The SPE is given by: S P E - ~ W,2

(6)

i-1

Simoglou et al, (2002) defined a number of metrics for monitoring the CVA states including the application of Hotelling's T 2 to the state space residuals, the excluded latent variables and the measurement residuals. 2.2 Wavelets and Multiscale PCA

The theory of wavelet transformations is based on multi-resolution analysis (Strang and Nguyen, 1996). The wavelet transformation can be applied to decompose a multivariate signal X into its approximate, A~ to AL, and detail, Dj to DE, coefficients for the first to L th level respectively. The idea of using PCA and wavelets has previously been reported Bakshi, (1998) who developed a multi-scale PCA (MSPCA) process performance monitoring framework. In this paper, the motivation for applying CVA and wavelets emanates from the fact that CVA deals with both the serial and cross correlation. However, the CVA states and residuals suffer from auto-correlation hence the metrics proposed by Simoglou et al, (2002) and Negiz and Cinar, (1997) for the monitoring of the CVA states and residuals will materialise in an excess of false alarms. This is due to the fact that the control limits for the T: metrics are calculated based on the assumption that the data is serially independent. To address this issue, Simoglou et al, (2002) proposed the use of control limits based on the empirical reference distribution (ERD) (Willemain & Runger, 1996). In this work, multi-scale PCA is applied to the CVA states and residuals. Wavelet analysis removes the autocorrelation within the states and the residuals and PCA is then applied to the wavelet coefficients to remove the correlation inherent within the states. The resulting scores and residuals are monitored using Hotelling's 7~ and SPE. Figure 1 presents a schematic diagram of the proposed fault detection and diagnosis scheme. For on-line performance monitoring, a moving widow approach is adopted. A window of incoming states and residuals are analysed using the developed monitoring scheme.

1462 That is, multi-scale PCA is applied to the states and residuals and then Hotelling's T2 and the SPE are calculated for each level of the wavelet decomposition. Once a fault is detected at a certain scale, fault identification is carried out to identify the source of the fault. Contribution plots for Hotelling 7e of the states and the SPE of the measurement error in the time domain are derived based on the approach described in Westerhuis et al, (2000). This is in contrast to using contribution plots of the CVA states as proposed by Norvilas et al (2000) which are more difficult to interpret.

_•

INPUTSAND OUTPUTS

CVA-STATE I SPACEMODEL ~

STATES [ MSPCA

~

MONITORING INDICES

STATESPACE RESIDUALS

STATES&MEASUREMENTS RESIDUALS

I

[ 4 ...................................................................................................... YES

I DIAGNOSIS

Figure 1. Framework for fault detection and diagnosis

3. Case Study" Monitoring of a Polymerization Reaction The proposed detection and diagnosis method is now applied for detecting a subtle fault in the polymerization of vinyl acetate in a continuous stirred tank reactor. The polymerization process was modelled by Teymour (1989). In this study the same input and output variables as in Norvilas et al (2000) are considered with a CVA model comprising four states being developed. The four process variables considered were reactor temperature, conversion, reactor initiator concentration and polydispersity. The simulated fault is a gradual decrease of the overall heat transfer coefficient at time point 2000. The simulation was repeated 100 times to calculate the Average Run Length (ARL). The application of multi-scale PCA to the states and residuals for fault detection is compared with the theoretical control limits (TCL) and the ERD limits (Simoglou et al, 2002). 1

~cf

1

1

0

0

•

•

-0.5

-1 0

10

lag

20

Figure 2a. A CF of the CVA states

0

10

lag

20

Figure 2b. ACF of Hotelling's 7e of the CVA states

-10

10 lag

20

Figure 2c. A CF of the SPE of the CVA residuals

Figure 2 shows the autocorrelation function of Hotelling's T2 based on the states and the SPE utilising the state-space residuals. As is observed from the autocorrelation function (ACF) (Figures 2b and c) of both Hotelling's T2 and the SPE are n o t serially

1463 independent. Thus, the control limits calculated based on the assumption that the distribution of the data follows a F-distribution or a X2 distribution is incorrect, resulting in an excess of false alarms. However, to address this problem Simoglou et al, (2002), proposed using the ERD to derive the control limits. For the ERD, it is the in-control average run length (ARL) performance that determines the limits, however as a consequence of it not taking into account the serial correlation, wide limits result and hence the fault detection task is delayed. Consequently the issue of serial correlation is not addressed. This is illustrated in Figure 3. However, compared with the ERD limits, the theoretical control limits (TCL) have a higher false alarm rate. i-

States

[] Fault detection 7~False alarms

delay

ii- State s p a c e residtnals

20025015015000~ 0

......~

TCL

.:............ i .......

ERD

[] fault d e t e c t i o n d e l a y

[] F a l s e

300

alarms

500 400 300 200 100 0

.....

Multiscale

TCL

Figure 3a. Comparison o f performance o f d({ferent monitoring indices on the states for 1 O0 runs.

ERD

Multiscale

Figure 3b. Comparison o f performance o f d(fferent monitoring indices on the states space residuals f o r 1 O0 runs.

As a consequence of these issues, wavelet analysis was performed on the states and residuals. More specifically Daubechies filter with 6 scales was applied. The number of scales was determined as described by Rosen and Lennox (2000). The number of scales being chosen in such a way that it allows sufficient separation between the stochastic (noise) and deterministic components of the variables. 1

1

0. 6

1

0. 6 0

0

O.6

-

-0.6

0.6 " 0

1

10

lag

20

-10

10

2O

-10

10

lag

lag

Figure 4a. ACF of scale 1 of the states

Figure 4b. ACF o[' Hotelling's 7-' of the states at scale 1

Figure 4c. ACF of Hotelling's T2 of the state space residuals at scale 1

As can be seen from Figure 3 the application of multi-scale analysis to the states reduces the time to fault detection and the false alarm rate. By using wavelets, the observation of each state is decomposed into several scales, and the monitoring chart is defined at each scale. Thus, the state can be monitored according to the dynamic frequency thereby making it possible to detect a subtle fault in the monitoring chart for the small detail rapidly. Also, this approach suppressed false alarms because the individual decomposed signal does not exhibit auto-correlation as can be observed from the autocorrelation fimction tbr scale I (Figure 4). Once the fault has been identified, a

1464 contribution plot of the states and measurement residuals in the time domain is used to identify the variables that are indicative of the fault. Since fouling affects the difference in inlet and outlet jacket temperature of the reactor, it has a direct impact on the reactor temperature. This is confirmed by the Hotelling's T 2 contribution plots which show that temperature is primarily contributing to the fault. Hotteling

T 2 States

7000

2 1,8

6000

5000

i 1.2

4000 3000 2000 1000

.

.

.

00

.

.

.

1~0

4000 Ti~

Fig. 4a. Hotelling's T: for the states

!i

/ 1

2

3

4

v~ab~s

Fig. 4b. Contribution plot for Hotelling's 7~

4. Conclusions This paper proposed a methodology for fault detection and diagnosis using the conjunction of CVA and wavelets. The performance and sensitivity of the proposed methodology was assessed using the Average Run Length (ARL) and the false alarm rate for different monitoring metrics. The results from the study demonstrated that the proposed methodology outperforms the conventional CVA monitoring metrics proposed by Simoglou et al (2002) for the detection of subtle faults. In addition the proposed methodology gave rise to fewer false alarms. References Bakshi, B. R., 1998, Multiscale PCA with Applications to Multivariate Statistical Process Monitoring. AIChE Journal, 44, 7, 1596-1610. MacGregor, J.F., T. Kourti, 1995, Statistical Process Control of Multivariate Processes, Control Engineering Practice,3,3,403-414 Negiz, A., A. Cinar, 1997, Statistical Monitoring of Multivariate Dynamic Processes with StateSpace models. AIChE Journal, 43, 8, 2002-2020. Norvilas, A., A. Negiz, J. DeCicco, A. Cinar, 2000, Intelligent Process Monitoring by Interfacing Knowledge-Based Systems and Multivariate Statistical Monitoring, Journal of Process Control, 10, 341-350. Simoglou, A. E.B. Martin, A.J. Morris, 2002, Statistical Performance Monitoring of Dynamic Multivariate Process using State Space Modelling, Comp.Chem.Engg, 26, 909-920 Rosen, C.; Lennox, J. A., 2000, Adaptive and Multiscale Monitoring of Wastewater Treatment Operation. Water Res., in press. Strange, G., T. Nguyen,1996, Wavelets and filter bank. Wellesley-Cambridge Press. Tymour, F.,1989, The Dynamic Behaviour of Free Radical Polymerization Reactions in a Continuous Stirred Tank Reactor. PhD. Thesis, University of Wisconsin, Madison. Westerhuis, J.A, S.P Gurden, A.K Smilde (2000). Generalized contribution plots in multivariate statistical process monitoring. Chemometrics and intelligent laboratory systems, 51, 95-114 Willemain, T. R, G.C Runger (1996). Designing Control Charts using an Empirical Reference Distribution. Journal of Quality Technology, 28,1,31-38. Acknowledgements A.A would like to thank the UK ORS Scheme and Chemicals Behaving Badly (CBBII) (EPSRC Grant GR/43853/01) for providing funding for his PhD studies.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1465

Predictive Functional Control Applied to M u l t i c o m p o n e n t Batch Distillation Column D. Zumoffen/a), L. Garyulo tc), M. Basualdo TMb)* and L. Jimdnez td) alnstituto de Fisica Rosario, CONICET, Universidad Nacional de Rosario Bv. 27 de Febrero 210 Bis, 2000 Rosario, Argentina. bGIAIQ, Universidad Tecnoldgica Nacional (FRR) Zeballos 1341, 2000 Rosario, Argentina. CDepartamento de Electrdnica, FCEIyA, Universidad Nacional de Rosario Riobamba 250 Bis, 2000 Rosario, Argentina. dDepartamento de Ingenieria Quimica y Metalurgia, Universidad de Barcelona Marti i Franqu6s 1, 08028 Barcelona, Spain.

Abstract This work describes the implementation of a Predictive Functional Control (PFC) algorithm on a ternary batch distillation column to control temperature by manipulating the reflux ratio. The PFC is tuned off-line by using simplified models obtained by applying identification techniques. The temperature set point is described by a polynomial related with an optimal dynamic behaviour determined to achieve the composition specifications. The separation performance is closely checked with the help of a soft sensor, based on a non linear Hammerstein model described in a previous work, which input is top temperature and the outputs are the estimated compositions. Additionally the model composition estimations are employed for calculating the accumulated compositions for each tank. Therefore a type of split range control for the corresponding valves of each tank is programmed in order to storage each component under quality requirement. Experiments were performed on a rigorous model developed in HYSYS.Plant '~ with data of a real pilot column. All concerning to control policy was implemented in MATLAB. Results comparing optimal PID and PFC are presented.

Keywords: Batch distillation columns; Non-linear model; Predictive Functional Control Soft-sensor.

1. Introduction The Predictive Functional Control (PFC) technique is the third generation of a family of Model Algorithmic Control (MAC), developed by Richalet and coworkers during the last decades (see Richalet, 1993). It resides on representing the plant with certain model, generate the control algorithm for one or more coincidence points with the reference trajectory, solve it and apply the calculated input action. The later can be constrained on its maximum and minimum values and its rate of variation. No report was found in the

Author to whom correspondence should be addressed: [email protected]

1466 open literature showing the application of this kind of control technology to batch distillation. The internal model, which gives the relationship among top temperature (controlled variable) and reflux ratio (manipulated variable), is obtained by linear identification techniques named N4SID, detailed in Jimenez et al (2002), and used here for predictions. In addition, a non linear identification technique is used for obtaining a reduced order Hammerstein model working as the soft sensor presented in Ruiz et al. (2004). It can handle the correlations among temperature and compositions of the batch distillation column. The case study analyzed here consists on an experimental batch column given by Nad and Spiegel (1987) to separate the ternary system of toluene, n-heptane and cyclohexane. The soft sensor is used to correct the temperature set point if the estimated instantaneous compositions do not match with the optimally specified ones. In addition the soft sensor allows to predict the accumulated composition in the different vessels and determine how to manipulate the valves corresponding to the main and off cuts.

2. Case Study: Multicomponent Batch Distillation The pilot plant shown in Figure 1 which data are taken from Nad and Spiegel (1987) is briefly described here. The distillation column has a 162 mm inner diameter filled with structured packing Sulzer Mellapak 250 Y (packing height of 8.0 m). The system involves a ternary mixture of cyclohexane, n-heptane and toluene. The whole column including reboiler and condenser has 20 theoretical plates. The initial charge is 40.07% of cyclohexane, 39.40% of n-heptane, and 19.90% of toluene. The duration of each step and the corresponding reflux ratio profiles are given in Jimenez et al. (2002).

Figure 1. Batch Distillation Column in HYSYS Plant*-{

3. Control Project Steps The main control objective consists in the implementation of PFC for the top temperature of the column which follows an optimally specified set point to achieve the required composition profiles. The control implementation is shown in Figure 2. This project involves the steps of system identification, controller design and implementation with the basic library of the communication protocols between software. It allows to connect the control routine in MATLAB TM to all other elements of the plant simulated by HYSYS.Plant ®.

1467

[ Te ~.p

R

I

D

l~t~ 1

l ReU-5~,

I

I

] vloo I --n'-'-~ rabbi° I

"1~1 0 4

vl

Sotp~nlt

Tcnnpi

o

o~1

I

Re.~l cow.position dat~ e a c h 3 0 ~cin.

F/gure 2. control structure applied to the batch distillation.

3.1 Identification Techniques Applied to Obtain the Internal Model In this section will be given the fundamental equations used for implementing the predictive control structure over the plant shown in Figure 2. A reliable state-space model, obtained following the 4SID methods, which considers a LTI system with n inputs and m outputs is described by Xk #1 -- AXk + BUk + Wk

(1)

Yk --CXk -+- DUk + Vk

where Xk is the state vector, U k is the input vector (RR), Yk is the output vector (T), and Wk and Vk are the process noise and output measurement noise vectors respectively. The estimated matrices were given in Ruiz et al. (2004) and are detailed in eq. 2. A-

E'°°°90.0006 -°°6'81 I::,6179 0.9324;

B

1716

D-0 (2)

The system given by eq. 2 can be transformed in a discrete transfer function available for implementing the internal model of the PFC which consists on a first order with integrator model: G-

-0.08495 z + 0.08487 ?

(3)

z- - 1.933 z + 0.9333 3.2 Controller Design The main PFC controller elements are: a) independent model approach which predicts the dynamic behavior of the plant on a prediction horizon given by eq. 3; b) for this case, where the plant transfer function presents an integrative element, decomposition principle for unstable system must be considered; c) exponential reference trajectory corresponding to first order closed loop response; d) polynomial structuration of the

1468 future manipulated variable that minimize the difference between reference trajectory and model prediction at one or most coincidence points; f) constraints on manipulated variable (MV) and state variables; g) tuning in time and frequency domain. 3.3 Mathematical Calculations for PFC Design

Since the identified transfer function was of first order plus integrator it is decomposed as shown in Figure 3. u

Y~ b._ v

oO.Z+Cl

-I

z - - O~rn

Y'p

I~I 1- ~_____~1 2- ~ m l

Figure 3. Decomposition of the integrator term.

I Tsl

aml -- exp -

(4)

Tdesc

Tdesc is the decomposition time generally considered equal to the closed loop time response.

ym(n + hj) - Yml(n + h j ) + Ym2(n + hj)

(5)

~p(n + hj) = Ym(n + hj) +~(n + hj)

(6)

The control law is calculated by minimizing the difference between predicted output ( y ) and reference trajectory (YR)-

nh

2

D = ~j=l { , p ( n + h j ) - Y R (n+h J )}

8D so, -0-c 3 ~=t

(7)

(8)

c(n + h i ) - YR(n + hi) - 2hJ.(c(n) - yp (n)) Where C represents the set point, and hj each coincidence point considered then

P c(n + hj) - Z c j ( n ) i=0

ij

(9)

P indicates the total number of extrapolation terms to describe the set point trajectory based on specific number of its past values. By doing the calculations, D becomes 2

N

D(n) =

de

fl(n)T .yB (hj) + amhj.Ymi (n) + c(n)+

~p(n+ hj)

i__~lej (n).(-i) j .h j -c(n+ h j)+ 2 hj .(c(n)-yp(n)) ,

(10)

YR(n+hj)

de

d(n) = ahmJ.Ymi(n) + e(n) + Z e j (n).(-i)J.hj - c ( n + hj) +/~hj .(c(n)- yp (n)) j=l

(ll)

1469 /l(n) = Y B c ' Y B .d(n)

(12)

YB and YBc values are known because they correspond to the output information for selected UB input base functions such as steps, ramps or parabolas.

YBC

_

YB(hi).y B(hj

)T

(13)

j=l

Y B - [YB(hl)YB(hx) .... YB(hN)]

(14)

3.4 T e m p e r a t u r e Set Point Configuration The last point is to configure a proper temperature set point which is based on the composition specification. The proposed problem is to maximize the amount of distillate for a given time (4.5 hours) and a 0.98 molar fraction for cyclohexane because it is considered to be the most important product to obtain. It is solved taking into account the following relationships:

maximize j Rt

~

0

dD.dt_ dt

()

V .dt Rt + 1

(15)

r v ~!

( ' ~.dr R, +1 "x~

subjected to xD~,,, =

r

V

=x

(16)

R,+I 4. Results In Figure 4 the instantaneous temperature and the set point values are presented when PFC is implemented together with the reflux ratio given by the control algorithm of eq. 12. Results indicate that a good servo-behaviour with smooth movements of the manipulated variable, except at the initial interval of the distillation, are achieved. In Table 1 the accumulated composition and level on each tanks of main cuts for both PFC and PID, respectively. Table 1. Accumulated composition on each tan]( and % level afier first batch time.

Component/% level

PID

PFC

Cyclohexane (V 104)

0.984

0.982

Level (V 104) N-heptane (V 102) Level (V102)

49.84 0.2103 20.73

48.83 0.2772 33.5

Toluene (reboiler) Level reboiler

0.4656 8.62

0.4692 8.5

1470 Data for PID was taken from a previous work (Ruiz et. al., 2004) where the composition from soft sensor estimation was the controlled variable. Table 2 shows the same as Table 1 but for the slop cuts where it is clear that less reprocessing material is needed when PFC is implemented. Table 2. Accumulated composition on each tank and level after the .first batch time f o r both slop cuts.

First slop cut (V103) PID PFC

"

Second slop cut (V105) PID PFC

Cyclohexane

0.95772

0.96141

0.53556

0.38764

n-heptane

0.00185

0.00177

0.11452

0.16741

Toluene

0.04043

0.03682

0.34991

0.44495

Level (%)

18.23

6.29

44.37

22.27

I

l 3O

,

,,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

°

.......

! ....

~ ....

~ ....

,~ ....

i---i

....

:.....

i

i

i

i

i

!

i

:-I'---: ....

;:I', !

......

1

....... ::/%~i~.... ....... i~..... ....:,'~=~-~,':--~--=::: ..... !.....:.....!..... - ~ -~:~;{----! ....I 70

'

0

100

'

200

.

300

.

400

.

.

500

Time

I

i

l

i

.j.

i-.,.! .....

.

600

.

700

1

800

900

°

! .... i .... i .... i .... i .... i;/4 :

:

:

:

20o

300

400

'l! " i~L~

:

.... 4-i .......

:-":i .... i ....

'

!

i

!-[ .......

1000 1ClO

500

6130

7130

800

900

100

~me

Figure 4. Simulation results with HYSYS.Plant ~ and MA TLAB rMof temperature and its corresponding reflux ratio f o r optimal cyclohexane recovery.

5.

C o n c l u s i o n s

PFC tuning involves several parameters, obtained by off-line optimization using both N4SID and Hammerstein simplified models, which help significantly to reduce the computational time. It allowed a good setpoint tracking with smooth movements for the manipulated variable during the first batch time. In addition, a comparison with the optimal PID is included remarking that PFC allows to achieve a better profitability by reducing the reprocessing operation time. References

Jimenez, L., M. Basualdo, J.C. Gomez L., Toselli, and M. Rosa, 2002, Nonlinear Dynamic Modeling of Multicomponent Batch Distillation: a Case Study. Braz. J. of Chem. Eng. 20 (2). Nad, M. and L. Spiegel, 1987, Simulation of Batch Distillation with Experiment, Proceedings of the CEF'87: The Use of Computers in Chemical Engineering, Taormina, Italy, p. 737. Richalet J., (1993), Pratique de la Commande Pr6dictive, Editorial Hermes, Paris, France. Ruiz, J., P. Zumoffen, M. Basualdo, and L. Jimenez Esteller, 2004, A nonlinear soft sensor for quality estimation and optimal control applied in a ternary batch distillation column, ESCAPE 14, Lisbon, Portugal.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1471

Fault tolerant control with respect to actuator failures Application to steam generator process A. AItouche ~ and B. Ould Bouamama b a LAGIS UMR CNRS 8146, ERASM-HEI 13, rue de Toul, 59046 Lille Cedex, France bLAGIS UMR CNRS 8146, Polytech'Lille Cit6 scientifique, 59655 Villeneuve d'Ascq, France

Abstract This paper deals with the analysis of nonlinear reachability and fault tolerant properties of multiactuator nonlinear systems. In this case, the process is a steam generator process containing a set of actuators. After occurrence of one or several actuator faults detected and isolated by Fault Detection and Isolation (FDD approaches, a quantitative analysis of the faulty system properties helps us to determine whether the faulty system can go on operating or not. Nonlinear reachability analysis that has been presented in this paper allows us to determine the minimal number of actuators that are n e c e s s a u to keep the system under control.

Keywords: Fault Detection and Isolation, Fault reachability, actuator failures, steam generator process. 1.

Tolerant

Control,

nonlinear

Introduction

Fault tolerance is highly required for modern complex control systems. Sensors, actuators or process failures may drastically change the system behavior, ranging from performance degradation to instability. Fault tolerant control systems are needed in order to preserve the ability of the system to achieve the objectives that has been assigned, or if this turns to be impossible, to assign new objectives so as to avoid catastrophic behaviors. Fault tolerant control implements the solution of control problem in which the system objectives can be achieved in spite of faults. The design of fault tolerant controllers needs the system to remain controllable in the presence of failures. Controllability or reachability (the ability of a state or a functional of a state to be controlled or reached by the inputs) is a property which characterizes the system and its actuators. In this paper, we intend to characterize the nonlinear reachability of a system under actuator failures, and to identify those subsets of actuators whose failure keeps that system property unchanged, thus providing the control engineer with fault reconfiguration possibilities. Before studying fault tolerant properties based on the analysis of nonlinear reachability, we suppose that the faulty actuators are detected and isolated by an FDI algorithm such as structural analysis, based on the elimination of the

1472 unmeasured variables of the system and only the healthy actuators are used to reconfigure the control law. Generation of residuals could be based on the technique of structural analysis (Blanke et al., 2003). This approach consists in finding analytical redundancy relations which contain only known variables. Those relations are satisfied if the residuals are null during the normal system functioning and non-null when the system fails. The bipartite graph is built representing the process model. This graph is constituted by a set of nodes related each over by a set of arcs. Each node represents a variable of the system or a function related those variables. From this bipartite graph the incidence matrix and then the residuals are obtained. The set of residuals generates a binary sequence where "0" represents a null residual and " l " a non-null residual. Those binary sequences are called signatures. By comparing those signatures with theoretical, known signatures representing the faults, faulty actuators can be deduced. Fault tolerance of sensor (namely fault tolerance estimation) systems has recently been studied in nonlinear systems based on the use of observability indices (Lienhardt et al, 2004). Because of the non duality between observability and controllability of nonlinear systems, the results can not be extended to fault tolerance analysis of actuator systems. Then, the definition of non linear teachability in terms of the Lie algebra (Isidori, 1997) has been used. The proposed analysis rests on the definition of minimal and redundant actuator sets using the individual nonlinear generic reachability indices. Some properties of redundancy and minimality are introduced with reference to the system reachability. Minimal redundancy means that the loss of any actuator causes the system to be uncontrollable and redundancy means that the loss of subset of actuators remains the system to be unreachable (the functional of state is based on the healthy actuators). The properties of the minimal and redundant sets are analyzed and used in order to build an algorithm which uses redundancy degrees for actuator losses. For some given degree (or/and reliability) the reachability property in the case of actuator failures could be guaranteed. Fault tolerance control strategy in the case of actuator faults can be represented by figure 1.

Faulty actuators detected and isolated

=1

i

Faulty actuators

I

Healthy actuators

Objectives FDI

[

Control

~.~

I

,..I

No faulty actuators detected

Nonlinear system

1 Figure 1. Fault tolerance control strategy

~] Accomodation I --I~

Not used in our case

Reconfiguration , I

1473 Our paper is organized as follow: description of the steam generator process, reachability analysis, redundancy and minimality and application to the steam generator process.

2. Process description Let us consider the pilot process whose global view is shown on figure 2. The test plant designed to be a scale-model of part of a nuclear plant is a complex nonlinear system. This installation is mainly constituted of four subsystems: a receiver with the feed water supply system, a boiler heated by a 60kW resistor (steam generator), a steam flow system, and a complex condenser coupled with a heat exchanger. In the present paper is considered only a part of the pilot process composed of the steam generator and the steam flow system as shown on Figure 2. The dynamic global model can be consulted in (Thoma and Ould Bouamama, 2000). The feed water flow, taken from the receiver tank, is pressurised via the feed pump which is controlled by a relay to maintain a constant water level inside the steam generator. The heat power is determined based on the available accumulator pressure. When the accumulator pressure drops below a minimum pressure, the heat resistance delivers maximum power; on the contrary, when the accumulator reaches a maximum pressure, the electrical feed of the heat resistance is cut off. As state variables used: the internal steam generator temperature T~v, the total mass stored by the boiler M~v

, the mean

temperature of the body of the boilerTMG and the displacements of the control valves Zv, and Zv2. As inputs used: the inlet feedwater flow

Qal,, the heating power/3H, the

pressure imposed by the external system (condenser)

t~:c and the control signals

Ovc and Or7 acting respectively to the valves VM~(automatically controlled valve) and VM2 (manually controlled valve) F L O W ~/IE,:.-~.~ S Y S T £ M VM]] 2"

~ED WATE~strm_vSYSTEM ~.-~, ± ..

,.

i

-I::::::c'.ii,',Il:: / I, I P~

Feed w a t e f l l o w Pmap

..... :;: ::

gggw

]-,]~A T P.ESISTAI~-~E

Figure 2. Technological schematic of the model

According to some modelling hypothesis, the simplified nonlinear state space model of the steam generator process is given by:

1474

TGV=)L1 QAL q-~2 (TGv--TMG)lt.~3 PI'H MGV

MGV

MGV

TMO=;~4(TGv--TMG)

QALTGv MGV

(1)

ZVI=~5Zv1-Jr-Ovc Zv2--~5Zv2nt-OvT ~'IGV=)%(Kv, -Kvz)T~v +(Kvl -Kv2)PEc +QAL where

the

state

vector

is: x(t)=(Tcv TMo Zvl Zv2 M o v y and

the

input

vector u(t)=(PEc Pm QA,~Ovc Ovr y'.

Parameters ( ,;h,d.a,Z~,,;h) depend on thermal capacity of the fluid and others coefficients. Parameters ~ and ~ have been identified (Thoma and Ould Bouamama, 2000). Let's assume that the parameters ,;L~(i=1,2 ..... 6) are constant. Kvl and Kv2 respectively the position of valve VM1 and VM2 are given by the constructor.

3. Reachability analysis of the system Definition (Isidori, 1997)" a state x ¢ 0 is said to be reachable (from the origin) if, givenx(0)=0, there exist a finite time interval [0,T] and an input {u(t),t~ [0,T]}such that x(T)= x . If all states are reachable, the system is said to be completely reachable.

3.1 Reachability analysis of an affine nonlinear system Given an affine nonlinear system" •

m

(2)

x= f(x)+ Egi(x)ui i=1

with m inputs u 1,u z ..... u mwhere f and gi are n dimensional vector functions. Mathematically, the analysis of the generic teachability is generated in three steps: The initial distribution is:

(3)

Ao=span{g,,g2 .... gin} This is extended by Lie-brackets of f and g in the first step &=A0+[f, A0]=span{g, ..... g ....[f , gl ] .... [f , gm

(4)

with The second step then gives the following m

_

.,

A2=AI+[f.A,]+~2[g.A,]

(5)

i=1

and recursively, A,,+I=A,,+[f,A,,]-I-£[gi,A,,]

(6)

i=1

The sequence terminates at k=k' if

Ak.+~=Ak.(at most, k'=n-1 where n is the dimension

of the state). To conclude about the teachability, the last step consists of determining the

1475 dimension of A~ which corresponds to the dimension of the reachable space. The system is generically reachable if and only if dim(Aa.,)= n .

3.2 Individual generic reachability indices vector The vector v , defined such that v = (v~..... v,,,), 1_
v; is called the individual generic reachability indice of the input i. In other words, the vector v is the vector of individual generic reachability indices, if the integer

Vi

iS the dimension of the space generically reachable only by the actuator i.

3.3 Redundancy and minimum sets Let's consider the following nonlinear s y s t e m •

ill

x=f(x)+~-' g j(x)vj ,/=1

Let I,. be a set of actuators, J be a subset of I,. and I,. \ J its complementary in I,. Redundancy and minimality notion are introduced according to recovery possibilities of system instrumentation.

A set of actuators

I

is said minimal with respect to the state space if and only i f (7)

J c L , ~I, \J (Z:~ Where ~1, and ~

are respectively the space recovered by the set I,. of actuators and

by the state. In other words, a set of actuators Ic is said minimal with respect to the state space if and only if the state space is generically reachable with Ic but generically unreachable with IcV, V(Je:~)cL. A set of actuators I,. is said redundant, if and only if : 3 J c I , with J:/:{~}, such that f~,~\,,c~

(8)

A loss of actuators in a minimal set makes the state space unreachable and a loss of actuators in a redundant set can lead either to another redundancy set either to a minimal set or to a set unable to keep the state space reachable.

4. Application to a steam generator process o The application is about a steam eenerator process in which"

2c2 ( T(;v -TM(; ) M~;v A4T~;v +)c~T~,~(; Z~ ZI.'I ~,Zv2 T,4 f(x)= A7(Kvl-Kv2 ) ~;v

0

and

2C3 /5 M(;v M ~ v g(x)= 0 0 0 0 0 0 (Kvl-Kv2) 0

T~;v 0 MGv 0 0 0 1 0 O 1 0

0 0 0 l 0

The computation of the algorithm of section 3.1 leads to the results given in table l"

1476 Table 1. Reachability analysis of the steam generator process

State xj \input ui

u~

u2

u3

u4

u5

PTH

QAL

OVC

OVT

X5(MGv)

PEc 1 l 0 0 1

1 1 0 0 1

1 1 0 0 1

1 1 1 0 1

0 0 0 1 0

Vi

3

3

3

4

1

Xl (TGv)

x2(TMG) x3(Zvl) X4 (Zv2)

In table 1, xj is generically reachable by the input ui if and only if the cellular corresponding to the line of xj and to the column of ui is equal to 1. Table 1 shows that state x3 and x4 are respectively generically reachable only by input u4 and us. Also, u4 can generically reach the state Xl, x2,and xs. So inputs u4 and u5 are necessary and sufficient to generically reach the state and therefore have to be detected and isolated without false alarms. So, the set of actuators {u4, u5 } is a minimal set of actuators. All sets of actuators which don't contain both actuators u4 and u5 are neither minimal or redundant. Finally, all sets of 3 actuators or more and containing actuators u4 and u5 are redundant. The choice of the set of actuators containing u4 and u5 depend on the desired weak redundancy degree (Lienhardt et al, 2004). For instance, if the desired weak redundancy degree is equal or up to 1, {ul, u2, u4, Us},{ul, u3, u4, us},{u2, u3, u4, u5},{Ul, u4, u5},{u2, u4, us},{u3, urn, us} could be chosen. A reliability study could be computed in order to give the set of actuators having the best reliability.

5. Conclusion Reachabilty studies in case of faulty actuators are used to determine minimal and redundant sets of actuators to keep the functional reachable and then to know the maximal number of actuators which can be lost while keeping the system reachable or controllable. Our approach depends on isolation of faulty actuators and only the best healthy actuators that satisfy the properties of fault tolerant control are used to reconfigure the system. Our work can be extended to the condenser model, which was previously used for Fault Detection and Isolation studies (Aitouche et al, 1999).

References Lienhardt, A.M, A. Aitouche and B. Ould Bouamama, 2004, Fault tolerance for multisensor nonlinear systems, I3M- IMAACA, Genova, Italy, Vol. 2, pp 177-181. Isidori. A., 1997, Non linear control systems 1, 3 rd edition,, Springer Verlag. Blanke, M., M. Kinnaert, J. Lunze and M. Staroswiecki, 2003, Diagnosis and Fault-tolerant Control, Springer Verlag. Thoma, J.U. and B. Ould Bouamama, 2000, Modelling and Simulation in Thermal and Chemical Engineering. Bond Graph Approach, Springer Verlag. A~touche, A., F. Busson., B. Ould Bouamama and M. Staroswiecki, 1999, Multiple Sensor Fault ~ t i o n of Steam Condensers, Computers and Chemical Engineering, Elsevier Science Ltd, Vol. 23, pp $585$588.

European Symposiumon ComputerAided Process Engineering- 15 L. Pui~janerand A. Espufia(Editors) @2005 Elsevier B.V. All rights reserved.

1477

Open/Closed Loop Bifurcation Analysis and Dynamic Simulation for Identification and Model Based Control of Polymerization Reactors M.P.Vega ~'*and M.R.C. Fortunato a

a

Universidade Federal Rural do Rio de Janeiro- Departamento de Engenharia Quimica BR-465, km 7, Serop6dica, Rio de Janeiro, Brasil, CEP. 23.890-000

Abstract All steps of nonlinear system identification represent very challenging theoretical and practical problems, for a general theory is not available. As a result, further investigation on systematic techniques for nonlinear model validation is a relevant research issue that needs to be explored for proper model based controller implementation. Bifurcation analysis and dynamic simulation were employed for proper model identification and synthesis of model based controllers. The nonlinear model based control of batch and CSTR polymerization reactors are analyzed, as a case study. It is suggested that dynamic simulation analysis and the investigation of bifurcation diagrams (open/closed loop analysis), using reactor jacket temperature and weight average molecular weight set point as the bifurcation parameters, should be included as a synthesis criteria for nonlinear identification and model based control purposes.

Keywords: Model based control, Stability analysis, Polymerization, Dynamics 1. Introduction As pointed out by Pearson and Ogunnaike (1997), a well-developed theory for nonlinear system identification is not available. Vega et al. (2001a, 2004) developed investigations on systematic techniques for nonlinear model validation using bifurcation diagrams. Advanced controller design techniques take nonlinear behavior of the process into account. This category of methods includes feedback linearization and nonlinear model predictive control. In the case of model based process control, simplicity is a very important required characteristic, as the model has to be solved many times at each sampling interval. One typical example is the nonlinear model predictive control (NMPC), where an optimization problem based on the internal model has to be solved iteratively at each sampling interval (Henson, 1998). Bifurcation analysis and control theory are two areas of research that have been developed independently from one another. Bifurcation analysis by continuation involves linearizations of generally nonlinear process models. This often causes confusion as readers assume that linearizations inevitably imply that the analysis is local Author/s to whom correspondence should be addressed: [email protected]

1478 only. Bifurcation analysis by continuation can in fact be used for more than local analysis of nonlinear systems, despite using linearizations, for they are carried out along curves of steady states (Hahn et al., 2004). While both bifurcation analysis and nonlinear control theory deal with stability of nonlinear dynamic systems, the vast majority of the literature on bifurcation analysis has nevertheless focused on open-loop processes. Exceptions include Zhang et al. (2002) that performed bifurcation analysis on the open loop process in order to determine appropriate operating points for designing a controller. Chen et al. (2000), Recke et al. (2000) and M6nnigmann and Marquardt (2002) studied bifurcation control field: control of the dynamic behavior in the parametric vicinity of a bifurcation. Stability analysis was performed at one operating point (Ananthkrishnan et al., 2003; Chang and Chen, 1984), for varying a parameter of a model (Paladino and Ratto, 2000) or the gain of a PI controller (Giona and Paladino, 1994) or the gain of a P controller (Cibrario and Ldvine, 1991). Hahn et al. (2004) implemented bifurcation analysis to a closed loop system using state feedback linearization controller. The main objective of this paper is using open/closed loop bifurcation analysis for proper nonlinear empirical model (internal model) and model based control (nonlinear model predictive control) synthesis. The solution polymerization in CSTR and batch reactors is studied. The methodology for confident identification and model-based control uses open/closed loop bifurcation and dynamic simulation analysis. As a result, the methodology should be included as genesis criterion in the nonlinear system identification/control scenarios.

2. Bifurcation analysis and dynamic simulations Bifurcation theory provides tools for a system stability analysis under its parametric changes. As the parameters undergo changes, the existence of multiple steady states, sustained oscillations and traveling waves might occur for highly nonlinear processes (Ray and Villa, 2000). The quality of the different models was evaluated by comparing their dynamic structure (attractors and respective stability characteristics) to the dynamic behavior of the "real" plant for the CSTR configuration. In order to do that, bifurcation and stability analyses were carried out to unveil attractors, employing well-known continuation methods. The computations presented in this paper were carried out with routines provided by AUTO (Doedel, 1986). Branches of steady state solutions and periodic solutions were calculated with the arc-length method developed by Keller (1977). Nonlinear system theory states that if all eigenvalues of the Jacobian matrix lie in the open left half of the complex plane, the system is stable. Conversely, the steady state is unstable if the Jacobian matrix has at least one eigenvalue in the open right half of the complex plane. The empirical model (internal model based on neural networks) is described as a discrete model, so that the stability characteristics are determined by the eigenvalues of the Jacobian matrix of the nonlinear map, which relates present data with the future process output. The stability characteristics of the closed loop (discrete system) are also determined by the eigenvalues of the Jacobian matrix of the nonlinear map: Steady states are stable if all eigenvalues of the Jacobian matrix are inside the unity circle. If any of the eigenvalues is outside the tmity circle, the solution is unstable. At a Limit

1479 Point, an eigenvalue becomes identically equal to + 1. At this point, multiple steady state solutions usually appear and a change in stability occurs. At a Hopf (Thorus) Bifurcation Point, a pair of complex eigenvalues crosses the unit circle with non-zero imaginary component and a branch of oscillatory solutions may appear. At a Period Doubling Bifurcation Point an eigenvalue becomes equal to -1 and branches of periodic solutions usually develop. AUTO automatically detects bifurcation points and provides routines for computation of the multiple steady state solutions, oscillatory and periodic solutions that arise at these special points. Unstable behavior usually occurs in the vicinities of these bifurcation points. The quality of the different models describing a batch polymerization reactor was evaluated by analyzing their dynamic structures, it is assumed here that a good empirical model should exhibit a dynamic behavior that resembles the one of the original process. Fhis means that the empirical models should present the same modes of operation of the original process. Therefore, in our particular case, a good empirical model should not display multiple solutions and unstable operation conditions. As a result, the identification of the bifurcation diagram and dynamic structure of open/closed loops may allow the understanding of how and why the empirical models tail at certain process operation conditions, even when allowing a satisfactory one step ahead prediction of process dynamics, required by traditional validation methods (Sriniwas et al., 1995), producing spurious controller performances. 3. T h e process analyzed The solution styrene polymerization was the system employed for illustrating the methodology that develops reliable model identification and model based control of weight average molecular weight. Detailed description of the process may be found elsewhere, Vega et al. (2001a). There is much interest in the in-line monitoring and control of molecular weight distributions, as this may be regarded to be among the most important molecular properties of polymer resins. However, the analysis of polymer chain length using GPC, SEC, and light scattering, requires very expensive, sophisticated, time-consuming and unreliable (at industrial environments) instruments. From a practical point of view, the whole molecular weight distribution is not needed and significant amount of information about the end-use properties may be provided by the leading moments of the molecular weight distributions, such as the weight average molecular weight. Vega et al. (200 l b) developed a simple viscometrical method for inline monitoring and control of weight average molecular weight in solution polymerizations. As a result, the weight average molecular weight is the polymeric property chosen for being controlled. The dynamic simulation of the batch polymerization model is shown in Figure 1. The CSTR bifurcation and stability analysis diagrams are rendered in Figures 2 and 3. The CSTR model presents a stable steady state solution branch.

4. Results and discussion Nonlinear system identification involves model parameters selection, determination of the forcing function, which is introduced into the plant to generate the output response,

1480 estimation of model parameters and comparison of plant information and model predictions for data not used in model development. All steps represent very challenging theoretical and practical problems, for a general theory is not available. The neural network (NN) approach has proved to be a useful tool and is the most popular framework for empirical model development.

8,0x105

~.~

7,sx,o~

~

7,0x10s

•~ ~

6,5x10s 6,0x105 0 ~pq2x103 4xl

3

~?sa 6

~

oLu

1x104

300

-~

,.l~¢.,~O.~)e~'~ -t~f~'

Figure 1. The batch model dynamic simulation 1E+6 1,08E-5

oz= o >

-

~

',

0,5-

",,

6E-5 L

'\

0,0..=

~:~ g 4 E - 5 " ~ _9.0 O 2E-5

L

\ -0,5-

~

"- ..........

. -l,0-4x 104

O

SIT["

300

="

" [ --r

= ' "']

320

' T ''"

T '

340

"~

....

F

-2x I 0 -~

0

2x 10-;

4x 10.4

. . . . . . . . . . .

360

380

Real

part

Temperature,K Figure 2. The CSTR model bifurcation diagram

Figure 3. The CSTR model stability analysis

In order to control polymer quality (weight average molecular weight) a NMPC strategy was developed (Henson, 1998), using a NN as the internal model, named empirical model, by manipulating the reactor jacket temperature. All NNs present 2x4xl architecture (reactor jacket temperature and conversion as inputs and weight average molecular weight as output). Empirical models were compared with the corresponding bifurcation diagrams and dynamic simulations of the phenomenological models, regarded as the real processes. Vega et al. (2004) pointed out that the use of traditional validation tests was not enough to guarantee successful use of NNs as the internal models of NMPCs. Care must be taken regarding the strategy for data generation, as the simple manipulation of the number of data points, neuron activation functions, NN architecture and initial guesses used for NN training are not enough to guarantee the building of proper models. As shown in Figures 4 and 5, the complex dynamic behavior displayed by the model (build with incomplete data set) may be completely different from the one displayed by the plant, resulting in poor control efficiency. Good controller performance was obtained when model and plant showed similar dynamic simulations.

1481 The empirical model bifurcation diagram (Figure 6) displays a CSTR phenomenological model similar behavior. All Floquet multipliers are inside the unity circle ensuring stable steady states (Figure 7). For closed loop bifurcation diagram synthesis (Figure 8) the output of the controller (reactor jacket temperature) serves as input to the system and has to be removed from the set of variables to be used for bifurcation analysis. Then, the set point of the system (weight average molecular weight) is the continuation parameter. As a result, the analysis can be performed over an entire operation region of the process rather than for a particular fixed value of the set point. Figure 9 shows that the closed loop system remains stable under parametric uncertainty and unmodeled dynamics over the entire operating region. Requiring stability of the closed loop system over the entire operating region is important because bifurcation analysis only results in steady state information, and it has to be ensured that the system trajectories cannot leave the regions of attraction of the steady state operating point. 2.0E+6

1.2E+6 Model Identification

a=

Mathematical model

•~

Model based

y= .~

control

O

Closed loop - nonlinear neural model 1

A

Closed loop - nonlinear neural model 2

1.6E+6 t~

Nonlinear neural model 1

A

Nonlinear neural model 2

~:

1.OE+6

1.2E+6

8.0E+5

~

,~ .,... ~D

,

~

°o

~ 6.0E+5 ~ .,--~ ~D

4.0E+5

o °

~~

4.0E+5

0.0E+0 280

320

360

400

440

Temperature, K

Figure 4. Model identification- batch model

4.0E+5

6.0E+5

8.0E+5

1.0E+6

1.2E+6

Weight average molecular weight set point

Figure 5. Model based control- batch model

/

Nxl0 +.~

o

6x 105

4x 10 ~ >~ 0,0 ,~'-~

2x105

280

,,, . . . . . . . . . , . . . . . . . . . , . . . . . . . . . , . . . . . . . . . 300 320 340 360 380

-0,5

Temperature, K - l,l)

~ -1,0

, -0,5

0))

0,5

Real part

Figure 6. CSTR open loop b(fi#'cation diagram

Figure 7. CSTR open loop stabiliN analysis

5. C o n c l u s i o n s it was observed that nonlinear models built to represent polymerization reactors may present incompatible complex dynamic open loop behavior, producing incompatible controller performance, unveiled by dynamic simulations and bifurcation theory. Bifurcation diagrams and dynamic behavior indicate whether spurious model responses

1482 are present and, therefore, indicate whether additional effort is needed for proper model development. Bifurcation analysis was used as an efficient tool for validating nonlinear models, which were built in a supervisory fashion, using available first principles mathematical modeling data. Following the data selection procedure (number, range and distribution) for nonlinear system identification, unknown systems can be unveiled if the convergence of the bifurcation diagram to a final structure is used as a quality index in an iterative procedure. This sophisticated validation procedure is indicated for complex units operating in a large range of operating conditions and using nonlinear model based controllers. Finally, it was shown that bifurcation analysis was successfully implemented for closed loop system analysis under phenomenological model and plant (internal model) mismatch of a NMPC scheme.

9x 1(15

~

0,5

sx05

Uz~ 7xo' ._~ ~'~

6xlO 5 6x 10 s

;>~ 0,0 ~

•

.-

7x 10 5

8x 10 5

9x 10 5

-0,5

Continuationparameter (Weightaveragemolecularweightsetpoint) - 1.0 - 1,0

-0,5

0,0

0.5

1.0

Real part

Figure 8. CSTR closed loop b!fiwcation diagram

Figure 9. CSTR closed loop stability analysis

References Ananthkrishnan, N., Vaidya, U.G., Walimbe, V.W., 2003, Journal of Power and Energy, 217, 279-286. Chang, H.-C., Chen, L.-H., 1984, Chemical Engineering Science, 39,1127-1142. Chen, G., Moiola, J.L., Wang, H.O., 2000, Int. Journal of Bifurcation Chaos, 10, 511-548. Cibrario, M., Ldvine, J., 1991, Proceedings of the 30 th Control Decision Conference, 1551-1552. Doedel, E., 1986, California Institute of Technology, Pasadena. Giona, M., Paladino, O., 1994, Computers and Chemical Engineering, 18, 877-887. Henson, M.A., 1998, Computers and Chemical Engineering, 23, 187-202. Keller, H.B., 1977, Applications of Bifurcation Theory, Academic Press, New York. MOnnigmann, M., Marquardt, W., 2002, Proceedings of the 15 th IFAC World Congress, Barcelona, Spain. Paladino, O., Ratto, M., 2000, Chemical Engineering Science, 55, 321-330. Pearson, R.K. and Ogunnaike, B.A., 1997, Nonlinear process control. Prentice-Hall. Ray, W.H. and Villa, C.M., 2000, Chemical Engineering Science, 55,275-290. Recke, B., Andersen, B.R., Jorgensen, S.B., 2000, Proceedings of the ADCHEM 2000, Pisa. Sriniwas, G.R., Arkun, Y., Chien, I-L and Ogunnaike, B.A., 1995, Journal of Process Control, 5, 149-162. Vega, M.P., Coimbra, K.B., Mattos, J.A., Scheid, CM., 2004, Proceedings of the DYCOPS-2004, Cambridge, Massachusetts. Vega, M.P., Lima, E.L., Pinto, JC., 2001 a, Proceedings of the ADCHEM 2000, Pisa. Vega, M.P., Lima, E.L., Pinto, JC., 2001 b, Polymer, 42, 3909-3914. Zhang, Y. C., Zamamiri, A.M., Henson, M.A., Hjortso, M.A., 2002, Journal of Process Control, 12, 721-734.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) ~©2005 Elsevier B.V. All rights reserved.

1483

Effect of Recycle Streams on Energy Performance and Closed Loop Dynamics of Distillation Sequences S. Hernfindez a'*, J.G. Segovia-Hernfindez a, J. Carlos Cfirdenas a and V. Rico-Ralnirez b aFacultad de Quimica, Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., 36050, M6xico bDepartamento de Ingenieria Quimica, Instituto Tecnoldgico de Celaya, Av. Tecnoldgico y Garcia Cubas s/n, Celaya, Gto., 38010, Mdxico

Abstract This paper presents the retrofit of five conventional distillation trains for the separation of quaternary mixtures of hydrocarbons for feed compositions with high or low content of intermediate components. The retrofit implies the incorporation of liquid or vapour recycle streams among the conventional distillation columns. Each recycle stream removes one condenser or one reboiler. The introduction of thermal links can lower the energy consumption tip to 40% in contrast to conventional distillation trains widely used in the industry. This efficiency in the use of energy is achieved because the recycle streams, introduced in the conventional distillation trains, reduce the remixing associated with higher energy consumption. Also, the introduction of recycle streams can improve the dynamic responses in contrast to those obtained in the conventional distillation sequences. Hence, the introduction of recycle streams in the conventional distillation sequences can improve both the energy consumption and the control properties.

Keywords: Distillation Sequences, Energy Savings, Dynamic Responses 1. Introduction Conventional distillation trains are characterised by large demands of energy in the reboilers (Tedder and Rudd, 1978; Glinos and Malone, 1988; Fidkowski and Krolikowski, 1990); as a restllt, researchers and engineers are interested in developing new distillation arrangements that can reduce energy consumption. Most of those arrangements involves the use of thermally coupled distillation sequences (TCDS) which, in the case of the separation of ternary mixtures, can decrease the energy requirements around 30% in contrast to conventional distillation trains (Triantafyllou and Smith, 1992; Finn, 1993; Wolff and Skogestad, 1995; Hernfindez and Jimdnez, 1996, 1999a, 1999b; Shah, 2002; Schultz et al., 2002). Thermal links reduce remixing in conventional distillation schemes, which contributes to the energy savings achieved in thermally coupled distillation sequences (Triantafyllou and Smith, 1992; Hernfindez et

Author to whom correspondence should be addressed: [email protected]

1484 al., 2003). Nevertheless, mixtures with more than three components have not been studied to the same degree as ternary mixtures (Rong et al., 2003; Christiansen et al., 1997; Rong and Krawslaski, 2002). Therefore, in this paper we present a study of the retrofit of conventional distillation sequences for the separation of quaternary mixtures of hydrocarbons (A,B,C,D) with low or high content of intermediate components; such choice of the compositions was made because, in the case of ternary mixtures, the energy savings depend strongly on the amount of the intermediate component. The TCDS obtained are subjected to a study of their dynamic properties under the action of feedback control. It is well known that the separation of a quaternary mixture can be done using the five conventional distillation trains (King, 1980) shown in Figure 1. Figures 1A and 1B shown two classical distillation trains: the direct distillation train, in which the components are removed one by one in the overheads, and the indirect distillation train, in which the components are obtained one by one in the bottoms products. These sequences are widely used in industry. Conventional distillation trains can be changed into thermally coupled distillation sequences by removing a condenser and introducing a liquid recycle stream or eliminating a reboiler and adding a vapour recycle stream to the bottom of the column (Figure 2). For example, in the case of the conventional direct distillation train (Figure 1A), the reboiler of the first column is replaced by a recycle stream of vapour from the second column, and the reboiler of the second column is eliminated with a vapour recycle stream from the third distillation column. At this stage, recycle streams have been introduced, but it is necessary to optimise their flowrates in order to guarantee optimal energy consumption. Recycle streams are varied until the minimum energy requirement is detected, as reported in Hernfindez and Jim6nez (1996, 1999b). The number of stages remains fixed in both types of distillation arrangements because in the retrofit design only recycle streams are introduced and condensers and reboilers are eliminated. i~

.i~~

~

ii:i~...........

~,~ ii~- ............

i

.......

i~ ~J

J ~. ~

! ......ii~i¸~

~

~.....~. .... [ .......

Figure 1. Conventional distillation sequences

i!J

.........

Figure 2. Thermally coupled distillation sequences

~.

,J

1485

2. Case of Study We have explored energy consumption, remixing and closed-loop dynamic behaviour of the five conventional distillation sequences shown in Figure 1 and the corresponding thermally coupled distillation schemes of Figure 2, for the separation of two quaternary mixtures of hydrocarbons (Table l) and two feed compositions (Table 2). The study was carried out via rigorous simulations by using the process simulator Aspen Plus

11.1TM

Mixture M1 M2

Table 1. Mixtures analysed. Components (A,B,C,D) n-pentane, n-hexane, n-heptane, n-octane n-butane, i-pentane, n-pentane, n-hexane

Table 2. Feedjlowrates for each feed Obmol/h). Feed Flowrate (A/B/C/D) F1 30/20/20/30 F2 20/30/30/20

3. Results 3.1 Energy in the first phase of the analysis, energy consumptions in the conventional distillation trains were obtained and compared (Table 3). For the case of mixture M1 and the two feed compositions, the CDS I (Figure 1A) was the most energy efficient; savings in energy of 37% and 11% for feed F1 and F2 respectively were obtained in comparison with the worst conventional distillation train. When the mixture M2 was considered, the sequences CDS V (Figure 1E) and CDS IV (Figure 1D) were the optimum options for the separation of feeds F 1 and F2 respectively with savings of 58% and 41%. In the second phase of the study, thermal links were introduced in the conventional distillation trains. As stated before, in order to obtain the optimum design in the use of energy, the interconnecting flows were varied until the minimum demand of energy was achieved. This task was completed with the process simulator Aspen Plus 11.1TM In the optimisation procedure the interconnecting streams were changed one by one and the optimisation curves were obtained. The optimum energy consumptions found for the thermally coupled distillation trains are shown in Table 4. It can be observed, for the case of the separation of mixture M I and the two feed compositions, that the TCDS I (direct thermally coupled distillation train) of Figure 2A was the most efficient and presented energy savings of 27% in comparison to the CDS I scheme (direct distillation train). It is important to note that in these cases, the conventional direct scheme was the optimum sequence for both feed compositions when thermal links were introduced. For the separation of mixture M2 and the two feed compositions, the optimum thermally coupled distillation trains presented savings of 40% and 30% in contrast to the conventional distillation sequences.

1486 In summary, the introduction of thermal links in the conventional distillation trains produced savings in energy of up to 40% in comparison with the optimum conventional distillation train.

Feed F1 F2 F1 F2

Feed F1 F2 F1 F2

Table 3. Energy consumptions (Btu/h) of the conventional distillation CDS I CDS II CDS III CDS IV Mixture M 1 3741914.2 3961719.8 5 0 1 0 9 4 1 . 4 1 3916616.7 4064516.6 4558954.6 4251316.04 4226684.6 Mixture M2 8440246.2 6164263.7 10555639.9 4609531.7 6741223.1 10555639.9 6359215.8 6174523.4

Table 4. Energy consumptions (Btu/h) of the thermally TCDS I TCDS II TCDS Ill Mixture M 1 2712669.4 3070826.3 3688361.6 2860660.9 3640303.3 3382957.9 Mixture M2 4318728.7 4596249.2 5544802.0 4400424.2 6935670.6 4946987.2

trains. CDS V 5936384.3 4596499.9 4423507.7 6944047.3

coupled distillation trains. TCDS IV TCDS V 2788522.1 2925223.3

3141563.5 3205683.6

292522.3 4448687.7

2624437.5 5714816.2

3.2 Remixing Remixing, presented naturally in conventional distillation trains, causes inefficiencies in the use of energy. These inefficiencies increase the energy of the reboilers required for the separation. In Figure 3 we observe the composition profiles for the four components in the first column of the CDS I for the separation of the mixture M1 and feed F1, as a typical example. The composition of component B increases until a maximum of 0.57 and then decreases to 0.28 in the bottom of the column, that is a consequence of remixing for component B. . . . . . . . . . . .

+A

. . . . . . . . . .

0.8 0.6 "5 u_

-5 0.4 0.2

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Stage

Figure 3. Remixing in the conventional distillation sequences

17

1487 A similar effect is presented in the composition of component C in the second column of the conventional distillation train CDS I. Having analysed all the mixtures and feed compositions, it was found that any conventional distillation column with at least one multicomponent product will have remixing.

3.3 D y n a m i c behaviuor

The optimum conventional and thermally coupled distillation sequences were subjected to a study of their dynamic responses under the action of feedback PI controllers. Changes in set points were considered and the optimal responses were chosen in terms of their IAE (integral of the Absolute Error) values. Through the use of Aspen Dynamics 11.1TM, the values of the controller gains (Kc) and reset times ('c~) that provided a minimum value of IAE for a set point change for each separation scheme were computed. Regarding the dynamic responses under the action of feedback controllers for changes in the set points, Table 4 showns the IAE values for a positive set point change in each product composition. TCDS I outperformed the dynamic responses of CDS I for set point changes in components A and B as shown in Table 4; however, for components C and D, CDS I presented better values of the IAE. When a negative set point change of the same magnitude was implemented in each composition, a similar result was obtained. CDS I presented the best dynamic behaviour according to its lower values of the IAE (Table 4) in comparison to TCDS I for components B and D; on the other hand, when the set points of compositions of the products A and C were perturbed, TCDS I presented better dynamic responses than those obtained in CDS I. Table 4. IAE results for set point changes in the distillation sequences.

Distillation Sequence

Product stream A

CDS I TCDS I

0.0143109 0.00494638

CDS I TCDS I

0.00037819 0.00026217

B

C

Positive change in set points 0.0142759 0.0001042 0.0005048 0.0049209 Negative change in set points 0.00023645 0.0007281 0.00107824 0.0000397

D

0.0004593 0.0099678 0.0000745 0.0003016

4. Conclusions The retrofit of conventional distillation trains was studied introducing thermal links for the separation of quaternary mixtures of hydrocarbons. Energy savings of up to 40% were obtained because the retrofit reduced the inefficiencies of the conventional distillation trains. This result is important because the retrofit involved only the introduction of recycle material streams. The recycle streams decreased significantly the remixing effects presented in the conventional distillation trains, associated with higher energy demands. Also, the dynamic responses of thermally coupled distillation

1488 sequences were as good as those obtained in conventional distillation sequences and, in some cases, the dynamic responses of thermally coupled distillation sequences were better than those of conventional distillation schemes. These results can establish that the energy savings are achieved without adding potential control problems. The lower control efforts (lower values of IAE) required by TCDS for some of the case studies indicate that these options may also provide a more efficient use of energy during its transient times.

References Christiansen, A.C., Skogestad, S. and K. Lien, 1997, Comput. Chem. Eng., 21, $237. Fidkowski, Z. and L. Krolikowski, 1990, AIChE J., 36, 1275. Finn, A.J., 1993, Chem. Eng. Progress, 89, 41. Glinos, K. and M.F. Malone, 1988, Chem. Eng. Res. Des., 66, 229. Hernfindez, S. and A. Jim6nez, 1996, Trans. Inst. Chem. Eng., 74, 357. Hernfindez, S. and A. Jim6nez, 1999a, Comput. Chem. Eng., 23, 1005. Hernfindez, S. and A. Jim6nez, 1999b, Ind. Eng. Chem. Res., 38, 3957. Hernfindez, S., Pereira-Pech, S., Jim6nez, A. and V. Rico-Ramirez, 2003, The Can. J. Chem. Eng., 81, 1087. King, C. J., 1980, Separation Processes, 2nd Edition, McGraw-Hill, New York, USA. Rong, B.G., Kraslawski, A. and I. Turunen, 2003, Ind. Eng. Chem. Res., 42, 1204. Rong, B.G. and A. Kraslawski, 2002, Ind. Eng. Chem. Res., 41, 5716. Shah, P.B., 2002, Chem. Eng. Progress, 98, 46. Schultz, M.A., Stewart, D.G., Harris, J.M., Rosenblum, S.P., Shakur, M.S. and D.E. O'Brien, 2002, Chem. Eng. Progress, 98, 64. Tedder, D.W. and D.F. Rudd, 1978, AIChE J., 24, 303. Triantafyllou, C. and R. Smith, 1992, Trans. Inst. Chem. Eng., 70, 118. Wolff, E. A. and S. Skogestad, 1995, Ind. Eng. Chem. Res., 34, 2094.

Acknowledgements The authors acknowledge financial support received from PROMEP and Universidad de Guanajuato, M6xico.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) 6') 2005 Elsevier B.V. All rights reserved.

1489

Expert system for the control of emergencies of a process plant Dr. M L Espasa, Ing. F B Gibert Secci6n de Sistemas Expertos, Institut Quimic de Sarrifi, Universitat Ram6n Llull Via Augusta 390, 08017 Barcelona (Spain)

Abstract The chemical industry due to its great potential of danger, as much for the human health and for the environmental one, requires exceptional safety measures. Not in vain there appear new more strict norms concerning the systems of control and study of the consequences of a possible accident. The investigation group has been developing an expert system for the integral management of the procedures of emergency of a refinery, the greatest and most complex of the chemical industries. The tool has two missions that are fundamental for the safety of any chemical plant, on one side advises to the operator for the actions to take in case of an emergency and on the other hand the expert system makes a complete program of formation for new workers. In this formation it simulates emergency situations that the user must solve successfully. In order to achieve this double objective, almost a year has been dedicated to the compilation of all the information necessary to nourish the knowledge base. The inference motor governed by logics rules will use all this information for, under several premises, to decide which the best action to take is. In addition the system is able to complete the formation of new technicians simulating emergency situations, soliciting data of equipment, safety norms, and function of the units... Due to the structure with which the expert system has been constructed, is easy to export it to another type of process plants. It as easy as finding an expert who, with the aid of a knowledge engineer, would introduce in the data base the particularitities of that type of industry.

Keywords: Expert System, Emergency procedures, Safety, Refinery 1. Introduction When this project began, the collaborating refinery trusted the answer to any alarm on its experts' knowledge. The operators based on their experience, decided the actions to take in order to avoid that risk situations became serious emergency situations. This scenario raised an amount of inherent problems to human condition like loss of capacity to reason in case of a panic attack, negligence by the excess of confidence and suppression of apparently unnecessary actions among others.

1490 In view of this situation the company decided to invest in a research program to construct an Expert System that provides a second opinion in case of real emergencies, as well as a program for complete training of new operators. The Expert System must accomplish the following objectives: • It must contain all the necessary information for making the correct decisions and, when there is a lack of a necessary parameter, it should formulate a question asking for it. • It must include all the plant units for considering the repercussions of each action taken and for avoiding, therefore, the denominated 'domino effect'. • It must be very clear and easily understood by users. • It must provide a complete training module on which users can complement their formation about the Plant and about specific subjects on safety. • It must have an updating subsystem so that the responsible person can introduce all changes occurred in the Plant.

2. The Expert System The first step for the construction of the Expert System is the knowledge database design, where the information that the inference engine will use for taking decisions is stored.

2.1 The Logical Tree The information of the knowledge database must be structured following logical rules in order to associate concepts in the same way that the human brain of the expert would. For this purpose, logical trees used for making decisions have been developed. A logical tree defines chain actions related by cause-effect associations. The relation between two actions can be direct or be associated by other conditions, appearing in this way, necessary conditions, sufficient conditions and both necessary and sufficient conditions.

[

Bloq~J~ar la ~ r d ~ a ~ y .~alida d~ la :[Jn~d~d de P~?~

Figure 1. Logical Tree

1491 As it can be observed in Figure 1, the logical tree presented has three kinds of relations between the actions: the consecutive relation (blue colour), the dilemma relation (green colour) and the waiting relation (red colour). • Consecutive relation This relation is necessary and sufficient, the following action is essential among the list of actions to take, but because of logistic reasons the order on which actions have to be taken is not of forced accomplishment, again, the decision is leaved to the operator. • Dilemma relation: This relation is necessary and sufficient, the following action is essential among a list of actions to take, but because of logistic reasons the order on which the actions are taken is not of forced accomplishment, the decision is left to the operator. • Waiting relation: This relation creates the possibility to execute different actions depending on the particular reasons of the emergency during the actions sequence. The difference with the previous bifurcation is that in this kind of relations two different branches of the tree can be taken to be merged later on. Besides the information concerning the actions to take in case of an emergency the database contains the specifications of the equipment in the plant and their operation conditions. Once the database contains all the information, the inference engine is able to predict the possible consequences of an alarm or incident and suggest in this way, the recommended actions to take in order to avoid further problems that would lead to more serious problems. This information is useful for the staff as a reminder and as a second opinion in case of doubt but never makes an action in the plant. The operator has the task of acting and feed the expert system with the required information as well as introducing the actions already taken.

I

. . . . li II I ........ i111li ...... .... iiili Iiiilii111111: ..... .... I:1...... III Iliiiiilill.......... i11111111 IIIIII C~,-:~'rar Y bloq~.se&r li~ vL'~lvufa.~ V 11 de ,'ntri:,da de ~li~s pllol.o i:~ kls tr,..'s horlrl4}S, t.l/Jr.ttr et [.if(:l~l.e~.l[iJ;r, f.:oil--qo~i{i,..tl la.~~

Figztre 2.Action List

1492 As it can be seen in figure 2 the structure given to the action form has been studied in a way that results simple to use and allows to see 10 actions at once, giving in this manner a general vision of the emergency procedure to follow.

2.2 Training System With the information present in the database a learning subsystem has been prepared in a way that generates simulated emergency situations. Once the warning pops up the operator must decide what actions have to be taken. The questionnaire is organized in a test form in a way that four possible answers are presented and only one of them is correct. In these test series, questions about the equipment and concepts related to safety can be asked. ~ii~i~~i~iiiiiiiiiii~iiiiiiii~iiiiiiiiiiiiiiiiiiiiiiiiiiiTiiiiiiii iiiii i i i!ii ~iiii i i iiiiiliiiiii i i i iil i i i i i i i i i i iiii~iii~iiiiiiiiiiiiiiiiii iiiii!ii i i i i i iTiiiiiii iii~!iiiiiiliilliill~iiiliiiii i iT~iTi~

"~!i'~, ~!i'~~"~, i~i!~~!ii!i~i,!!:~:~i ,'~,~'~+,i,!~i ,~i~!;Wi~~i,~i,i71~i : i~,~i~Wk! ~ii~,;:~,iii~'iilL~ii~i,~i,;i,i,!;~i~!~i~L~:i iii~ !,;:,i~i ,i~;~i ii!~~ii!ii~i~il;~711! ,~i, iil;,~i~i,ii,i,171L~ ,~i~i i~il;~i,~ii~i i i~i,i~i,ii~~,iiiil~i i ~i i i i i i,',~!ili i i ~i~iiii! !i!:ii i!i!i!~iil ~i;i I(]0~tl litt ti~!i Cltilttril ~llJ:~'lt~l~ll,~ Clil~ ~tt rrlli~t~ltltil ttri

t~rt

Figure 3. Training test

Finally, the application was provided with multiple options that make its use more dynamic and easy, like the possibility of consulting the map of the section where an item of equipment or a particular accessory appears. In this way it results more simple to understand its utility and predict the consequences of its malfunction. In the figure 4 appears an example of a unit diagram.

1493 ::: ....

:

::

:

i~i~iiiiiiiiii~}~ii:~iiiiiiii~iiiiii'~ii:~ii'~i'~i'i:,,iiii:,):~ :i!ii~ii i il;iiiii:~i~i:~i~iiiiiiiii:~;~ ~ :~i:;i ::: : :

iii~:i:~ii :

::

:

::

::;::

:::

::

:

: ~

Figure 4. Unit diagram

3. C o n c l u s i o n s An application has been developed with the purpose of accomplishing two main functions, it gives an objective second opinion to the operator concerning the actions to be taken in case of an emergency, and also, is a suitable tool to teach, train and update the personnel. In order to build the application it has been necessary to acquire a deep knowledge of the refinery units and the definition of the emergency procedures, structured in logical trees and saved in a database. The designed inference engine acts on this database, it manages all the information, suggesting the necessary actions that have to be taken in case of an emergency. Furthermore, it generates the questionnaires that will be used in order to train the staff. Besides this features a device that maintains the application has been integrated; it allows the user to update the system (add items or modify the database), without using the source code, making the application non dependent on the original programmers.

References Hopgood, A.A., CRC Press, 2001, Intelligent Systems for Engineers and Scientists. USA. Krishnamoorthy, C.S., Rajeev, S., CRC Press, 1996, Artificial Intelligence and Expert Systems for Engineers. USA

European Symposiumoil ComputerAided Process Engineering- 15 I,. Puigjanerand A. Espufia(Editors) (c;,2005 Elsevier B.V. All rights reserved.

1495

An expert system for a semi-batch pilot scale emulsion copolymerisation facility R. Chew, B. Alhamad, V.G. Gomes, J.A. Romagnoli Laboratory for Process Systems Engineering, Department of Chemical Engineering, The University of Sydney, NSW 2006, Australia

Abstract A knowledge-based system (KBS) has been developed for a semi-batch pilot scale emulsion copolymerisation reactor facility. A simulation model was developed for the feed of styrene and MMA monomers as well as surfactant and initiator to control the particle size distribution (PSD) and molecular weight distribution (MWD) over the entire monomer conversion. The expert system architecture provides continuous support and rectification of product off-specs, monitoring and maintaining safety functionality, as well as retaining process continuity. Process events such as the particle growth and secondary nucleation could be picked up by the rule-based expert system. The knowledge-based system is built under multiple layers of a proposed supervisory architecture. This expert system was built using G2 TM (Gensym Corp). The expert system provides diagnostic and decision support to the operator. The diagnostic module triggers alarm and send message queues whenever a process upset occurs. The decision support system (DSS) incorporates several features such as intelligent polymer recipe input interface to pre-select optimal pump controls. The expert system was put to test on the actual facility and has been aiding the operator running the facility.

Keywords: Knowledge-based Systems, Copolymerisation, Fault Diagnostic System

Supervisory

Control,

Emulsion

1. Introduction Knowledge-based systems (KBS) or commonly known as expert systems are computer systems that assist the operator in making critical decisions under various operational scenarios with the capabilities of emulating the process behaviour based on knowledge of process characteristics. The KBS usually consists of a knowledge base, decision rules, and an inference engine. The knowledge base is comprised of facts pertaining to a specific process, while the decision rules are typically of the IF/THEN conditional statements.

1496

Hopgood [1] states "Rules are an elegant, expressive, straightforward and flexible means of expressing knowledge" and in knowledge representation, Moore [2] pointed out that experts used their knowledge of plant structure, knowing how the connected process units affect each other, it is thus useful to use graphical form of knowledge representation, so experts can define the plant structure and interactions by connecting objects on a computer workstation. KBS development software such as G2 is designed to permit the process engineer to define the knowledge in natural forms with the capability of symbolic processing. In this paper, the application of G2 is focused on a lab-scale semi-batch pilot scale emulsion copolymerisation facility. Supervision of an emulsion copolymerisation process is needed specifically for monitoring and control of monomer conversion as it is crucial both for proper process operation so as to aid the downstream separation, and for obtaining products with desired properties due to the influence of conversion on polymer molecular weight and particle size distributions [3]. Not only this, the decision support system (DSS) can easily be implemented by G2 and any other features to aid the operator.

2. Experiment The laboratory setup of this facility consists of a 5 litre jacketed stirred reactor; a Julabo heating circulator provides heating/cooling water through the external jacket; 4 Prominent dosing pumps to introduce feed of the two monomers, surfactant and initiator; 3 RTDs for temperature monitoring; and 4 precision balances to determine the quantities of reactants used. Data acquisition is achieved via Honeywell's PlantScape DCS. On-line control of process equipments can be done on the graphical-user-interface (GUI) which is developed on Honeywell's system (see Figure 1). A schematic diagram of the reactor system built using G2's Dynamic Display utility is shown in Figure 2. Semi-batch emulsion copolymerisation of styrene (99% purity) and MMA (99% purity) were carried out at 70, 75, 80 and 85°C under slight nitrogen pressure.

~i.......i!......................!~!

Figurel. GUI in Honeywell DCS.

Figure 2. Process monitoring in G2.

3. Architecture of the supervisory KBS The supervisory KBS is designed to embody expertise in a particular domain. It usually has two components; the knowledge module is called the knowledge base while the

1497 control module is called the inference engine. The explicit separation of knowledge from control makes it easier to add new knowledge either during program development or in the light of experience during the program's lifetime, [ 1]. The proposed architecture or expert system shell is divided into four different domains, namely the operator/user domain, the expert supervisor domain, the simulation/processing domain and lastly the plant/action domain. Advice

Level 4" Expert System

Supervisory ~ . Module

Level 3" MPC ~..J

Level 2' DCS ~l

Level 1' Online Simulation

~l ~

I

On-line Calorimeter

KnowledgeBase

~,,....~

Monitoring & Control

......

..I i i i

,,~ _ _i

Emulsion Copoly.... isation Process

Figure 3. Scheme of the supervisory architecture. •

•

•

The operator domain comprises of a DCS workstation manned by the user which allows human intervention of the process. Advices, notifications and alarms can be read and acknowledged by the user. In the expert supervisor domain, the supervisory module acts as a manager of the distributed knowledge base as well as managing prioritised alarms if multiple errors appear. The artificial intelligence (AI) comes solely from the developer, who imparts the extensive knowledge and rules into the KB. For the simulation domain, the on-line calorimeter provides inferential conversion monitoring and control through calorimetric measurements of reaction temperature. An on-line diagnostic module is also added for processing detected faults, and to provide corrective control action to the plant.

4. Software Four commercially available software have been utilised for the implementation of the architecture. These are outlined in this section.

gPROMS (Process Systems Enterprise, UK)." For numerical simulation purposes, the sets of differential mass and energy balances, the kinetic equations and the population balance equation were solved using gPROMS. Excel VBA (Microsoft Coworation, USA). MS-Excel was used extensively throughout the development of this KBS. The programming language was used to develop the communication bridge between G2 and the physical reactor. G2 utilises a tool called

1498 "ActiveXLink" and is compliant with any Microsoft Windows based programs. Example of VB code fragments used in this application include" Read data:

G2Gatewayl.Call ("procedure-name" arguments);

Write data: Variant)

G2Gatewayl_RpcStarted

(By Val Name As String, InArgs As

PlantScape r500 (Honeywell Corporation)" The uploading and configuration of the control schemes to the controller is done using the software called Control Builder TM. Control Builder allows analogue inputs of plant instruments for a series of conventional PID control over the plant.

G2 (Gensym Corporation, USA)." This real-time expert system development tool uses several different knowledge representations: rules, object-oriented platform, connection stubs. These entities has classes and workspaces assigned, allowing the developer to define the knowledge in natural forms. An example of how our metering pump (Prominent gamma/L) is defined in G2 is illustrated in Figure 4.

ii!i!!!iil,ili!iii!ii! i¸ ...........................

:~,~ ..........

:

i .....

................................. :i~!:!!!¢!ii,!i:2?,;ii!:=!!~:i:iii~:~::::< ~!:il,:. . .

Figure 4. A workspace showing a pump definition.

Figure 5. Screenshot of user interfacefor recipe selection

5. Features/Improvements In order to allow the knowledge base to respond to various conditions, rules are used and they can be easily defined in plain text format. Rules describe knowledge in a manner that allows the KB to draw conclusions from existing knowledge, to react to certain kinds of events, and to monitor the passage of time. A total of 23 rules were by date updated into the KBS. Example of a rule used to investigate "secondary nucleation" by referencing historical data with present data is as follows: whenever the conversion of soft-sensor receives a value and when the conversion of soft-sensor > 0.5 and the rate of change per minute of the polydispersity of softsensor during the last 15 seconds > 0 and the rate of change per minute of the

1499

particle-number of soft-sensor during the last 15 seconds > 0 then post for the next 5 seconds "Secondary Nucleation".

In this paper, several added features were also presented. An automatic software launcher was developed in G2 which eliminates the complicated startup an operator has to face before running the experiment. One of the key features that were developed would be the recipe scheduler. It was built based upon the graphical language component in G2 known as the G2 Diagnostic Assistant (GDA) tool. As with the above mentioned software launcher, this feature automates the task of selecting the optimal feed profile in Control Builder. The user/customer only needs to enter his/her preferred polymer properties press enter and the recipe formula would be selected accordingly to the matched logic structure developed in GDA. Figure 5 shows a screenshot of the user interface along with the structure of our feed recipe formula. An experimental results logger was also implemented via GDA. An interface allows the user to key in a filename which will automatically record all process events and major alarm messages in a text format. 6. R e s u l t s a n d O b s e r v a t i o n s

The most obvious use for GDA would be the diagnostic support that would be utilised for early fault detection and perform corrective measures. Pre-analyses problems were targeted to test-run this prototype, which includes detection in pump flow deviations, pump/pipe blockages, product off-specs due to rate of reaction and abnormal reaction temperature and early detection of monomer feed run-out. An alarm panel appears when a process upset occurred.

:ii:i : :/i:::¸¸:iii:¸¸

::¸ :/¸

i¸ ::

t

i:¸

Figure 6. Screenshot of GDA structure and the a/arm.for "l)ump running dtr3 " "

•

Figure 7. Screenshot of "Secondary Nucleation

Example of a common fault that was purposely created is preventing the pumps from running dry. The user inputs in the amount of feed used, GDA will calculate the safe

1500 level to be left in the feed bottle and when the safe level has been breached, GDA alarms and automatically shuts the pump. Figure 6 shows the pop-up of the alarm panel for this event. To validate the above mentioned rule, 2 trend plots showed that the rule can be constructed to correctly identify "secondary nucleation". Figure 7 clearly shows that at approximately 4.20pm, the rule initiates the message which coincides with the decrease in the particle size and the number of particle increases. The validation of optimal trajectories carried out with experimental runs is stated in literature, [4].

7. Discussions and Conclusion A particle size distribution analyser (Polymer Laboratories) has recently been installed for the primary purpose of measuring PSD of samples from the batch. On-going research has been undertaken to enable online measurement during the batch process. A detailed (validated) mechanistic model has been developed to calculate set-point trajectories to ensure the production of a copolymer with a defined PSD [4]. In G2, an interface has been created to allow manual inputs of sampled PSD. This operator value will be validated with the current simulation, which will provide the eventual knowledge for rule generation and thus providing a more robust supervisory module when the analyser becomes online. We tested this expert system and it has periodically been running for some experiments. The system gets periodic data and performs diagnostic support with no trouble. Recipe selection allows the GDA structure to target the Control Builder feed profile with exact precision. If a profile could not be matched, an online working model would be generated to find a new optimal profile/recipe for the user. This of course, would be included in our future work. Overall, this expert system maintains a continuous automated process, from the initial pre-run check, the less complicated software startup, the recipe selection step, the monitoring of secondary nucleation and particle growth events, the fault detection and corrective measures, to the eventual online sampling of PSD with G2 in an all-in-one package.

8. References [ 1] Hopgood, Adrian A., 1993. Knowledge-based systems for engineers and scientists.

[2] Moore, Robert L., Rosenof, H., Stanley, G., 1989. Process Control Using The G2 Real-time Expert System. Gensym Corp, Cambridge, MA, USA. [3] Zeaiter, J., Romagnoli, J.A., Barton, G.W., Gomes, V.G., Hawkett, B.S., Gilbert, R.G., Operation of Semi-batch Emulsion Polymerisation Reactors: Modelling, Validation and Effect of Operating Conditions, Chem. Eng. Sci., Vol. 57, No. 15, 2955-2969 (2002). [4] Alhamad, B., J.A. Romagnoli, and V.G. Gomes. Optimal Control for Emulsion Copolymerization: Application within a DCS environment, in 7th International Symposium on Dynamics and Control of Process Systems. July 5 -7, 2004. Boston, USA.

European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) ~;' 2005 Elsevier B.V. All rights reserved.

1501

Integrating Data Uncertainty in Multiresolution Analysis Marco S. Reis a*, Pedro M. Saraiva a a GEPSI-PSE Group, Department of Chemical Engineering, University of Coimbra P61o I I - Pinhal de Marrocos, 3030-290 COIMBRA, PORTUGAL

Abstract Multiresolution decomposition frameworks are instrumental when one needs to focus data analysis at a particular scale or to separate the several contributions to the overall phenomenon, arising from different scales either in time or length. On the other hand, measurement uncertainties are now frequently available along with raw value measurements. In this paper we address the development of multiresolution decomposition methodologies that are able to cope with difficult data/uncertainty structures often met in industrial practice, like missing data and heteroscedastic uncertainties. A guideline is provided regarding their adequate use and an example illustrates the potential benefits associated with the suggested approach.

Keywords" multiresolution analysis, multiscale decomposition, wavelets, missing data, measurement uncertainty. 1. I n t r o d u c t i o n Multiscale approaches have received considerable interest from several widely different branches of science, including PSE, where wavelet theory, and in particular Mallat's (1988) concept of lnultiresolution analysis have been playing an important role, particularly in what concerns data analysis applications (Mallat, 1998; Alsberg et al., 1997). Another theme that has gained considerable importance in the last years regards the specification and incorporation of uncertainty information in data analysis. Uncertainty is defined as a "parameter associated with the result of a measurement that characterizes the dispersion of the values that could reasonably be attributed to the measurand" (more details on ISO, 1993; Lira, 2002). With the appearance of new sensors, the development of metrology and the increasing enforcement driven by standardization organizations, one has now frequently available for analysis not only measurement values but also their uncertainties, i.e., two tables containing important information: one with raw data and another with their associated uncertainties. In this paper we address the development of multiresolution decomposition methodologies that incorporate data uncertainty information, and are able to cope with difficult data/uncertainty structures that are often met in industrial practice, like missing data (i.e., when there are blanks in the raw data table due to, for instance, the existence of variables with different acquisition rates or problems either in the process or in the sensor/transmission/storage intbrmation chain) and heteroscedastic uncertainties Author to whom correspondence should be addressed: [email protected]

1502 (signals noise with a variance that changes over time). In the next section we present two uncertainty-based multiresolution decomposition frameworks, and in section 3 we provide a general guideline for their use. Section 4 illustrates the potential benefits associated with the proposed approaches, and in section 5 we conclude by discussing some issues concerning the use of these approaches as well as other application contexts.

2. Accounting for Decomposition (MRD)

Data

Uncertainties

in

Multiresolution

Under the heading of multiresolution approximation, Mallat (1989) presented a framework where coarser approximations of a given signal at the finest scale can be considered as projections to approximation subspaces indexed by a scale index (j), Vj, that span progressively shorter regions of Lz (IR), and that have a nested structure (Vj+~ c ~,~+~ ~: Vj ). On the other hand, the details that are lost in the process of projecting the signal to increasingly coarser approximation spaces can also be considered as projections to complementary subspaces, the details spaces, Wj, that, in conjunction with the approximation space, span the space of the original signal. This allows us to write a given signal at the finest scale, say f0, as the sum of its projection to the approximation space at scale j, .~, plus all the details relative to the scales in between, {w; };:~......j. These projections can adequately be written in terms of linear combinations of the basis functions for the spaces, multiplied by the expansion coefficients. The expansion coefficients are called approximation coefficients, akJ (k ~ Z) (multipliers of the basis functions for the approximation space), and details coefficients, d~, (i = 1.... ,j; k ~ Z)

(multipliers of the basis functions for the detail

spaces), and are usually referred to as the orthogonal wavelet transform or wavelet coefficients. For the purposes of this paper, we will call "multiresolution decomposition framework" to the algorithm that provides the expansion coefficients, which, for the classical situation, is just the wavelet transform. However, this classical procedure can not be straightforwardly applied in less conventional situations, like those with missing data, something that occurs quite often in industrial scenarios, and furthermore does not take explicitly into account data uncertainties, when these are available. In the next subsections, we will present two methodologies that handle these issues, for situations with missing data and homoscedastic (constant) or heteroscedastic (varying) uncertainties (Method 1 and 2). 2.1 Method 1" Adjusting filter weights according to data uncertainties. The Haar wavelet transform, perhaps the simplest of all known wavelet transform families, attributes a very clear meaning to its coefficients: approximation coefficients are averages of non-overlapping blocks with two elements (scaled by a factor of 1/x/~ ), and detail coefficients are calculated as the difference between the average and the first

1503 element of the block. Cascading this procedure along the sets of approximation coefficients results in the Haar wavelet transtbrm. Such a process gives equal weights to both values involved in the calculation of their average (coarser approximation coefficient). With data measurement uncertainties at our disposal, the averaging process can be modified so that the calculation of the coarser approximation coefficient (ai'~)~2i) gives more weight to the datum with less uncertainty. This can be achieved by using (-,/~ I.I /--,/+1.2

different averaging coefficients ( L iX/2~ , ,~F~/~? ) applied to each datum ( a::, a/k+, ): /+~':. uFk/2 "~r,~-/2~"a~~. + ¢"~-/2] -/+~ ~ - F'/+~l

(1)

a / :,.+l

where [-x~ is the smallest integer n _>x. Adequate weights can be set using formulas for the MVUE (minimum variance unbiased estimator) of the (common) average, suggesting the averaging coefficients associated to each datum presented in equation (2). Detail coefficients are given by (3).

v,...(-;) /

q'""

=

/

2

,, ~

k +1

'4J+l - t'-'J+ll • (a)! i--) I - ~ j + I . 2 _ aj "~u-/-,l '- iu-,~ <'~ -aik/21 < '- Fk/2i "( aft-~21 ~+~ )

where uric(x)

(3)

means the uncertainty associated with value x. Data uncertainty of the

approximation coefficients at scale./should also be propagated to the approximation and detail coefficients at the next coarser scale j + l , so that the averaging procedure can continue to coarser scales, and to enable the specification of the uncertainties associated with each coefficient for posterior use. This can be done by applying the law of propagation of uncertainties (LPU) to the present situation (Lira, 2002):

/+l,~ 2 •,,-(<) uric(u:k/'2~ ~/÷') = ~ ( Cw,::)

2

"-F~/2~ ) . uric(a,+' , )2

(4)

where it is assumed that the errors from two successive observations are independent, but more complex situations can also be considered. By conducting a multiresolution decomposition using this procedure, we give more weight to the values with less uncertainty associated during the calculation of the approximation coefficients. Extending this reasoning further, we can see that this calculation scheme allows tbr the integration of missing data in the analysis, as a missing datum can be considered to be any finite number with an infinite uncertainty associated, that essentially removes it from (2)-(5). In this case, the coarser approximation coefficient will have the same value as the non-missing datum and the coarser detail coefficient will be zero. For the case where there is no missing data and data uncertainties are homoscedastic, this multiresolution decomposition framework will provide the same values as the Haar transform (up to a scaling factor of 2 '/-~ for the coefficients of scale j).

1504 2.2 Method 2: Use Haar wavelet filter, accommodate missing data and propagate data uncertainties to coarser coefficients In this second approach for incorporating data uncertainties, the averaging and differencing coefficients are kept constant and equal to the ones suggested by the Haar filter. When there are no data missing, the uncertainty of the finer approximation coefficients is propagated to the coarser approximation and detail coefficients, using the law of propagation of uncertainties. If there are missing data, we calculate the next coarser coefficients by successively applying the following rules to each new pair of

approximation coefficients at scale j, (~ak/ , a k+l / J~ • • No value is missing ~ use Haar and calculate uncertainties using LPU; • tak,is missing ~

aFk/2~J+l-- aJk+l' blHc[aFk/2 j+l

• a k/ +l is missing ::> ui~/2 -J+~~ - a k/ , u n c • {a~, a kj+l } are missing ~

)

- u n c , (a ' k+l ,~ ' Hj+I ~[-k/2~ -

/+~~ - u n c aFk/2

¢'l~k/2~-J=+lm i s s i n g ,

O, urtc(dik/2~)]+l

a kJ , ,4/+1 ~'Fk/21 = 0,urtc~,.,Fk/27)

: O;

- 0;

a~k/27J+' ) - missing;

u n c [[

d S k/27 ' = missing,unc(dF~)~21

) -

missing.

From the rules above, we can see that when no missing data is present, the procedure consists of applying the Haar wavelet with uncertainty propagation. When we have missing data, it can also happen that it remains present at coarser scales (see the fourth rule). This can be instrumental when analysing the information content at different scales, and enables the development of tools for scale selection.

3. Guidelines on the Use of Uncertainty-Based M R D Frameworks Methods 1 and 2 differ deeply on how they implement the incorporation of uncertainty information. In this section we provide a general guideline about which of the two approaches to use and when. Let us consider an artificial piecewise constant signal, where the values are held constant in windows of 24 - 16 successive a), to which proportional noise with uncertainty assumedly known is noisy signal (Figure l-b), it is possible to calculate its approximations ( j = 1, 2,... ) using the two types of approaches and then to see which

values (Figure ladded. Using the for coarser scales method performs

better in the task of approximating the true signal when projected at the same scale, j. Our performance index is the mean square error between the approximation at scale j, calculated for the noisy signal, and that for the true signal, MSE(]). Figure 1-c summarizes the results obtained from 100 simulations. These results illustrate the general guideline according to which, from the strict stand point of the approximation ability at coarser scales, Method 1 is more adequate then Method 2 for constant signals and for piecewise constant signals until we reach the scale where the true values begin to vary from observation to observation, i.e., for which the piecewise constant behaviour stops. As the original signal has constant values along windows of 16 values, the piecewise constant pattern breaks down after scale j - 4. This occurs because Method 1 is based on the MVUE estimator of an underlying constant mean for two successive values, thus leading to improved results when this assumption holds, at least

1505 approximately as in the case of piecewise constant signals, being overtaken by Method 2 when such an assumption is no longer valid. True signal I

a~ 0

r~

~L !

~

~[~ •

±

7'i

-o.2

~._i q

J

-0.6 Noisy signal

"-~-0.8 F i

-lc

L

-1.2, -1.4

J

c~

-1.6i, i

2

3

4

5

6

Scale index (j)

Figure 1. (a) true signal used in the simulation; (b) a realization of the noisy signal and (c) box plots for the d(fference in MSE at each scale (j) obtained for the two methods 1O0 simulations).

4. An Uncertainty-Based De-Noising Application Wavelets found great success in the task of "cleaning signals" from undesirable components of stochastic nature, called noise, if we are in such a position that we do know the main noise features, namely measurement uncertainties, then we can use this additional piece of information to come up with simple but effective de-noising schemes. As an illustration, consider a smoothed version of a NIR spectrum as the "true" signal, to which heteroscedastic proportional noise is added. The standard denoising procedure was then applied to the noisy signal, according to the following sequence of steps: 1. Decomposition of the signal into its wavelet coefficients; 2. Application of a thresholding technique to the calculated coefficients; 3. Reconstruction of the signal using processed coefficients. This procedure is tested for the classic Haar wavelet with the threshold suggested by Donoho and Johnstone (1992), T-6-x/21n(N ) , where 6- is a robust estimator of the noise (constant) standard deviation, along with a "Translation Invariant" extension of it, based on Coifman's "Cycle Spinning" concept (Coifman and Donoho, 1995): "Average[Shift- De-noiseUnshifl]", where all possible shifts were used. We will call this alternative as "TI Haar". These methods are to be compared with their counterpart procedures that have the ability of using explicitly the available uncertainty information: "Haar + uncertainty propagation", "TI Haar + uncertainty propagation" (only 10 rotations were used in this method). All the tested methods used the same wavelet (Haar), threshold constant

1506 (~21n(N)) and thresholding policy ("Hard Threshold"). Figure 2 presents results for the MSE scores of the reconstructed signal (scale j - - 0 ) relatively to the tree one, obtained for 100 realizations of the additive noise. A clear improvement in MSE is found for the uncertainty-based methods, relatively to their classic counterparts.

2.5 ..................l.................

........ i ................................t

+

............... j i

1.5

0.5

Haar

Haar+unc.

prop.

TI H a a r

TI H a a r + u n c .

prop.

Figure 2. De-noising results associated with the four alternative methodologies ("Haar" "Haar+uncertainty propagation . . . . TI Haar" and "TI Haar+uncertain~ propagation ").for 1O0 noise realizations.

5. Conclusions In this paper, we propose two methods for handling the issues of missing data and data uncertainty in MRD. Both Methods 1 and 2 are not extensions of the wavelet transform in a strict sense, as some of their fundamental properties do not always hold, such as the energy conservation property (in the sense of the Plancherel formula; Mallat, 1998). However, they can lead to improved results by effectively incorporating uncertainty information and allow one to extend the wavelet MRD to contexts where it could not be directly applied, namely when we have missing data, as well as provide new tools for addressing other types of problems in data analysis, such as the one of selecting a proper scale for data analysis.

References Alsberg, B.K., A.M. Woodward, D.B. Kell, 1997, Chemometrics Intell. Lab. Syst. 37, p. 215-239. ISO, 1993, Guide to the Expression of Uncertainty. Geneva, Switzerland. Lira, I., 2002, Evaluating the Measurement Uncertainty, NJ: Institute of Physics Publishing. Mallat, S., 1989, IEEE Trans. on Pattern Analysis and Machine Intell. 11, 7, p. 674-693. Mallat, S., 1998, A Wavelet Tour of Signal Processing. San Diego [etc.]: Academic Press.

Acknowledgements The authors would like to acknowledge Portuguese FCT for financial support through research project POCTI/EQU/47638/2002.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1507

Integrated Process and Product Design Optimization" a Cosmetic Emulsion Application Fernando P. Bernardo* and Pedro M. Saraiva GEPSI-PSE Group, Department of Chemical Engineering, University of Coimbra, P61o II - Pinhal de Marrocos, 3030-290 Coimbra, Portugal

Abstract A simultaneous approach to address optimal product and process design is presented and applied to a cosmetic lotion case study. The problem formulation integrates product quality, as assessed by customers, a model predicting lotion viscosity as a function of its composition and a process model linking process design and operation with lotion composition and microstructure. The solution of such a problem identifies the optimal lotion composition together with the interrelated process optimal specifications. This integrated design approach is shown lo provide better solutions than the ones obtained when product and process design problems are solved separately.

Keywords: Process and Product Design, Optimization, Cosmetic Emulsions.

1. Introduction Integrated chemical product and process design may be understood as the specification of a chemical-based product together with the design of the correspondent manufacturing process. The product/process specification should take into account product functionalities and attributes valued by customers, as well as feasibility and profitability of production at a commercial scale. Generic methodologies to guide the solution of such an integrated problem along the way from customer needs to product manufacturing have started to be developed (Cussler and Moggridge, 2001; Wibowo and Ng, 2001, 2002). The basic idea under these methodologies is to drive decisions by product quality factors related to customer satisfaction, that once identified are then translated to a product/process technical specification. |n a previous work (Bernardo and Saraiva, 2004), and accordingly to the above qualitydriven perspective, we have proposed an optimal design formulation that integrates a product quality function together with product and process models. Based on this optimization problem, and handling its associated uncertainties, we have then presented a method to analyse the value of obtaining additional knowledge regarding a particular problem level. A cosmetic lotion case study was used to illustrate the application of our approach dealing with uncertainties in the prediction of product viscosity, which is correlated with customer satisfaction, but at that stage the interconnected manufacturing process design was not considered. Corresponding author, e-mail address: [email protected]

1508 In this paper, we focus on the simultaneous optimization of product and process design and its application to our previous cosmetic lotion case study, now enlarged with an approximate model of the manufacturing process. Our main objective here is thus to illustrate how both product and process design decisions may interact with each other and therefore verify to what extent an overall formulation that accounts for product quality, as well as process costs, may lead to improved solutions over the common sequential approach, where product and process design are handled separately.

2. Optimal Product/Process Design Formulation Although it may be further generalised, our design formulation is primarily dedicated to consumer formulated products, such as pharmaceutical, cosmetic, and cleansing products. Usually, such products comprise a mixture of several ingredients, combined in a structured system, such as an emulsion, suspension, foam or gel. Table 1 presents a set of variables and parameters relevant to the design of these products. Table 1. Product~process design variables and parameters.

QF y p

Xl

Z2

02 03

Description Product quality factors valued by customers Quality variables: product properties p or states x related to quality factors Product physicochemical properties or effects during usage Product design variables (process independent): ingredients used and their proportion Product state variables (process dependent): product structure Product operating variables: external conditions during product usage Process design variables: flowsheet configuration and equipment dimensions Process operating variables: operating procedure (recipe) and equipment operating conditions Process parameters: physicochemical properties and kinetic/equilibrium parameters Additional parameters, such as economic coefficients or market indicators

Cosmetic Lotion Example Skin feeling Lotion viscosity Lotion viscosity Oil-in-water emulsion (water, thickener, oil, emulsifier, etc) Droplet size distribution of the oilphase Shear rate of lotion application on skin Mixing equipment dimensions Impeller speed Heat transfer coefficient in mixing/heating tank Quality loss coefficient, electricity cost

Our design methodology is therefore based on three main groups of relationships: 1. The quality function, relating quality factors QF with product quality variables y; 2. The product function, which predicts product properties as a function of its related variables: p= fl(dl,Xl,Zl) ;

(1)

3. The process function, linking product and process variables: f2 (dl, d2, z2,02, Xl ) = 0 .

(2)

Regarding quality functions, we will assume here that, for each y variable, there is an optimal y* value, from the customer point of view, and that the quality loss L associated with a deviation ( y - y*) is well quantified by a Taguchi loss function:

1509 (3)

L = k ( y - y*)2,

where k is a quality loss coefficient to be estimated based on customer satisfaction surveys and panels. Other quality function definitions may be used as an alternative and are easily incorporated in the proposed methodology. Given the above mappings, leading all the way from customer perceptions to process operating conditions, our integrated product/process design problem can then be formulated as follows: max P(dl,Xj,zl,p,d,,z,,02,03)_ _ ~11,d2 ,:2

(4)

s.t. p - . f l (dl ,xl ,zl) A gl (dl ,Xl ,zl, P) <- 0

,];2(dl ,d2 ,z2,02,xl ) A g2 (all ,d2,z2,02, xl ) -< 0 . Here, P stands for an overall performance criterion, including a quality cost term based on loss functions (3) and also production and investment costs; gj _< 0 and g2-< 0 represent respectively product and process inequality constraints. A multi-criteria optimization approach can also be adopted, with product quality and process costs being handled as two opposing objectives and the trade-offs between them evaluated.

3. A Cosmetic Lotion Case Study A cosmetic lotion is usually an oil-in-water emulsion with the typical formulation shown in Table 2 (Williams and Schmitt, 1992; Wibowo and Ng, 2001). The lotion main function is to maintain the skin hydrated, by adding water from its own composition and reducing water loss from skin due to occlusive ingredients, such as mineral oils and fatty acids, and also humectants, such as glycerol. Emulsifiers that adsorb at the surface of oil droplets promote emulsion formation and stability, lowering the oil/water interfacial tension. Thickener additives, usually water-soluble polymers, largely control emulsion flow properties and also contribute to its stability, by increasing the continuous phase viscosity. Table 2. Tyt?icalformtdation of a hand and bo@ lotion.

Part A (10 to 15% (v/v) of the total) Stearic acid (occlusive) Cetyl alcohol (occlusive) Petrolatum USP (occlusive) Mineral oil, 70 mPa.s (occlusive) Isopropyl pahnitate (occlusive) Glyceryl monostearate (emulsifier) PEG-40 stearate (emulsifier)

% (w/w) 25.5 10.3 10.3 20.5 20.5 10.3 2.6 100

Part B Deionized water (solvent) Glycerol (humectant) Xanthan gum (thickener)

% (w/w) q

.

s

.

5-12 0.5-1.5 100 Part C (-0.25%(w/w) of the total) Preservatives Fragrances

3.1 Quality Function Lotion quality primarily depends upon its hydrating effect, but also relies on other factors, such as stability, flow properties and several sensorial attributes. Here, we will focus our product quality characterization strictly around the sensations experienced during its application on skin, the so-called skin feeling.

1510 Sensory panel tests (Brummer and Godersky, 1999), discriminated in sensations at the beginning and end of lotion application, indicate a significant correlation between these two quality factors and the correspondent viscosities lal and la2 (quality variables). From such results, two loss functions (3) are constructed, with ideal values lal * = 375 and la2* = 0.0242 Pa.s, and both losses L~ and L2 measured in % of product lost value. 3.2 Product Function

The main variables determining lotion viscosity are: thickener (xanthan gum) content in the aqueous phase (wv), glycerol content in the aqueous phase (wG) and oil-phase volume fraction (~). These are product design variables (d~) to be optimized, under the limits shown in Table 2, while the rest of the lotion formulation is considered fixed. For the viscosity of xanthan gum aqueous solutions, experimental data are available showing that three different regions may be distinguished: an approximately Newtonian region, for lower shear rates, followed by a strong shear-thinning region, and then again a nearly Newtonian region for high shear rates (Pal, 1995). These data are fitted to a Carreau model (Tanner, 2000), in which the glycerol contribution is incorporated assuming that it only influences the limiting viscosity for high shear rates. One thus obtains a model that predicts continuous (aqueous) phase viscosity: lac = lac(Wx,W~,~,). The theoretical model of Yaron and Gal-Or (Pal, 2001) is then used to predict emulsion viscosity from single-phase individual viscosities: la = la(lac,lad,q~), where lad stands for the oil-phase (Newtonian) viscosity. Our resulting product function is then of the form: = A (w~,wG,,~,~).

In order to estimate quality variables la~ and la2, the correspondent shear rate of lotion application must be known. For oil-in-water lotions, the typical final shear rate is ]/2 -5000 s-~. The initial shear rate ~'1 is calculated as the transition point between the nearly Newtonian region for low shear rates and the strong shear-thinning region. 3.3 Process Function

A batch process is considered (Figure 1) comprehending the following operations (Williams and Schmitt, 1992; Wibowo and Ng, 2001): 1. In tank T-1: (i) charge part A; (ii) dissolve solids, heat and mix; 2. In tank T-2: (i) charge part B; (ii) heat and mix; (iii) add part A; (iv) cool and mix (pre-emulsion formation); (v) add part C and mix; 3. Homogenization in colloid mill CM-1 (continuous operation); 4. Filling and packaging. Besides mass and energy balances, our process model includes droplet breakage relationships (Shimizu et al., 1999; Wieringa et al., 1996) that predict the maximum droplet diameter at the exit of tank T-2 ( D 2 , m a x ) and after homogenisation in the colloid mill (D3,max). These droplet sizes correspond to an equilibrium situation of maximum size reduction and the time necessary to attain such a state is also estimated. The overall process model has the following structure: inputs - d~ (product design variables), d2 (batch size and equipment dimensions), z2 (operating temperatures and mixing speeds) and 02 (process parameters); outputs - D3,max (product state variable), operating times and energy consumptions. Given the annual production required, and assuming some process scheduling data, the effective batch time (time between two consecutive batches) and the annual operating time are also estimated.

1511 part A (oil)~(Pre_mixing and heating1 25 °C (tank T-1 --

part B (water),~(Pre-mixin~ ~ and heating1 25 °C r ] (lank T-2)

part C Mixing and cooling (tank T-2)

Mixing 1 (tank T-2) o

Final product ~'

( Fillingand ~.,, (. packaging 7

'

[ ttomogenization ((colloid mill CM-I)

Figztre 1. Lofion mam(/'acmring process.

3.4 Integrated Product/Process Design Our integrated product/process design problem is therefore formulated as follows" given the annual production required, find d~, d2 and z2 that minimize an overall annual cost, equal to the sum of investment, production and quality loss costs. Quality costs are considered proportional to the total loss (L~ + L2) and estimated as 30% of production costs when (L~ + L2)- 25%. Operating temperatures are not optimized, since the process model at this stage does not incorporate the dependence of interracial tension with temperature. Therefore, temperatures are considered fixed and equal to the values shown in Figure 1. Since the adopted quality function does not include the effect of droplet size, which is known to be related with product stability and smoothness, a restriction D3.max -< Ot is imposed, and the problem solved for different values of or. In order to guarantee a sufficiently refined pre-emuMon, the constraint D2,max -< 200 btm is also considered. The optimization problem is implemented and solved using GAMS/CONOPT3. 3.5 Results and Discussion Figure 2a shows a set of optimal solutions obtained for an annual production of 2000 ton/yr and for different ot values (D3,,,l~x < or). The rise in total cost is mainly due to the process intensification, namely as a result of an increase in colloid mill dimensions. Quality loss essentially remains the same, which means that the optimal product formulation does not change when the production of a thinner emulsion is imposed. For ct _< 6 btm, the process becomes infeasible. Let's consider now that a more concentrated emulsion is allowed for (~ < 0.2). In this case, both optimal product and process decisions are affected by the ¢t value. When a thinner emulsion is imposed, the optimal solution adjusts product composition in order to alleviate the process, with a consequent increase in quality loss (Figure 2b). We also compare the results obtained when the product and process design problems are solved simultaneously and separately, in particular for ~ < 0.2 and ~ = 10 pm (Table 3). The design resulting from a decoupled solution (product design followed by process design) corresponds to higher investment and production costs, although the differences found are not very high. However, it should be noted that such differences become more significant as cz decreases.

1512 Table 3. Simultaneous versus decoupled product/process design solutions. WT

WG

Costs (thousand Euro/yr)

(~

(% w/w) (% w/w) Simultaneous Decoupled

0.8454 0.8515

12.00 12.00

0.1813 0.1667

a. dO-< 0.15 QualityLoss (%) 5 i4

350 340

2

330 .1~_

~

1 0

320

7

Quality 2.0 0.0

Total 333.0 335.4

b. qb_ 0.20

Total Cost (thousandEuro/yr) 360

6

Investment Production 86.8 244.2 88.3 247.1

8

9 10 11 12 D3rmx (micrometer)

13 14 15

Total Cost (thousandEuro/yr) 360

QualityLoss (%) 5

350

4 3

340 330

""~~~..~

320 6

7

2 1

~--~---*~'-'*"~----~ ! 0 8 9 10 11 12 13 14 D3max(micrometer)

Figure 2. Optimal solutions for different emulsion droplet sizes

4. C o n c l u s i o n s We have presented an integrated product/process optimal design formulation and applied it to a cosmetic lotion case study. The results obtained clearly illustrate how decisions regarding product formulation and structure interact with process design and operation, as well as how a decoupled sequential solution of product and process design problems may lead to suboptimal solutions. Therefore, an integrated point of view seems to provide a much sounder approach for addressing this kind of problems. References Bernardo, F. P. and Saraiva, P. M., 2004, Computer-Aided Chemical Engineering, BarbosaP6voa, A. and Matos, H. (eds.), 18, 151. Brummer, R. and Godersky S., 1999, Colloids & Surfaces A: Physicochem. Eng. Aspects 152, 89. Cussler, E. L. and Moggridge, G. D., 2001, Chemical Product Design, Cambridge University Press, Cambridge. Pal, R., 1995, AIChE J. 41,783. Pal, R., 2001, Chem. Eng. Journal 81, 15. Shimizu, K., Minekawa, K., Hirose, T. and Kawase, Y., 1999, Chem. Eng. Journal 72, 117. Tanner, R. I., 2000, Engineering Rheology, 2 nd ed., Oxford University Press, Oxford. Wibowo, C. and Ng, K. M., 2001, AIChE J. 47, 2746.. Wibowo, C. and Ng, K. M., 2002, AIChE J. 48, 1212. Wieringa, J. A., van Dieren, F., Janssen, J. J. M. and Agterof, W. G. M., 1996, Trans. IChemE. 74, part A, 554. Williams, D. F. and Schmitt, W. H., Eds., 1996, Chemistry and Technology of the Cosmetics and Toiletries Industry, 2 na ed., Blackie Academic & Professional, London.

Ae knowledgements

The authors acknowledge financial support provided by FCT through research project P OCTI/EQ U/32647/2000.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1513

Design Synthesis for Simultaneous Waste Source Reduction and Recycling Analysis in Batch Processes Iskandar Halim a and Rajagopalan Srinivasan a'b* a Institute of Chemical and Engineering Sciences (ICES) 1 Pesek Road, Jurong Island, Singapore 627833 b Department of Chemical and Biomolecular Engineering, National University of Singapore 10 Kent Ridge Crescent, Singapore 119260

Abstract The issues of waste generation in batch process plants differ in many aspects from those in continuous plants. Despite the smaller-scale of processing, complexities from discontinuities and run-to-run variations make waste minimization in batch plants more challenging. In this paper, we introduce an integrated qualitative-quantitative methodology and decision support system, called Batch-ENVOPExpert, for assessing waste minimization opportunities in batch processes. First, a qualitative analysis is performed to identify the sources of wastes and to derive recipe-level waste minimization solution. This is followed by cletailed analysis at process variables level using mathematical simulation. The application of the methodology is illustrated using a propylene glycol case study.

Keywords" Waste Minimization; Expert system; Process improvement

1. Introduction Batch process operations are prevalent in industries such as specialty chemicals, foods, agricultural chemicals, pharmaceuticals and other high value-added chemicals. Unfortunately, batch operations produce high waste-to-product ratio. In the past, batch process industries could tolerate large waste generation due to the high values of final products, which justify the waste treatment and disposal costs. However, due to increasing regulations, waste has become more expensive to deal with while market forces have constantly kept the product prices down. Today, this true cost of waste generation has provided a huge incentive for batch manufacturers to actively seek strategies for waste minimization. Computer simulation has been applied to solve waste minimization problem through maximizing water reuse (Almato et al, 1999), recovering solvent (Lee and Malone, 2000) and minimizing environmental impacts (Jensen et al, 2003). One common shortcoming of the current simulation approach is due to the complexities involved in modelling industrial-scale process with large number of interconnections between the streams and units. Another shortcoming arises from the fact that this approach requires considerable skill and expertise of the user. We have previously addressed this important problem of industrial significance by developing a novel methodology for Author to whom correspondence should be addressed: [email protected]

1514 identifying waste minimization opportunities in continuous chemical processes (Halim and Srinivasan, 2002a). An intelligent decision support tool, called ENVOPExpert, has also been implemented based on the methodology to automate waste minimization analysis in continuous plants (Halim and Srinivasan, 2002b, c). ENVOPExpert has been successfully tested on several case studies including hydrocarbon separation process, chemical intermediate manufacturing, hydrodealkylation (HDA) of toluene to benzene and acrylic acid production. In this paper, we extend the ENVOPExpert methodology to batch processing environment. While the equipment used in batch process are readily available in continuous plant, the modes of operating them are significantly different. Unlike in a continuous plant, wherein each equipment is dedicated to one type of operation, the same equipment in batch plant is commonly used to perform multiple operations. These fundamental differences between batch and continuous operation necessitate new developments in the underlying knowledge representation and inference schemes that were implemented in ENVOPExpert. In the next section, we discuss our proposed methodology called Batch-ENVOPExpert and apply it to solve an industrial case study involving a propylene glycol process.

2. Waste Minimization M e t h o d o l o g y of Batch Process Our methodology has been developed with the following task: given a flow diagram, production recipe and process chemistry of a batch process plant, the objective is to identify potential waste minimization alternatives. For this, we implement a two-stage approach for source detection, diagnosis and waste analysis i.e. (1) Waste source tracing, and (2) Waste minimization options generation. In the first stage, the origin of each material component that makes up the waste stream is determined. As multiple operational tasks may be performed in the same piece of process unit, analysis of the production recipe thus plays a central role for identifying the waste generating operation. Once the waste sources are identified, the next stage is to derive waste minimization alternatives, i.e. source reduction or segregation and recycle of the useful materials for other purposes. This requires an integrated qualitative-qualitative methodology comprising Grafcet, process graph (P-graph) and mathematical modelling.

2.1 Grafeet model Grafcet has been used for representing the production recipe of batch processes (Viswanathan et al, 1998). In our Grafcet model, each action in the product recipe is modelled using steps and the conditions associated with each action by transitions separating adjacent steps. Fig.1 shows a typical Grafcet representation. The recipe depicted in this figure describes a reaction-separation activity and can be explained as follows: (1) Two reactants (A and B) are charged into a vessel, (2) The vessel is heated to a specified temperature, (3) The mixture reacts to form product C and waste byproduct D, and (4) The mixture is separated into product and waste stream.

2.2 P-graph model We have used P-graph (Friedler et al, 1994) to describe the state condition of materials at the input and output of each process unit. Our P-graph takes a slightly different approach from the original P-graph, in which, a bar is used to represent an operation in the product recipe and a circle for state of materials of a unit operation or a stream. Fig.2 illustrates the P-graph representation for the recipe described in Fig.1. After the materials flow throughout the process has been established, the next step is to diagnose each operation that produces wastes as well as inefficient separation that causes the

1515 escape of valuable materials into the waste streams. This is done by tracing each waste material backward, starting from each of the waste streams and upstream to the material flow network composing the product recipe. Fig.3 depicts the origins of waste stream shown in Fig.2. As shown in Fig.3a, the presence of product C in the waste stream is caused by inefficient separation process [Task 6]. The presence of by-product D, on the other hand, is caused by the reaction in the vessel [Task 4] (see Fig.3b). [1 ] Charge A to vessel

1

3

.4 it7 vessel

"~' D'

5

[2] Charge B to vessel B i, vessel

[3] tteat vessel mixture

© C,D

.4 a m / B at temperature 7"am~pressure P

[4] React mixture

O A,B.C

Figure 2. Material./7ow diagram

A. B, C a , d D iH ~'esse/ I

[5] Send mixture to separator

A

5

3

A,B

C

,4. B. C a n d D it7 separator

[6] Separate mixture irl separator ('-D at top..4-(" at bottom

[7] Discharge top-phase C-D dischar~, ed as waste

l

cO 3

A,B

D

Oc

-

[8] Discharge bottom-phase A- (" discharge'd as pro&let (b)

Figure 1. Grajcet o/a product recipe

7 =:~

DO Figure 3. Waste /7ow diagram

2.3 Recipe-level waste minimization solution Once the waste origins are identified, alternatives to eliminate or minimize them can be proposed. For this, we have derived a set of top-level waste minimization heuristics on the basis of P-graph analysis. These heuristics are implemented through IF-THEN rules set as the following: • IF useless materials (e.g. impurities) are present in feed stream or feed equipment THEN remove those useless materials prior to usage. • IF useful materials (e.g. reactants or products) are present in waste stream THEN recover and recycle those materials for other purpose.

1516 • IF useless materials are generated during a reaction or other phenomena THEN eliminate or minimize the generation through better operating conditions. • IF useful materials (e.g. reactants) are transformed at low conversion rate THEN increase the conversion rate for those materials. • IF useful materials are ineffectively separated THEN improve the separation process to eliminate or minimize the escape of useful materials. The heuristic approach provides a very top-level view of waste solutions. The next step in the quest for minimizing waste is to identify more detailed solutions at the process variable level that can be incorporated into the plant operations. The detailed analysis would provide suggestion on which process variables or parameters should be manipulated in order to achieve the desired waste reduction. To derive such detailed alternatives, cause-and-effect among the process variables need to be known and this can be obtained from signed digraph model or from mass and energy balance equations.

2.4 Detailed waste minimization solution Signed digraph can be used to describe the cause-and-effect relation between two variables in a qualitative manner. It consists of nodes which represent process variables and directed arcs connecting the nodes to describe the relationship ("proportional" or "inversely-proportional") between the nodes. The advantage of signed digraph model is it is simple to develop, especially when the availability of process data is limited. The main disadvantage is it cannot be used to describe variables with non-linear relationship such as variables with J-Curve relationship. Other disadvantage of signed digraph arises from ambiguities or incorrect relationship that may arise from multiple variables interaction. As an example, consider an output variable "flow", which is connected to two input variables "pressure" and "heat-input" of "proportional" and "inverselyproportional" relationship respectively. Here, we will have ambiguity in describing the value for variable flow when both the input variables are increased. To avoid ambiguity, a more concise variables interaction model needs to be used. In our model, this is done using balance (mass and energy) equations. We have developed sets of balance equations of several unit operations commonly found in a batch plant. Each unit operation model is directly linked to each activity in the product recipe that takes place in that unit. For example, the task of reaction in an agitated vessel can be modelled by mass and energy balances of stirred tank reactor, while the separation task will represented by flash-separator, distillation column models, and so on, depending upon the type of separation unit utilized. To illustrate this concept more clearly, consider a waste minimization alternative "improve the reaction operating conditions to minimize waste by-products generation" that is derived using the P-graph model. Provided we have adequate process data, we can simulate the effects of different variables such as pressure, temperature and heat-input of the reaction to obtain the exact amount of waste being generated. This can be done through changing (either by increasing or decreasing) those affecting variables individually or simultaneously and comparing the results obtained in terms of the amount of waste produced and end product as well as economics. Consequently, process changes that cause waste to be reduced will be our waste solutions.

3. Intelligent Decision Support System

Batch-ENVOPExpert (BEE) has been implemented in an object-oriented framework using Gensym's G2 expert system shell. BEE consists of two solutions domain: qualitative solution based on recipe analysis and quantitative solution based on

1517 simulation of process variables. For the quantitative part, we have used HYSYS simulator as our modelling tool, although other commercial simulators could also be used. Fig.4 shows the overall framework of BEE. First, different stand-alone unit operation models are developed using HYSYS simulator. These models are then interfaced with Microsoft Excel through HYSYS-Browser program, which has been developed by AspenTech. The Excel program will consist of sets of input-output variables connected in two-way direction with their related unit operation in the HYSYS simulator. In this way, any changes to the input values in Excel will be passed to HYSYS for simulation and the results of calculation obtained will be transferred from HYSYS back to Excel. To link between G2 and Excel, an ActiveX based connection has also been developed in G2 system to interpret the simulation results on the basis of waste minimization and economic objectives.

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4. C a s e Study" P r o p y l e n e

Glycol Process

We have tested our BEE by performing waste minimization analysis on a case study involving propylene glycol production (see Fig.5). The recipe for this process involves charging reactants (propylene-oxide and water) into a vessel in the presence of sulphuric acid as catalyst and methanol as the reaction aid. Besides (mono) propylene glycol product, the reaction also produces di- and tri-propylene glycol as the by-products. After a certain time, the reaction is quenched with sodium hydroxide solution before being sent to batch-distillation column for separation. The only waste stream of this process comes from vapour venting of the vessel and this stream contains mainly the excess reactants, methanol and mono- and di-glycol. For more detailed information on the production recipe and kinetics of this process, the reader is referred to Elgue et al

(2003). Our P-graph analysis for this case study reveals the following waste sources: reaction by-products and useful materials in the waste stream (vent). Based upon this diagnosis, the recipe-level and detailed waste minimization alternatives to the sources can then be derived. Table I shows some of the waste minimization results of BEE. In this case, we are able to successfully identify the basic qualitative and quantitative solutions.

1518 However, the table also shows conflicting suggestions. Decreasing the pressure is found to reduce di-glycol in waste stream while increasing it can reduce propylene oxide from becoming waste. Such conflict is not uncommon in a waste minimization study, where trade-off between various options is always required for the most optimum solutions.

5. Conclusions The issue of cleaner production has challenged the batch manufacturing industries to initiate new approaches to tackle waste problems. We have developed a methodology for automating identification of waste minimization strategies in batch processes and successfully implemented it as an intelligent system called Batch-ENVOPExpert. The methodology has been shown capable in generating waste minimization solutions both in qualitative and quantitative manner. Our future work will include incorporating environmental impact and economic analysis into the current framework for trade-off analysis between the solutions. Table 1. BEE solutions

............

Waste Minimization Qualitative Direct-recycle or recovery-recycle of useful materials from vent. Improve the design and operation of vessel. Improve reaction condition. Change from homogeneous catalyst to heterogeneous one. Consider using reaction agents to suppress byproducts formation.

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Quantitative Decrease 5% of feed pressure during reaction reduces di-glycol in waste stream from 574.6 kg/h to 567 kg/h. Increase 5% of feed pressure during reaction reduces propylene oxide in waste stream from 100.7 kg/h to 84.3 kg/h. Decrease 5% of feed temperature during reaction reduces di-glycol in waste stream by 574.6 kg/h to 572.5 kg/h.

References Almato, M., A. Espuna and L. Puigjaner, 1999, Comp. Chem. Eng. 23, 1427. Elgue, S., J.M. Le Lann, M. Cabassud, L. Prat and J.Cezerac, 2003, Chem. Biochem. Eng. Q. 17(1), 43. Friedler, F., J.B. Varga and L.T. Fan, Eds., 1994, Pollution Prevention via Process and Product Modifications. American Institute of Chemical Engineers, New York. Halim, i. and R. Srinivasan, 2002a, Ind. Eng. Chem. Res. 41 (2), 196. Halim, I. and R. Srinivasan, 2002b, Ind. Eng. Chem. Res. 41 (2), 208. Halim, I. and R. Srinivasan, 2002c, Env. Sci. Tech. 36(7), 1640. Jensen, N., N. Coll and R. Gani, 2003, Clean Tech. Env. Pol. 5,209. Lee, Y.G. and M.F. Malone, 2000, Ind. Eng. Chem. Res. 39(6), 2035. Viswanathan, S., C. Johnsson, R. Srinivasan, V. Venkatasubramanian and K.E. Arzen, 1998, Comp. Chem. Eng. 22(11), 1673.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) :~ 2005 Elsevier B.V. All rights reserved.

1519

Design and Control Structure Integration from a ModelBased Methodology for Reaction-Separation with Recycle Systems Edgar Rarairez and Rafiqul Gani Computer Aided Process Engineering Center, Department of Chemical Engineering, Technical University of Denmark, DK-2800, Kgs. Lyngby, Denmark

Abstract This contribution presents the latest results of a systematic model-based methodology for the design and analysis of processes with a Reaction-Separation with Recycle (RSR) structure. The methodology subdivides the problem into three main stages, where the first two stages identify a common set of design and process (control) related variables and their role in design and operation of the process using simple but appropriate models for the specific analysis tasks. Based on this analysis, the methodology determines the design-operation targets, the design-process variables that can attain these targets and the operational ranges for a stable operation. The main features of this model-based methodology is presented and illustrated through a case study involving the Tennesse-Eastman (Challenge) Problem.

Keywords: Integrated Design, Model-based analysis, Reaction-Separation-Recycle.

1. Introduction Integrated process and control (structure) design aims to satisfy simultaneously, the increasing demands for the development of environmentally benign, economically profitable yet technically operable processes. In order to achieve this, the recycle of mass and energy within the process, which introduces new challenges to modelling, design and control of the process, need to be considered (Luyben, 1994; Morud and Skogestad, 1996). Also, Russel, et al. (2002) highlighted the roles of models in the simulation, design and control of chemical processes and suggested a more intelligent use of models in an advice role to solve process engineering problems related to synthesis, design and control. Several approaches deal with process design or control issues. A very well known approach is the hierarchical-based method of Fisher, et al. (1988), which principally relies on experience and heuristic based rules. Bildea et al. (2000) utilize mainly a nonlinear analysis of the models where the control structure proposed is already selected at the start. Therefore, it is more like a trial-and-error approach. Optimization-based approaches (Mohideen, et al. (1996)) involve large NLP or MINLP problems in order to find an optimal design of the process. However, through a systematic model-based parametric sensitivity analysis of the RSR structure, some of Author to whom correspondence should be addressed: rag~kt.dtu.dk

1520

the complex interactions in the non-linear behaviour of the processes can be understood helping to characterize them. The objective of the parametric sensitivity analysis is to identify a common set of design and process (control) variables that affect the decisions related to the design as well as control (structure) of the process, the desired values for these variables and their upper and/or lower bounds without necessarily formulating an optimization problem. Since these variables affect the design and control related decisions, their effect can therefore be evaluated through the behaviour of the process measured in terms of a set of performance criteria. Therefore, integration of aspects of design and control of a chemical process with an RSR structure can be achieved in the early stages of the design process if the model-based analysis is performed simultaneously with the conceptual design calculations. The objective of this paper is to present some of the new features of the model-based methodology developed earlier by Ramirez and Gani (2004) and highlight its application through the well-known Tennessee Eastman Challenge Problem (TE). 2. M e t h o d o l o g y

Overview

The model-based methodology comprises of three successive stages where special purpose models are used for parametric sensitivity analyses in the first two stages and validation in the third stage. Since integration of design of the process and its control structure involves simultaneously solving these two problems in the early stages of the design process, it is necessary to use appropriate models representing specific features (operation, behaviour) of the process and the variables which may affect them. Design Variables (Manipulated Variables)

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Figure 1.The roles of design and process variables in Stages 1 and 2.

Figure 1 highlights the roles of a class of design and process (control) variables typically found in processes with an RSR structure and are listed on the left hand side of Fig. 1. In Stage 1, some of the design variables are combined together into coupled parameters or dimensionless numbers (such as Da, the Damk6hler number). The models in Stage 1 are therefore based on these coupled variables and the objective is to find the values of these variables where the process has the optimal behaviour. Therefore, for different values of the design variables (listed in Fig. 1), the model equations are solved to obtain values of the process variables (listed in Fig. 1), which are then used to estimate the variables that determine the process behaviour (performance). This helps to decide target values for the coupled (design) variables (corresponding to the desired process performance), the operational limits (in terms of the process variables) and

1521 desired (target) of the process behaviour. All these variables, affect the design of the process as well as the design of the control structure. In Stage 2, the coupled parameters or dimensionless numbers are decoupled, generating therefore, a new model, which obviously, is more complex than the model in Stage 1. The objective here is to find the design variables (listed under Stage 2 of Fig. 1) that can match the process behaviour (defined by the process variables) and the target values of the Stage 1 design (coupled) variables. If the Stage 1 design targets cannot be matched, new targets are set until a match is found. As highlighted in Fig. 1, the results from the model-analysis determine the operational feasibility of the process as well as the search space for the design-process variables. In Stage 2, the overall design targets are set and the values for a minimum set of design and process variables that matches this target is found. This means that all the design-control structure related decisions needed to make in the early stages of the design process has been made. The process can be described in terms of the performance it will give, the values of the design variables that can achieve it and values of the process variables that will be attained by the process. From a control structure point of view, these process variables will need to be controlled by manipulating the identified design variables. Also, these calculated values correspond to the set points for the manipulated and controlled variables. The models in Stages 1 and 2 are quite simple as they only include the features of the process that need to be studied, in Stage 3, a rigorous model of the process is used to validate the design decisions and if necessary, to improve the design. The results from Stages 1 and 2 are used as initial estimates, therefore, the robustness and efficiency of the rigorous modelbased solver is improved. Typically, steady state as well as dynamic simulation models can be used at this stage, while in Stages 1 and 2; mainly steady state models are used.

3. Study Case The TE Problem (Downs and Vogel, 1993) has been selected in order to highlight some of the new features of the model-based methodology for integrated design and control structure. Details of other examples can be obtained from the authors.

3.1. Process Description The TE process produces two products (G & H) from four reactants (A, C, D, E), while B and F are an inert and a byproduct, respectively. The reactions, which are all irreversible and exothermic, are modelled by the following kinetic rate expressions, A(g)+C(g)+D(g)------~ A ( g ) + C ( g ) + E(g)

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One of the main characteristics of the TE problem, also studied by others (for example, McAvoy (1994) and Ricker (1995)), is the high non-linearity and open-loop unstable behaviour of the process, due mainly to the reactions occurring in the system.

1522

3.2 Stage 1" Use of models with coupled (design) parameters A model that includes the reaction kinetic expressions for the reactor but the separation operations are modelled for specified separations (fixed separation factors) has been developed according to the method outlined by Ramirez and Gani (2004). The important behaviour to model is the effect of the recycle flow on the reactor operation, since it is the chief source of non-linear behaviour and assuming that the separation problem can be designed to match the separation factors used. The derived Stage 1 model has the following assumptions: 1. A constant pressure is assumed in the reaction zone, so pi,- = Yi.rPr.r 2. Reaction 1 is taken as a reference due to its highest sensitivity to temperature 3. The feed flow rate of component A is considered as the reference flow rate 4. No recovery of products or byproducts is considered The steady state mass and energy balances for all the unit operations are represented in their compact from by,

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(2)

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(6)

--

F 4,1

3.2.1 Model-based Analysis The model represented by Eqs. 2-5 represent a set of non-linear algebraic equations in terms of vector x, requiring the specification of the fixed parameters vector p and the adjustable design variables vector d. Figure 2 shows the results for the G/H selectivity or mass ratio (ScH) and reactor heat duty (Q<) for different values of recovery factors ac with respect to Da. It can be noted that the recycle of reactants back to the reactor has a positive effect on its performance, evaluated through SeN. However, as ac increases, the heat content in the reactor also increases, due to the production of component G which is the most exothermic of the reactions taking place. Therefore, as the amount of reactants in the reactor increases, the heat in the reactor increases until the desired operation can no longer take place. Another measure of the process performance is the conversion of component A, XA, which may be considered as a limiting reactant as it is present in all the reactions.

1523 Figure 3 shows the behaviour of x4 vs. Da for different values of ~4. Since high recoveries are usually preferred, a low Da number operation can achieve higher conversions, although this may imply high sensitivity to disturbances and short operating ranges. It is well known that in processes with RSR structures, at low Da, the process usually has the snowball effect on the recycle flow due to disturbances in the feed flowrate (Ramirez and Gani (2004)).

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From the above analysis, the target values for the design variables (Da and aA) can be selected, which in turn, will lead to the desired performance. Also, the model solutions at the selected design variables provide the corresponding process variable values. Selecting upper and lower bounds on the design variables, define therefore, the operational window, within which undesired and/or unstable process behaviour (such as snowball effect) can be avoided. Note that choices of the design variables for the above process variables, also determine the optimal value for the recycle flow and its effect on the process. The objective here is to make these decisions without the need or use of rigorous model based simulation, since at this early stage of the design, enough data or information is usually not known to perform such calculations.

3.3 Stage 2: Use of models with decoupled design variables The results from Stage 1 are used as targets that will now be matched with design variables typically encountered in process design and/or control. For example, Eq. 6 is now used to replace Da in the model and the process performance and design targets are matched with the adjustable variables from Eq. 6 (the feed flow rate FAt). Also, all assumptions considered in Stage 1 are now removed. That is, the separation process is modelled to match the separation factor used in Stage 1 (this will now give, for example, the temperature and pressure where a single stage vapour-liquid separation will take place). The model used in this work is that proposed Jockenh0vel, et. al (2003), where energy balances for the reactor, the product separator, the stripper and the mixing zone have been added to the models given by Downs and Vogel (1993).

1524

3.3.1. Model-based Analysis The developed model can be used for steady state as well as dynamic simulations and contains 30 ordinary differential equations and 160 algebraic equations. The model has 11 manipulated (design) variables and fixed process parameters. The objective has been to first match the steady state design obtained in Stage 1 and then to study the dynamic behaviour in open-loop and in closed-loop (by incorporating a control scheme using the set of identified manipulated and control variables from Stage 1). While the steady state design can be matched, the process shows highly non-linear process behaviour and the open loop instability, which without any control action reaches shutdown limits within approximately 60 minutes from the start of operation. Detailed simulation results, the model equations and its analysis for Stages 1 and 2 can be obtained from the authors.

4. Conclusions The results obtained from the systematic model-based parametric sensitivity analysis has been useful not only to identify operational constraints and/or limiting conditions, but also to identify set of manipulative and control variables that may be useful for control structure design. The analysis also provides the set-point values for the control variables matching the desired target performance of the process. The final step of validation through control schemes is currently being developed. For the TE problem, as far as validation of the design is concerned, stage 3 is not necessary since the stage 2 simulations validate the reported design. Current work is also developing a collection of case studies with their corresponding models and model analysis results.

References Bildea, C.S., A.C., Dimian and P.D. Iedema, 2000, "Nonlinear behavior of reactor-separatorrecycle systems", Comp. Chem. Eng., 24, 209-215. Downs, J.J. and E.F. Vogel, 1993, A Plant-wide Industrial Process Control Problem, Comps. Chem. Eng., 17 (3), 245-255. Fisher, W.R., M.F. Doherty and J.M. Douglas, 1988, "The Interface between Design and Control. 3. Selecting a Set of Controlled Variables", Ind. Eng. Chem. Res., 27, 611-615. Jockenh6vel, T., L.T. Biegler and A. W~.chter, 2003, Dynamic optimization of the Tennessee Eastman process using the OptControlCentre, Comps. Chem. Eng., 27, 1513-1531. Luyben, W.L., 1994, Snowball Effects in Reactor/Separator Process with Recycle, Ind. Eng. Chem. Res., 33,299-305. McAvoy, T.J. and N. Ye, 1994, Base control for the Tennessee Eastman problem. Comps. Chem. Eng., 18, 383-413. Mohideen, M.J., J.D. Perkins and E.N. Pistikopoulos, 1996, "A framework for process design and control", Proceedings of International Conference in Control, vol. 2, 918-923. Monad, J. and S. Skogestad, 1996, Dynamic behaviour of integrated plants, J. Proc. Cont., 6, 2/3, 145-165. Ramirez, E. and R. Gani, 2004, A Systematic Approach for the Design and Analysis of ReactionSeparation Systems with Recycle, CACE-18, Barbosa-Povoa & Matos (Editors), Elsevier, The Netherlands, 469-474. Ricker, N.L., 1995, Optimal Steady-state Operation of the Tennessee Eastman Challenge Process, Comp. Chem. Eng., 19 (9), 949-959. Russel, B.M., J. P. Henriksen, S.B. Jorgensen and R. Gani, 2002, Integration of design and control through model analysis, Comps. and Chem. Eng., 26, 213-225.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors)
1525

Modelling and Optimisation of Industrial Absorption Processes" An EC Collaborative Research Project P. Seferlis a *, N. Dalaouti a, E. Y. Kenig b, B. Huepen b, P. Patil c, M. Jobson c, J. Klemes c, P. Proios d, M. C. Georgiadis d. E. N. Pistikopoulos d, S. Singare e, C. S. Biidea c, J. Grievink e. P. J. T. Verheijen~, M. Hostrup f, P. HarperS; G. Vlachopoulos ~, C. Kerasidis ~, J. Katsanevakis h, D. Constantinidis h, P. Stehlik ~, and G. Fernholz i CERTH -Chemical Process Engineering Research Institute (CPERI), PO Box 361, 570 01 Thermi Thessaloniki, Greece Department of Biochemical and Chemical Engineering, University of Dortmund, PO Box 44221, Emil-Figge Str. 70, 44227, Dortmund, Germany c Centre for Process Integration, CEAS, The University of Manchester PO Box 88, Sackville St., Manchester, United Kingdom d Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom e Delft Chem Tech, Delft University of Technology, Julianalaan 136, 2628 BL, Delft, The Netherlands f CapSolva- Integrated Process Solutions ApS, Kronprinsessegade 46 E, DK-1306 Kbh. K, Copenhagen, Denmark Phosphoric Fertilizers Industry S.A., P.O. Box 10183, 54110 Thessaloniki, Greece h ESTIA Consulting S.A., Makrigianni 61, 57001 Thermi Thessaloniki, Greece i Institute of Process and Environmental Engineering, Technical University of Brno, Technicka 2, 61669 Brno, Czech Republic J Process Systems Enterprise Ltd, Bridge Studios, 107a Hammersmith Bridge Road, London, W6 9DA, United Kingdom

Abstract This work summarises the research and technological achievements of the EC funded research project OPT-ABSO. The major innovation of the present project is the development of a fully integrated set of modelling, simulation, and optimisation methodologies, and computer-aided tools tbr the design, synthesis, control, and efficient operation of sustainable industrial absorption processes. The aim of cost, waste and energy reduction and the development of realistic operating strategies for practical implementation are facilitated through an interactive software framework.

Keywords: Absorption, Modelling, Synthesis, Optimisation, CAPE tools

Author/s to xvhom correspondence should be addressed: [email protected]

1526

1. Introduction Reactive absorption is attracting the interest of the chemical industry as it provides an efficient alternative for the recovery of significant pollutants and useful compounds from industrial gas streams in relatively mild operating conditions. Considering the environmental impact of reactive absorption that necessitates the operation under tight specifications it is imperative that reliable and accurate modelling tools become available for the design and operation simulation, optimisation and analysis. The current work summarises the developments in the modelling technology of reactive absorption achieved in OPT-ABSO a European collaborative project. Furthermore, a brief description of the integrated tools that cover the synthesis, optimisation and heat integration studies tailored to the specific needs of reactive absorption is provided.

2. Modelling of Reactive Absorption Processes Design, optimisation and analysis of reactive absorption processes require the use of reliable process models that predict with the desired degree of accuracy the interactions between the multiple phenomena occurring within the column. Tray and packed absorption columns can be described as a sequence of equivalent stages. These stages are modelled using a rigorous rate-based model, which incorporates the mass and heat transfer mechanisms and the complex reaction schemes involved in industrial reactive absorption operations (Kenig et al., 2001). The model is based on the two-film approach that considers mass and heat transfer resistance concentrated within two film regions adjacent to the interface, where phase equilibrium is assumed to hold (see Figure 1). The models cover a wide range of absorption processes including electrolyte systems and reacting systems in both the liquid and gas phases. Furthermore, the dynamic dimension of the models enables the prediction of the transient behaviour and the evaluation of the control system performance during operation.

r-

_• :BuI~ ~:

interface !

.~1~Film

-q

Fil~

Figure 1. Schematic of the rate-based stage model

Process design and real time applications however, may require the use of simplified or reduced-order models that enable quick calculations to verify the feasibility of the separation. Techniques varying from orthogonal collocation on finite elements (OCFE) to balanced residualisation (Singare et al., 2003) are employed to construct reducedorder models of variable resolution and controlled accuracy (Figure 2). Most notably, OCFE formulation allows for a continuous representation of a staged column in a compact form. Simplified models based on the Kremser group method allowed for preliminary design studies of the gas sweetening absorption-desorption flowsheets with

1527

multiple feed

and recycle streams (Patil and Jobson, 2004).

Packed Column ,

.

Staged Column

Orthogonalcollocation on finite elements

Short-cut

----_.__.

i

•

2-----

Equivalent stages

Polynomial approximation

Compartmental

Figure 2. Alodelling approximations

2. Synthesis, Design, Control and Optimisation 2.1 Synthesis of absorption sequences The Generalized Modular Framework (GMF) is a flexible methodology for process synthesis based upon superstructure optimisation techniques. The GMF method produces a compact mathematical formulation, which can be subdivided into components, consisted of a Structural Model, and a Physical Model (Figure 3). The Structural Model acts as the generator for the process structural alternatives, while the function of the Physical Model is the evaluation of feasibility and optimality of each structural alternative generated based upon a valid representation of the underlying physical phenomena. The synthesis methodology allows the optimal design of process flowsheets while achieving the tight separation targets under model and process related uncertainties. GMF/OCMass/HeatModule

GMF Mass/HeatModule

...........

•

...... : . . . . . . . . 7 1 / . . . .

. 7:, . ,, i _ % / . .

, 7.1.. i,

. ~•• 7 .

i, ••.~ • ~

.......

.i•

Fl~ure 3. GMF module and its discretised (orthogonal collocation) equivalence.

1528

3.2 Controllability analysis of reactive absorption units Controllability analysis examines the impact of process design on the performance of the control system; an issue of paramount importance considering the stringent constraints that absorption units have to satisfy (e.g., as pollution prevention units in NOx removal or waste incineration gas cleaning). A number of instruments have become available for the process characterisation and controllability analysis of reactive absorption units ranging from interaction analysis to static and dynamic disturbance rejection properties. Reduced-order linear approximations and nonlinear models in combination with advanced optimisation and linear algebra techniques are utilised in the evaluation, rank ordering and screening of alternative design configurations for the absorption columns.

4. Validation and Industrial Case Studies Validation was performed with experimental data from pilot plant columns for coke oven gas purification (electrolyte system) and NO× removal and two industrial columns for nitric acid production (see Figure 4). Good match of the model predictions to the actual data was possible without any tuning of the model parameters (Figure 5). The effect of design decisions and particularly the location of the side feed and recycle streams, the cooling policy, and the nominal operating conditions on the dynamic behaviour of the column were investigated. Design decisions influence the dynamics of the column and consequently the performance of the control system. The analysis focused on the ability of the column and the implemented control system to alleviate the effects of disturbances in the temperature and concentration of the inlet gas stream to the product streams (Dalaouti and Seferlis, 2005). The evaluation criteria involved the steady-state impact of the disturbances on the controlled and manipulated variables (static controllability index) and the characteristics of the dynamic response (Table 1). Heat integration studies of new plants and retrofit design of industrial absorption units using pinch-analysis revealed an area of great potential for essential energy saving opportunities. Optimisation-based techniques have been applied on two industrial cases (nitric and sulphuric acid production flowsheets) with proposed design modifications that reduce significantly the energy requirements of the existing plants. In flue gas cleaning (e.g., waste incineration gases) an optimised Venturi scrubber (Figure 6) was designed that generated strong turbulence due to the increased velocity and allowed intensive mixing of the liquid agent (e.g., water solution of NaOH) with the off-gases. A novel equipment design the "O-element" (Figure 7) resulted in significant reduction of the pressure drop for the gas stream and enhanced absorption efficiency. Table 1. Static controllability index for simultaneous disturbance on the inlet gas temperature and NOx content (preferred config. 20-55)

Disturbance variation (%) Side stream Recyclestream position position 20 55 20 60 30 55 30 60

5

0.529 0.525 0.580 0.588

10 15 20 Static controllability index 0.780 0.773 0.884 0.870

1.030 1.016 1.152 1.132

1.227 1.270 1.423 1.405

25

1.445 1.494 1.614 1.670

1529

NOx [ 1

Flue gases t

specification]

20 18

\

16

--y_NOx

% ~,

14 -'~

I

~.d P'-

~,

'~' 12

H30, HNO3 _

.

• y NOx (exp.) % %

~

x_HNO3 (exp.) -%

e-

E 8

--~

(sim.)

- - 'x_HNO3 (sim.)

-,,,, -%

6

-%

-%

A,p-

N .00 r

\'~ ~ J

0.02

0.04

0.06

0.08

0.10

0.12

molar fraction [-]

Air, NO, 1 Figure 4. Reactive absorption for HN03 production

Figure 5.Rate-based model validation for the absorber in the HN03 production

5. S o f t w a r e F r a m e w o r k The entire suite of models and tools for absorption processes has become available through a software prototype framework (note: version for evaluation and testing is available, www.opt-abso.org). The software prototype comprises a set of interconnected components for input specification, execution management, output visualisation, and review, a set of model libraries (model defining sets of equations) and model server components (for the evaluation of the model equations) and a set of activity execution components (e.g. simulation, optimisation, calculation or analysis). Excel ® is the platform for the input, output and execution management communication, while the basic simulation and optimisation engine is gPROMS ~' (Process Systems Enterprise, 2004). Additional third party software components can be linked to the prototype to perform the required analysis tasks (e.g., MATLAB). The main modelling options included in the software prototype: (i) rate-based model for steady-state and dynamic simulation, (ii) OCFE with rate-based balances for design and operation optimisation and controllability analysis, (iii) OCFE with equilibrium balances for column synthesis (iv) simplified process model with Murphree efficiencies for synthesis, and (v) reduced state space models for controllability analysis. In addition, a tool for solvent selection in natural absorption processes was developed. In principle, given the information on desired properties relevant to the separation system (e.g., solubility) and the type of compound (e.g., aromatic, cyclic, number of C, ester, alcohol) a set of compounds is derived that satisfy the separation specifications. The tool's ability to handle mixtures of compounds enables greater flexibility and makes it suitable for problems of industrial relevance. The key activities that are available in the OPT-ABSO software prototype are summarised in Table 2.

1530 •~'~

Spray application of absorption solution

Figure 6. Venturi scrubber for flue gas cleaning

Cleaned gas

Polluted gas inlet

Spray application of -i

solutionabs°rpti°n

Figure 7. O-Element for flue gas cleaning

Table 2. Tools and features of the OPT-ABSO software prototype.

Reactive absorption

Simulation

SynthesisOptimisation

Controllability Heat analysis integration

steady-state dynamic Nitric acid production Sulphuric acid production Coke-oven gas Gas sweetening CO2 absorption

X

X

X

X

X

X

X

x x x x

x

x

6. Conclusions The comprehensive software framework of integrated tools provides the state-of-the-art technology for the synthesis, design, and optimisation of reactive absorption units. Issues that may need further exploration are concentrated in the developments of correlations for mass and heat transfer coefficients for trays and packings with specific geometry through the analysis of experimental results, and the detailed study of system hydraulics (e.g., effect of liquid phase maldistribution). The application of the models and tools to biotechnological systems shows great potential for future research.

Acknowledgments The financial support of the European Commission (Growth programme G 1RD-CT2001-00649) is gratefully acknowledged.

References Dalaouti N., and P. Seferlis, 2005, J. Cleaner Prod., (in press). Kenig E.Y., R. Schneider, and A. Gorak, 2001, Chem. Eng. Sci., 343, 56. Patti P., and M. Jobson, 2004, ESCAPE-14, 457. Process Systems Enterprise, 2004, gPROMS v.2.3.1. User's Guide. Proios P, and E. N. Pistikopoulos, 2003, ESCAPE-13,263. Singare S., C. S. Bildea, and J. Grievink, 2003, ESCAPE-13,929.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1531

An integrated approach to modelling of chemical transformations in chemical reactors Tapio Salmi, Dmitry Yu. Murzin, Johan W~irn~, Matias Kangas, Esa Toukoniitty, Ville Nieminen Abo Akademi, Process Chemistry Centre, Laboratory of Industrial Chemistry FIN-20500 Turku/Abo Finland, fax +358-2154479, e-mail [email protected]

Abstract An integrated approach to the modelling of chemical reactors, particularly catalytic ones is presented. The modelling approach starts from quantum-chemical calculations, mechanistic hypothesis, derivation of kinetic expressions in order to achieve an appropriate kinetic model. The model parameters are determined by regression analysis and the complex behaviour of fixed bed reactors, including catalyst deactivation is described in an adequate manner. A general flowsheet for the procedure is proposed.

Keywords" kinetics, reactor, modelling, quantum chemistry

1. Introduction Mathematical modelling of chemical reactors is one of the most demanding tasks in chemical engineering because of the interaction of several simultaneous phenomena, such as chemical kinetics, mass and heat transfer as well as fluid dynamics. In recent years, a lot of attention has been paid on detailed modelling and calculation of fluid dynamics (CFD). However, the crucial point in the description of a chemical reactor is the chemical transformation itself. In addition, a majority of industrially operating chemical reactors involve the presence of two or three phases, which emphasizes the role of interracial mass and heat transfer. For heterogeneously catalysed processes, the modelling of intraparticle mass and heat transfer is included. The tendency in chemical reaction engineering research is nowadays to move more from bulk chemicals to fine and specialty chemicals. Thus the system cannot be described by few reactions, but a complex reaction network appears. The kinetics of the incorporated reactions is usually experimentally measurable, but the development of rate equations requires a deep-going insight on the reaction mechanism. The general chemical intuition can give inspiration to mechanistic considerations, but more rigorous calculations provided by quantum chemistry are needed to confirm/reject the kinetic hypotheses. In the current paper, we present an integrated approach to the modelling of chemical reactors. The goal is to achieve as good but as simple as possible model. The integrated modelling approach was applied on several catalytic systems, such as three-phase hydrogenation of aldehydes and ketones as well as hydrocarbon transformations (i.e.

1532 skeletal isomerizations of alkenes) over mesoporous and microporous catalysts. The characteristic feature of the systems considered is that a simplistic, rough modelling approach discarding the detailed reaction mechanisms leads to inappropriate rate equations, which are not able to describe the progress of the reactions and the development of the product selectivities correctly.

2. Case study Skeletal isomerization of linear alkanes to branched counterparts has attracted attention to a large extent, since increasing the degree of branching of alkanes can boost the octane quality of a gasoline fraction. The application of branched hydrocarbons is an environmentally more acceptable alternative compared with other techniques, such as blending with aromatics or oxygenates (Ertl et al 1997, Guillaume et al 2003, Hou~vi6k et al. 1997, Nieminen et al. 2004, Ouno 2003). Kinetics of n-butane isomerization over bifunctional Pt-H-Mordenite was studied in a catalytic fixed-bed reactor by varying reactant partial pressure and temperature. The main products were isobutane, propane and pentanes. The state of adsorbed species inside the catalyst pores (channels) was investigated by quantum-chemical calculations, which suggested that alkoxy species are formed inside the channels- an example of the calculations is displayed in Fig. 1. The reaction rate showed complex dependence on the reactant partial pressure. Three kinetic models were developed based on the current understanding of the reaction mechanisms including hydrogenation and dehydrogenation steps on the metal sites, skeletal isomerization on the acid sites and deactivation due to the coke formation. Model A enabled monomolecular isobutane formation path, model B bimolecular and model C both reaction paths.

©

Fig. 1 1-butene in the zeolite channel according to quantum chemistry.

A kinetic model based on the experimental results was developed. Only the reactions proposed in the literature to produce the main products, propane, isobutane and pentanes, were taken into account while other reaction paths, such as hydrogenolysis and monomolecular butane cracking were omitted. The reason for this is that the amount of by-products is minor and neglecting them keeps the model reasonably simple containing less estimated parameters while still being able to capture the main kinetic features of the reaction. The pentanes, isopentane and n-pentane, were lumped together,

1533 because both of them are (hydrogenated) cracking products of Cs~ ----> C 3- + C [ . The reaction network on the catalytic sites is displayed in table 1.. Table 1 Reaction ;Tetwork on lhe catalytic sites

1. n -

C*;;' 4,~, ~-~ i s o - (~.H' "~ 4.~,

2. 2 n •

C 4,o *;;~

C*;; ~ *n' S.o +

,

c,tt'

'

4. C;,~

-I-- H - C415 --~ 3C3, o + 2 *'v'

5 C£,~H, + * ' ; •

~

.

--> 2iso - c * " ' "'-

NII~

NI21

N~3~

N~4~

NI5,

1

o

o

o

0

(1)

0

1

1

I

1

(2)

o

o

o

1

1

(3)

0

0

0

0

1

(4)

0

1

0

0

0

(5)

o

o

1

o

o

(6)

o

o

o

-1

-1

(7)

1

2

1

2

3

(8)

-1

-2

-1

0

0

(9)

0

0

0

-1

0

10

4.o

6.

C s,o *;;+ + *;;' ---> i s o - - C 4.o *;;+ + n - - C4,o *" A. C3," + B.

*H +

+

/'/--84o

*H*

E C3, , . H + ,..,

~

n-C4,

.H + °

c. i s o - C 4 ,, + * " - E i s o - C *;;+ ,

D. C5, o +

*H ~

' 4,0

*H ~

E C~.~,

On the right hand side of the equations (1)-(10) above, the stoichiometric numbers (N) the of steps along independent routes are presented. Model A corresponds to monomolecular isobutane formation and included route N (~ as the sole path to isobutane. Routes N ~4~ and N ~5~ describe byproduct formation. In model B isobutane is formed bimolecularly (N ~3.) and the monomolecular path for isobutane formation is neglected. The valid routes are NI3LN ~5~. Model C includes routes N t~t, Nt3LN 15~. Thus, in model C isobutane can be formed either monomolecularly or bimolecularly. The rate equations of Langmuir-Hinshelwood type were derived using the assumption that ratelimiting steps are the surface reactions on the catalyst

k~ ( K , , : . .

, P ( ~ - K i c;.H +P i c: K , ' )

r4=

Z3

k 2 K c 2~, H + P~c2

r(=

Z2

(2)

1534

where Z

-1+

Z K i , H + P i +O'c2,H+ i,ole/in i¢C~

and

Oc2,H, -

0c~ H÷ ~ OV

(3)

The rate constants and their temperature dependencies were modelled with the Arrhenius equation, modified in order to improve simultaneous estimation of preexponential factor and activation energy. Since catalyst deactivation is a profound feature, it was included in a general way in the model. The rate of the reactions are given by equation below, where r0.i is the initial reaction rate for reaction i, and a denotes the relative activity: r i = ro,ia

(4)

where the activity factor is calculated from p a-

[

1

1 + (a -1)k'c e,0 ~-'

a - e x p ( - ilk'cp,o~-I t)

a~l t

(5)

a -1

(6)

Reaction and deactivation were assumed to be uniform throughout the reactor bed and the catalyst particles. The component mass balance is written as (p-partial pressure).

dpj dr

= m~trja

j - C 3, C 4,i - C 4 , C s

(7)

where r is the space time of the fixed bed. The overall generation rates of alkanes are determined by the isomerization of olefins on acid sites giving generation rates rc~ - r3 + 3 r 4

(propane)

l/'i-C 4 =]el "of-]e6

(isobutane)

]eC4 -- --]el

-2r3 - r 4

-r6

rcs =r3 - r 4

(n-butane) (pentane)

ru~ -- rc~,, - %; - rc; = . . . = 0 The reactor model equations were solved numerically by a stiff ODE-solver during the parameter estimation which was carried out by a Levenberg-Marquardt algorithm implemented in the software Modest (Haario 2001). Examples of the fit of the model to the experimental data are provided by Figs 2-3. The figures reveal that the description of the conversion a l o n e - including the catalyst deactivation- is not enough, but a detailed analysis of the product distribution is needed, as revealed by the selectivity analysis (Fig. 3). The detailed kinetic modeling

1535 enables us to judge, which mechanism is prevailing under specified conditions (pressure, temperature). The model, which enabled bimolecular reaction path for isobutane formation, had a good fit on the selectivity to isobutane at high reactant pressures but was incapable to predict the increase in selectivity to isobutane with decreasing n-butane pressures. At the same time, the above mentioned tendency was very well predicted by the models enabling monomolecular mechanism for isobutane formation. The kinetic modelling also supported the proposal that excess of propane compared to pentanes is due to consecutive codimerization of formed C f with C 4 to C~- followed by cracking to three C 3 species. 30

673 K, n-butane:H 2 40"60 25Z 6 ©

20

=- 15O

.,.-,

0o ;>

\

10-

7 ~ i Model

eel

0 _

0

i

I

50

0

100

i

I

150 TOS/min

I

200

250

Figure 2. Examples o/convetwion as a./imction of time on stream at 673 K by the kinetic models compared to the experimental values.

9O 6

80

O

d +...,

=

A

~;~

70-

--o-- Model ~+- Model QModel

,½

60-

©

•©-~ 50+..a

>' 40-

.+..a

;>

. ,..-~ .,..a

¢)

3020 0.0

673 K l

0.1

l

I

[

I

0.2 0.3 0.4 0.5 n-Butane partial

l

0.6

0.7

Figure 3. Selectivity to isobutane at TOS = 10 min as a function of n-butane partial pressure at 673 K by the kinetic models compared to the experimental values.

1536

3. Conclusions The approach applied is briefy summarized in the flowsheet sketched below. Successful modelling of catalytic reactors requires a strongly integrated approach. Due to the progress of applied quantum chemistry it is possible to get ideas and inspiration for mechanistic hypothesis, which are brought to kinetic equations including catalyst deactivation. Furthermore, models for heat and mass transfer as well as flow models are incorporated. Efficient and robust numerical algorithms are used to solve the kinetic and reactor models. The approach should not have a single missing link, since the final goal is a reliable design tool for chemical reactors integrated to surrounding process units. Construction of stoichiometric scheme

Quantum J chemical calculations

,4

-

~- Check of overall thermodynamics

l fypoth esis o n reaction mechanism

Derivation of rate 4 equatiolls

Kinetic experiments

4 Model for test reactor Estimation of kinetic parameters v Mass and heat transfer correlations and experimentation

Kinetic model Mass and heat transfer i,. model

4, REACTOR P" MODEL

-

Experimental verification offlowcond ifion s

Flow ¢, model

References Sie, S. T. Handbook of Heterogeneous Catalysis, eds. Ertl, G.; Kn6zinger, H.; Weitkamp, J. VCH/Wiley, 1997, p. 1998. Guillaume, D.; Surla, K.; Galtier, P. From single events theory to molecular kinetics-application to industrial modelling. Chem. Eng. Sci. 2003, 58, 4861. Nieminen, V.; Kumar, N.; Salmi T.; Murzin, D. Yu. n-Butane isomerization over Pt-H-MCM-41. Catal. Comm. 2004, 5, 15. Haario, H. Modest Users's Guide 6.0, ProfMath Oy, Helsinki, 2001. Hou~vi~ka, J.; Ponec, V. Skeletal isomerization ofn-butene. Catal. Rev.-Sci. Eng. 1997, 39, 319 Ono, Y. A survey of the mechanism in catalytic isomerization of alkanes. Catal. Today 2003, 81, 3.

Acknowledgements This work is part of the activities at the Abo Akademi Process Chemistry Centre within the Finnish Centre of Excellence Programme (2000-2005) by the Academy of Finland

European Symposiumon ComputerAided Process Engineering 15 L. PuiNaner and A. Espufia(Editors) ¢~)2005 Elsevier B.V. All rights reserved.

1537

An MILP Model for Optimal Design of Purification Tags and Synthesis of Downstream Processing Evangelos Simeonidis a, Jose M. Pinto b and Lazaros G. Papageorgiou a'* aCentre for Process Systems Engineering, Department of Chemical Engineering UCL (University College London), Torrington Place, London WC 1E 7JE, U.K. UDepartment of Chemical and Biological Sciences and Engineering Polytechnic University, Six Metrotech Center, Brooklyn NY 11201, U.S.A.

Abstract Downstream protein processing in biochemical production plants can be improved significantly with the use of peptide purification tags: comparatively short sequences of amino acids fused onto the product protein, which modify the physical properties of the desired product in a way that enhances its separation from contaminants. A two-step MINLP framework that integrates the selection of optimal peptide tags with the synthesis of downstream processing has previously been developed by the authors. The objective of this work is to transform this framework to a simpler MILP model. The methodology is validated by an illustrative example based on experimental data.

Keywords: protein purification processes, peptide tags, mixed integer linear programming

1. Introduction Recent advances in biotechnology have given immense impetus to the introduction of biopharmaceutical and biotechnological products. Downstream processing is typically among the most difficult and complex stages and the source of a large portion of the manufacturing and investment costs in a biochemical production plant. The quality of the product is predominantly determined at the purification level, which may therefore be regarded as the most important production stage. Early systematic methods for the synthesis of downstream protein processing made use of expert knowledge systems for selecting operations (Lienqueo el al., 1996). Vasquez-Alvarez and Pinto (2004) presented a mixed integer linear programming (MILP) framework, in which mathematical models for each chromatographic technique rely on physicochemical data on the protein mixture that contains the desired product, and provide information on its potential purification. Considerable improvement of downstream protein purification processes can be achieved with the use of peptide purification tags (Steffens et al., 2000, Simeonidis et al., 2004). Peptide tags are comparatively short sequences of amino acids, genetically fused on the protein product, in order to modify its physicochemical properties in a way that will enhance the separation, thus simplifying the purification flowsheet. The Author to whom correspondence should be addressed: l.

papageorgiou@ucl,

ac. uk

1538 development of a framework for the optimal design of case-specific peptide tags that alter the properties of a particular protein product in the most beneficial way, and the concurrent synthesis of downstream protein processing has been previously presented by the authors (Simeonidis et al., 2004); a methodology based on a two-step, mixed integer non-linear programming (MINLP) framework has been developed. In this work, the above model is reformulated as a mixed integer linear programming (MILP) model through piecewise linear approximations of the nonconvex, nonlinear functions. The new model utilises physicochemical property data to specify the amino acid composition of the shortest and most advantageous peptide tag configuration, and concurrently select operations among a set of candidate chromatographic techniques in order to achieve a specified purity level. The applicability of the model is demonstrated by an example that relies on experimental data.

2. Problem Statement Overall, the problem of simultaneous optimal tag design and synthesis of downstream protein processing can be stated as follows:

Given" • a mixture of proteins (p: 1,...,P) with known physicochemical properties; • a set of available chromatographic techniques (i: 1,...,/) each performing a separation task by exploiting a specific physicochemical property; • the properties of the twenty amino acids (k: 1.... ,20); and • a minimum purity level for the desired product (dp). Determine: • the amino acid composition of the shortest and most advantageous peptide tag; • the physicochemical properties of the tagged protein (desired product + tag); and • the flowsheet of the high-resolution purification process. So as to optimise a suitable performance criterion.

3. Mathematical Formulation Next, the main components of the proposed mathematical framework are briefly described. The resulting MILP representation, designed for the synthesis of purification bioprocesses, so as to consider the optimal design of purification tags, extends an earlier MINLP formulation (Simeonidis et al., 2004).

3.1 Physicochemical property constraints The tagged protein's net charge (Qdp) is predicted based on the methodology suggested by Mosher et al. (1993). Q,.~,~-

~)~.+ + ~ keBA

nk K k_~_ 1

II4+L

-

~

nk

keAA ___-[H+]J ~ 1

x~

(1)

1539 where BA and AA are the acidic and basic amino acid groups respectively; R) is the ionisation constant; 17x is the integer number of amino acids k in the tag and Q,.+ is the initial product charge. The tagged protein's hydrophobicity (H,o,) is estimated using the work by Lienqueo et al. (2002). The calculation is based on the relative contribution of each amino acid to the surface properties of the product protein and the knowledge of its 3D structure. 3.2 D i m e n s i o n l e s s r e t e n t i o n t i m e s

Dimensionless retention times KD]], are defined as a function of net charge Qo, or hydrophobicity H,. For ion exchange chromatography, retention times for the tagged protein product are estimated based on approximations of the chromatograms by isosceles triangles and on physicochemical property data for the product and contaminants (Vasquez-Alvarez eta/., 2001). The methodology presented by Lienqueo et al. (2002) is used to estimate the dimensionless retention times for hydrophobic interaction (KDm.],). Both relationships between retention t i m e - physicochemical property are nonlinear; therefore piecewise linear approximations are used for their linearisation, as presented in Figure 1. --

~

7~

KD

-

A

£

-

110 ]K D .....

-

0.8

i

0.3

KD c6

!

." . ' ' ' ' "

0.6

".11

-3.0

-2.0

-t0

~'"

0.0 O ,op

1.0

2.0

I

0.4

!

O.2

I 3.0 I

i0.0

i ,F i

o.17

0.22

0.27

0.32

Hop

:

Figure 1. Piecewise linear approximations of retention times for ion exchanq, e chromatogt'aphy (AE." anion c
Deviation factors D F o, indicate the distance between the protein product's chromatographic peak and a contaminant's chromatographic peak. They are defined as the difference between the dimensionless retention times of the product and each contaminant p for each particular chromatographic step i. D I~,,. -DF,,, = K D, + - K D,,,

V i, p :1: dp

(2)

DF]* ~_M'xi/'

gi, p ¢ dp

(3)

DF-, < M . (1 - x,,, )

gi, p ¢ dp

(4)

D C = DF; + D~,,

vi, p * @

(5)

where DF~ , D F are auxiliary positive continuous variables; and x#, is a binary variable equal to 1 if DFi], is positive and 0 otherwise.

1540 3.4 Concentration factors Deviation factors are used to calculate the concentration factors CFip, which represent the ratio of the mass of contaminant p after chromatographic step i to the mass of contaminant p before step i. The relationship between deviation factors and concentration factors is also nonlinear (Vasquez-Alvarez et al., 2001), so another piecewise linear approximation is needed, as presented in Figure 2. 3.5 Purity constraint The mass mz,dp of protein product dp after the last chromatographic step I must meet a specified purity level, SP. Since it is assumed that the separation is performed without product loss, the final product mass mz,dp is constant and equal to the initial mass mo.dp. m,,a,, > SP. Z m~,,, ~ (1 - SP). mo.,o, > SP. E m~.,, p

(6)

p~dp

The remaining m a s s mi,p o f each contaminant protein p after the final technique I is calculated from the initial mass m0,o by: m,.p = mo.,, . n

CFip

(7)

v p ¢: dp

i=l

where

CF ,~ - CF:,,

if

w, = 1

CF,~ = 1,

if

w, = 0

V i, p =/:dp

Binary variable wi is used to indicate the selection of technique i. Variables CF,,, can be expressed as an exponential function of concentration factors CFip and decision variables wi" CF,p = e

(In OF, ).,~

(8)

V i,p , dp

Therefore, using equations (7) and (8), purity constraint (6) can now be rewritten as" (1- SP) . mo,dp >_SP. E mo,p "e'

(9)

p,dp

where ~,~ - ( l n C F , p).w,. Constraint (9) incorporates the nonlinear factor e '

, which

can also be linearised with a piecewise linear approximation (Figure 2). D F ip i

-

i i

i

0.2

0.3

•

1

0.8 0.6

~

I n C F jp

~ ~. . . . . . . . . . . . . . . . .

-10

. . . . .

~

-8

. . . . .

y ~~p

Figure 2. Piecewise linear approximations for concentration factors CFip and for ~ip

i':

1541

3.6 Solution approach The overall problem is formulated as an MILP model, in order to identify the chromatographic techniques and the shortest amino acid sequence that can produce the optimal flowsheet of the purification process. The objective is to minimise the total number of selected chromatographic steps i in the purification process and, using a penalty parameter c, to force the model to select the minimum number of amino acids na in the tag.

minimise ~

(10)

w~ + c . Z n,~ k

First the MILP is solved without the use of a peptide tag for the purification of protein

dp. Then the MILP is solved again with a tag fused to the product protein; but this time the candidate chromatographic steps i are chosen only among those selected in the first stage of the solution.

4. C o m p u t a t i o n a l Results Solutions were obtained with the GAMS software (Brooke et al., 1998), using the CPLEX 6.5 solver. All computational experiments were performed on an IBM RS6000 workstation. The methodology was tested with a four-protein mixture: thaumatin (dp), conalbumin (p 1), chymotripsinogen A (p2) and ovalbumin (p3). The physicochemical properties of the mixture are presented in Table 1.

Table 1. Phvsicochemicai properties o[protein mixture. Protein

Dp pl p2 p3

too4, (mg/mL) 2 2 2 2

MW/,

Hp

(Da) 22200 77000 23600 43800

0.27 0.23 0.31 0.28

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A maximum number of 6 amino acids per tag is imposed on the number of amino acids that can be present in the peptide tag, so as to avoid interference with the tertiary structure of the protein product, as well as the possibility of formation of an alpha-helix or a beta-sheet from the tag itself. At the same time, hydrophobic amino acids should be balanced by polar residues so that the tag is soluble and does not bury itself within the protein. This possibility is avoided by imposing an upper bound to the number of hydrophobic residues that may be included in the peptide tag. The purity level required for the desired product (dp) is 98%. There are 11 available chromatographic steps: anion exchange chromatography (AE) at pH 4, pH 5, pH 6, pH 7, pH 8, cation exchange chromatography (CE) at pH 4, pH 5, pH 6, pH 7, pH 8 and hydrophobic interaction (HI). From these, CE pH 6, CE pH 7, CE pH 8 and HI are needed for the purification without the use of a peptide tag fused to protein dp, which achieves a product purity of 98.1%. The solution is significantly improved with a tag of 3 lysine residues; a purity of 98.1% can be achieved with only three separation steps: CE pH 7, CE pH 8 and HI. The results are illustrated in Figure 3.

1542 Step

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Figure 3. Optimal result for protein mixture with no tag and with a tag of 3 lysines

The MILP solution is almost identical to the one provided by the MINLP model presented in Simeonidis et al. (2004), which selected the same 3 chromatographic steps and a tag with lysines only. The selection of a peptide tag that only contains lysine amino acids implies that the increase of the product charge benefits the purification and that a hydrophobicity increase would be detrimental. Even though there are amino acids with a stronger effect on charge than lysine, they would increase hydrophobicity as well, which remains unchanged when lysine is used. Indeed, when the model is tested with a pre-fixed tag containing any amino acids that would increase hydrophobicity, a purity of 98% is not achievable.

5. Concluding remarks An optimisation framework for the simultaneous selection of optimal peptide tags and the synthesis of chromatographic steps for the purification of protein mixtures in downstream protein processing has been presented. The framework was formulated as an MILP mathematical model, developed from a previous MINLP model (Simeonidis et al., 2004) through piecewise linear approximations of nonlinear functions. The methodology was validated through its application on an example protein mixture involving 3 contaminants and a set of 11 candidate chromatographic steps. Results were indicative of the benefits of peptide tags in purification processes and provide a useful guideline for both downstream process synthesis and optimal tag design.

References Brooke, A., D. Kendrick, A. Meeraus, and R. Raman, 1998, GAMS: A User's Guide. GAMS Development Corporation, Washington. Lienqueo, M.E., E.W. Leser and J.A. Asenjo, 1996, Comput. Chem. Eng. 20, S 189. Lienqueo, M.E., A. Mahn and J.A. Asenjo, 2002, J. Chromatogr. A 978, 71. Mosher, R.A., P. Gebauer and W. Thormann, 1993, J. Chromatogr. 638, 155. Simeonidis, E. J.M. Pinto and L.G. Papageorgiou, 2004, Proc. ESCAPE-14, Portugal, 289. Steffens, M.A., E.S. Fraga and I.D.L. Bogle, 2000, Comput. Chem. Eng. 24, 717. Vasquez-Alvarez, E., M.E. Lienqueo and J.M. Pinto, 2001, Biotechnol. Progr. 17, 685. Vasquez-Alvarez, E. and J.M. Pinto, 2004, J. Biotechnol. 110, 295.

European Symposiumon ComputerAided Process Engineering- 15 L. Puig~ianerand A. Espufia (Editors) :~c)2005 Elsevier B.V. All rights reserved.

1543

An U p p e r O n t o l o g y based on ISO 15926 Rafaei Batres ~*, Matthew West b, David Leal c, David Price d, Yuji Naka a aTokyo Institute of Technology 4259 R l- 19 Nagatsuta Midori-ku Yokohama 226-8503, Japan /'Shell Information Technology International Limited London SE 1 7N A, U K CCAESAR Systems Limited 29 Somertrees Avenue, Lee London SE 12 0BS, UK ~Eurostep Ltd. Cwttir Lane, St. Asaph, Denbighshire L L I 7 0 L Q , UK

Abstract Ontologies reflect our view of what exists and developing ontologies for a given domain requires a common context. This context can be characterized explicitly by means of an upper ontology. Upper ontologies define top-level concepts such as physical objects, activities, mereological and topological relations from which more specific classes and relations can be defined. As an effort to support the development of domain ontologies, we are developing an OWL ontology based on the ISO 15926 standard. This paper presents the development to date of this standard and discusses its benefits and applications in the process engineering domain.

Keywords: ontologies,

ISO 15926, temporal parts, four dimensionalism

1. Introduction Ontologies describe a shared and common understanding of a domain that can be communicated between people and heterogeneous software tools. We construct an ontology by defining terms such as classes of concepts, their taxonomy, the possible relations between the concepts, and axioms for those relations. A class represents a category of similar 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 less_than, connectedto, and part_of. Class taxonomies are defined with the use of the subclass relation. A class is a subclass of another class if the former represents a set of things that subsumes the set of things represented by the latter. A number of ontologies have been developed in the process engineering domain. Among these, OntoCAPE defines a comprehensive number of chemical engineering concepts implemented in DAML+OIL (Yang and Marquardt, 2004) based on CliP (Bayer, 2003) which uses a systems-theoretic view of the world.

Author to whom correspondence should be addressed" [email protected]

1544 Ontologies can be developed using top-down or bottom-up approaches. The bottom-up approach starts with the most specific concepts in a domain of application. A bottomup approach results in ontologies that are difficult to modify and integrate with ontologies developed for other domains or applications (Uschold and Gruninger, 1996). Top-down approaches start with high-level concepts that are assumed to be common to many application areas. The top-down approach facilitates integration of applications with ontologies that are easier to maintain. Unfortunately, engineers using the topdown approach are susceptible of imposing arbitrary high-level categories which often tend to be prescriptive (what will be), not meeting the user's requirements. These problems can be avoided with an upper ontology. Upper ontologies define top-level concepts such as physical objects, activities, mereological and topological relations from which more specific classes and relations can be defined. Examples of upper ontologies are SUMO (Niles and Pease, 2001), Sowa upper ontology (Sowa, 2000), Dolce (Gangemi et al. 2000), CliP (Bayer, 2003), and ISO 15926-2 (ISO 15926-2, 2003). Engineers can start by identifying key concepts by means of activity modeling, use cases and competency questions. This concepts are then defined based on the more general concepts provided by the upper ontology. This avoids reinventing the wheel while having a better integration and maintenance. As an effort to support the development of process engineering ontologies, we are developing an upper ontology in the OWL language based on the ISO 15926 standard. Specifically, ISO 15926 Part 2 (standardized as ISO 15926-2:2003) specifies an ontology for long-term data integration, access and exchange. It was developed in ISO TC184/SC4-Industrial Data1 by the EPISTLE consortium 2 (1993-2003) and designed to support the evolution of data through time. The upper ontology contains 200 concepts including a meta-model for extending the ontology through what is known as a Reference Data Library (about 20,000 concepts from the engineering domain). We have translated the original EXPRESS code (ISO 10303-11, 1994) of ISO 15926-2 to the OWL language that can be used directly in a number of inference software packages (W3C, 2004). Axiomatic definitions are currently being added to implement some semantics of the standard that are not represented in the EXPRESS schema.

2. Temporal parts ISO 15926-2:2003 is founded on an explicit metaphysical view of the world known as four dimensionalism. In four dimensionalism, objects are extended in space as well as in time, rather than being wholly present at each point in time, and passing through time. An implication of this is that the whole-part relation applies equally to time as it does with respect to space. For example, if a steel bar is made into a pipe then the pipe and the steel bar represent a single object. In other words, a spatio-temporal part of the steel bar coincides with the pipe and this implies that they are both the same object for that period of time. This is intuitive if we think that the subatomic particles of the pipe overlap the steel bar.

http://www.tc 184-sc4.org/ 2 http://www.epistle.ws/

1545 Information systems have to support the evolution of data over time. For example, let us assume that a pump was designed and identified as P-101. Some time later, a manufacturer delivers a pump with serial number 1234 that meets the design specifications of P-101. Pump 1234 is installed and after a period of operation the pump fails. Therefbre, maintenance decides to replace it with pump 9876. This situation can be easily modeled using the concept of temporal parts as shown in Figure 1. ISO 15926-2:2003 defines the class junctional_physical_object to define things such as pump P-101 which have functional, rather than material continuity as their basis for identity. In order to say that pump 1234 is installed as P-101, P-101 is defined as consisting of S-1 (temporal part of 1234). In other words, S-1 is a temporal part of 1234 but is also a temporal part of P-101. In fact, because S-1 and P-101 have the same spatio-temporal extent they represent the same thing. Similarly, after a period of operation 1234 was removed and pump 9876 takes its place. In this case, S-2 (temporal part of 9876) becomes a temporal part of P-101. Objects such as P-101 are known as replaceable parts which is a concept common in artifacts in many engineering fields such as the process, automobile, and aerospace industries (West, 2003).

3. Top level concepts thing is the root concept in the ontology that subsumes abstractobject and possible_individual classes. A thing is anything that is or may be thought about or perceived, including material and non-material objects, ideas, and activities. Every thing is either a possible_individual, or an abstract_object. Members of possible_individual are entities that exist in space and time, including physical objects like a compressor or ideas that exist in our imagination. Individuals that belong to abstract_object can be said to exist in the same sense as mathematical entities such as numbers or sets but they cannot exist at a particular place and time. possible_individual is divided into arranged_individual, actualindividual, whole_lije_individual, activity, physical__object, period_in_time and event (see Figure 2).

4. Mereotopology Mereology expresses the part-whole relations of an object, which means that a . . . . E v e n t . 1 2 3 4 is

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1546 component can be decomposed into parts or subcomponents that in turn can be decomposed into other components. Mereological descriptions are possible by means of composition_of individual and its subproperties, composition_of_individual is transitive. Subproperties of composition_of_individual include containment_of_ individual (used to represent things that are inside others) and relative_location (used to locate objects on a particular place). Topology refers to the connectivity between Objects. Topological descriptions are based on the use of the property connection_of individual which is defined as symmetric and transitive. For example, a reasoner can infer that pipes A and B are connected because their flanges F and G are connected (Figure 3). F G

Figure 3. Connectedpipes andflanges and its corresponding OWL code

4. Physical objects A physical_object is a possible_individual that is a distribution of matter, energy, or both. Examples of physical_object are a table, a pump, a piece of metal, a laser beam. Physical objects can be instances of arranged_individual which defines those possible individuals that have parts each of which plays a distinct role. Instances of physical objects can be related to instances of abstract_object. For example, the liquid contained in a tank that has the phase liquid. In the ontology, phase is abstract.

5. Activities Activities can have temporal boundings linking events as well as points_in_time because activity is a subclass of possible_individual which has a life cycle bounded by beginning and ending. The activity concept can be used to represent physicochemical behaviors, plant operations, abnormal situations, etc. Activities bring about change by causing an event. Causality is described by means of the cause_of event relation. Events mark the beginning, or the ending of a possible_individual. An activity consists of the temporal parts of those members of possible_individual that participate in the activity. For example, the mixing activity shares the temporal parts of the tank and agitator. An example of the use of activities, events and participating objects is shown in Figure 4. <ending> <event rdf:ID="pump-off"> <participation>

1547 <event r d f : I D = " p u m p - o n " / > < p h y s i c a l __o b j e c t rdf :I D = " p u m p " > < e n d i n g rdf :r e s o u r c e = " # p u m p - o f f "/>

Figure 4. OWL code thclt shows the use ofactivities, events" and participating objects.

6. P h y s i c a l q u a n t i t i e s Following the arguments presented by Gruber and Olsen (1994) the upper ontology supports the idea that physical objects and activities should not be allowed to define quantities as attributes because a quantity is not an inherent property. For example, the setpoint of a temperature controller (a physical object) can be defined as an instance of class_ofindirec£properO,. The class_of indirect_property is a rdfs:subClassOf owl:FunctionalProperty whose domain is given by members of class_ofjndividual and whose range is given by members of properO:_space. It is a relation whose range is tenlperature_quantiO,, temperature_quantity is an instance of property_space. Furthermore, proper~_space is a subclass of class_of_property, which means that temperature quantiO, is also an instance of class_ojboroperOp (Figure 5). For the units of measure JSO 15926-2:2003 suggests to classify the property_quant(fication, in other words a classification relation is used to map an instance of properO,_quantification to an instance of scale. The approach used here defines scale as an OWL:property. <propertyspace

rdf : ID= " t e m p e r a t u r e _ q u a n t i t y " / >

Temperature Controller

TIC-01

<xsd:float rdf:value="800.0"/>

1548 < / r d f :D e s c r i p t i o n > < /t e m p e r a t u r e _ s e t p o i n t < / I i s :p h y s i c a l _ o b j ect >

>

Figure 5. 0 WL Code illustrating the definition of physical quantities. We can also specify temporal boundings (beginning and ending) to temporal_part_of_TIC_01_at_800K to indicate the time interval in which the setpoint of TIC-01 was at 800K.

6. C o n c l u s i o n s Industries around the world recognize that some of the keys to compete in the everincreasing global markets, as well as to meet increasingly tighter safety and environmental constraints lie in improved work flow processes and in the integration of information systems. However, many current information systems can be integrated only at great cost because of their incompatible proprietary representations of information. One approach to integration of information systems is by means of shared ontologies. In particular, upper ontologies define top-level concepts such as physical objects, activities, mereological and topological relations from which more specific classes and relations can be defined. We have provided a brief overview of an upper ontology based on ISO 15926-2:2003 which has been implemented in OWL. The ontology is being used as an approach to represent and query knowledge generated during Hazards and Operability Studies, and it is also the upper ontology for defining and searching modeling services. It would be of great benefit to the process engineering community to explore the integration with other efforts such as the OntoCAPE ontology. The upper ontology in OWL format can be downloaded from: http://www.ompek.org/

References Bayer, B., 2003, Conceptual information modeling for computer aided support of chemical process design. VDI Verlag GmbH, Daseldorf. ISBN 3-18-378703-2 Gangemi A., N. Guarino, C. Masolo, A. Oltramari, L. Schneider, 2000, Sweetening Ontologies with DOLCE. Proceedings of EKAW 2002. Siguenza, Spain ISO 10303-11, 1994, Industrial automation systems and integration - Product data representation and exchange - Part 11: Description methods: The EXPRESS language reference manual ISO 15926-2, 2003, ISO-15926:2003 Integration of lifecycle data for process plant including oil and gas production facilities: Part 2 - Data model Niles, I. and A. Pease, 2001, Towards a Standard Upper Ontology. 2nd International Conference on Formal Ontology in Information Systems (FOIS), Ogunquit, Maine, October 17-19 Sowa, J., 2000, Knowledge Representation: logical, philosophical, and computational foundations. Brooks/Cole Uschold, M. and M. Gruninger, 1996, Ontologies: Principles, Methods and Applications Engineering Review 11 No. 2 (1996) 93-113 West, M., 2003, Replaceable Parts: A Four Dimensional Analaysis Proceedings of the Conference on Spatial Information Theory (COSIT), Ittingen, Switzerland, September 24-28 W3C, 2004, OWL Web Ontology Language Overview, W3C Recommendation, [Online] Available: http ://www.w3.org/TR/owl-features/ Yang, A. and W. Marquardt, 2004, An Ontology-based Approach to Conceptual Process Modelling. Proceedings of ESCAPE-14, Portugal.

European Symposiumon ComputcrAided Process Engineering 15 L. Puigjaner and A. Espufia (Editors) g~ 2005 Elsevier B.V. All rights reserved.

1549

Multi-Agent Systems for Ontology-Based Information Retrieval R. Bafiares-Alcantara ~ , L. Jimdnez b and A. Aldea c ~Department of Engineering Science, Oxtbrd University Parks Roads, Oxford OXI 3PJ, UK bDepartment of Chemical Engineering and Metallurgy, University of Barcelona Marti i Franqu~s 1, Barcelona 08028, Spain CDepartment of Computing, Oxford Brookes University Wheatley Campus, Wheatley, Oxford OX33, UK

Abstract The Web offers a huge amount of valuable intbnnation, but it is very hard and time consuming to retrieve thousands of web pages related to a concept, filter the relevant ones, analyse this intbrmation and integrate it in a knowledge repository. This paper describes one component of a knowledge management platform (h-TechSight project) that performs these tasks, the multi-agent search module (MASH). MASH employs a domain ontology to search for web pages thai contain relevant information to each concept in the domain of interest. The search is then constrained to a specific domain to avoid as much as possible the analysis of irrelevant information.

Keywords: ontology; multi-agent system; knowledge retrieval.

1. Introduction A good use of knowledge management practices can greatly benefit knowledge intensive industries, such as chemical process industries. Maintaining an up-to-date knowledge of the domain is of capital importance for those industries. The WWW offers a huge amount of information, but it is impossible for a person to retrieve thousands of web pages related to a concept, filter the relevant ones, analyse their content and integrate it in the company knowledge repositories [Batres et al., 2002]. Knowledge management tools can help by providing tools that automatically update technological domains, and monitor and assess how products, services, and technologies evolve, emerge, mature or decline. Furthermore, engineers typically identify the evolution of their disciplines by reading journals, attending conferences or by hearsay. All this information can be found nowadays on the web, but it is weakly structured, scattered, distributed and impossible to analyse manually. Traditional search engines allow users to retrieve information by combining keywords. This type of search can cause several problems: the number of

Author to whom correspondence should be addressed: [email protected]

1550 pages retrieved may not be manageable; some of the retrieved documents are irrelevant while some of the relevant documents may have not been retrieved. Fensel (2001) argued that the performance of a search engine could be improved by using ontologies. In its conventional form, an ontology can be seen as a representation of the concepts which are relevant to a particular domain. Ontologies provide a semantic view that helps to sort out web pages with relevant information about a concept from web pages that contain data with just syntactic similarities to the concept. The aim of the EU research project h-TechSight (h-TechSight, 2001) is the construction of a knowledge management platform (KMP) (Stollberg et al., 2004; Kokossis et al, 2005), which can be used by knowledge-intensive industries to keep a dynamically updated knowledge map of their domain. This paper describes in detail one of the main components of the KMP, the MASH search module, which main task is to find web pages with relevant information about a predefined field represented by a domain ontology (Aldea et al., 2003).

2. The Multi-Agent Search Engine (MASH) The search engine requires a domain ontology to perform the search, so the user must generate that ontology or use an existing one to start the procedure. The implementation of the search module is based on the agent technology (Wooldridge, 2002) where several software agents work together in an asynchronous, concurrent and intelligent way that can be distributed among several computers.

2.1. Domain ontology The search is driven by the domain ontology which is represented by a hierarchical taxonomy of concepts. Every concept (class) is connected to a parent concept (superclass) and thus a class and all its ancestors define a class path (for example, in Figure 1: Biosensor\Application\Environment\Air analysis). Every class (e.g.. air analysis ) contains a set of slots which represent the properties and characteristics that are important for this specific class in the general domain of interest (e.g. biosensors). Every class also inherits all slots defined in its ancestors (Fensel, 2001). Figure 1 depicts a part of one domain ontology (biosensor ontology) used in this work. For instance, the concept biosensor application in health care is represented by the subclass "health-care" within this class, the user decided to include two slots "researcher-field" and "re searc h-top ic". During the search process, the difference between classes and properties is that classes define the search domain, while properties are used to evaluate to what extend the retrieved pages have the sort of information required by the user. The use of synonyms in the definition of classes and slots extends the domain ontology with the possibilities of having alternative terms as, for example, "domain" and "field", acronyms as "computer fluid dynamics" and "CFD", chemical formulas as "sodium sulphate" and "NazSO4" or language differences as "generalisation" and "generalization".

1551 •[ ~ Biosen sot .

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2.2 The search process Once the domain ontolo~, and the search parameters have been defined by the user, the multi-agent search process starts. This task combines several stages: splitting the domain ontology, retrieving the web pages, rating and filtering the retrieved pages, and the classification of the results. The domain ontology is first dividing into query ontologies. A q u e ~ ontology consists of a class with all its slots (own and inherited) and the class path. The query ontologies

1552 are used by the search agents and as a result, for every search a set of web pages is retrieved. The constraints web site (e. g. yourcompany.net or mycompany.com), language (e. g. German) and country (e. g. mx or jp), are also considered. Moreover, MASH is able to search databases or documents available on the intranet (*.pdf or *.doc). If the number of web pages retrieved does not reach the MaxLinks parameter predefined, the system raises a complementary process, based on an expansion tree of the initial query, as can be depicted in Figure 2 where query for the class airanalysis has been expanded. The query building process is as it follows: each node of the tree is expanded with sub-nodes representing queries where one of the keywords has been removed, except the name of the current class (right bottom side of Figure 2). When one of the parents of "air analysis" (i. e. "environment", "application", or "biosensor") is removed from the initial query, the nodes A, B, E are respectively expanded, while "air analysis" (AA) is in all three sub-nodes. The number of web pages found for each node is depicted in the white box inside each node in Figure 2. An alternative way to extend the number of web pages to reach the MaxLinks parameter is to use the Depth parameter. This value indicates to what extend the search process takes into consideration the links contained in the retrieved pages. So, if Depth is 0 only pages recovered by the search engine are considered. But if Depth is set to 1, also pages directly linked from Depth 0 pages are retrieved, rated and filtered. Depth values above two are not recommended because the time increases exponentially. The final stage of the search process is rating and filtering the retrieved pages according to their relevance to the query ontology. The rate is calculated with the function: number of attributes encountered (p,A)" 100 Rc(p, A) =

(1)

total number of attributes (A)

where p is the web page recovered for a class C and A is the set of attributes (inherited or not) of C. Rc (p,A) defines the relevance of the web page p with respect to the class C. After normalisation (range [0, 1]), and during the filtering step, this value is used to discard pages below the Threshold parameter, and finally, to rank pages.

_ ~-I n t e r n e t I'~ ... ~,, II .n. ...... . , o nt olo~. WWW ! ,[.Agent(IA)f",,.~(classes+arts) f~ ~...... -, ~ - ~ ~...,/ i/ ......~...... Set o f "1",,,.~ -. ., ] ' ....: r a t e d ~ ' " - ~ C o o r d inator]-, I -"~( ~:~ Retrieve ............ages .....i J . . . . . . /-" "%..i:\\::;i ! pages ......./.,au~ /JAgem I,L,/4, U i ;~ fromW ...:.~.... .. / / ...... :

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1553 in the final step, all pages obtained for all classes of the domain ontology are combined into a single information ontology.

2.3. MASH Architecture The search process was implemented in the Multi-Agent JADE environment (Bellifemini, 2001). Four different types of agents were identified (Figure 3): one user agent (UA), which interacts with the user, n internet agents (IA) which access, retrieves, rates and filters the information from the web, one weight agent (WA) that supports the search and supplies alternative queries when requested, and one coordinator agent (CA) that rules the overall process, particularly during splitting and amalgamation of the tasks performed by the IA. The way these agents collaborate can be explained following the interactions contained in Figure 3, a more detailed description of the platform can be found in Moreno et al. (2004). • The user interacts with the system through the UA, providing the domain ontolo~: and setting up the parameters described in section 2.2. • The CA receives and divides the domain ontology into the quew ontologies that are spread out across all the available IAs (configurable with Internet Agents). • Each IA uses the search engine (configurable with the SearchEngine) and the semantic information of the quew ontolo~: received from the CA to filter and to sort the web pages, and sends them back to the CA. if the IA does not recover enough pages, the WA supplies alternative queries to complete the list. • In this case, the WA explores the expansion tree and proposes the most restrictive query. For instance the alternative query at level 2 corresponds to node A (Figure 2). • Finally, the CA waits for all the iAs to supply the results or until the Deadline is reached. Then the CA amalgamates all the results and sends a unified ontology to the UA, who shows the results to the user. Both the input and the output of the search process are handled using a web interface where the user can edit, create, retrieve, import and export ontologies as Resource Description Format files (W3C, 2001).

3. Tests a n d R e s u l t s The MASH search engine has been extensively used in different domains such as biosensors, chemical engineering, and process engineering employment agencies (Aldea et al, 2003). A more detailed analysis of the search module to study the evolution of the relevance of the retrieved pages depending on the input parameters has been produced in the field of biosensors. Some of these studies show that the number of pages about biosensors that have been updated during the last three months are above 94800. For such amount of information and dynamics, the use of automatic intelligent search systems, such as the one described in this paper, is compelling. One first benefit is to reduce the number of retrieved pages to a manageable quantity, by keeping for each concept of the ontology only those pages which are the most relevant to the concept and its attributes, within the context of the ontology. Three main outcomes arise from the analysis of the results. Firstly, the lack of attributes in a class produces a deceptive appearance of high relevance in comparison to other classes with attributes. A deeper analysis shows that the reason is that the search is less

1554 demanding as the number of attributes decreases. Secondly, the average quality of the pages has a slight descending trend as the number of pages required increases. This result confirms that when MASH is forced to recover more pages, and thus new pages, which are progressively less relevant, are considered. Finally, it is also interesting to observe that the average relevance of the pages associated with a class is typically higher than the average relevance of the pages of their subclasses, but this difference is smaller as we move deeper in the ontology hierarchy. The reason is twofold, when the classes become more specific (deep in the hierarchy) they are more restrictive and as consequence less good pages are found. However, if the number of recovered pages is kept constant for all the classes, those classes that are more restrictive are forced to include less relevant pages, and the average rate descends.

4. Conclusions MASH, a multi-agent search engine has been described in this paper. MASH is able to detect web pages related to a domain ontology and calculate the relevance of each one. Additionally, the search parameters allow the user to control some aspects of the search (Deadline, SearchEngine, MaxLinks, Threshold and Depth). The system was tested to analyse the relevance of the pages as the user parameters are modified. The multi-agent system has been developed to make the whole process asynchronous, concurrent, intelligent and distributed.

References Aldea, A., R. Bafiares-Alcfintara, J. Bocio, J. Gramajo, D. Isern, L. Jimdnez, A. Kokossis, A. Moreno and D. Riafio, 2003, An Ontology-based Knowledge Management Platform, Workshop IIWEB'03 at IJCAI'03, Acapulco, Mdxico: 177-182. Batres, R., R. Chatterjee, R. Garcia-Flores, C. Krobb, A. Yang and X. Z. Wang, 2002, Software Agents, in B. Braunschweig and R. Gani, Software Architectures and Tools for Computer Aided Process Engineering, Amsterdam, Elsevier 11: 455-484. Bellifemine, F., A. Poggi and G. Rimassa, 2001, Developing Multi-Agent Systems with a FIPA Compliant Framework, Software Practice and Experience, 31:103-128. Fensel, D., 2001, Ontologies: A Silver Bullet for Knowledge Management and Electronic Commerce, Heidelberg, Germany. h-TechSight, 2001, IST Project (IST-2001-33174). prise-serv.cpe.surrey.ac.uk/techsight (Access: January 2005). Kokossis, A., R. Bafiares-Alcfintara, L. Jimdnez and P. Linke, 2005, h-Techsight: a Knowledge Management Platform for Technology Intensive Industries, European Symposium on Computer Aided Process Engineering (ESCAPE-15), Barcelona, Spain. Moreno, A., D. Riafio, D. Isern, J. Bocio, J. Sfinchez and L. Jim6nez, 2004, Knowledge Exploitation from the Web, 5th International Conference on Practical Aspects of Knowledge Management (PAKM'04), Viena, Austria. Stollberg, M., A. Zhdanova and D. Fensel, 2001, H-TechSight: a Next Generation Knowledge Management Platform, J. of Information and Knowledge Management, 3 (1): 47-66, 2004. W3C, 2001, Resource Description Framework. Wooldridge, M., 2002, An Introduction to Multiagent Systems, John Wiley and Sons Ltd, New Jersey, USA.

Acknowledgement This work has been funded by the h-TechSight EU project (IST-2001-33174).

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) ~22005 Elsevier B.V. All rights reserved.

1555

An agent-based approach for supply chain retrofitting under uncertainty Gonzalo Guill6n, Fernando D. Mele, Francisco Urbano, Antonio Espufia and Luis Puigjaner* Universitat Politbcnica de Catalunya, Chemical Engineering Department, E.T.S.E.I.B., Diagonal 647, E-08028, Barcelona, Spain

Abstract In this work, decisions that have a long lasting effect on the SC such as the design and retrofit of a production/distribution network are considered. The retrofitting tasks are accomplished by using a SC agent-oriented simulation system, which model each entity belonging to the SC as an independent agent and represents in a functional way the interactions between the components of the SC. The starting point is a set of possible design options for the existing SC. For each design alternative a performance index is obtained through the agent-based framework, which is coupled with a genetic algorithm (GA) that looks for the best value of the operational variables associated to the resulting network.

Keywords: Retrofit, SCM, agent, discrete-event simulation

1. Introduction The concept of Supply Chain Management (SCM), which appeared in the early 90s, has recently raised a lot of interest. A lot of attempts have been made to model and optimise the SC behaviour, currently existing a big amount of deterministic and stochastic derived approaches. Supply Chains (SCs) are made up of several elements whose behaviour affects the performance of the entire system (Perea-L6pez et al., 2000) being the relationships that constitute this system not simple at all. Then SCs, as many real-world systems, cannot be evaluated analytically using mathematical methods to obtain exact information on questions of interest, being therefore more appropriate to consider the SC by means of dynamic simulation. Uncertainties also substantially contribute to the complexity of the SCM. In addition to none stationary random demands at each retailer, equipment breakdowns and uncertainty in processing times greatly influence the SC operation.

1.1 Simulation approaches for SCM Simulation is one of the best means for analysing SCs because of its capability for handling variability. Although managers were able to try 'what if' scenarios with input To whom all correspondence should be addressed.

1556 data and simulation to obtain potential solutions, an optimisation procedure helps to eliminate the need for random trial and error (Wan et al., 2003). In distributed artificial intelligence (DAI), an agent is defined as a computer system that is situated in some environment, and that is capable of autonomous action in this environment in order to meet its design objectives. SCM problems are both distributive in nature, and require extensive intelligent decision-making. Thus, in the last few years, multi-agent systems have been a preferred tool for solving SC problems, and several approaches using multi-agent systems have been proposed (Julka et al., 2002). Such architectures are particularly recommended for modelling complex networks which are driven by a combination of heuristics rules and mathematical programming tools. Moreover, this kind of systems can also handle the perturbations caused by stochastic events in the supply chain. This study presents an approach for SC design and retrofit that considers the eventdriven nature of real SCs through a dynamic simulation of a set of independent agents. Each agent represents one SC entity or node. The agents store the real-world SC data and emulate the behaviour of the entities by means of a set of specific algorithms based on a state-transition description that they have implemented. The system includes a "central" agent that coordinates the activities among the rest of the agents and manages the information between them. The multi-agent system able to carry out the discreteevent simulations of the SC is coupled with Genetic Algorithms (GAs) as a useful tool that identifies better values for the operational variables associated to a given network. This procedure in two stages allows managers to make strategic decisions in a reliable manner. The main contribution of such approach in comparison with previous methodologies is the combination of the multi-agent system (discrete-event simulation) with an optimization algorithm. The former allows a realistic modelling of the SC and also handles uncertainty, while the latter improves the performance of the overall network regarding inventory control policies, transport and production decisions. ~.J,~,, gl

Di

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Figure 1. Structure of the case study

2. Motivating example Let us consider a SC consisting of nine interconnected entities as the one shown in Figure 1. The network comprises two plants (F1 and F2), two distribution centres (D 1 and D2) and five retailers (R1 to R5). The plants manufacture final products A, B and C from raw materials provided by external suppliers. Final products are transported from plants to warehouses and from warehouses to retailers where they become available to customers. In such SC, there is a material flow that moves from the plants to the

1557 customers and an information flow (ordering flow) which does it in the opposite direction. It is supposed that the demand of the system can be modelled as a set of events distributed over the time horizon tinder study, each of them involving an associated amount of material and time of occurrence. Both parameters, the amounts and the interarrival intervals between events, are assumed to be time-variant. The material quantity of each demand event follows either a uniform or a normal distribution law, while a Poisson probability distribution is used to model the inter-arrival times between orders (Law and Kelton, 1991). Moreover, processing and transport times are also assumed to follow normal probability distributions. A periodic revision strategy is implemented at the distribution centres, being R the time period between two consecutive inventory reviews. Every R time units, the inventory position l n v is checked. If the value of I n v is below the reorder point s, a replenishment quantity u = S - hTv is ordered to raise the stock level to S. If the position is above s, nothing is done until the next review. Thus, the strategy has three parameters whose values have to be determined: R, S and s. For the retailers, a similar but continuous revision strategy is considered. The retrofit of the above described SC could be in principle addressed by means of mathematical programming tools. However, this would lead to high computation times owing to the scale and complexity of the resulting formulation. On the one hand, a global optimisation approach, which requires an extensive computation effort, would be necessary for optimizing the inventory control policies applied in the warehouses. On the other hand, a complex multi-stage stochastic formulation requiring also high computation times, should be applied to provide a 'walk through the timeline' concerning the decisions to be taken under uncertainty in the demand, the processing and the transport times.

3. Proposed Approach The overall SC design problem is hierarchically-decomposed into two levels, a higher strategic level and a lower tactic/operational one. This leads to tractable problems and avoids monolithic formulations that require an extensive computation time and become impossible to solve in the case of large-scale SC problems. At the strategic level, the capacities of the plants and storage sites are considered. At the lower level, which comprises tactical and operational decisions, the quantities manufactured in the factories, transported between nodes, and the values for the parameters of the inventory control policies, are computed by applying a genetic GA on the multi-agent system. The overall algorithm is depicted in Figure 2. In first place, it is necessary to provide a set of design candidates from which the final configuration should be selected. A Monte Carlo sampling is next performed over the probability distributions that characterise the uncertain parameters (demand, processing and transport times), thus generating a set of scenarios with given probability of occurrence. For each SC alternative a GA, that provides an oriented search mechanism that decreases the computation effort required by rigorous optimization techniques, is applied for optimizing the operational variables associated to the selected configuration. There~bre, the fitness function is obtained by running for each scenario generated by Monte Carlo sampling, i.e. for each set of values

1558 of the uncertain parameters, a discrete-event simulation and computing the average value of the objective function, in this case profit, over the entire range of them. The different configurations are finally compared in terms of the expected total profit (profit) associated to the best set of their operative variables computed by the GA. The profit index computed for each configuration measures the operational cost of the SC achieved over the simulation time horizon and basically considers revenues, storage, manufacturing, and transportation costs. Unlike other works in the literature, we assume that some of the demand can actually be left unsatisfied because of limited production capacity. J

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The revenues (revenues) are computed from the sales of products:

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k

where t represents each simulation step, Sk,t is the unit price at retailer node k and time t, and Uk,t is the amount sold at retailer entity k and time t. The storage cost IC accounts for the opportunity cost related to the value of the inventoried material and also for the expenses incurred in running a warehouse:

IC=ZZIk,tlCk,, t

(2)

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In this equation, IC~,t is the unit holding inventory cost at entity k and time t, and Ik.t is the inventory level at the entity k in the SC and at time t. The manufacturing cost MC is calculated by means of equation (3):

1559

t

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where MCa,, represents the unit manufacturing cost at entity k and time t, and Ua,, is the amount produced at a manufacturer entity k and time t. Regarding the transportation cost (TrC), these are computed by applying equation (4):

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where Tr(_~..,is the unit transportation cost at entity k and time t, and Uk., is the material delivery quantity at every entity k and time t. Finally, the total profit over the time horizon is given by: profit = r e v e n u e s - ( I C + MC + TrC) (5) 34

0

20

40

60

80

100

120

140

160

180

200

Figure 4. Average objective fimction evolution during the GA run.

4. Results The case study presented before is solved by applying the proposed strategy. Three sets of different capacity values for the distribution centres are evaluated. For each value of the design variables, a GA properly designed and tuned is run over the discrete-event simulator. The GA handles 27 variables: the s and R inventory parameters at the distribution centres (12 variables), and the s parameters at the retailers (15 variables). Real-valued encoding and maximum number of generations as termination criterion are used. A one year horizon of time is considered with daily precision for each simulation run. The multi-agent system has been developed in C# language and has been operated in an AMDK6 computer, 2.16 GHz, 512 MB. Concerning lhe implementation of lhe GA applied in this work, it should be mention that this has been coded using MATLAB® (Chipperfield et al., 1994). With regard to the CPU time, for each configuration only a few hours are required to evaluate the expected profit. It is also important to notice that this time depends on the number of simulation runs to be made, which is given by certain tuning parameters of the GA such as the number of generations and the number of individuals in each population. Figure 3 shows the inventory level evolution at distribution centre D1 for the best solution and tbr a solution found using other configuration, as it appears in the graphical

1560 user interface of the multi-agent system. Figure 4 shows the evolution of the objective function (expected profit) through 200 generations. The curve represents the average value of profit for about ten GA runs. Repeating the same procedure for each of the remaining configurations, the decision maker can determine the best strategic decision to be implemented in the network in terms of the resulting expected profit achieved within the time horizon of the analysis.

5. Conclusions In this work, the SC design and retrofit problem has been addressed. Strategic decisions have been made taking into account their impact at a lower level. The performance of each SC configuration has been assessed through a dynamic multi-agent model that has been coupled with GAs in order to optimise the operation variables associated to each design candidate. The computation cost of the proposed approach depends on the problem dimension and its level of complexity. However, the time requirement is reasonable for such a longterm decision. On the other hand, the use of multi-agent systems allows modelling in a very realistic manner complex SCs, particularly those which imply the combined use of heuristic rules and mathematical programming tools and operate under uncertainty.

References Chipperfield, A., Fleming, P., Pohlheim, H., and C. Fonseca, 1994, Genetic Algorithm Toolbox for Use with MATLAB®. User's Guide 1.3. Law, A. M. and W. D. Kelton, 1991, Simulation Modeling & Analysis. McGraw-Hill International Editions. Julka, N., Srinivasan, R. and I. Karimi, 2002, Agent-based supply chain management-l: framework, Comp. and Chem. Eng., 26, 12, 1755-1769. Perea-L6pez, E., Grossmann, I., Ydstie, E., and T. Tahmassebi, 2000, Dynamic Modeling and Classical Control Theory for Supply Chain Management. Comp. and Chem. Eng., 24, 1143-1149. Wan, X., Orgun, S., Pekny, J. F., Reklaitis, G. V., 2003, A simulation based optimization framework to analyze and investigate complex supply chains. In Proceedings of the Process System Engineering, Elsevier, Amsterdam, 630-635.

Acknowledgements Financial support received from the Spanish "Ministerio de Educaci6n, Cultura y Deporte" (FPU programs), "Generalitat de Catalunya" (FI programs) and from GICASA-D 00353) and OCCASION (DPI2002-00856) projects is gratefully acknowledged.

European Symposium on Computer Aided Process Engineering - 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1561

Pharmaceutical Informatics" A Novel Paradigm for Pharmaceutical Product Development and Manufacture Chunhua Zhao, Girish Joglekar, Ankur Jain, Venkat Venkatasubramanian*, G.V.Reklaitis {chunhua, gjogleka, jainl 8, venkat, reklaiti} @ecn.purdue.edu Institute for Advanced Pharmaceutical Technology Purdue University West Lafayette, IN, USA

Abstract The compelling drivers for the pharmaceutical industry are minimizing the time between a drug's discovery and its delivery to the marketplace, and maintaining high productivity in the manufacturing processes. During a product's lifecycle many complex decisions must be made to achieve these goals. To better support the development and manufacturing processes at each stage, we have proposed a new paradigm to facilitate the management and transfer of data, information and knowledge. A prototype for the informatics paradigm has been successfully developed. As a first step, the feasibility of the proposed informatics framework is demonstrated using a case study based on a pilot plant operation.

Keywords: Pharmaceutical informatics, Drug development and manufacture, Process development tools, Information modeling and integration

1. Pharmaceutical Informatics: the grand vision The major tasks involved in bringing a pharmaceutical product to the market are outlined in Figure 1. Under ideal circumstances, each stage operates in isolation and generates process knowledge according to certain expectations. The knowledge is then passed on to the next stage at the appropriate time. However, in reality considerable amount of "starting over" occurs due to the changes in overall direction as more knowledge is gained at each stage. The information flows between the various stages of this process tend to be voluminous and there is high level of uncertainty in the underlying technical and commercial data. In addition, the technical specifications and information base which must be developed to support production are very extensive and the regulatory oversight requirements are very demanding. The current industrial response to all these challenges is sub-optimal. There are many individual islands of automation and no comprehensive, integrated, environment that links these islands. Therefore, practitioners must make do with a limited computer-based assistance to acquire, manage, analyze and interpret complex product and processing information with enormous amounts of human intervention. This increases the inefficiencies, Author to whom correspondence should be addressed: [email protected]

1562 uncertainties, costs, delays, and product quality concerns all along the product development. Sm~scate Erpeti~ ll4hrket Studies

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Figure 1. Major tasks in the product development and manufacture

We propose a new paradigm for pharmaceuticals development and manufacture that can effectively address the challenges faced by the industry. In this paradigm, a web-based informatics infrastructure is developed to support the key decisions spanning the entire process, including product portfolio selection, capacity allocation decisions, process monitoring and quality control, production planning and scheduling, process safety analysis, and supply chain management. The data/information/knowledge flows in the entire process development are modeled. We call this infrastructure Pharmaceutical Informatics (PI). In this novel paradigm, we adopt an information-centric view instead of current application-centric view as discussed in next section.

2. Information Centric View At present, the scope and representation of a process are limited to the requirements of a specific stage, and are often influenced by the tools used in that stage. Therefore, only a partial representation of the process is required. For example, a simulation tool does not need to have material safety related data for its execution, but this kind of information is crucial to process safety analysis. Furthermore, different tools are structured in different ways to present the same process information. The lack of a coherent and unified process view results in islands of information with virtually no provisions for the computer assisted exchange of knowledge between these tools. We call this paradigm application-centric view. The most important aspect of the proposed informatics infrastructure is the separation between the underlying process information and the tools which use the information. Information is central to the infrastructure in the new paradigm, not the tools that use the information. Various applications become providers as well as consumers of the information. We believe that only by dramatically changing the current application-

1563 centric view to information-centric view it is possible to develop the vision we have proposed in previous section. Thus, in the new paradigm, instead of entering the process specification into individual tools, the task here is to describe the information. Instead of encoding process specifications in objects in a particular programming language or tool specific constructs, the process information should be explicitly described. A repository of process information will be at the core of the informatics infrastructure. The repository will cover a wide range of information blocks such recipes, equipment configurations, experimental data, plant operation data and so on. Furthermore, the information is separated from its presentation, contrary to what is currently implemented in many process development tools. Though new to pharmaceutical process development, this separation of tools, information, and presentation have been very well studied and adopted in other disciplines, for example, it is very easy to make analogy with business logic, data, and presentation in business process. The explicit description of domain concepts and relationships between these concepts is known as an ontology. The recent developments in the field of ontology have created new software capabilities which greatly facilitate implementation of the Pharmaceutical Informatics infrastructure. Ontology is defined as an explicit specification of a conceptualization (Gruber, 1993). The shared understanding is the basis for a formal encoding of the important entities, attributes, processes and their inter-relationships in the domain of interest. Ontologies can be used to describe the semantics of the information sources and make the contents explicit, thereby enabling integration of existing information repositories, either by standardizing terminology among the different users of the repositories, or by providing the semantic foundations for translators. Web Ontology Language (OWL), recommended by W3C, is used as the language to specify the ontologies. OWL can formalize a domain by defining classes, properties of these classes, and relations between them. OWL can also define individuals and assert properties about them, and furthermore reason about these classes and individuals to the degree permitted by the formal semantics of the OWL language. As a very first step towards the information-centric paradigm, we demonstrate that it is feasible to explicitly describe the information related to pharmaceutical development process, and it is achievable for various application tools to access the information. So the goal here is not to construct a comprehensive ontology for the information. We demonstrate the feasibility of the proposed framework using a pharmaceutical pilot plant operation.

3. Process Ontologies We first create ontologies for the domain of process recipe information. As the first step, the existing standards related to process information and literatures on process ontologies were reviewed because they summarize a common view of the process information from industrial practitioners. The standards can be grouped into three categories: equipment specifications (AP231, FIATECH, STEP), process engineering

1564 computations (CAPE-OPEN), batch recipe specifications (ISA $88, $95). Although there is no single standard that has been accepted in the industry and that can adequately describe a pharmaceutical process, the review provided a good basis for developing the required ontologies. Whenever appropriate, the same terminology and keywords were used in the new ontologies. For process engineering area, OntoCAPE has been developed define conceptual data models (Yang, 2004). However, this extensive development is targeted for continuous process design and simulation. At present it does not accommodate the general recipe, the most important concept in pharmaceutical processes. We use Prot6g6 (see URL), an ontology and knowledge-base editor, for creating ontologies and Racer (see URL), a Description Logic reasoning system, as the inference engine to check data consistency and validity. Complex rules for checking data consistency are processed using Jess (Ernest J. Friedman-Hill, 2003), which is a rule engine and scripting environment. The higher level concepts in the process ontology include Material, Equipment, Reaction, Separation as well as RecipeElement under which Operation and UnitProcedure are defined. Other important concepts include Stream and Port. OWL provides the capability to describe complex relations between the concepts in the process information. For example, hasUnitProcedure property in Operation and hasOperations in UnitProcedure are inverse functional relations. The hasOperation property in Port has cardinality restriction of 1. The inference engine can clarify the hierarchy of classes, and furthermore, check consistency to ensure the completeness and validity of the process information based on predefined consistency rules. As an example, a consistency rule is used to require that the has UpstreamPort and hasDownstreamPort of a Stream be different.

4. Pharmaceutical Informatics Infrastructure Figure 2 shows the overall architecture of the new paradigm. Process ontologies are first created as well as the logic embedded in the rules to ensure the completeness and validity of the process information. Based on the ontologies, instances of the concepts and relations are created for a particular process using the web based information management facility. A web-based interface for information management was developed because the web is the natural environment for the use of the infrastructure with such a wide scope. Additionally, development of thin-client applications in web environment has become feasible due to the recent advances in web technologies. The process information repository is in OWL format or related databases. Given the diversity of the tools that will access the process information, a middle layer consisting of controller, adaptor or translator is created for the tools as well as the web interface to access the repository. In this work, we investigated and critically assessed various technologies in order to make this infrastructure work, including the link between web interface to the information repository and different scenario for tools to access the information. A Web

1565 based process information management prototype has been developed. The current effort is to use the interface to create a specific process based on the ontologies. The design guideline is to minimize the code to be written in order to create the presentation. Thus XSL.T is used to link the OWL files to the presentation, and XForms is used to define forms for various process information. SVG is used as the format to generate recipe network or PFD from process information. A portal is also created to manage the process information.

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Figure 2. Pharmaceutical bTjbrmatics infrastructure The software tools that will use the process information defined in OWL. can be grouped into the following three types: 1. Tools that have native interface for the ontologies, that is, tools that are developed based on the ontologies defined in this work 2. Tools that have the ability to read or import process information from databases or XML Tools that use proprietary input and output formats. °

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Figure 3. bTteractions between the process repository and application tools A simple pharmaceutical API process has been used to demonstrate the technical feasibility of the infrastructure. The interactions between the process repository and software tools are shown in Figure 3. The process consists of four batch unit procedures: Reaction, Filtration, Drying l and Drying2, involving 20 operations. All the three scenarios for tools to consume the process information in OWL are successfully

1566 implemented. As an illustration of a category 1 tool, Java classes were created using Kazuki (see URL) and to analyze the details of a given operation. As an illustration of a category 2 tool, the repository was mapped into XML read into PHASuite (Zhao, 2002) for safety analysis. To illustrate the use of a category 3 tool, a Batches (Batch Process Technologies, 2003) simulation model of the process was created using Kazuki and Jena Framework. We also demonstrate a representation layer of the repository using Web interface adapting XML based web technologies, including XForms for entering information, and SVG for generating graphic views. We are currently working on integrating information generated from tools to the information repository. From what we have shown, the process information can be sufficiently described using OWL, which can act as a process information repository. The open and explicit description of the information provides a solid foundation for better use, sharing, and integrating process information.

5. Summary and Future Research Plan In this paper, we proposed a novel paradigm to facilitate transfer of data, information and knowledge using ontological models to better support the development and manufacturing processes. The main concept behind the proposed pharmaceutical informatics infrastructure is the separation of process information from the tools that use this information, and furthermore, the information is described explicitly. A prototype of the informatics infrastructure has been developed for process information in the pilot plant stage, to demonstrate the feasibility of the framework. Major components of this infrastructure were identified. Process ontologies have been created, and methodologies for using the ontologies to describe the process information and share information for tools are discussed. Work is in progress to further expand and implement the informatics infrastructure to the entire pharmaceutical development process and its various tasks and decision levels.

References Batch Process Technologies, Inc., 2003, Batches Reference Manual, W. Lafayette, IN. Ernest J. Friedman-Hill, 2003, Jess 6.1 manual. Sandia National Laboratories. Gruber, T. R., 1993, International Workshop on Formal Ontology. Italy. Golbreich, C. and Imai, A., 2004, 7th International Protdg6 Conference. Haarslev V., M611erR., 2001, Lecture Notes in Computer Science. Jena Semantic Web Framework: http://jena.sourceforge.net/ Kazuki: http://projects.semwebcentral.org/projects/kazuki/ Protdgd. http://protege.stanford.edu/ OWL Overview: http://www.w3.org/TR/owl-features/ SWRL: http://www.w3.org/Submission/2004/SUBM-SWRL-20040521/ Tim Berners-Lee, James Hendler, Ora Lassila, Scientific American, May 2001. Yang A., W. Marquardt, 2004, ESCAPE 14. Zhao, C., 2002, Ph.D. Thesis. Knowledge Engineering Framework For Automated HAZOP Analysis, Purdue University.

Acknowledgements The authors gratefully acknowledge funding support from The Indiana 21 st Century Research and Technology Fund.

European Symposiumon ComputerAided Process Engineering- 15 1,. Puigjanerand A. Espufia(Editors) (¢2)2005 Elsevier B.V. All rights reserved.

1567

A Web Service Based Framework for Information Integration of the Process Industry Systems Xiangyu Li, Xiuxi Li, Yu Qian* School of Chemical Engineering, South China of University of Technology Guangzhou 510640, P. R. China

Abstract Many process industry subsystems were developed separately. They didn't collaborate efficiently, which makes it difficult for information integration. In this paper, a web service based framework is presented to address this problem, in which every process industry subsystem is described as a web service by web service wrapper and registered in the UDDI register centre, according to different information integration schemes, these web services can then be integrated dynamically. Also presented is the accomplishment of the framework architecture. Finally the practicability and validity of the integration technology are verified through the application in the establishment of information integration platform of TE procedure.

Keywords: system integration, web service, legacy system, agent 1. Introduction The information integration is very important to the process industry. On the other hand, however, it is very difficult. In the past years, a number of information integration systems implemented in the process industry are based on Agent (Maguire, 1998) or CORBA technology (Object Management Group, 2002). There are some limitations in these schemes in terms of real time, security and stabilization in inlbrmation communication. These systems are characteristic of point-to-point connection and difficult to maintain. They lack agility thus do not cope with change of the process systems dynamically. For a rational and better implementation of the information integration in process industry systems, a novel web service based framework is proposed in this paper. In the proposed information integration framework, different subsystems are described as web services according to their functions. These web services are then represented with WSDL language (Yu, 2004) and lheir communicalion interfaces are defined. Finally, these web services are registered in the UDDI (universal description, discovery, integration) register centre. When different subsystems need to be integrated, it is not necessary for engineers to be familiar with inner details of each subsystem. What engineers should do is to understand the communication interface of each web service, to cope with the change of integration strategy dynamically. At the same time, web

* correspondence author: [email protected]. Phone and Fax: +86(20)87112046

1568 service wrapper is used to encapsulate the functions of the subsystem, thus ensure their safety and stabilization.

2. Information Integration of Process Industry Systems 2.1 Basic requirements for information integration Considering the particularities of process industry systems, to implement the information integration of different subsystems, the four basic requirements must be considered. (1) The integration should be the integration of factual applications, it should support the information communication among different operation modules and isn't the simple connectivity among different process industry subsystems. (2) The integration should be dynamic; it can be changed easily when the enterprise changes integration strategy or production process. (3) To process industry systems, security and stabilization are very important, when they are integrated, the integration technology should assure their former security and stabilization in the integration framework. (4) The integration is to extend the functions of process industry systems; it can't neglect the functions of subsystems entirely (Qian, 2003).

2.2 Information integration framework of process industry systems Considering the basic requirements for information integration of process industry systems, in the framework for information integration, every subsystem is wrapped as web service, so it is modified with a little amount, as a result, the security and stabilization of every subsystem aren't changed in the integration framework. When process industry subsystems are defined as web services, they are registered in the UDDI register centre (Yu, 2004). When these web services are called, they may be accessed at UDDI register centre. Agents are generated accordingly and return results what we want. The information integration framework of process industry systems is shown in Figure 1. Search Windows Client

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Figure 1. Information Integration Framework of Process Industry Systems The system architecture is as follows. (1) When a client sends a request with soap, the application server accepts the request;

1569 (2) Application server searches web service which meets client's need from UDDI register centre; (3) UDDI register centre returns message to application server; the message is associated with the location of certain web services and other related information; (4) Based on the message, Application Server creates web service agents and binds the agent to the web service that meets client's need; (5) Application Server calls the web service to serve the client request and to return results to the client. In this architecture, web service is used to implement cooperation among different subsystems, which are regarded as web service providers; Web service wrapper encapsulates the functions of subsystems and hides the inner complexity. XML language is adopted for message communication among different web services tbr different operation systems. The web service technology is particularly applicable to integrate different legacy subsystems running in different operation systems and different network environment as a distributed architecture. Data and messages may communicate among them, while security and stabilization of legacy systems are retained in the information integration platform.

2.3 Peculiarities for the integration framework The peculiarities for the integration framework are as follows. (1) SOAP is used to implement the exchange of information among different subsystems. It uses XML to describe information and uses HTTP as transport protocol; as a result, it is possible to integrate different subsystems running in different system platforms. (2) The functions of every subsystem are encapsulated as web services, so the characteristics of every subsystem aren't influenced in the integration framework. (3) According to different integration schemes, process industry subsystems can be integrated dynamically. (4) Based on web service technology, process industry subsystems can be integrated with multi-interface; this assures the agility of information integration of process industry systems. 2.4 Key technologies used in the integration framework To implement the web service based framework for information integration of process industry systems, there are many key technologies and criterions involved, includes: (1) UDDI (Universal Description, Discovery and Integration). UDDI is bought forward by Microsoft and Ariba and used to detect web services. By UDDI, clients can find and locate to certain web service that is provided by different corporations (of course, corporations must register the web service in the UDDI register centre firstly). The information model of UDDI is defined with XML Schema. In the proposed information integration framework, to every web service, it is registered in the UDDI register centre, when clients want to call certain web service, the UDDI register centre can implement the quick detection of web service with certain arithmetic and send information about the web service to clients, then clients can call the web service and get the return result. (2) WSDL (web service description language). WSDL is an XML based language, and it is used to describe web service. To every web service, clients can get its

1570 description information by its WSDL document, such as functions, parameters, and return value.

2.5 Difficulties in the integration of process industry systems The difficulties in the integration of process industry systems are as follows. (1) Security. To process industry systems, Security is very important (Cheng, 2003), so when we integrate different process industry systems, we must take into account this problem seriously. At present, web service technology hasn't taken pertinent measures to assure the security of web service. To us, during the integration of different subsystems, a new scheme is used to assure the security of web service. In this scheme, when a client calls a web service, the header of SOAP transfers its information, then the application server gets its information and verify its power, if the client has no access to call the web service, it is refused. According to the experimental result, this scheme is valid to assure the security of web service. (2) Compression of alternant information. Dealing with large numbers of data is a common characteristic of process industry systems (Chen, 2002), so when we integrate different subsystems, for decreasing the time of information exchange among different subsystems, we must compress alternant information to a minimal quantity. By the extension of SOAP, we make use of certain arithmetic to compress alternant information among different web services; as a result, 85 percent of redundant information is wiped off. (3) Discovery of web service. Real time is an important speciality of process industry systems (Shen, 1999), so it is necessary to study excellent arithmetic to implement the quick discovery of web services. In the proposed information integration framework, to the discovery of web services from UDDI register centre, an arithmetic based on ontology is bought forward. In this arithmetic, according domains and functions, different web services are classified; and client's query is standardized. This arithmetic assures timely discovery of web services, so users can get return result from web service what they call with a very short time.

3. Case Study TE procedure is a process control case based on practical process industry, during these day, we have done some research in this field, such as, fault diagnosis system based on ART2 nerve network (developed with G2 platform) (Qian, 1999), data monitor system based on wavelet analysis (developed with Matlab), procedure attemper and optimization system (developed with Games). Based on the proposed information integration scheme, an information integration platform is developed and implemented for a case study of TE procedure. It integrates three subsystems of data collection, data reconciliation, and fault diagnosis, which run in different computers with different operation systems. The subsystems are described as web services, which are registered and called when they are needed. Real time message in XML format is communicated among the three subsystems. Issues on security and stabilization are considered in building of the system. The information integration platform for TE procedure is shown in Figure 2.

1571 Search

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Fig, re 2. Mformation integration pla(form for TE procedure When client sends a request to change the operation pattern of TE procedure, application server queries the pertinent parameters of the web service for TE procedure simulation, and then calls the web service to implement the simulation of TE procedure under certain operation pattern, subsequently the web service for data reconciliation is called to emend data that is produced from the simulation, and the web service of attemper and optimization optimizes the data, finally, the fault diagnosis system uses the data to diagnose whether there are faults during the simulation of TE procedure. At the same time, the optimal result of every certain pattern is sent to the client terminal. Under optimal condition, the values of 10 variables and cost of four patterns are shown in Table 1. Table 1. The values o['10 variables and cost o/jbur patterns under optima/condition

1 2 3 4 5 6 7 8 9 10

Feedl Feed2 Feed3 Feed4 Recycle valve Purge valve Separator valve Stripper valve Steam valve Reactor coolant Total cost $/h

Base 63-10 53.8 24.6 61.3 22.2 40.0 38.1 46.5 47.4 41.1 170.6

Modell 60.9 50.2 26.3 62.1 0.9 21.9 40.3 45.2 1.0 32.9 12.1

Model2 12.6 89.7 29.6 54.7 1.0 50.4 35.9 42.8 1.0 21.9 180.8

Model3 90.6 7.4 21.8 52.5 787 9.5 29.8 42.1 1.0 32.7 48.3

Model4 99.2 80.2 4.0 96.5 1.0 45.6 60.1 74.5 1.0 65.8 278.2

1572

4. Conclusions The information integration of process industry systems is very important and difficult. Considering the peculiarities of process industry systems, a framework for information integration of the process industry systems is proposed, and the intrinsic problems that traditional technologies of information integration often meet have been solved. Finally, the practicability and validity of the integration technology were verified through the application in the establishment of information integration platform of TE procedure.

References Cheng, H.N., 2002, Dissertation, agent-oriented analysis, modelling and integration of process operation systems, South China University of Technology. Maguire, P.Z., A. Struthers, D.M. Scott and W.R. Paterson, 1998, The use of agents both to represent and to implement process engineering models, Computers and Chemical Engineering, 22(Supp 1.), $571. Object Management Group, 2002, http://www.omg.org/. Qian, Y., P.R. Zhang, 1999, Fuzzy rule-based modelling and simulation of imprecise units and processes, Canadian Journal Chemical Engineering, 77(1), 186. Yu, K., X.L. Wang and Y. Zhou, 2004, Underlying techniques for web services: a survey, Journal of Software, 15(3), 428. Qian, Y., X.X. Li and H.N. Cheng, 2003, Integration of chemical process operation systems, Journal of Chemical Industry and Engineering, 54(4), 557. Shen, J.Y., J. Hang, 1999, CORBA based tele-collaboration workflow mode, Computer Applications, 19(9), 19. Cheng, H.N., Y. Qian and X.X. Li, 2003, Agent-Oriented approach for integrated modelling of process systems, Journal of Chemical Industry and Engineering, 54(1), 128. Acknowledgements Financial supports from the Outstanding Young Scientist Fund (No.20225620), the National Natural Science Foundation of China (No.20376025 and 20476033), and the State Key Development Program for Basic Research of China (No.G200000263) are gratefully acknowledged.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1573

A Library for Equation System Processing based on the CAPE-OPEN ESO Interface G. Schopfer a, J. Wyes a, W. Marquardt a~, L. von Wedel b a

Lehrstuhl t'tir Prozesstechnik, RWTH Aachen, D-52056 Aachen, Germany b AixCAPE e.V., D-52072 Aachen, Germany

Abstract In this contribution we present the LptNumerics library for processing of equation systems that are provided via the CAPE-OPEN ESO interfaces. The library provides functionality for the pre-processing of an equation system and its solution. Here the term pre-processing refers to the steps required prior to solving a model in an equationoriented solution approach. The library is implemented in C++ and can be used within any equation-oriented application. This contribution discusses the design and implementation of the library and presents two application examples.

Keywords: CAPE-OPEN, process modelling, object-oriented design

1. Introduction In the EU-funded project CAPE-OPEN and its successor project Global CAPE-OPEN standard interfaces for process modelling tools were defined. The goal of these projects and the follow up organization CO-LaN is to achieve interoperability of process modelling tools by means of standardized interfaces that make modules exchangeable across tools from different vendors (CO-LaN, 2004). These modules include unit operation models, thermodynamic calculation packages and solvers. Within the "numerics" work package of CAPE-OPEN, interfaces were developed for simulation and optimisation of models that are defined in an equation-oriented approach. In this approach, models are typically defined in some modelling language in terms of equations describing the process behaviour and variables denoting process quantities (von Wedel et al., 2002). In case of a process consisting of several process units the equations of all process units are aggregated to one system and solved by a numerical equation solver. In case of recycles in the process model, the equation system has to be solved iteratively. For example for an algebraic equation system, in each iteration step the equation solver evaluates the differences of left- and right-hand sides of each equation for a given set of variable values. Based on these equation residuals and their derivatives with respect to the variables, called Jacobian matrix, the equation solver determines the variable values for the next iteration step. A solution of an equation system is obtained when all residuals are (close to) zero.

Correspondence should be addressed to W. Marquardt, [email protected]

1574 In the CAPE-OPEN project, the representation of an equation system in the form suitable for evaluation by an equation solver is called "Equation Set Object" (ESO). The CAPE-OPEN standard distinguishes between ESO that represent only algebraic equations, defined by the interface ICapeNumericAlgebraicESO, and ESO that evaluate additionally differential equations, defined by the interface ICapeNumericDifferentialAlgebraicESO. in the remainder of this paper, we refer to both interfaces as the CAPEOPEN ESO interfaces. These interfaces allow to set variable values and to evaluate the corresponding residuals and the jacobian matrix. In case of a differential-algebraic ESO, an independent quantity (e.g. time) can be set additionally and the derivatives of the differential variables with respect to it are considered as additional unknowns of the system. The work of the numerics work package resulted in a draft interface specification that is implemented by the commercial process modelling tool gPROMS (Process Systems Enterprise, 2002) and the final interface specification that was implemented prototypically by Belaud and co-workers (Belaud et al., 2001). However, CAPE-OPEN only deals with the definition of interface standards and does not provide any kind of functionality. Especially in the area of equation-oriented modelling, there is a large set of functionality which is required by many applications. Hence, reusable software components for existing process systems would be of great help to the modelling engineer. In this contribution, we present the LptNumerics library for the processing of equation systems based on the CAPE-OPEN ESO interfaces with the goal of exploiting this opportunity of reuse. The LptNumerics library provides reusable functionality for preprocessing of equation systems and their solution in equation-oriented modelling tools. Here the term pre-processing refers to several steps required prior to solving a process model, e.g. the aggregation of the equations of subordinate process unit models and the specification of input values. The structure of this paper is as follows. Section 2 describes the conceptual architecture of the LptNumerics library and discusses its benefits. Section 3 describes the implementation of the library in terms of actual classes. Section 4 presents applications of the library. Section 5 concludes the paper with a summary and an outlook on future work.

2. Conceptual architecture of the LptNumerics library The conceptual architecture of the LptNumerics library can be described by a layered model as shown in Figure 1. On the Tool Layer we consider equation-oriented process modelling tools such as gPROMS, Aspen Custom Modeler (AspenTech, 2004) or UnitGen (a research prototype from our lab to generate a CAPE-OPEN ESO from a Modelica specification) (Geffers et al., 2001). gPROMS and UnitGen provide their models in terms of the CAPE-OPEN ESO interfaces, whereas the current version of Aspen Custom Modeler does not provide the CAPE-OPEN ESO interfaces to external applications. However, since the equation-oriented approach of Aspen Custom Modeler allows the realisation of the CAPE-OPEN interfaces at least in principle and a future version might actually offer them, it is considered here as an additional example. On the Tool Level it has to be considered that different technologies can be used for the implementation of the CAPE-OPEN interfaces. For example gPROMS and UnitGen use the CORBA distributed object technology. On the other hand, since Aspen Custom

1575 Modeler generally makes use of the COM middleware, we assume that it eventually will provide a CAPE-OPEN ESO via COM interfaces. In the Wrapper Laver the technically different CAPE-OPEN ESO interfaces from the tools are wrapped to one C++ interface, called LptESO. For the integration of gPROMS and UnitGen, this layer contains a CORBA Wrapper that establishes a bridge between the CORBA CAPE-OPEN ESO interfaces and the LptESO interface. For Aspen Custom Modeler a COM wrapper would be required for establishing a bridge between the COM CAPE-OPEN ESO interfaces and the LptESO interface, in the following we refer to classes that realise the LptESO interface as LptESO and classes that realise the CAPEOPEN ESO interface as CAPE-OPEN ESO for short. Based on these wrappers, the modules of the Pre-processing Laver are implemented. These modules realize functionality that might be required for pre-processing of process models before they can be solved. In case that not all derivatives of a CAPE-OPEN ESO are provided, the Perturbation Module provides methods that add missing derivatives through perturbation strategies. When the different process unit models of a process model are realized in different CAPE-OPEN ESOs, the Aggregation Module is used. It provides methods that aggregate several ESOs to a single overall one and allow to enforce identity constraints between variables of different ESOs, e.g. to represent connections between two process unit models. Finally, the SpecilTcation Module is concerned with imposing constraints on individual variables, such as the assignment of model inputs for a steady-state or a dynamic simulation.

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Figm'e l. Conceptual Architecture o/'the LptNumerics Library The modelling engineer controls and designates the pre-processing steps, which are executed from LptNumerics. After that, the fully specified ESO does not reveal any remaining degrees of freedom. It can hence be solved by one of the algebraic equation (AE) solvers or differential-algebraic equation (DAE) solvers of the Solver Laver. The introduction of a wrapper layer between the CAPE-OPEN interfaces of the tools and the pre-processing layer has several advantages. Firstly, it decouples the technically different realizations of the CAPE-OPEN interfaces from the pre-processing layer. Furthermore, in reality different tools realize even semantically slightly different versions of the CAPE-OPEN ESO interface. For example, gPROMS in its current version implements a draft standard of the CAPE-OPEN ESO whereas (Belaud et al.,

1576 2001) implement the final specification of the standard. By implementing the preprocessing layer based on the LptESO interface, adaptations of the tool interfaces and the integration of new tools only affects the corresponding class of the wrapper layer, whereas the pre-processing layer remains unaffected. Another advantage of mapping the COM and CORBA interfaces to a C++ interface is the reduction of the complexity of the pre-processing classes and the improvement of their runtime performance. This is due to the higher complexity of COM and CORBA implementations compared to pure C++ implementations and the overhead of communicating through a middleware compared to in-process communication. Note that all elements of the pre-processing layer implement the LptESO interface and interact with each other only via this interface. Furthermore, this interface is used by the solvers of the solver layer to access models. For this reason, the elements of the preprocessing layer can be combined flexibly as required in a specific application.

3. Implementation of the LptNumerics library Figure 2 gives an overview on the implementation of the LptNumerics library that consists of three parts: the interface classes, the wrapper classes, the pre-processing classes and the solver classes. The interface classes comprise the model interface class LptESO and the solver interface classes LptAESolver and LptDAESolver for AE and DAE solvers, respectively. The interface classes are realized as pure virtual C++ classes. By defining inheritance relations between the interface classes and the processing, wrapper and solver classes it is enforced that these classes realize the corresponding interface. Interface Classes

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Figure 2: Overviewof the LptNumerics implementation (UML) The wrapper classes comprise the classes CQto Lpt ESO and Lptto_CO ESO. The class CQto LptESO accesses a CAPE-OPEN ESO and provides it to the processing classes via the LptESO interface. The class Lptto_CO ESO realizes the CAPE-OPEN ESO interface and allows providing a LptESO as a CAPE-OPEN ESO. It is used for example by UnitGen, which first generates an LptESO and then provides it linked with the wrapper class as a CAPE-OPEN ESO. Both wrapper classes use the CORBA framework, i.e. the class CQto Lpt ESO is implemented as a CORBA client and the class Lpt_to_CO_ESO is implemented as a CORBA server.

1577 The pre-processing classes comprise the classes PerturbationESO, AggregationESO, and SpecificationESO with the functionality of the corresponding modules discussed in Section 2. The class PerturbationESO evaluates missing elements of the Jacobian matrix by means of numerical perturbation and provides an LptESO with a complete Jacobian matrix. The class AggregationESO aggreagtes several LptESO to a single overall LptESO and adds further equations for the identity relations between variables of different LptESOs. Finally, the class SpecificationESO provides a mechanism for assigning variables either to constant values (for AEs) or time dependent functions (for DAEs) and provides an LptESO with additional equations for the assignments. The solver classes serve as wrappers for integrating different numerical solvers into the library. In order to make all solvers accessible through unified interfaces, each solver is integrated by one wrapper class that inherits from the corresponding interface class (i.e. LptAESolver for AE solvers and LptDAESolver for DAE solvers). Furthermore, the wrapper classes access the equation system through the LptESO interface and pass the corresponding numerical information to the solver in the format it requires. Currently, the algebraic equation solvers NLEQls and NLEQ2 (Nowak and Weimann, 1991) and the DAE solver Limex (Deuflhard et al., 1987) are integrated into the library. For this purpose the solver classes N/eqlsWrapper, Nleq2Wrapper and LimexWrapper were implemented. The LptNumerics library is implemented in C++ using the Microsoft Visual C++ compiler. For the implementation of CORBA interfaces the CORBA framework omniORB (omniORB, 2004) is used.

4. Applications Two applications have been realized using LptNumerics. The first one is the program UnitGen, which generates solvable models from a model specification written in the Modelica language. From this model specification, UnitGen generates C++ code that provides the model as an LptESO. In a second step a SpecificationESO is created based on a configuration file that specifies which variables serve as model inputs and assigns their values. Then a solver of the LptNumerics library can be applied to solve the model. Alternatively, the LptESO can be combined with the wrapper class Lpt_to_CO ESO and be exported as a CAPE-OPEN ESO. The second application is CHEOPS (Schopfer et al., 2004), an integration platform for chemical process modelling with models that are provided by different modelling tools. Cheops creates an image from a flowsheet using nearly all LptNumerics classes of Figure 2. Here, the LptNumerics library is used for integrating process unit models provided as CAPE-OPEN ESO as LptESO (using the class CO_to Lpt ESO). For providing the model as a module that calculates the outputs given the inputs (as well referred to as closed-form representation), it is combined with the class Spec!ficationESO, which assigns the process units inputs, and a numerical solver. In case of missing derivatives of the jacobian matrix, the PerturbationESO is added during runtime. Furthermore, on the process model level, the LptESOs from different unit models can be aggregated (by using the class AggregationESO) to a single overall LptESO and solved subsequently.

1578

5. Conclusions In this contribution, we have presented the LptNumerics library that provides functionality which is applicable in different equation-oriented modelling and simulation tools. The functionality supports the integration of CAPE-OPEN ESO, their aggregation to one overall equation system, the specification of variable assignments and the solution of the resulting, square equation system. Wrappers are used to decouple the functionality of the library from the technically (and sometimes semantically) different realisations of the CAPE-OPEN interfaces. These wrappers map the CAPEOPEN interfaces to a C++ interface, the LptESO interface. Based on the LptESO interface, a purely C++ based implementation realizes the pre-processing functionality of the library. The approach of implementing the pre-processing functionality based on a C++ interface instead of using directly the CAPE-OPEN COM or CORBA interfaces considerably reduces the complexity of the implementation and improves its run-time performance. Furthermore, it makes the library implementation independent of the different technologies used to implement the CAPE-OPEN ESO interfaces and makes it more robust towards changes in the interface implementations. In the architecture chosen, such changes only affect the wrapper implementations and new communication technologies (e.g. COM) can be realized simply by adding a new wrapper. The architecture offers the possibility to extend the library with additional software modules at little effort. Currently work focuses on extending the library interfaces and implementation towards optimisation, including providing second order derivatives, as it is required by Newton-type optimisation algorithms. References AspenTech (2004): Product information available online at http://www.aspentech.com/ B. L. Braunschweig, H. Britt, C. C. Pantelides, and S. Sama (2000): Process modelling, the promise of open software architectures. Chemical Engineering Progress, pages 65-76. CO-LaN (2004): CAPE-OPEN Laboratories Network webpage: www.colan.org P. Deuflhard, E. Hairer, and J. Zugck (1987): One-step and extrapolation methods for differentialalgebraic systems. Numerische Mathematik, (51):501-516. W. Geffers, L. yon Wedel, J. Wyes, W. Marquardt (2001): Integration of declarative and executable models in open simulation environments. In K. Panreck and F. D6rrscheidt, editors, 15. Symposium Simulationstechnik, pages 579-586, Paderborn, Germany, 11.9.-14.9.2001, SCS International. Process Systems Enterprise (2002): gPROMS introductory user guide, release 2.1.1, Process Systems Enterprise, London, UK U. Nowak and L. Weimann. A familiy of newton codes for systems of highly nonlinear equations. Technical Report TR-91-10, Konrad-Zuse-Zentrum f't~rInformationstechnik, Berlin, 1991. omniORB (2004): homepage: http://omniorb.sourceforge.net/ J.-R Belaud, K. Alloula, J.-M. Le Lann, X. Joulia (2001): Open software architecture for numerical solvers: design, implementation and validation, ESCAPE 11 Conference, Kolding, Denmark. Available in Computer-Aided Chemical Engineering, 9, Elsevier, Editors R. Gani & S.B. Jorgensen, pp 967-972. G. Schopfer, A. Yang, L. von Wedel, W. Marquardt (2004): CHEOPS: A tool-integration Platform for Chemical Process Modelling and Simulation, International Journal on Software Tools for Technology Transfer Vol. 6, No. 3, 2004, 186-202. L. von Wedel, W. Marquardt, R. Gani (2002): Modelling Frameworks. In: B. Braunschweig, R. Gani (Eds.): Software Architecture and Tools for Computer Aided Process Engineering, Elsevier Science, 89-126.

European Symposiumon ComputerAided Process Engineering- 15 L. Pui~ianerand A. gspufia(Editors) :~<,2005 Elsevier B.V. All rights reserved.

1579

On the Optimal Synthesis of Micro Polymerase Chain Reactor Systems for DNA Analysis Toshko Zhelev, Stokes Research Institute University of Limerick, Ireland

Abstract The paper makes an overview of the problems related to a new and challenging research direction, namely, the application of the process system engineering approach for the efficient design and operation of micro-bio-chips. It intents to analyse some general aspects of process synthesis including trade-offs, important variables, possible optimisation, energy integration, system's layout and important aspects of systems' design and operation. Presented analysis and discussions are focused on specific type of micro-systems represented by the micro-polymerase chain reactor systems (MPCRS) designed for DNA analysis. It attempts to formulate the problems of primary importance faced by process systems engineers in their attempt to assist the design of highly reliable, flexible and controllable MPCRS.

Keywords: micro systems, DNA analysis, systems engineering, integration 1. Introduction Nowadays the goal of chemical engineers may very well be equally reformulated as activities of scaling-up from laboratory to industrial scale or scaling-down from laboratory into micro scale, where the processes are much more intensive and efficient. In many cases, the challenges and difficulties associated with the process of scaling down can be even avoided through application of micro-systems. Because of their complexity, dynamic and sensitive environment of operation, the system approach may best suit simultaneous problems consideration. In this case the process systems engineer's activities are focused again at modelling, simulation, optimal design and operation of highly efficient, reliable, flexible and controllable processes. Our strategy is to step on the already developed micro-unit operations and focus on the practical needs of the system as a whole in terms of design sophistication, resources management and minimisation benefiting from the recent advances in process systems engineering and process integration.

2. Micro PCR system The focus of this study is on a class micro-total chemical analysis systems ( g - T A S ) the micro polymerase chain reaction systems (MPCRS) used for DNA analysis. The polymerase chain reaction (PCR) is an enzyme-catalysed amplification technique, which allows any nucleic acid sequence to be generated in vitro. Since its introduction

1580 in 1983, PCR has been playing central role with applications in DNA analysis, sequencing of human genome, drug discovery, genotyping for rapid medical diagnostics, food production, validation and control, forensic science and medicine, micro-fuel cells design, environmental analysis, molecular biotechnology, pharmaceutical industry, biological weapons detection, etc. The heart of these systems is the polymerase chain reactor, a bio-chemical catalytic reactor for nucleic acid amplification and replication of certain part of the DNA molecule. PCR is a temperature controlled process conducted by cycling a reaction mix through three-temperature step, typically: denaturation at 94 °, annealing at 50-60 ° and elongation at 72 °. A typical PCR reaction thus goes through 20-40 cycles. What is the motivation to miniaturize the PCR system? (a) Low design cost (small footprints, compact design); (b) Low running cost (reduced reagent consumption); (c) Reduced waste production; (d) High speed analyses (ultimately more rapid thermal cycling), parallel architectures, high throughput; (e) Low contamination risk.

3. Micro-Devices' Specifics Since transport phenomena are scale-dependent, micro reactors, as a new type of unit operations, have some unique characteristics. Heat transfer coefficients exceed those of conventional heat exchangers by an order of magnitude. This leads to re-evaluation of neglected terms. The heat transfer in the longitudinal direction cannot be neglected because the ratio of wall volume to channel volume is large enough. The increased surface to volume ratio in micro reactors has implications for surface-catalysed reactions. Scaling down theory led to the conclusion that g-TAS are mainly diffusioncontrolled systems (molecular diffusion, heat diffusion or flow characteristics control the process efficiency).

3.1 Scale Fundamental scaling issue is the so called Cube-Square Law. It simply reflects the fact that volumes scale with the cube of the typical length scale, while areas scale with the square of the length scale. Thus, as a device shrinks, surface phenomena become relatively more important than volumetric phenomena. The most important consequence of this is the observation, that the device mass (and inertia) becomes negligibly small at the micro-scales. Regarding the miniaturization, the arising question is should all components be sub-millimetre scale? Some authors pledge that the perception of shrinking everything down to small scale is misleading for micro reactors. The question is if this is valid for g-TAS systems?

3.2 Pumping In g-TAS reactors fluids flow through a network of micro-channels without turbulence. Main differences in flow conditions depend on pumping strategy that formulates a pressure-driven or shear driven flow with the usual assumption of a slip-velocity condition. The time in this case is regarded as a surface and is proportional to the square of the typical length (tube diameter, or other). The liquid velocity in the case of electroosmotic flow (EOF) is constant across the channel except for the diffuse layer very close to the wall. Unlike EOF, pressure driven flow produces a parabolic velocity profile with high velocities in the channel centre and slow velocities near the wall. The

1581 EOF velocity is independent of the channel cross section dimension; whereas the volumetric flowrate does depend on channel dimensions. A mixture of EOF and pressure driven flows can be practical.

3.3 Mixing The fluids can only mix by diffusion. Micro-mixers can reduce mixing time to milli- or nano-seconds. For the usual flow velocities in the range of 0.1-1.0 mm/s and Reynolds numbers <10 the mixing of two fluids at a T-junction occurs by inter-diffusion because both fluids retain their laminar flow patterns in the joint flow. If for instance the channel width is of 100 btm and diffusion coefficient of 0.5 m2/s, the time for mixing of two streams at 1 mm/s will be 100 s, i.e. quite unsatisfactory long time. The more efficient way of mixing is through the "flow-inject-flow", where a slug of one fluid is produced within a flowing stream of a second fluid.

4. Design Implications The design, i.e. the architecture, is perhaps the most important feature of a microchip as it defines the t'unction and sequence of processes taking place in the device. Miniaturisation of the PCR system provides significantly improved thermal energy transfer than provided by macro-scale systems, thus enabling an increased speed of thermal cycling. The design implications in the micro-scale are quite different compare to the macro scale. For instance, the reserves (over-design, design margins) accounting for possible deviations from the nominal operation condition, can not be used as flexibility compensation in the case of micro reactors, because any over-sizing can substantially affect the function of the device. As stated by Hasebe (2003), the shape factor plays much bigger role in the design of micro devices compare to conventional unit operations. Terms such as perfect mixing, overall heat transfer coefficient, plugflow, steady state, etc. are usual assumption and their values do not depend on the location in the device. The shape of the device has large degree of freedom and needs to be constrained. New types constraints are to be introduced such as average residence time; residence time distribution and temperature distribution have to be included in the design problem. If shorter residence time in connection device is desirable the system structure is to be amended. It is difficult to measure and control the flow conditions in the micro device, so an invariant to changes of the physical properties design should be suggested.

5. Modelling and Simulation The major difficulties in modelling p-TAS systems are in solving the three-dimensional, time dependent Navier-Stokes equations in complex geometric domain. Thus, efficient flow solvers are critical to the success of the integrated microfluidic device simulators. One example of such integration is the experience in combination of SPACE simulator, realizing time-domain transient analysis and Ne~c~o~r- a general purpose CFD. In many cases the FLUENT code, based on control volume method, was used to solve conservation equations of mass, momentum and energy, but it does not consider the polymerisation changes of DNA amplification process, characteristic for the systems in question. An attempt to develop this missing part was reported recently by Viljoen (2004).

1582 It has to be realized that the anticipated benefit of micro devices development will come from new designs yet unknown; therefore micro devices simulation based on fullphysical models may still (but not for long) be more appropriate for exploring new concepts.

6. Process Systems Engineering Impact PCR system consists of large number unit operations synchronized in particular order. There are filters, mixers, micro pumps, valves, reactor, separators, heaters, coolers, sensors, electrophoresis unit, pipes (channels), etc. Concerns are related to raw materials, products, wastes and utilities management, problems related to detection/measurement, controllability, flexibility, robustness, energy conservation, contamination elimination, etc. The type of micro-unit operation can substantially affect the optimal system structure. The time allowable to transfer material to the next device has to be considered. The objective functions in process optimisation has to be reconsidered (throughput and time are the most important once). Stepping on the Stokes Research Institute's (http://www.stokes.ie) experience in microfluidics hydrodynamics, thermal analysis, measurements in micro-channels, microsensors, and the current intensive research in development of main components of micro-bio-chips such as mixers, centrifuges, reactors, detection units and heaters/coolers, our focus is on flexible system design, intelligent control and resources management. Walsh & Davies (2004), conclude that one major problem of the design of a PCR system is the cross contamination. The optimisation criterion targeting increased PCR efficiency is according to Mohamed Gad-el-Hak (1999), the cycle time minimisation, leading further to ramp-rate optimisation. This consequently leads to minimisation of sample fluid volumes (in order to minimise the lumped heat capacity and transition times between temperature zones allowing for controllable residency times in each of the stages of the cycle and user controlled temperatures in each of the zones of the device as suggested by Walsh and Davies (2004)). The new design presented by same authors target handling of large groups of samples and is an alternative to the parallel processing. It tackles many samples in small time intervals.

7. Integration Much options remains to be explored so that rational tools can be developed for the design and efficient operation of ~t-TAS, witnesing an explosive growth during the last decade. •

Micro-electro-mechano-chemical integration

Recently micro-electro-mechanical systems (MEMS) have been upgraded into microelectro-mechano-chemical systems challenging a new generation of interactions between with chemical or bio-chemical processes. The impact of such a kind of microprocess-systems-engineering approach would facilitate the identification of interesting micro-systems phenomena, specific properties and design guidelines. The new paradigm for process-systems on chip (PSoC) has analogy with the Systems on chip (SoC) announced by Benini (2003). It brings the problems of micro-network synthesis and micro-network integration and resources management onto the domain of optimal design and optimal operation.

1583 • Architecture of micro-system (structure, topology) As it can be expected, the architecture of micro-system plays substantial role in total efficiency consideration. The production rate can be increased by increasing the number of micro-units operating in parallel. The structure varies from aggregated micro devices, through a combination of conventional and micro devices, to a hybrid system. The production rate can be changed by changing the number of parallel reactor units. • "Horizontal" and "vertical" integration The development of systems featuring '~horizontal" integration by building parallel lanes for high throughput applications, and "vertical" integration by implementing several functions on a single device is the most exciting trend in the microchip world. Often the maior push of the integration is towards portability and decreased reliance on external infrastructure. Benini & Micheli (2003), introduce the network-on-chip paradigm for the system on chip design. Their prediction is promoting design methodology to support plug-and-play fashion, reliable operation of interacting components, minimum energy consumption forming micro-network of components and micro-network adapting the protocol stack principle. In other cases the integration concept is related to the number of components in a system. Nguyen (2002) refers to the density of components, concluding that the degree of integration in micro devices fbllows Moore's law, doubling integration density every 18 months. This growth currently is limited by the photolithography technology, slowing the forecast to doubling integration density every 24 months. 7.1 Control issues Different from the conventional plants, in the case of micro-systems it is almost impossible to add new measurement devices after construction. Thus, the ~a-TAS system and the instrumentation and control systems must be designed simultaneously. 7.2 Heat integration As reported by Punch et al (2003), the Biot number (the ratio of conductive to convective thermal resistance) is a key parameter in the thermal analysis of micro-PCR device. It was found that the velocities changes within 0.1 - 1.0 mm/s have little effect on the temperature profile along the micro-channels. The design options for controlling the cycle-number (CN) and the temperature in three zones of the micro-device are as follows: (a) Solid resistors fixed under the meanders of channels - classical PCR cycler. The obvious sequence of heating/cooling zones assists the efficient energy management. The flow after being heated to 93°C passes without meanders trough 72 degree zone, assisting the beginning of cooling and is further cooled in the meanders of the 58 degree zone. Next, passing quickly through the 72 degree zone the sample is preheated helping to reach required temperature in the tbllowing 93 degree zone, and so on. The length of the channel in each zone/the wide of the heater, the volumetric flowrate/pumping abilities and the minimum size of the channel are in strong relation, where the pressure drop and contamination in parallel with the rigid control options are of major concerns. Temperature and CN control is possible through the number of heating sections or the meanders; (b) Rotational device of Walsh & Davies (2004) arranges the droplets of sample fluid to float in a carrier immiscible fluid to prevent contamination. A third fluid comes in direct contact with the carrier fluid fulfilling two functions - pumping and

1584 heating/cooling and leaving the channel in particular point. The control is much more flexible and easy. The optimal energy management structure can be found using the Pinch concept. Our experience shows a typical threshold problem case where ATtain < ATthre, hold holds corresponding to non-constrained case. In collaboration with Professor Olaf Strelow, University of Giessen, Germany we developed deterministic methodology and a program code for heat integration of portable two and three-fluid PCR systems (to be reported During the HEFAT conference, Egypt, September 2005). More complex integration problems arise when the system design envisages parallel reactor layers for throughput maximisation and flowshop of DNA analysis, and where the temperature, ramp rate and cycle numbers are different for each layer.

7.3 Synthesis task An important design optimisation tasks would be: For given process specifications such as number of cycles and temperature ranges, find the best values of design variables and structure of a system that can lead to quickest DNA amplification. Currently the fluidic PCR process is considered as a continuous process, though one should not forget that the time parameter plays a central role. Considering our experience in batch process systems engineering, we found quite similar design tasks that were subject of number of successful approaches commonly formulated as MINLP problems. The immediate design tasks are: (a) Build a mathematical model of MPCRS and perform sensitivity analysis through computer simulation; (b) Design a micro-bio-chip for a wide (but prescribed) range of DNA analysis characterized by high throughput and minimum time. 8. C o n c l u s i o n s It is clear that combination of expertise in areas such as process systems engineering and micro-bio-chips can lead to interesting amalgamation and confident ability to face the challenge of solving micro-systems engineering problems. Grossman & Westerberg (2000) analysing the future challenges of process systems engineering profession, note that increased attention at the synthesis and design of micro systems may give a rise to design problems that have not received much attention in the past. In line with this prediction we initiated corresponding activities and the results are to be reported soon.

References Benini, L., G.De-Micheli, 2003, Networks on Chip: A New Paradigm for Systems on Chips Design, http://akebono.stanford.edu/users/nanni/research/net/papers/dateO2.pdf. Gad-el-Hak, M., 1999, The Fluid Mechanics of Microdevices, J.Fluid Engng., 121, 5. Grossman, I. & A.Westerberg, 2000, Research Challenges in PSE, AIChE J., 46, 1700. Hasebe, S., 2003, Process Systems Engineering 2003, Elsevier Science, 89. Nguyen, N-T., 2002,Fundamentals & Application of Microfluidics, Artech House. Punch, J., B.Rogers, D.Newport & M.Davies, 2003, IMECE-41884, Washington, 1. Viljoen, H., Principles of PCR: Mathematical modelling, ChlSA, Prague, 2004, 1403. Walsh, P. and M. Davies, 2004, 7 th Annual Sir Bernard Crossland Symposium, 1. Acknowledgements The author acknowledges the valuable help in reviewing the literature by Mr Yi Liu and the ideas and advices given by Professor Reginald Mann- University of Manchester.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) ~/)2005 Elsevier B.V. All rights reserved.

1585

An Agent-oriented Approach to Integrated Process Operations in Chemical Plants Magid N ikraz and Parisa A. Bahri* School of Engineering Science and A. J. Parker Centre for Hydrometallurgy Murdoch University, Dixon Road, Rockingham WA 6168, Australia

Abstract Integration of process operations involves the coordinated management of operational tasks in a process plant. In the context of chemical process plants, these tasks can be categorised as data acquisition, regulatory control, data reconciliation, process monitoring, fault diagnosis, supervisory control, scheduling and planning. While each of these tasks is responsible for a particular function, they are also dependent on each other and thus cannot be treated in isolation- this is why integration is necessary. The focus will be on the use of agent-oriented techniques to achieve integration. Limitations of previous integration techniques in the context of chemical plants will be outlined and this will elicit the need for a more powerful software engineering paradigm utilising software agents. The main barriers to achieving integration will then be discussed and how an agent-oriented approach represents a logical solution to these problems. Finally, a pilot plant application of the proposed technique will be presented.

Keywords: integration, agent, chemical process plant

1. Introduction Agent-oriented software engineering techniques present a possible solution to the problem of integration of process operations. The tasks which come under process operations in the case of chemical plants can be loosely classified as data acquisition, regulatory control, process monitoring, data reconciliation, fault diagnosis, supervisory control, scheduling and planning. Integration in this context refers to the process of bringing these separate tasks together under a coordinated framework (Venkatasubralnanian, 1994). Though integration is highly desirable, its achievement is made more difficult by the complexity of today's chemical process plants and the different approaches to each of the tasks. Agent-oriented techniques are suited to the problem of integration primarily because they provide a unitbrm means of communication between the modules representing the individual operational tasks. Furthermore, agents can encapsulate legacy systems written at different times and bring them into the integrated framework. The focus of this study is on the software aspects of integration and the relationship between the individual tasks. A brief review is presented of previous integration

Author to whom correspondence should be addressed: [email protected]

1586 techniques and their limitations. Then, some barriers to achieving integration are outlined and the role of agent-oriented techniques in providing a solution is discussed. Finally, a pilot plant application of the proposed technique is presented.

2. Review of Previous Integration Techniques The • • • •

major works in the area of integration of process operations can be classified as: Functional hierarchy (Sardis, 1983) Blackboard architecture (Fjellheim et. al., 1994) A framework for integrated process supervision (Rengaswamy, 1995) Coordinated Knowledge Management Method (Power, 2004)

2.1 Functional hierarchy The idea is based on the hierarchy shown in Figure 1. There are three levels: execution level, coordination level and organisation level. The low levels require more precision and less intelligence, while for higher levels, this requirement is reversed. Layers are added on top of each other one by one, with each layer being tested and accepted before another more complex layer is introduced on top of it. The new layer then acts on the lower layer, which modifies the status of the objects associated with them. A very rigidly structured organisation with many levels functions best when environmental conditions are relatively stable. Unstable environmental conditions, which are prevalent in the chemical processing industry, require a flexible organisation that can adapt quickly; hence, a rigid structure is no longer considered appropriate. 2.2 Blackboard architecture The idea involves a group of generic problem solvers or experts which look at the same blackboard recording individual states of the ongoing problem solving process. Each expert takes appropriate actions based on the information presented on the blackboard. A key feature of this structure is that the problem solving states are made available in the form of global data structures, while maintaining the isolation of each of the modules. The blackboard model consists of three major components: 1. knowledge sources, which are independent but complementary subsets of the knowledge about the process; 2. blackboard data structure, where all the knowledge sources have exclusive access for retrieval and storage modification of information; 3. control mechanism, which consists of the knowledge sources responding to the changes of the blackboard.

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Figure 1. Functional hierarchy applied to chemical processing plants

1587 The blackboard model only outlines the organisation principle and does not specify how the system is to be realised as a computational entity. Application of the blackboard framework often requires extensions to the framework. Also, when applying the blackboard framework, one must address the problem of maintaining data consistency in the blackboard by controlling asynchronous references to shared data. 2.3 A framework for integrated process supervision This framework, shown in Figure 2, attempts to integrate the lower and mid-level process operational tasks for continuous operations.

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Fig-m'e 2. Frame+workfor integrated process SulaervMon The framework is useful for considering the information flow, however, no mention is made as to how coordination of tasks is achieved in the references cited nor if the information has been applied. 2.4 Coordinated Knowledge Management Method This method, shown in Figure 3, allows tasks to commtinicate directly with the coordination mechanism dispensing with the requirement of an external control mechanism. Hierarchy is present but it is not as rigidly structured as in the functional hierarchy. As in the case of the blackboard framework, tasks represent knowledge sources and act autonomously. However, the blackboard is no longer present; instead, a Petri-net is used to: 1. coordinate tasks, 2. monitor the system, 3. activate the knowledge sources (tasks), 4. request data to be updated in the data structures and 5. receive notice when the task is completed. Visualisation of the state of the system is achieved through the moving tokens in the Petri-net. Each individual module contains information (including rules+ procedures, Petri-nets, optimisation and neural networks), which enables each module to operate autonomously.

1588 Modules Planning & Scheduling

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Module interaction, organised through the structure of the hierarchical timed place Petri net (low-level net), is adequate for a small plant. However, as plant size increases, not only are there module interactions, but also plant section interactions; so, the integration Petri-nets must be extended to coordinate both module and section interaction. This extension will mean that the Petri-net model will become very complex and difficult to manage.

3. An Agent-oriented Solution The paradigm of agent-oriented programming was introduced by Shoham in 1993 as a specialisation of object-oriented programming (Shoham, 1993). The meaning of the term agent is fuzzy and a subject of ongoing debate. However, one popular characterisation is (Jennings and Bussmann, 2003): "an agent is an encapsulated computer system that is situated in some environment and is capable o f flexible, autonomous action in that environment in order to meet its design objectives" In addition, most problems require or involve multiple agents which interact with each other in a common environment; such an environment is referred to as a multi-agent system. For an introduction to agent-oriented software engineering, the reader is referred to Wooldridge (2002). A major problem when attempting to integrate a system is heterogeneity. This refers to the fact that some software may be pre-existing. Furthermore, the pre-existing (nonagent) software may incorporate different solution techniques for different tasks, each of which may have been developed at a different time by different people. One of the benefits of using agents is that it permits the use of pre-existing software through encapsulation using a wrapping mechanism. The wrapping software looks like another agent from the outside, while serving as an interface to the legacy components at the same time. As pointed out by Jennings and Bussmann (2003): "this ability to wrap legacy systems means that agents may initially be used as an integration technology" Furthermore, this capability permits a more flexible system structure and ultimately results in time and cost savings since new software is not required to be developed. Flexibility is a major advantage of the agent oriented approach which is lacking in the previous techniques presented in Section 2.

1589 Another requirement for integrating systems is that the software components must be able to interoperate with each other by exchanging information and services. An agentoriented solution permits communication between the software components using a universal communication language. The framework shown in Figure 3 highlights the vital need for communication between the individual software components. Some may argue that objects also have means of communication through message passing. This is true, but the advantage of an agent-oriented approach is the use of a common language with agent-independent semantics (Genesereth and Ketchpel, 1994). There are also several other important differences between agents and objects, which have been indicated in the literature (Jennings and Bussmann, 2003). The notion of permitting heterogeneity in the system and a universal communication language for information exchange make an agent-oriented approach effective from the perspective of integration. Furthermore, this approach also addresses the shortcomings of previous techniques discussed in Section 2 by permitting flexibility and an effective means of information exchange for all components.

4. Pilot Plant Application The pilot plant representing the Bayer Process at Murdoch University is being used as a base for testing the agent-oriented approach to integration. The necessary modules representing the tasks have been developed: data reconciliation, process monitoring, fault detection and diagnosis and supervisory control. Some modules are pre-existing (via Honeywell SCAN 3000): data acquisition and regulatory control. Furthermore, the scheduling and planning have not been implemented because they are application specific and implemented over a timescale of months or years. The proposed model for integration is shown in Figure 4. The system consists of a group of pre-existing and custom-built heterogeneous agents. The agents communicate via an agent communication language (ACL) standardised by FIPA (FIPA, 2004). The use of the wrapper agent can be observed, which serves as an interface between the preexisting modules and the other agents. The agents are situated over several pilot plant computers. The user agent acts as a means of integrated information exchange between the system and the user. ('ontrol room c ()mlmlCr(s) . . . . . . . . . . . . . . . .Scan . . . . . . .3000 ............. Pilot

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1590 Each of the modules in Figure 4 has a known function. Based on this, the dependencies between the modules can be defined through a brainstorming session. The dependencies are transformed into cooperative actions or interactions between the agents. Once the interactions between the agents are known, a suitable interaction protocol for each interaction, possibly one defined by FIFA is selected depending on the nature of interaction between the agents. For example, if the fault detection and diagnosis agent needs to know whether the pilot plant is at steady-state, it will need to interact with the monitoring agent which is responsible for determining whether the plant is at steadystate. The fault detection and diagnosis can communicate with the monitoring agent using a FIPA-Query interaction protocol, which returns a True of False value depending on whether the plant is at steady state. It must be noted that the only means of agents communicating is via ACL and an agents methods can not be accessed directly by other agents contrary to objects where this requirement does not exist. Once the interactions and the interaction protocols have been defined and ontology formed, the system can be implemented using a FIPA compliant agent framework such as the Java Agent Development Framework (Bellifemine et. al., 2001).

5. C o n c l u s i o n s The need for an integrated framework for coordination of tasks in a processing plant stems from the growing complexity of current systems, as well as from the traditional expense, time constraints and limited availability of human expertise. In light of the many benefits, very little attention has been devoted to finding a solution to the problem of integration with respect to chemical processing plants. As a result, many plants today operate without realising the benefits of integration via software inter-communication. It has been suggested that an agent-oriented solution presents an effective approach to solving this problem by providing a powerful mindset to the engineer and allowing the system to expand relatively easily and in a modular fashion.

References Bellifemine, F., A. Poggi and G. Rimassa, 2001, JADE: a FIPA2000 compliant agent development environment, Agents 2001, 216-217. FIPA, 2004, Foundation for Intelligent Physical Agents, http://www.fipa.org. Fjellheim, R.A., T.B. Pettersen, B. Christoffersen and A. Nicholls, 1994, Application Methodology for REAKT Systems, proceedings of the IFAC Artificial Intelligence in Real Time Control, Valencia, Spain, 325 - 332. Genesereth, M.R. and S.P. Ketchpel, 1994, Software Agents, Comm. of the ACM, 37(7), 48 - 53. Jennings, N.R. and S. Bussmann, 2003, Agent Based Control Systems, IEEE Control Systems Magazine, 23(3), 61 - 64. Power, Y., 2004, The Development of an Integrated Process Operation Management System, Doctor of Philosophy Thesis, Murdoch University. Rengaswamy, R., 1995, A Framework for Integrated Process Monitoring, Diagnosis and Supervisory Control, Doctor of Philosophy Thesis, Purdue University. Sardis, G.N., 1983, Intelligent Robotic Control, IEEE Trans. on Auto. Control, 28, 547 - 557. Shoham, Y., 1993, Agent-oriented programming, Artificial Intelligence, 60(1), 51-92. Venkatasubramanian, V., 1994, Towards Integrated Process Supervision: Current Status and Future Directions, proceedings of the IFAC Computer Software Structures Integrating AI/KBS Systems in Process Control, Lund, Sweden, 1 - 13. Wooldridge, M., 2002, An Introduction to Multiagent systems, John Wiley and SonsLtd.

European Symposiumoil ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) :~i,2005 Elsevier B.V. All rights reserved.

1591

Entire Supply Chain Optimization in Terms of Hybrid in Approach Takeshi Wada a, Yoshiaki Shimizu a and Jae-Kyu Y o o a aProduction Systems Engineering, Toyohashi University of Technology 1-1 Hibarigaoka,Tenpaku-cho, Toyohashi, Aichi 441-8580 Japan

Abstract As an essential part of decision-making in recent business processes, this study has called attention on entire network associated with supply-chain management. To optimize such large-scale and complex systems, we proposed a hybrid method compose of meta-heuristic method and mathematical programming after decomposing the problem into two sub-problems in a hierarchical manner. Then we provide a unique method to adjust and unify each result of sub-problems solved individually. Through numerical experiments, we verified the performance of the proposed method.

Keywords: supply chain optimization, hybrid method, multi-level model, capacitated hub problem, meta-heuristics 1. Introduction Recently, industries have been paying keen interests on supply chain management (SCM) that might be viewed as a re-engineering method managing life cycle activities of business process. It tries to deliver value-added products and services to customers in just-in-time and agile manners. As an essential part of SCM, many researchers have engaged in logistic optimisation known as p-hub center problem, p-median problem, etc. from a variety of approaches (for examples, Campbell, 1994; O'Kelly and Miller, 1994; Drezner & Hamacher, 2002; Ebery et al., 2000; Lee et al., 200l) as well as classical location problems (Shimizu, 1999). Taking a p-median problem of distribution center (DC) problems in SCM, we also developed previously a method to optimize the total transport cost with respect to location of DCs and route from plants to customers via DCs (Shimizu & Wada, 2004). However, since none of those have called attention on the entire system composed both of the DC problem and collection center (CC) problem, we can concern with decisionmaking on economical partnership in SCM more relevantly by optimising the entire system. To deal with such large-scale and complex problems practically, in this study, we decompose the problem into two sub-problems in a hierarchical manner, and apply a hybrid method employing meta-heuristic method and mathematical programming. Through numerical experiments, we will examine validity of the proposed method.

2. Problem Statement Taking a supply chain network (SCN) composed of suppliers, CCs, plants, DCs, and customers as shown in Figure 1, we have formulated the problem under the conditions

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that capacity of facility is constrained, and demand, supply and per unit transport cost are given a priori. Moreover, multiple and single-stage routing is allowed for CC problem while single and two-stage routing for DC problem. After all, it refers to a non-linear integer programming deciding simultaneously the location of hub centers and routes to meet the demands of all SCN members while minimizing total cost.

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r,s,t • {0,1}, x,y • {0,1},u,v •Real number

where binary variables xi and yi take 1 if each center i is open, and ro., so., t o. become 1 if there exist routes between customer i and DC j, DC i and DC j, and DC i and plant j, respectively, and 0 otherwise in all cases. On the other hand, u o. and v o. denote shipping

1593 amounts from C C j to plant i and from supplier j to CC i respectively. Moreover, D: is demand of customer i, and P:, Qi, S: and T; represent capacities of DC, plant, CC, and supplier, respectively. On the other hand, terms from 1st through 5th of the objective function denote transport costs, and the 6th and 7th terms fixed charge costs of DC and CC respectively. Moreover, each constraint means such that : Eqs.(1), (3), and (5) require each customer, DC and plant must select only one location respectively in the downstream network; Eqs.(2), (4), (6), (8), and (10) stand for the capacity constraints on the 1st and the 2nd stage DCs, plant, CC, and supplier respectively; Eqs.(7) and (9) represent balances between input and output of plant and CC respectively. Owing to the product terms among the binary variables in objective function and Eqs.(4), (6) and (7), this refers to a mixed integer non-linear programming problem (MINLP).

3. Hierarchical Procedure for Solution 3.1 Decomposition into sub-models Since solution of MINLP belongs to a NP hard class, developing a practical solution method is more desirable than aiming at rigid optimality. With this point of view, we decompose the original SCN into two sub-networks originating from the plants, i.e., upstream chain, and downstream chain. The former solves a problem how to supply raw materials from suppliers to plants via CCs while the later how to distribute the products from plants to customers via DCs. Then, to obtain a consequent result of the entire supply chain from each solved individually, we have given an effective way to combine them consistently by adjusting a coupling constraint. That is, instead of using Eq.(7) directly as the coupling constraint, we transfonn it into a suitable condition for operating auction mechanism based on an imaginary cost that makes trade off gains between the sub-networks. For this purpose, let us assume first that the optimal cost associated with the procurement in the upstream chain is C'proc* , i.e. (1 1)

Z Z C4 k:u~' + Z Z C5:,, v:,,, + Z F2: v: = C ,:,.,,, k~K

IcL

l~L

m~.~/

IEL

Then, dividing Cpro,* into each plant according to the amount of production, i.e., Cp~o~* = Y~k V~, we can view V~ as a certain shipping cost from each plant. Now, writing such unit procurement cost by p:, we obtain the equation like

Using this as a coupling condition instead of Eq.(7), we can decompose the entire model into each sub-model as follows. Downstream network model

Y,Y(Y

Min i~l

jE.I

~.

j'.~.

1

i~

subject to Eqs.(1)--(6) and Eq.(12)

• Y Y(Y(V "~,

~

" . ~,

) /c.]

1594 Upstream network model subject to Eqs.(8) --(10) and Eq.(13) k ~ K IEL

Rk =

u k, =

l~L m E M

l~L

D;d sij. t j.k

Vk • K

(13)

where asterisks means the optimal value for the downstream problem. 3.2 Coordination between sub-models

It is apparent that as long as the optimal values of the coupling quantities, i. e., V~and Rk are known a priori, we can derive the consistent solution straightforwardly by solving each sub-problem individually. However, since this is not true presently, we need to take an adjusting process as follows. (1) For the tentative Vk(initially not set forth), solve the downstream problem. (2) After calculating Rk based on the above result, solve the upstream problem. (3) Re-evaluate Vkbased on the above upstream optimization. (4) Repeat until no more change of Vkhas been observed. Increasing quality of information on Vk and/or Rk along with iteration may guarantee qualitatively the convergence of such coordination. In addition, we can rewrite the objective function of the downstream problem by relaxing the coupling constraint in terms of Lagrange multiplier as follows.

~DiCj~J ~' /i'J+j~Jj~.~JI~Di)'/i~,

C2~j,sj~.+~Y,~xj-~.kVk+~[j~jk~(~Di,i/j~j J'~J

Si/.l(C3j.k+.~kp~,)rj.j ' (14)

Then we notice the last term implies that re-costing the transport cost C3jk will conveniently play this role of coordination. In practice, we can perform it as C3 jk "-C3 j~ +Constant × p . After all, so far statements claim the coordination will be viewed as an auction on the transportation cost so that the procurement becomes most suitable for the entire chain. 3.3 Procedure for coordinated solution

To reduce load of computation, we break down each sub-problem further into two levels, i.e., the upper level problem for locating and the lower for routing. Taking such hierarchical approach, we have the following advantages. 1. In the upper level problem, we can shrink searching space dramatically by confining the search just to the location. 2. We can transform the lower level problem into what is solvable very effectively by using an appropriate mathematical programming. As a drawback, we need to solve repeatedly one of the two subject to the foregoing result of the other in turn. However, the previous study revealed computational load of such adjustment was moderate and effective. Consequently, we solve the downstream problem simply following the previous method that applies a meta-heuristic method like complete local search with memory (CLM; Ghosh & Sierksma, 2002) for the upper level and a mathematical programming like Dijkstra method for the lower. In contrast, we have developed newly a similar hybrid method that is peculiar to the upstream problem where we use linear programming (LP) to solve the lower level problem. Eventually, the proposed approach is summarized as follows.

1595 Step 1. Set all parameters at their initial values. Step 2. Under the prescribed parameters, solve the downstream problem using the hybrid meta-heuristic method. • Provide the initial location of DCs. • Decide the routes covering the plants, DCs, and customers by the revised Dijkstra method. • Revise the DCs' location repeatedly until the convergence of CLM search will be attained. Step 3. Compute the necessary amount at the plant based on the above result. Step 4. Solve the upstream problem using another hybrid meta-heuristic method. • Provide the initial location of CCs. • Decide the routes covering the suppliers, CCs and plants by LP. • Revise the CCs location according to CLM search. Step 5. Check the convergence criterion. If it is satisfied, stop. Step 6. Re-cost the transport costs between plants and DCs, and go back to Step 2.

4. Numerical Experiments We evaluated the performance of the proposed method by solving a variety of benchmark problems whose features are summarized in Table 1. They are produced by generating the nodes whose appearance rates become approximately 3:4:1:6:8 among suppliers, CCs plants, DCs, and customers. Then distributing them randomly over the grid point drawn on the plain, we give the value related to Euclid distance between each node as the transport cost per unit demand. On the other hand, demand and capacity are given randomly between certain intervals. The results summarized in Table 2 reveal that the proposed method can improve the initial feasible solution and expansion of computation load is considerably slow along with the increase in problem size. On the other hand, due to the complicated non-linear structure not reconfigurable by CPLEX, it could not solve the present model. (We showed outstanding advantage of our hybrid approach over CPLEX for the downstream problems (Shimizu & Wada, 2004). However, due to our unsophisticated implementation of LP, we cannot always outperform it for the upstream problems.) In Figure 2, we present the convergence features including those of downstream and 250000

optimal

200000

150000 e0

o (D

. . . . . . -.5.. • ............................................................................................... 100000

50000 Entire Distribution Procurement 0

5

10

15

........... 20

Iteration [ - ]

Figure 2. Convergence.feature along iteration. (FI-1 O)

1596 upstream problems. There, we observe that the proposed coordination method works adequately to reduce the total cost by making the gain at the procurement chain overwhelm the loss at the distribution chain, and only small number of iterations is required by convergence (See also Table 2). Moreover, relying on the good performance of the hybrid method compared with CPLEX for each decomposed subproblem, we can claim the converged solution might attain almost at the global optimum by virtue of the generic nature of meta-heuristic algorithm employed presently. Table 1. Feature of bench-mark problems.

Data set ID F1-04 F1-06 F1-08 FI-10

Customer 32 48 64 80

Table 2.

Data set ID

DC 24 36 48 60

Number of Plant 4 6 8 10

CC 16 24 32 40

Supplier 12 18 24 30

Number of {(binary, real), constraint} {(1480, 256), 180} {(3300, 576), 270} {(5840, 1024), 360} {(9100, 1600), 450}

Results of benchmark problems.

Objective value Initial Converged

Improved rate [%]

F 1-04 129031.8 127555.4 1.1 F 1-06 175894.5 167199.7 5.2 F 1-08 192049.0 186287.5 3.1 F 1-10 241648.4 236349.8 2.2 PC={CPU:Athlon 1.0 GHz, Memory:256MB}

Computation time [ s e c ] 98 859 3680 6842

Number of coordination 3 5 12 18

5. Conclusion This study has extended the foregoing distribution problem to the entire supply chain environment while expecting the advantage brought about by expanding the system boundary. To realize a practical resolution method, we have given an idea that tries to decompose first the entire supply chain into the sub-chains, and then combines consistently each result solved individually. Applying two kinds of hybrid methods of meta-heuristic and mathematical programming, we have given an effective algorithm depending on the peculiar feature of each sub-problem and examined its effectiveness through numerical experiments. References Campbell, J. F., 1994, Studies in Locational Analysis, 6, 31. Drezner, Z. & H. W. Hamacher, 2002, Facility Location: applications and theory, Springer, Berlin. Ebery, J., M. Krishnamoorth, A. Ernst & N. Boland, 2000, Europ. J. of Oper. Res., 120, 614. Ghosh, D. & G. Sierksma, 2002, J. of Heuristics, 8, 6, 571. Lee, H., Y. Shi, S. M. Nazem, S. Y. Kang, T. H. Park, & M. H. Sohn, 2001, Europ. J. of Oper. Res., 133,483. O'Kelly, M. E. & H. J. Miller, 1994, J. Transport Geography, 21, 31. Shimizu, Y., 1999, J. of Chem. Engng. Japan, 32, 51. Shimizu, Y. & T. Wada, 2004, Hybrid Tabu Search Approach for Hierarchical Logistics Optimization, Trans. ISCIE, 17, 6, 241 (In Japanese).

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1597

A Computer Architecture to Support the Operation of Virtual Organisations for the Chemical Development Lifecycle Adrian Conlin a, Philip English b, Hugo Hiden a+, Julian Morris b, Rob Smith ~ and Allen Wright b ~Department of Computing Science bDepartment of Chemical Engineering and Advanced Materials University of Newcastle upon Tyne United Kingdom, NE1 7RU

Abstract Fine chemical and pharmaceutical manufacturers focus on new product development as a means of growth, with time to market as a key driver. Time to market improvements are, however, limited by a company's infrastructure; for example, in-house design and manufacturing capacity, ability to respond to a dynamic environment etc. In many marketplaces, there is an increasing trend towards outsourcing and operating networks of specialist providers. Different specialist companies may be involved at all stages in the R&D lifecycle, providing services ranging from basic research or safety testing, to industrial scale manufacturing. This outsourcing concept can be generalised to support advanced notions of collaboration such as loosely-coupled but highly integrated networks of companies cooperating as a single enterprise. These networks can be described as dynamic Virtual Organisations (VOs) (Demchenko, 2004). This paper will outline a computer based architecture developed to address the operational difficulties associated with the creation and operation of this type of VO and present it within the context of the chemical development lifecycle.

Keywords: Virtual Organisations, Chemical Development, Lifecycle Management

1. Introduction An early example of a speciality chemical development VO, was reported by Wright (2004). The company employed chemists to develop synthetic routes, whilst most other functions were outsourced. This approach led to reported reductions of 92% in product development costs, and time to market savings of 66%. Although technically successful, this VO was not scalable due to the difficulties associated with the co-ordination of the individual companies and the management and distribution of the intbrmation generated during the process. To improve scalability, a improved infrastructure is required, which can provide services to address the problems reported during this virtual development

+ Author to whom correspondence should be addressed: [email protected]

1598 exercise. The architecture presented in this paper describes such an infrastructure, outlining a system that can demonstrate the following attributes: • Security: Chemical companies participating in a VO may be mutually distrusting and security mechanisms must be provided to protect against misuse of shared resources and to form a basis for the establishment and maintenance of trust relationships. • Auditability: In order to comply with statutory regulations and to monitor and manage interactions between collaborators, all actions performed within the system must be recorded and made available for audit. • Flexibility: The chemical R&D lifecycle is highly dynamic and unanticipated direction changes can occur throughout the process. The infrastructure must provide mechanisms to recognise and respond to changes, including changes in VO membership, type and content of information managed, and business relationships. • Usability: Companies typically have their own infrastructures: technical, procedural, cultural, etc. It is a requirement that they be able to participate in VOs without substantial changes to their legacy systems. 1.1 The Chemical Development Process and the Data it produces Although the chemical development process is complex, it can be broken down into discrete stages, a representative selection of which, including the various forms of data generated, is shown below in Table 1. Table 1. Example Chemical requirements. Stage

Chemical route development

Business analysis and justification

Scale up studies

Production

development

stages

and

Generated Data Types Lab notes References to previous work Chemical route information Related patents Competing companies Economic information Hazard/safety analysis Results data Operational specification Equipment availability Plant performance data QA results

information

Data Scope Local Global X X X X X

X

Table 1 also indicates specific cases where data has Global scope and may be shared between several stages within the development process. If the development is being performed within a VO, global data must be shared between different VO member companies. This implies a need for security and access control methods to be in place. Section 2.1.2 outlines some of the approaches that are relevant to the problem of securely transferring data between VO members.

1599

2. Service Oriented Approach In general, requests Ior intbrmation and action from one VO member to another should be trivial. However, fulfilling theses requests may require a complex internal process. Providers can hide that complexity by encapsulating it into a service with a simple interface defining how consumers can interact with it. This is referred to as a Service Oriented Architecture (SOA) (Erl, 2004). The service-based approach conveys a number of important benefits. Most importantly, encapsulation, which can provide a solution to the problem of loose coupling but tight integration between organisations. Web Services (Skonnard, 2002) are a standards based approach to implementing a SOA, making it possible to leverage a wide variety of open standards and protocols and integrate different software applications running on different platforms. This helps to address the usability requirements lbr a VO, as described in Section 1. 2.1 Services to support Virtual Organisations Two levels of infrastructure are required to support VOs: a basic level facilitating fundamental VO functionality, such as communication, coordination and accountability and an application specific level which, in this case, will allow VOs to be deployed within a chemical development context. VO Services

Current VO member companies

................... Structure services: • VO Members • Member capabilities

\ VO membership structure

] ] •Activity co-ordination ]

Information services: • Information storage • Information search

VO can expand to include new member ..........companies over its

Companies"p,u.,..blish capabiliti~

'k.

Q by VO "'...... ,.......... .., VO activities '".,.

Captures data gener~Red

Trust services: oNon-repudiation • Contract monitoring • Audit generation

......,. .............. ~

]

1

Monitors and records

"\'.................. .

)f

"',,,,,

f" ......../" m

.............•..........................................

O%7o;O,oOm;n2/O

Figure 1" Services to support VO management and operations Figure 1 illustrates a VO, comprised of a number of member companies being managed and controlled by the basic set of services described above. 2.2 Core VO functionality 2.1.1 Structure services One of the key requirements for the operation of VOs is to be able to support a dynamic environment in terms of the participating member companies. For example, the

companies involved during the initial investigative phases of the chemical development process are likely to be different to those involved during the final manufacturing stages. In order to monitor and control this dynamism, structural services should be provided to manage the VO and allow companies to coordinate their activities within it. In Figure 1, these structure services maintain information regarding the VO(s) that are

1600 currently operating, their member companies companies that can be invited to join.

and additional

potential

member

2.1.2 Security and trust services Security is a key concern when sharing information between VO members. Access to resources must be configured locally for security purposes but to prevent excessive management overhead in a dynamic environment it must be policy based. This removes the need tk~r resource owners to possess information about individuals in other organisations and reduces the possibility of misconfiguration and error. Access control should be supported by authentication using digital certificates (for example, Choua and Yurovb, 2004) to provide a consistent security framework across organisational boundaries. The basis of most business relationships is trust, however trust is difficult to achieve in a dynamic environment. This means that the facilities must be provided within the architecture to enable the establishment and management of trust relationships. These facilities should include electronic contracts for specifying interaction requirements (Molina-Jimenez et al, 2004), and need to be complimented by non-repudiable messaging (Cook et al, 2004) and audit trail generation to provide consistent, irrefutable evidence in the event of a dispute. The trust services in Figure 1 achieve this by monitoring the interactions between VO members and logging activities in a centralised location. 2.1.3 Information management Sharing and integration of information is a key component of VOs. Member companies may store their information in very different ways and yet a VO must be able to integrate these heterogeneous data sources and provide a consistent interface across organisational boundaries, which behaves like a single database (see, for example, Chervenak, et al, 2003, who outline a grid enabled distributed data storage architecture). The information management services should also include features such as notification so that changes to information repositories and VO structure are propagated across organisational boundaries as appropriate.

2.3 Supporting the Chemical Development process Creating and managing a VO is one aspect of a chemical development focussed VO. In addition, the VO must be able to support the various forms of data and business interactions that are anticipated within the chemical development process (Table 1). In accordance with the detailed discussion of the interactions and data types encountered during the chemical development process presented by Bayer and Marquardt (2004), we propose to build upon the Core VO functionality described in Section 2.2 in the following ways:

2.3.1 Extensions to handle chemical data types A selection of data types that are encountered during the chemical development process are presented in Table 1. What is clear from this table is that there are a wide variety of different data formats and structures that must be managed by the VO. Some of this information, for example chemical route information, is available in a highly structured form (such as the Chemical Markup L a n g u a g e - CML (Murray-Rust et al, 1995) which can be used to describe chemical specific information) and can be supported and

1601 indexed directly by the information storage services provided within the VO. Other information, for example, laboratory notes may be available only in a proprietary format (such as MS Word), which must be stored as binary data within the information services. In these cases, additional Meta-Data (Date, 1999) can be attached to facilitate future search operations. Information regarding the capabilities of VO members to generate chemical development specific infiwmation is stored within the Member Capabilities service shown in Figure 1. 2.3.2 Trust and Secltri O' extensions to facilitate chemical business interactions

Whilst the business interactions occurring during the chemical development process are likely to be common to may types of business processes, the chemical industries have a higher than normal statutory duty lk)r auditing and traceability. For example, the FDA regulations and 2 1 C F R l l requirements lk)r digital signatures (FDA, 2003). These capabilities are integrated into the core trust and security services (Section 2.1.2) in a manner that generates access logs that conform to FDA (and other relevant statutory) requirements.

3. Examples of VO Operations This section presents some examples of the interactions between individual services during typical VO operations.

3.1 Creating a new VO This example describes the steps required to create a new VO (assuming a suitable VO does not already exist) and invite a set of members to participate. Table 4." Creating a VO

Action

Service Group

Create a new empty VO Search for potential member companies Invite members to collaborate Members accept / decline invitation

Structure Structure Structure Structure

Services invoked Members Capabilities Co-ordination Co-ordination

3.2 Requesting and storing data This example describes the tasks performed when a VO member requests data to be generated by another VO member. This data is then stored and made available fi)r other VO members to access. l'able 5. Requesting data fronl a VO nwmber

Action Identify member that can produce the required data Request data from member On completion the data is stored Notifies requestor when the data is complete Requestor retrieves the data from storage

Service Group Structure Member Infl)rmation Information Information

Services invoked Capabilities Data Generation Storage Notification Storage

1602

4. Conclusions and Further Work This paper has presented an architecture to support the creation and operation of VOs for the purposes of collaborative chemical development. Although the services described in this paper have been presented in an implementation neutral fashion, they are currently being implemented using Web Services (Skonnard, 2002) which provide a widely used way of providing services over the intemet. Once complete, the VO services will be used to perform an example chemical development process which will demonstrate both the chemical specific and more general business interaction features of the architecture.

References Bayer, B. and Marquardt, W., 2004, Towards integrated information models for data and documents, Computers & Chemical Engineering, Volume 28, Issue 8, 1249- 1266. Chervenak, A.L., Atkinson M.P., Kunszt P., Narang I., Paton N.W., Pearson D., Shoshani A., Watson, P., 2003, Data Access, Integration and Management in The Grid 2: Blueprint for a New Computing Infrastructure Second Edition, November 2003. Choua, D.C., Yurovb, K, 2004, Security development in Web Services environment, Computer Standards and Interfaces, Article in Press. Cook, N.O., Robinson, P. and Shrivastava, S.K., 2004, Component Middleware to Support Nonrepudiable Service Interactions, In Proc. IEEE Int. Conf. on Dependable Systems and Networks (DSN 2004), Florence, Italy, 28 Jun.-1 Jul. 2004. Date, C.J., 1999, An Introduction to Database Systems, Addison Wesley Longman; 7th edition (October 1, 1999), ISBN 0201385902. Demchenko, Y, 2004, Virtual organisations in computer grids and identity management, Information Security Technical Report, Volume 9, Issue 1 , January-March 2004, 59-76 Erl, T., 2004, Service-Oriented Architecture : A Field Guide to Integrating XML and Web Services, Prentice Hall PTR, 16th April, 2004. ISBN 0131428985 FDA, US Department of Health and Human Services, 2003, Guidance for Industry Part 11, Electronic Records; Electronic Signatures- Scope and Application, US FDA, August 2003. Molina-Jimenez, C., Shrivastava, S., Crowcroft, J. and Gevros, P., 2004, On the Monitoring of Contractual Service Level Agreements, In Proceedings of the IEEE Conference on Electronic Commerce CECV04, The First IEEE International Workshop on Electronic Contracting (WEC), San Diego, 6-9, 2004 Murray-Rust, P., Rzepa, H.S., Leach, C., 1995, CML - Chemical Markup Language, Poster presentation, 210th ACS Meeting, Chicago, 21 st August, 1995 Skonnard, A, 2002, The XML Files: The birth of Web Services, MSDN Magazine, Volume 17, Number 10, October 2002. Wright, A.R., 2004, Turning Virtual Development Methods into a Reality, In BatchPro symposium on knowledge driven batch processes, Poros, Greece, 6th June 2004.

Acknowledgements This paper was produced as part the GOLD project, which is funded by the EPSRC and operated in collaboration with Unisys, Lancaster University Management School, CPACT, BRITEST, SOCSA and the North-East Regional Development Agency Centre of Digital Excellence (Codeworks).

European Symposiumon ComputerAided Process Engineering- 15 L. Pui~janer and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1603

An Approach for Integrating Process and Control Simulation into the Plant Engineering Process M. Hoyer:, R. Schumann ~and G. C. Premier b aForschungsschwerpunkt AUBIOS, University of Applied Sciences and Arts Hannover Ricklinger Stadtweg 120, D-30459 Hannover, Germany bSchool of Technology, University of Glamorgan Llantwit Road, Pontypridd, CF37 1DL, Wales, UK

Abstract The generation of plant models for simulation is in general a task for modelling experts which are seldom available during the engineering process of a plant. The paper proposes an automatic model aggregation concept which provides the planning engineer with a simulation model at the end of the plant engineering process, such that he can test and debug the plant functions by simulation before it is built. To demonstrate the feasibility of this approach, a prototype example illustrates the practical realisation.

Keywords: Chemical plant, process engineering, control engineering, model catalogue, graphical user interface

1. Introduction Testing of chemical plants is done mainly during the start-up and commissioning phase and in general requires a considerable amount of time and money to correct hardware and software problems. This costs could be considerably reduced by testing the simulated plant in advance before the plant has been built. Many developments in modelling and simulation are aimed to reduce such deficiencies already during the early engineering phases, see Fig. 1. In this early design stage, generic process models must be used and parameterised by modelling experts. An alternative to these bottom-up methods is the use of model based plant simulation directly at the end of detailed engineering. At this stage all components are completely specified- ready to o r d e r - and no degrees of freedom for parameterisation are left as in the early design phases. This paper describes an integrated approach to generate the required plant models automatically from a simulation model catalogue for physical components after completion of the engineering process, not requiring specific modelling expertise of the planning engineer to run the simulation. By this approach the main testing and faults correction could be done by simulation of the virtual plant with small additional effort thus reducing time and cost of the real start-up phase. The paper is organised as follows: First, the need for this approach is established by a critical literature review on current developments in modelling and simulation environments used during the plant engineering cycle. The detected markus.hoyer@mbau, fh-hannover.de

1604 deficiencies in supporting planning engineers by plant simulation have motivated this new approach for simulation and testing of the plant at the end of detailed engineering which is based on a simulation model catalogue. Then, the set-up of an integrated simulation environment is described comprising the basic plant-CAE system in which the simulation model catalogue is integrated, the standard process and control simulators and a new module for the automatic aggregation of simulation models using a smart GUI. Finally, an application example illustrates the potential of the new approach by showing the automated procedure guiding the planning engineer from the P&I diagram of the plant-CAE system to the associated simulation results. !iEiii~i!ii!i!ii!!!~!ii!!iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii!i~iiiiiiiiiiiiiiiiii!iii~iiiiiiiiiiiiiiiiiiii~iiii~ii~iii~iiiii~ii!iiiiii~iiiiiiiiiii~iiiiiiiiiiiiiiii{iiiiiiiiiiiiiii~iiii!iiiii!iiiiiiiiiiii i i i ! i j ~ } i i ~ i } i i { ~ 3

const[uc!ionI%~ ... ' ~ . Iiii

Figure 1. Simulation support for plant engineering process

2. Modelling and Simulation Environments for Plant Engineering Commercial or scientific modelling tools for the plant engineering process are classified into two groups utilising block-oriented or equation-oriented model descriptions, see Marquardt (1996) or Pantelides and Britt (1995). These tools are tailored to users with appropriate knowledge in their domains (control system engineering, chemical plant engineering, modelling and simulation). In general, the use of these tools requires knowledge from all domains. This makes a permanent presence of experts necessary during all modelling and simulation procedures and is realisable (although at high costs) in large industrial companies or in scientific research. However, in small or medium sized industrial companies (planning and engineering companies) such experts are in general not available at all. Due to the large variety of chemical process units and physical-chemical phenomena as well as increasing requirements on the sophistication of models, the development in knowledge-based modelling environments has increased in the past decade. The general idea of knowledge-based modelling environments is a methodology to lift the equationoriented modelling from detailed mathematical representations to the level of process knowledge (in general by using phenomenological building blocks) (Bogusch et al., 2001). The support for the modeller takes place with suitable dialogs, provision of information and modularisation of process models below the model unit level. The modularisation aspect of process models has been investigated by several authors (Ponton and Gawthrop, 1991; Marquardt, 1996; Perkins et al., 1996 and Preisig, 1996). All approaches contain a general systematic methodology for structuring the model with respect to later reuse and modification. Based on those general structuring concepts modelling languages and tools have been developed which permit a modular and highly structured model formulation. Examples are ModDev (Jensen and Gani, 1999), Modeller (Westerweele et al., 1999), TechTool (Linninger et al., 2000), ProMot (Tr~inkle et al., 2000) or ModKit (Bogusch et al., 2001). These modelling tools have provided the

1605 development of model libraries based on simple, flexible and reusable modelling units. Furthermore, they are mostly integrated in CAPE (Computer Aided Process Engineering) environments used for modelling procedures and plant analysis as well as for the synthesis of chemical plants or control systems. However, these approaches are dedicated to the conceptual design at the beginning of the plant engineering cycle. Simulation tools, based on a special web-based platform, such as Jarke et al. (1998) and K611er et al. (2001), use and provide components from different vendors by using a standardised open interface of the Global CAPE-OPEN-project, see Braunschweig et al. (2000). However, for the use of these component stores, expert knowledge is required. All described methods and tools are designed for modelling and simulation experts and for the early phases of the plant engineering process. In order to provide non-expert users like planning engineers with simulation support during the plant engineering process (in particular at the end of detailed engineering), a new approach has to be taken.

3. New Approach: Integrating Process and Control Simulation into Plant Engineering The new approach to integrate simulation at the end of detailed engineering is based on an extended CAPE (Computer Aided Process Engineering) concept which comprises the basic plant-CAE system (in the prototype realisation Comos PT by Innotec, 2003) and simulators for the chemical process (gProms by PSE, 2002) and its control system (Simulink by The Mathworks, 2003), Fig. 2. Ptant-CAE system (COMOS PT) Data base t~g ~1

based on ..........

1!i

i

"Smart" GUI ( G r a p h i c a l

::::i:.........(Simu!i nk)

.......... !gProms): ...........

User Interface)

Figure 2. General set-up including essential tasks

These modules have to be linked among each other by the new developed model aggregation module (MAM) and with the planning engineer by the "smart" GUI (graphical user interface) module designed to allow simulation of plant and control system functions without requiring the assistance of modelling or simulation experts. For setting up a plant model and its simulation the following tasks are accomplished: 3.1 Task 0: Collection of simulation models for the model catalogue in the plantCAE system The prerequisite for this approach is the availability of simulation models for all plant components. The component models required for simulation of the fully specified plant at the end of detailed engineering are models of its specific physical components (including the process control system), which will be built into the real plant. These simulation models, which do not have to be parameterised by the user, must become available from the component suppliers (as is the case in electrical engineering for PCB

1606 design) - this is a critical assumption- and should be stored in the database of the plant CAE system in a simulation model catalogue. To allow the use of sophisticated and dedicated simulators for chemical process components and control components it makes sense to store and simulate the models separately for the process and control domain, details see Hoyer et al. (2005a). 3.2 Task 1: Extraction of component information from P&I diagram (GUI) The GUI module realises the interactive selection of an area in the P&I-diagram to be simulated, Comos PT delivers the required component and connection information of the P&I-diagram in a component dataset. 3.3 Task 2: Analysis of P&I diagram and model aggregation (MAM) From the component dataset MAM detects the selected area to be simulated, the components within this area and their connections. From this information the simulation model is aggregated making use of the simulation model catalogue. For determination of boundary conditions for simulation the relations between the selected part and the rest of the P&I diagram are analysed and missing simulation parameters are detected by MAM.

3.4 Task 3: User dialogue for missing simulation data (GUI) The missing simulation parameters are specified by the user in a dialogue window collecting boundary conditions for streams, set points etc.. In the actual prototype version the GUI is just able to collect this information, in the final version the smart GUI will provide the non-expert user with assistance functions guiding him through this nontrivial specification procedure. 3.5 Task 4: Generation of simulation scripts (MAM) The complete simulation information is compiled by MAM into simulation scripts for the process and control simulator. In the prototype realisation a combined simulation script is generated and fed to Simulink (mdl-file) containing besides Simulink blocks for the control part the gProms block containing the gProms script for the process part. In this realisation gProms serves in S imulink as simulation engine for the process part through a standard interface (gOSimulink by PSE, 2002). 3.6 Task 5: Presentation of simulation results (GUI) In the actual prototype version simulation is still started manually and the simulation results are presented within Simulink. In the final version, the smart GUI will hide the complex simulation environment behind the P&I diagram from which the simulation is started directly, and all simulation results will be directly presented in the context of this P&I diagram allowing easy interpretation of results. 4. I l l u s t r a t i v e A p p l i c a t i o n E x a m p l e The functionality of the realised prototype is illustrated using an example from a fresh cheese production line, details see (Hoyer et al., 2005b). During detailed engineering of the fresh cheese production line with Comos PT, the component objects were arranged and specified in the P&I diagram and the corresponding object tree as shown in Fig. 3. The red dashed boundary marks the components of the production line to be simulated: the process part contains pipes, the separator with input stream (curd) and output

1607 streams (sour whey, fresh cheese), the control valve and the physical parts of the sensors for curd flow and dry matter. The control, system part includes the control loop FC 005 for the curd flow to the separator and the cascaded dry matter control loop QC 001. project

database

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)

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Figure 3. Flow control system in Comos PT (project database, P&l-diagram, user dialogue) and Simulink with gProms block

After selecting the plant parts to be simulated (red dashed lines) (Task 1), the component dataset is analysed (Task 2). Having specified the missing simulation parameters in the user dialogue window (here boundary conditions for input and output streams, set points for flow and dry matter control loop, Task 3), Simulink is started and automatically provided with the generated simulation script as mdl-file (Task 4). The simulation is then manually started by the user from the Simulink scheme (Task 5) and the simulation results are presented in Simulink fore, at. In the application example, the impact of the disturbance "disc fouling" on the dry matter control loop is illustrated with the dry matter and curd flow signal reaction to this disturbance after time t= 1000s.

5. Conclusion and Recommendation Aspects The extended CAPE concept proposed in this paper is intended to support the planning engineer with simulation at the end of detailed engineering and opens a new path to integrate simulation in the plant engineering process. To make the concept work in reality a comprehensive component simulation model catalogue must be accumulated in a combined effort between CAPE system designers and component suppliers, as has already been the case in electrical engineering (e.g. PCB design). Furthermore the question of validation arising within all simulation activities has to be deepened in future. The quality of models may be characterised by the experimental or theoretical conditions under which these models were derived - such modelling conditions must become an integral part of the model description supplied by the model developer (supplier) to allow qualification of simulation results. The general issue how to make sure that n o n -

1608 expert users can produce reliable simulation results in the absence of experts will have to be addressed step by s t e p - as has been the case in electrical engineering during the evolution of simulation during the last decades with still ongoing discussions. Having solved the remaining theoretical and technical problems the industrial application of such an extended CAPE system will allow testing and optimisation of the plant by simulation before it is built and thus may help to reduce start-up time and costs.

References Bogusch, R., B. Lohmann, W. Marquardt, 2001, Computer-aided Process Modelling with MODKIT, Comp. & Chem. Engineering, No. 25, pp. 963-995. Braunschweig, B. L, C. C. Pantelides, H. I. Britt, S. Sama, 2000, Process Modelling: The Promise of Open Software Architectures, Chemical Engineering Progress 9, pp. 65-76. Hoyer M., R. Schumann and G.C. Premier, 2005a, Model cat- A Model Catalogue Based Approach to Process Modelling. 16. IFAC World Congress, Praque 2005, to be published. Hoyer M., R. Schumann, E. W%t and G.C. Premier, 2005b, Feedback control system design for a fresh cheese separator. 16. IFAC World Congress, Praque 2005, to be published. Innotec, 2003, Comos PT. http://www.innotec.de/en/index.php Jarke, M., M. A. Jeusfeld, C. Quix and P. Vassiladis, 1998, Architecture and quality of data warehouses. Proc. CAiSE 98, Pisa. Jensen, A. K. and R. Gani, 1999, A Computer Aided Modelling System, Comp. & Chem. Engineering Suppl., pp. 673-678. K611er, J., T. List, M. Jarke, 2001, Designing a Component Store for Chemical Engineering Software Solutions, Proc. International Conference on System Sciences, Hawaii, pp. 1-9. Linninger, A. A., S. Chowdhry, V. Bahl, H. Krendl and H. Pinger, 2000, A Systems Approach to Mathernatical Modelling of Industrial Processes, Comp. & Chem. Engineering, Vol.24, pp. 591598. Marquardt, W., 1996, Trends in Computer-Aided Process Modelling, Comp. & Chem. Engineering, Vol. 20, No. 6/7, pp. 591-609. Pantelides, C. C. and H. I. Britt, 1995, Multipurpose Process Modelling Environments, AIChE Symposium Series No. 304, Vol. 91, pp. 128-141. Perkins, J. D., R. W. H. Sargent, R. Vfizquez-Romfin, J. H. Cho, 1996, Computer Generation of Process Models, Comp. & Chemical Engineering, Vol. 20, No. 6/7, pp. 635-639. Ponton, J. W. and P. J. Gawthrop, 1991, Systematic Construction of Dynamic Models for Phase Equilibrium Processes, Cornp. & Chem. Engineering, Vol. 15, pp. 803-808. Preisig, H. A., 1996, Computer-Aided Modelling: Two Paradigms on Control, Comp. & Chem. Engineering (Suppl.), pp. 981-986. PSE, 2002, gProms User Manual, Process Systems Enterprise Ltd., http://www.psenterprise.com/gPROMS The Mathworks, 2003, Matlab. http://www.mathworks.com Tr~inkle, F., M. Zeitz, M. Ginkel and E. D. Gilles, 2000, PROMOT: A Modelling Tool for Chemical Processes, Mathematical and Computer Modelling of Dynamical Systems, Vol. 6, No. 3, pp. 283-307. Westerweele, M. R., H. A. Preisig, M. Weiss, 1999, Concept and Design of Modeller, a Computer-Aided Modelling Tool, Comp. & Chem. Engineering Suppl., pp. 751-754.

Acknowledgements This work was supported in part by the Volkswagen foundation, AUBIOS (project ZN1195) and the British Council and Daad (Deutscher Akademischer Austauschdienst) through the Anglo-German Academic Research Collaboration Programme ARC, project No. D/03/20266-1216.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) ¢C>2005 Elsevier B.V. All rights reserved.

1609

Process Integration and Optimization of Logistical Fuels Processing for Hydrogen Production Fadwa T. Eljack ~, Rose M. Cummings ~, Ahmed F. Abdelhady, Mario R. Eden ~* and Bruce J. Tatarchuk h :'Department of Chemical Engineering, Auburn University 230 Ross Hall, Auburn, AL 36849-5127, USA ~Center for Microfibrous Materials Manufacturing (CM 3) 337 Ross Hall, Auburn, AL 36849-5127, USA

Abstract In this work, the preliminary results of a process integration analysis of a logistical fuels processing plant is presented. A simulation model of a bench scale test bed was developed using a commercial simulator (Pro/II) and used to generate the necessary data for performing a thermal pinch analysis. The analysis shows that considerable savings can be obtained through increased thermal integration of the system. The specific application of the fuel processing system is to power a portable radar system, thus reductions in energy requirements translates into equally important reductions in equipment size. To further increase the integration potential the use of heat pipe technology has been investigated. Heat pipes allow for near isothermal heat transfer and thus significantly reduce the required temperature driving force. A simple, systematic method for identification of optimum heat pipe usage in heat exchange networks is presented in this work.

Keywords: Fuels processing, process integration

1. Introduction Fuel cells are emerging as an important component of a renewable energy future for many utility and mobile applications. Proton exchange membrane (PEM) fuel cells are capable of achieving much higher energy efficiency levels since a fuel cell is not limited by the traditional Carnot cycle found in combustion engines. A very promising technique is to obtain the required hydrogen by reforming a liquid hydrocarbon fuel, which has a significantly higher energy density than gaseous hydrogen. Recent efforts are focused on reforming existing logistical fuels, e.g. diesel or JP-8 for use in fuel cell systems (Amphlett et al., 1998). This is particularly important for military applications, as it would allow for the US armed forces to move towards using one single logistical fuel. Since the overall energy efficiency of a fuel cell system is approximately three times higher than a combustion engine based generator, it would provide substantial savings for the US Army if alternative means of power production could be developed.

Author to whom correspondence should be addressed: [email protected]

1610 To meet these ends the Center for Microfibrous Materials Manufacturing (CM 3) at Auburn University has developed a bench scale test bed for investigating running a portable radar system of a Ballard Nexa TM PEM fuel cell stack by producing high purity hydrogen from reforming JP-8. The PEM fuel cell system consists of the fuel processing section and the fuel cell itself, with the former being the reformer and postcombustion cleanup steps. Such systems inherently possess tremendous integration potential, not just limited to recycling unused material, but also in terms of energy recovery (Godat and Marechal, 2003). The objective of this work is to develop a process simulation model of the fuel processing test bed and use it to generate the data required for subsequently performing a thermal pinch analysis in order to identify the potential energy savings attainable. As this system is targeted for mobile applications reductions in utility requirements will automatically result in reductions in the system size.

2. Process Description and Model Development A schematic of the fuel processing test bed is given in fgure 1. A central theme for the test bed is the use of microfibrous entrapped catalysts and sorbents. These microfibrous materials provide high contacting efficiency through a high surface area to volume ratio. This enhanced heat and mass transfer capability presents an opportunity for miniaturization of the processing units compared to conventional catalyst supports, such as packed beds. In figure 2, 500 lam water gas shift catalysts particles are entrapped in 10-50 ~tm Nickel fibres. Similarly 150 ~m particles of a precious metal catalyst on alumina support are depicted in figure 3 (Karanjikar et al., 2004). The simulation model was developed using a commercially available process simulator Pro/II (Simulation Sciences, 2004) augmented with a customized model for the fuel cell. It should be noted, that the simulation model is specified to match the experimental data. JP-8 ''"""''~t H~.O ~

Two Stage Reforming

Preformer (900~'C) Postformer (700:;C)

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Figure 1. Fuel processing test bed schematic

Figure 2. WGS catalyst in Nickel fibres

Figure 3. PROX catalyst on Al:03 support

1611 2.1 Reforming section There is no standard formula for jet fuels such as JP-8. The exact composition depends on the crude oil from which they were refined. Variability in fuel composition occurs because of differences in the original crude oil and in the individual additives. As a result of this variability, little information exists on the exact chemical and physical properties of jet fuels (Custance et al., 1992). JP-8 consist of a variety of hydrocarbons ranging from C7 to C~,, however the bulk of the fuel (over 80%) is made up by decane, dodecane, tetradecane and hexadecane (US Air Force, 1991). The steam-to-carbon ratio in the feed is 2.4, which has been reported as being the optimal choice (Zalc and L/Sft'ler, 2002). The mixture of steam and fuel is heated to 900°C and fed to the first reactor, which performs the majority of the reforming according to equations (1)-(3), while the second reactor reduces the methane content fi'om approximately 15% to 1%. Chromatographic analysis of the effluents for the preformer and postformer is presented in figures 4 and 5, respectively and the reactor models are specified to match the performance of the experimental test bed. CnHm + nH_~O ---> nCO + (n + 0.5m)H_~

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2.2 Reformate cleanup The purpose of the next sequence of units is solely to purify the hydrogen by removing or converting the reforming by-products. Analogous to the reformer models, the model specifications are based on experimental data. First step is removal of hydrogen sulphide as it serves as a catalyst poison. The removal is performed by a microfibrous entrapped ZnO/SiO2 catalyst. The removal rate is greater than 99%, thus reducing the H2S content to less than 1 ppm. Next are two water gas shift reactors, which convert carbon monoxide (which poisons the PEM fuel cell) into carbon dioxide as described by equation (3). The CO content after the shift reactors is reduced from 15% to less than 0.75%. The remaining CO is converted to CO2 through preferential oxidation (PROX), which reduces the CO content to less than 10 ppm. The selectivity of the PROX catalyst

1612 (Pt-M/A1203) is 60% towards the oxidation of CO, while the remaining 40% reacts with hydrogen to form water. The CO2 is then removed by adsorption on a microfibrous entrapped alkaline sorbent. The last unit before the hydrogen rich gas enters the fuel cell is an inline fuel filter, which is a series of microfibrous entrapped sorbents that can remove traces of HzS, NH3, CO and CO2 (Karanjikar et al., 2004).

2.3 PEM fuel cell The high purity hydrogen stream is sent to the PEM fuel cell along with a feed of atmospheric air. The fuel cell produces electrical power and heat along with pure water, some of which is then recycled back to the steam production section. For the specific application envisioned by the military, i.e. power supply for a portable radar system, this presents an additional benefit. Since there is a net production of water (on a molar basis roughly 6 times the water supplied for the steam reforming) in the system, the on board fuel processor is capable of providing drinking water for the personnel.

3. Process Integration Analysis Once the simulation model had been developed based on the experimental data obtained from the fuel processing test bed, a process integration study was performed to identify the potential energy recovery. By employing pinch analysis methods the global flow of energy in the system was mapped and analyzed. Assuming a 20°C minimum allowable temperature driving force, the pinch analysis showed that by extensive integration the external heating duty could be reduced by 58%, while the external cooling duty could be reduced 54%. These are quite significant savings when keeping in mind that these reductions in energy can be translated to reductions in equipment size as well. Furthermore, the fresh water requirement for steam production has been completely eliminated due to the fact that there is a net production of water in the system. Further investigations include dynamic simulation of the system, which may reveal that the hold-ups in the system require the water the recycle to be increased in order to run the system continuously. However it is still anticipated that a considerable amount of the fresh water produced can be used as drinking water.

4. Enhancing HEN Performance using Heat Pipes Implementation of heat pipe technology has the potential of significantly increasing the attainable integration potential for process systems as the required driving force is decreased (Gaugler, 1944; Chi, 1976). A heat pipe is a heat transport device that utilizes evaporation and condensation to transport high rates of heat almost isothermally. Figure 6 outlines the structure of a generic heat pipe, where the heat transport is realized by evaporating a liquid contained in the wick in the heat inlet region and then subsequently condensing the vapour in the heat rejection region. Closed circulation of the heat transfer fluid is maintained by capillary and/or bulk forces. Heat is transferred radially through the casing and into the wick causing the liquid to evaporate and thus transferring mass from the wick to the vapour core. This increases the pressure in the vapour core at the evaporator end of the pipe, thus allowing vapour to flow to the condenser end of the pipe. Heat is removed through a suitable heat sink attached to the pipe casing at the condenser end. The condensing vapour replaces previously

1613

evaporated liquid mass to the wick and capillary forces feeds the liquid back to the evaporation section (Harris et al., 2001). Besides the inherent benefits associated with nearly isothermal heat transport, an additional advantage of using heat pipes rather than conventional heat exchangers is that the pipe and the heat transfer liquid provides additional separation between the two streams exchanging heat. This ability reduces the dangers associated with transferring energy between incompatible materials, thus relaxing some of the conventional constraints encountered when designing heat exchanger networks (Harell, 2004). 4.1 Identification of optimal heat pipe placement Since heat pipes are an emerging technology available to the processing industry and thus still quite costly, it is imperative to use them efficiently. For a conventional heat exchanger network the minimum allowable temperature difference (ATtain) is usually between 10 and 20°C. Hence, for a given heat exchanger network the pinch analysis is first performed with ATtar,, equal to e.g. 20°C. Next, the utility targets for a heat pipe only network are identified by performing a pinch analysis with a significantly lower value of ATmio, e.g. 2°C. Now, an iterative procedure as outlined in figure 7 is employed to identify the placement and minimum number of heat pipes required to achieve these targets. The rationale behind the developed iterative approach is that in a standard heat exchanger network the thermal pinch point is the bottleneck, which must be overcome in order to transfer additional energy. Therefore the pinch location is the ideal point to implement a heat pipe. Once the first heat pipe has been implemented, the pinch analysis is redone and the utility targets evaluated. If another pinch point is identified, then a second heat pipe is added to remove this bottleneck. This procedure is continued until the utility targets identified from the 2°C pinch analysis have been matched, and thus no benefits will be obtained by adding additional heat pipes. HEATEXCHANGERNETWORK Thermal Pinch Analysis for AT,:,

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1614 The iterative procedure outlined in figure 7 ensures that wherever possiblethe bulk heat transfer requirements are carried out using conventional heat exchangers and the more expensive heat pipes are only implemented, where a lower temperature difference is required in order to achieve the desired utility targets.

5. Conclusions and Future Work Using commercial process simulation software a model of a logistical fuel processing system for mobile applications has been developed based on data from an experimental test bed. A process integration analysis showed that energy savings in excess of 50% are achievable through thermal integration of the system. A systematic method for evaluating the effect of using heat pipes in heat exchange networks has also been presented. The method is a simple extension to conventional pinch analysis methods. The presented method utilizes an iterative procedure where heat pipes are implemented at the pinch locations to overcome the thermodynamic bottlenecks. The implementation of heat pipes in the fuel processing system was found to potentially reduce the external heating and cooling demands by an additional 5% as well as providing a technology for reducing the physical size of the system. Future efforts will be focused on further developments of the simulation model including the use of alternative fuels, e.g. diesel, and different reforming schemes, i.e. partial oxidation and auto-thermal reforming. Furthermore, the design changes suggested by the thermal pinch analysis will be implemented on the test bed and the performance validated. Finally, the presented methodology for augmenting heat exchange networks with heat pipes will be extended from the current targeting approach to include actual network design. References Amphlett, J.C., R.F. Mann, B.A. Peppley, P.R. Roberge, A. Rodrigues, J.P. Salvador, 1998, Journal of Power Sources, 7 l, 179-184. Custance, S.R., P.A. McCaw, and A.C. Kopf, 1992, Journal of Soil Contamination 1(4), 379. Chi, S.W., 1976, Heat Pipe Theory and Practice, Hemisphere Publishing Corporation. Gaugler, R., 1944, Heat Transfer Device, US Patent 2350348. Godat, J. and F. Marechal, 2003, Journal of Power Sources, 118, 411-423. Harell, D.A., 2004, Ph.D. Thesis, Texas A&M University. Harris, D.K, D.R. Cahela and B.J. Tatarchuk, 2001. Composites - Part A: Applied Science and Manufacturing 32(8), 1117-1126. Karanjikar, M., B.K. Chang, Y. Lu, and B.J. Tatarchuk, 2004, Pre-prints of Fuel Chemistry Division, ACS Annual Meeting Philadelphia August 2004, 49(2), 910. Simulation Sciences, 2004, Pro/II User Guide. US Air Force, 1991, Supercritical fluid fractionation of JP-8. Aero Propulsion and Power Directorate, Wright Research and Development Center, Air Force Systems Command, WrightPatterson Air Force Base, OH. NTIS Publication no. AD-A247-835. Zalc, J.M. and D.G. LOffier, 2002, Journal of Power Sources, 111, 58-64.

Acknowledgements This work was performed under a U.S. Army contract at Auburn University (DASG 6000-C-0070) administered through the U.S. Army Space & Missile Defense Command (SMDC). This financial support along with support from the Auburn University Undergraduate Research Fellowship Program (AU-URF) is highly appreciated.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

1615

A Systematic Approach for Synthesis of Optimal Polymer Films for Radioactive Decontamination and Waste Reduction Tracey L. Mole a*, Mario R. Eden a, Thomas E. Burch a, A. Ray Tarrer a and Jordan Johnston b a

Auburn Engineering Technical Assistance Program (AETAP) Auburn University, AL 36849 b Orex Technologies 1850-E Beaver Ridge Circle, Norcross, GA 30071

Abstract In this work, an effective and systematic modelling technique is devised to generate optimal formulations for explicit polymer film engineering applications. These methods aim at developing quantitative values for not only intrinsic properties, but qualitative characteristics are developed in order to simultaneously optimize the formulation subject to the product specifications. The predictive modelling framework developed is comprised of material and energy balances, constraint parameters, constitutive equations, design/optimization variables and possible polymer synthesis techniques. A set of user defined design constraints produces a subset of different optimization formulations comprised of different polymer blends, molecular weights, hydrolyzation extents, solvents, and additives. This contribution illustrates a novel way to evaluate a wide range of polymeric fihn compounds and mixtures with fewer testing iterations.

Keywords: Formulation synthesis, material development

1. Introduction Formulation of new products and improvement of existing merchandise is practiced in many different industries including paints and dyes, polymers and plastics, foods, personal care, detergents, pharmaceuticals and specialty chemical development. Current trends in the engineering design community have moved towards the development of quantitative integrated solution strategies for simultaneous consideration of multiple product characteristics. The optimization variables are most often determined by qualitative attributes, stochastic variables, visual observations and/or design experience. The effectiveness of these approaches is limited by available data, bias towards specific solutions, reproducibility, and experimental error. Model insight is required for development of fast, reliable and systematic screening methods capable of identifying optimal formulations and reducing the number of subsequent laboratory trials. Author to whom correspondence should be addressed: [email protected]

1616

2. Model Development Methodology In order for the product to exhibit the desired performance, a combination of discrete constraints must be fulfilled. Identification of an optimal formulation that is suitable for the desired system requires integration of all the interlacing behaviours of the product constituents. These characteristics include the constituents used for construction as well as their inherent properties. This is accomplished by using a combination of novel modelling techniques. 2.1 Property integration This method consists of tracking functionalities instead of chemical species in order to represent the synthesis problem from a properties perspective. The conventional approach to product formulation development is selecting constituents that exhibit desired produced properties and optimizing the mixing ratios. In order to model the product characteristics, these pre-determined candidate components are required as inputs to the design algorithm. These inputs are based on qualitative process knowledge and/or design experience, which can exclude solutions involving other possible raw material sources. In this work, the concept of property integration for process development introduced by E1-Halwagi et al. (2004) is applied to product synthesis. This modelling approach allows for solution of many different engineering problems to be conducted on a property only basis. This method allows for identifying optimized solutions to specified chemical engineering problems by determining the desired output and solving backwards for the constituents and compositions. In the case study to be described in the next section, these techniques are used in conjunction with a model decomposition technique to allow for formulation of reverse property prediction problems.

Conventional Model Structure

~

Decoupled Model Structure

I Balance and Constraint Equations ] Mixing Rules & Formula Concentrations) ]

Balance and ConstraintEquations (Mixing Rules & Formula Concentrations)

Property and Constitutive Equations~" I (Phenomena Models & Intensive | Properties) ~]

REVERSE SIMULATION

Design Parameters and Limitations We" (Desired Behaviors & Attributes)

DESIGN TARGETS (Constitutive Variables) gp

(a~

REVERSE PROPERTY REDICTION

Design Parametersand Limitations (Desired Behaviors & Attributes)

(b] Figure 1. Decoupling of constitutive equations for reverse problem formulation

1617

2.2 Model decomposition and reverse property prediction These modelling techniques are useful tools to reduce the complexity involved when trying to simultaneously optimize balance and constraint equations with constitutive and property models. The development of these novel techniques has been described by Eden et al (2004). Although these procedures were created for process development, minor changes allow for application to product design. The main objective of the method is to separate the balance and constraint equations from the often complex and non-linear constitutive property relations. Figure 1 illustrates this decomposition principle by showing how the overall model (a) is divided into two separate models by defining target property variables (b). These target variables are a set of solutions to both the formula balance model and the constitutive property design model. Each mathematical system is solved independent of the other until valid sets of solutions are found that satisfies both networks. This technique is illustrated in the following case study.

3. Case S t u d y - Polymer Film for Nuclear Applications The desire to decontaminate surfaces inside nuclear power plants has been addressed with a number of different products. The implementation of latex-based pealable films has been used for many years. The coating serves to initially "fix" the contaminants in place for containment and ultimate removal. However, power plants have discontinued the use of these products because of their long drying times and expensive disposal costs, in the place of these products, protocol has turned to the use of steam jets to remove the radioactive particles and clean the exposed surface. This method has proven to be ineffective due to a build up of contaminants that, through molecular transport, become airborne and contaminate larger areas. The purpose of this work is to develop an effective and systematic model to synthesize a formulation of a water soluble polymer film coating for radioactive decontamination and waste reduction. This material development involves the use of a polymer matrix that is applied to surfaces as part of the decontamination system in place of the past latex products. Upon mechanical entrapment and removal, the polymer coating containing the radioactive isotopes can be dissolved in a solvent processor, where separation of the radioactive metallic particles occurs. Ultimately, only the collection of filtered solids must be disposed of as nuclear waste. The ability to identify such a product creates an attractive alternative to direct land filling or incineration. In order for the polymeric film to be a viable candidate, it must exhibit the desired performance that previous coatings are unable to. These characteristics include, drying time, storage constraints, decontamination ability, removal behaviour, application technique, coating strength and dissolvability processes.

3.1 Property integration of polymer coating model Identification of an optimized formulation that is suitable for this entire decontamination system requires integration of all the interlacing characteristics of the coating composition that affect the film behaviour. In order to accomplish this, an accurate representation of the system must be developed in order to solve the design parameters in terms of properties only. The representation of the design parameters along with the interactions between them and the overall formula behaviour is given in

1618 figure 2. This model could be solved as a reverse simulation problem using the final coating characteristics as input variables and the final polymer, solvent, and additive selections established as output solutions. The intricacy here is producing an accurate model, as the inherent non-linearity of the property relationships in conjunction with the complex formulation balance equations makes acquiring viable solutions difficult. In order to overcome these obstacles, model decomposition is employed. .............

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3.2 Decomposition of polymer film design problem The problem schematic shown in figure 2 is decomposed into three separate parts in order to reduce the complexity of the solution procedure. These subparts are comprised of formula equations, design parameters, and target property values. 3.2.1 Formula constraint equations The formula balance equations are separated into a reverse simulation problem that includes polymer, additive and solvent choices. Among these selections are available synthesis variables that affect polymeric properties such as molecular weight and extent of hydrolysis. With this information included in the model, not only can different polymer chains be compared, but also different variations of the same polymer and polymer blends. The ability to optimize the polymer synthesis as well as the film composition increases the possible formula combinations and improves the chances of acquiring an acceptable optimized formula. The additive options include components that enhance the desired film properties in order to fulfil the necessary constraints from

1619 the target property variables. This assortment of compounds contains wetting agents, surface tension reducers, biocides, cross-linking agents, elastomers, resin hardeners, dyes, pigments and dispersants. The choice of solvents is limited not only by the polymer selection, but also by the application. The list and amounts of volatile solvents allowed to be used on a nuclear power plant floor is extremely limited. The initial concentration of solvent present in the coating is the primary driving tbrce involved with drying time. It is imperative for this part of the overall model to simultaneously optimize the formulation so that target properties are exhibited and the overall film behaviour is superior to current competitor products.

3.2.2 Design parameters The design parameters and limitations represent a compilation of attributes that the final product must exhibit. Because this formulation is intended to fulfil a market niche that already exists, the final formula characteristics are well known. The primary design parameters are the decontamination ability, drying time and redissolvability. The ability for the film to remove contaminates is measured by the ratio of radiation detected divided by the radiation present before the film removal. This numeric value is known as the decontamination factor and is a major selling point that must be equivalent or better than other possible decontamination products and processes. Another parameter where the new formulation must out perform the competing processes is drying time. Nuclear power plant outages are very costly and the schedule is optimized to minimize profit losses. By producing an optimized formula with the customer's major objectives in mind increases the marketability of the product and improves possible sales. The issue of redissolvability mostly pertains to the manner in which the film is disposed of. The current operations in nuclear plants involve the use of many different polymer based products that are sent to processing stations for redissolving and filtering. It is desired that the film can be disposed of by utilizing these same processing procedures. Other constraints include a simple and effective means to apply the coating to the walls and surfaces inside the plant as well as removal techniques. The model's main objective is to determine what intrinsic properties govern the desired performance variables and develop a dynamic set of target properties. 3.2.3 Target property variables The development of a set of target properties allows this model to utilize reverse property prediction to identify the design alternatives. This is accomplished thru experimentation to determine what property ranges equate to final film behaviour. In order to illustrate the modelling techniques presented in section 2, we can simplify the system by assuming that the only major target property in figure 2 is viscosity. This seemingly simple model is decoupled into two separate systems, which is illustrated by figure 1; the chemical makeup equations that produce a given viscosity and the behavioural models which predict how the viscosity affects the design parameters and limitations. By conducting laboratory tests and simulation studies, the optimum fluid viscosity that produces adequate application behaviour can be determined to be a given value, 4000 centipoises for example. This value becomes the viscosity design target of the qualitative prediction model. By implementing the reverse simulation of mixing rules and formula concentration models, a set of viable product formulations that meet the 4000cps design target are determined. These techniques seem unnecessary when

1620 considering only one target property, but when numerous targets are set, these simplification processes are extremely advantageous.

4. Results The ultimate result of this model aided in the development of a product that increases the removal rate of radioactive contaminates by 69% while attaining a 33% reduction in drying time over the current marketed competitors. The finalized product formula will be available through the Orex Technologies Catalogue in Fall of 2005.

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5. Conclusions By employing novel model development techniques such as property integration and model decomposition; a complex product formulation development process has been simplified. In this work, these methods were illustrated by addressing a problematic phenomenon in the nuclear power industry. The utilization of these modelling techniques took an industrial idea to full scale testing and production in under 18 months by reducing the number of subsequent laboratory trials.

References E1-Halwagi, M.M., I.M. Glasgow, M.R. Eden and X. Qin, AIChE Journal, Vol 50(8), 2004. Eden, M.R., S.B. Jorgensen, R. Gani and M.M. E1-Halwagi, Chemical Engineering and Processing, 43, 2004. Eden, M.R., S.B. Jorgensen, R. Gani and M.M. E1-Halwagi, Computer Aided Chemical Engineering, 15B, 2003 Finch, C.A. 1992, Polyvinyl Alcohol Developments, Wiley & Sons, Chichester

Acknowledgements The authors would like to acknowledge the support of the National Science Foundation for their support of the Auburn Engineering Technical Assistance Program and Orex Technologies for this opportunity and the financial support to conduct this research.

European Symposiumon ComputerAided Process Engineering- 15 L. PuiNaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.

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Integration of Planning and Scheduling in Multi-site Plants" Application to Paper Manufacturing Munawar, S.A. a, Mangesh D. Kapadi b, Patwardhan, S.C. a, Madhavan, K.P. a, Pragathieswaran, S. b, Lingathurai, p.b and Ravindra D. Gudi a* aDepartment of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai- 400 076, India. bHoneywell Technology Solution Laboratory, Banerghatta Road, Bangalore- 560076, lndia.

Abstract In this paper, a general multi-level decomposition based framework has been proposed for integration of planning and scheduling in a multi-site, multi-product plant, with applications to paper manufacturing. The problem involves complex issues relating to large-scale production in a hybrid flowshop configuration, decisions relating to minimizing trim losses, while maintaining on-time delivery of orders. Due to these complexities, the overall problem of integrated planning and scheduling is logically partitioned into several levels, depending on the problem size. As followed in other decomposition-based approaches, the upper level models are equipped with appropriate abstractions of the lower level constraints. Also from a reactive scheduling point of view, some pro-active measures are embedded into the multi-level structure. The proposed multi-level decomposition scheme is demonstrated on a representative planning and scheduling problem.

Keywords: Planning, Scheduling, Integration, Decomposition 1. Introduction Integration of planning and scheduling in the process industries has received significant attention in the recent years by practitioners and academicians because of the high economic incentives and the challenges involved. Most of the large-scale multienterprise facilities currently employ some heuristics for this integration and are generally dissatisfied with the resulting inconsistencies in decision-making (Shobrys and White, 2000). Over the last few years, though some progress has been made in this direction tbr development of more superior frameworks for such integration problems, there is a large scope for additional improvements. In the literature there are several works on planning and scheduling. Shah (1998) gives a detailed review and current status on single and multi-site planning and scheduling. However, there has not been much work done in the literature towards the integration of planning and scheduling in the paper industries. Pinar et al. (2002) proposed an agent Author to whom correspondence should be addressed: [email protected]

1622 based decision support system termed as Asynchronous Team (A-Team) framework for central planning and scheduling of gross root paper industries based on heuristics. The challenges are in terms of the complex issues relating to handling large-scale advanced planning and scheduling problems leading to combinatorial explosion of the problem sizes for centralized decision-making. Moreover, the horizons of interest are broadly different in planning and scheduling models. Hence, decomposition based approaches have been increasingly gaining attention in the recent years. Additionally, in the decomposition based approach, the models at the upper levels must reflect accurate abstractions of the lower levels and should be revised as infrequently as possible when compared to the lower levels. The planning models must be consistent with lower level scheduling models, and the scheduling models must again be consistent with the plant level operation thus achieving the vertical integration. Traditionally, the decisions in an enterprise flow in a top-down manner leaving less degree of freedom at lower levels fbr rescheduling, leading to frequent revision of targets set by the top levels. Embedding contingency measures for integration of rescheduling has been ignored in most of the works published. With this motivation, in this paper an integrated multi-level decomposition based framework has been proposed for efficient integration of planning and scheduling for a multi-site, multi-product plant with applications to paper manufacturing. Productionplanning and scheduling for paper manufacturing in real world environment involves intricate issues related to large-scale production in a hybrid flowshop configuration. Issues related to minimizing trim loss while maintaining on-time delivery of orders need to be addressed. Typical real world problems have about 1000-5000 orders to be manufactured across 5-10 paper machines from 3-6 mills in 1-3 months time (Pinar et al., 2002). The resulting formulation involves solution of mixed integer linear/nonlinear problems with very large number of variables and constraints. Despite the significant progress in the computational resources in the recent years, such large models cannot be solved with the capabilities of the existing solvers. Hence a decomposition based solution approach is necessitated. In this work, we consider a mathematical programming based multi-level framework with minimal heuristics for the above integrated planning and scheduling problem. This is an extension of the earlier work (Munawar et al., 2003; Munawar and Gudi, 2004) but oriented for multi-site plants. This paper is organized as follows. In the next section, we discuss a general multi-level decomposition based framework. Later in section 3, the proposed framework is illustrated for solving the integrated planning and scheduling problem in a paper manufacturing industry, along with a representative case study.

2. Multi-level Decomposition based Framework Consider a general multi-site, multi-product planning and scheduling problem with several plants located in different geographic locations with product demands specified over a multi-period operation. Each product has different site dependent manufacturing/production cost, and depending on the customer location there is also an additional transportation cost involved from the manufacturing location. Furthermore, each site has some inventory cost for products produced earlier than their due date, and a tardiness penalty for products produced later than their corresponding due date. At

1623 each site, a generic hybrid flowshop configuration of various machines is assumed that can be easily simplified to any problem specific topology of series and/or parallel configuration of different stages. The global objectives are minimizing the overall costs discussed above and timely satisfaction of customer orders with minimal impact of the disruptions if any (machine breakdowns etc.), on the plant operation. The latter objective is achieved implicitly through the proposed proactive measures for local attenuation of the plant disruptions leading to infrequent revision of the commitments made to the customers. Based on the inherent, functional decomposition of the global objectives, the overall problem can be traditionally decomposed into two major levels, a primary level for strategic (or longterm) planning over a multi-period operation across multiple sites and a secondary level for tactical (or mid-term) planning and scheduling at each site in each time period. The primary level has multi-period demands over a longer horizon (say 1 year) and has an abstraction of each plant in terms of the average production and inventory capacities. Accordingly, based on minimization of the overall cost mentioned above, the abstract model at this level sets production targets for each plant. Additionally at this level we consider an abstraction of the other production losses that may possibly occur at the lower levels. The production losses could be either the trimming losses in cutting stock problems or the slopping losses during grade changeovers in refinery problems (Munawar and Gudi, 2004). The primary level is revised on a less frequent basis (say monthly/quarterly) to avoid frequent revision of the commitments made to customers. At the secondary level, for mid-term planning and scheduling at each site/plant with detailed plant constraints, the horizon of interest is smaller (1-3 months) catering to less number of customers, and the model here may be revised/updated on a frequent (say weekly/monthly) basis but without violating the global objectives. The lower levels have detailed constraints to account for the production losses mentioned above. Depending on the complexity of the problem these levels may further need to be decomposed as discussed later in section 3.2. From a reactive scheduling point of view, some pro-active measures are embedded into the multi-level structure; such as assuming higher production losses at the top levels; and appropriate relative penalties to some of the cost terms in the objective function. This is motivated towards better flexibility at later stages for reacting to unforeseen plant disruptions.

3. Application to Paper Manufacturing The major decisions in paper manufacturing are order allocation across multiple sites, run formation and order sequencing in each paper machine, trim schedule for minimum wastage of paper and a load schedule for order distribution to various destinations. In this work, we consider decision support for only the first three processes and propose ways of solving the integrated production planning and scheduling problem.

3.1 Paper Manufacturing as a Hybrid Flowshop Facility The superstructure of all the alternate products at any site can be viewed as paper machines for producing different disjunctive mode; i.e. only one paper

production routes for producing different paper a hybrid flowshop facility. For a site with two grades of paper, the paper machine operates in a grade can be produced at a time, and involves

1624 transition time for grade changeovers which might be sequence and machine dependent. Orders of smaller roll dimensions may often need to be further cut on common rewinders (parallel lines) before they are wrapped and packaged for dispatch. 3.2 M u l t i - l e v e l D e c o m p o s i t i o n

The proposed multi-level framework is shown in Figure 1. For small-size problems with fewer customer orders, a two-level decomposition may be adequate as shown in Figure 1(a), while for medium to large-scale problems a four level decomposition, as shown in Figure 1(b), is found to be necessary for obtaining the solution in real time.

Level-1

Z T Level-2

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Simultaneous Trim loss minimization & pattern sequencing

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Figure 1. Proposed multi-levelframework for multi-sitepaper manufacturing In Level-1 problem of Figure l(a), a MINLP formulation has been proposed for simultaneous order allocation and grade sequencing across multiple sites with assumed trim losses, which is later linearized to an MILP after removing the bilinearities. For addressing the complex issues related to large-scale production in a hybrid flowshop configuration at the upper levels, some simplifying assumptions have been made. Generally the production rates in a paper machine are much lower compared to processing in other downstream units. Hence, the order allocation problem is generally assumed to be based on the aggregate properties of the paper machine alone rather than based on the entire production route in the hybrid flowshop. For medium to large-size problems as shown in Figure l(b), the objective at the top sub-level (Level-la) is primarily order allocation (without sequencing) across multiple sites with assumed production losses; while at the next sub-level (Level-lb) the objective is sequencing of grades for each paper machine individually, with penalties for violation of due dates. Before going into the details of the lower level problem (Level-2) we first present the results of the upper levels for a representative problem.

Case Study on Small-size Planning and Scheduling Problem." Consider 4 paper machines at 3 paper mills located in distinct locations for meeting 21 orders placed from 5 different customers. All the MILP models in this work are solved using CPLEX solver on ILOG OPL STUDIO, while the MINLP model is solved using SBB solver on GAMS. When we applied the simple two-level decomposition shown in Figure 1(a), the MINLP problem at Level-1 takes long computational time (more than 1 hr). When the four-level decomposition shown in Figure 1(b) was applied, both the sublevels at Level-

1625 1 together are solved relatively faster to find the order-machine allocation and grade sequencing (for all 4 machines). On each paper machine, for the set of orders assigned to each time slot, the problem at Level-2 involves trim loss minimization and sequencing of optimal cutting patterns. In the literature, typically, the trim loss problems (Level-2a) and the sequencing of the optimal cutting patterns (Level-2b) are solved sequentially (Westerlund et al., 1998; Westerlund and Isaksson, 1998). Due to the current computational limitations, the traditional sequential approach (Level-2a followed by Level-2b) needs to be used for large-scale problems. In this work, it is demonstrated that for small to medium-size problems, the proposed novel approach (aggregate Level-2) shown in Figure l(a) for simultaneous trim loss minimization and sequencing of cutting patterns has more flexibility leading to better customer satisfaction and lower overall costs.

3.3 Simultaneous Trim loss Minimization and Sequencing of Optimal Cutting Patterns Consider the one-dimensional trim loss problem with fixed deckle size of the paper machine that allows variation only in the length of the cutting patterns. Given the problem parameters of the paper machine and winder, along with the data related to the customer orders, the total number of feasible cutting patterns can be enumerated using the explicit procedure listed in Westurlund et al. (1998). The link between the trim loss minimization problem and the pattern sequencing problem is through the use of the common decision variables for selection of optimal patterns and their corresponding optimal lengths. The resulting MILP problem formulation is not presented here due to space limitations. We assume as many time slots as the total number of feasible cutting patterns. Since all the cutting patterns may not be selected at the optimal solution some slots would be empty. (When the number of feasible cutting patterns is large it may lead to combinatorial problems and hence the proposed simultaneous approach is applicable to small to medium size problems, otherwise the sequential approach is recommended). We enforce unique allotment of a pattern to a time slot with the provision for some slots being empty. All the empty slots are pulled towards the beginning of the horizon and the corresponding decision variables are assigned to zero for these slots. The objective function includes penalties for tardiness and under production, in addition to the costs resulting from trim loss and knife changes (due to the transition between patterns).

Case Study." For illustrating the proposed model, consider a set of 7 orders of the same grade assigned to a single slot. For the given problem data, the total number of feasible patterns are enumerated to be 22. Using the trim minimization problem, 7 optimal set of patterns are selected (p5, p9, p14, p17, p 1S, p19 and p22) and the total cost is $20504. Then the pattern sequencing problem for these 7 optimal patterns yields a total tardiness cost of $2438. The overall results for the traditional sequential approach are: % Trim loss : 1.0312 Trim cost : S9899 Under production cost : $9906 Knife change cost : $700 Tardiness cost : $2438 The total cost : $22943 The optimal sequence is: p 17 --) p9 ---)p5 --) p 18 --) p 19 --) p22 --) p 14

1626 When we solve the proposed simultaneous trim minimization problem and pattern sequencing problem, the following output is obtained. 10 optimal patterns are selected. % Trim loss : 1.0313 Trim cost : $9901 Under production cost : $9907 Knife change cost : $1000 Tardiness cost : $1015 The total cost : $21823 The optimal sequence is: p17-) p12 --) p9 ---)p5 --) p21--) p19 --) p22-) pl 8--) p14 --) p7 A comparison of the above results reveals that, though there is an increase in the knife change cost for the 10 optimal patterns selected by the simultaneous approach, there is a drastic reduction in the tardiness costs for the same trim loss and underproduction costs and hence the overall costs for the simultaneous approach are relatively lower. Conclusions

In this paper, the integration of planning and scheduling in a multi-site, multi-product plant is discussed with applications to paper manufacturing. At the lower level a novel simultaneous approach is proposed for the combined trim loss minimization and pattern sequencing problem. Realistically (large) sized industrial problems would bring in further complexities (constraints) and challenges that require novel approaches for decomposition and global solution; this is an aspect of future research. References

Munawar, S.A. and R.D. Gudi, 2004, A multi-level, control-theoretic framework for integration of planning, scheduling and rescheduling, In: 7th International Symposium on Dynamics and Control of Process Systems (DYCOPS-7), July 5-7, 2004, Massachusetts, USA. Munawar, S.A., Bhushan, M., Gudi, R.D. and Belliappa, A.M., 2003, A multi-level, control-theoretic approach to reactive scheduling in continuous plants, In: 4 th Conf. on Foundations Of Computer Aided Process Operations (FOCAPO), 397. Pinar, K., Wu Frederick, R. Goodwin, S. Murthy, R. Akkiraju, S. Kumaran and A. Derebail, 2002, Scheduling solutions for the paper industry, Oper. Res., 50(2), 249. Shah, N., 1998, Single and multisite planning and scheduling: current status and future challenges, AIChE Symp. Ser., 94 (320), 75. Shobrys, D. E. and D. C. White, 2000, Planning, scheduling and control systems: why can they not work together, Comp. Chem. Eng., 24, 163. Westurlund, T., J. Isaksson and I. Harjunkoski, 1998, Solving a two-dimensional trimloss problem with MILP, Euro. J. Oper. Res., 104, 572. Westurlund, T. and J. Isaksson, 1998, Some efficient formulations for the simultaneous solution of trim-loss and scheduling problems in the paper-converting industry, Trans. IChemE., 76 Part A, 677.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) (©2005 Elsevier B.V. All rights reserved.

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Review of optimization models in the pollution prevention and control Emilia Kondili a, a Assistant Professor Dept. of Mechanical Engineering, Technological Educational Institute of Piraeus, Greece

Abstract The objective of the present work is to investigate the extent and effectiveness of the implementation of optimization methods for the solution of environmental problems. In order to fulfill its objective, the present work reviews a significant number of scientific / research papers dealing with the application of optimization approaches for the solution of environmental problems, in the areas of air pollution, solid, liquid and industrial waste management, and production integrated pollution control. The review focuses its attention to the identification of the basic problem parameters, the type of the optimization model for each particular problem category and the results obtained. Amongst its various other conclusions, the present work exhibits the contribution of the optimization modeling to the identification of all the characteristics of the environmental problems and their integrated approach.

Keywords: Optimization, Modeling, Pollution Prevention, Mathematical Programming 1. Introduction In many cases the solution of problems related to the environment require decisionmaking and selection between a number of alternatives that need to satisfy a number of technical and regulation constraints. Therefore, in parallel to various other efforts for the solution of the environmental problems, a significant number of scientific works have appeared in the literature, approaching the environmental issues through the development of optimization models and their implementation in practical cases. The objective of the present work is to investigate the extent and effectiveness of the implementation of optimization methods for the solution of environmental problems. In order to fulfill its objective, the present work reviews a significant number of scientific / research papers dealing with the application of optimization approaches for the solution of environmental problems. The review focuses its attention to the identification of the basic problem parameters, the development of the optimization model, i.e. the identification of the optimization criteria that drive the problem solution, the various different constraints that need to be taken into account in each specific type of problem, the algorithms being used for the solution of the optimization models and the results obtained.

1628

2. Optimisation methods and tools Optimisation methods and algorithms have lately become very valuable tools for the solution of a wide variety of complex engineering problems. Two recent excellent review papers of Biegler and Grossmann (2004) and Grossmann and Biegler (2004) analyse and classify the current situation and future prospects of optimisation methods and tools, as well as their applicability to the solution of various practical problems. Mathematical programming and optimization in general have also found extensive use in various types of environmental problems. The reason is that, in these problems, there is very often a need for decision making under conflicting objectives, since there is a number of alternative solutions and the optimal one needs to be chosen. Therefore, a list of mathematical and decision support techniques have been deployed in the past years to aid in forming policies or solving various environment-related design, operation, planning, scheduling and routing problems. The optimization techniques being implemented in the reviewed literature are deterministic and stochastic programming models. The deterministic optimization models range from simple Linear Programming, Mixed Integer Linear Programming, Non-Linear Programming, Dynamic Programming models, as well as multi-objective optimization models, depending on the specific characteristics of the problem under consideration. For problems including uncertainty stochastic programming models, such as Fuzzy linear programming, fuzzy integer programming, Interval linear Programming, are used. The use of multicriteria decision methods in a number of real environmental problems is described by Ladhema et. al (2000). The authors describe the methodology for approaching environmental problems with multicriteria analysis, supporting the view that this formulation provides a comprehensive framework for storing all relevant problem information, makes the requirement for new information explicit and thus supports the most efficient allocation of resources.

3. Optimisation methods in various environmental problems 3.1 General considerations A wide spectrum of environmental problems is solved with optimization methods, such as the environmental process synthesis and design, waste management and minimization, water resources management, energy management with environmental considerations. However, the present work only deals with a rather limited area of environmental problems, focusing its attention to the problems with most interest for the CAPE community (Table 1). Table 1. Environmental problems included in the present work

Air pollution Waste minimisation Environmental synthesis and design Facility location Supply chain with environmental considerations Solid waste management

1629 3.2 Air pollution Mathematical programming models are extensively used in air pollution management literature. Generally, the objective of these models is to optimise the cost of policy decisions with the great majority oriented to minimising the cost of control and removal methods. The main possibilities are the minimisation of the pollutants, the minimisation of the pollutants reduction cost and the minimisation of the pollutants concentration in the most sensitive receptors. The constraints being developed express the conformity to pollution standards. A very comprehensive survey of mathematical programming models in air pollution management is presented by Cooper et al (1996). However, since then, various papers have appeared in the literature, dealing with a number of interesting aspects of air pollution management. For example, Shaban, Elkamel and Gharbi (1996) have developed a Mixed Integer Linear Programming model for the selection of the best pollution control strategy to achieve a given pollution reduction level. The objective of the model is to minimise the total control cost, consisting of operating and investment costs. Various constraints are imposed on the model, including a prescribed pollution reduction level and maximum budget available for investment. The model gives the optimum set of control options along with their optimum set-up times. 3.3 Waste minimisation Wu and Chang (2003) have developed a method and procedure for the optimisation of a textile dyeing manufacturing process in response to the designated waste minimisation alternatives, the new environmental regulations and the limitations of production resources. They use a nonlinear integer optimisation framework. The objective function is the profit maximisation, including benefits from product sales as well as the emission/effluent charge and water resources fees required by new environmental regulations. The constraint set includes capital and labour limitations, equipment availability, demand requirements, water balances and capacity limitations. The optimisation method that is used is based on the Genetic Algorithm and uncertainties are dealt with via an interval analysis. Chakraborty et. al. (2003) introduce a systematic planning methodology for obtaining a long-term waste management strategies for entire batch manufacturing sites. Their work introduces a dynamic view of designing optimal waste management strategies for a planning horizon of 5-10 years. The objective function minimises the net present cost that includes the operating cost, the annualised capital investment and the maintenance costs. The operating cost is obtained as the probabilistic average of the operating cost in the individual waste forecast scenarios. This term takes into account penalties for capacity constraint violations. The problem constraints include corporate-wide budget limitations, special permit constraints, emission trading opportunities, emission limitations. The resulting model is an MILP model. Alidi (1996) proposes a multiobjective optimisation model based on the goal programming approach to assist in the proper management of hazardous waste generated by the petrochemical industry. The analytic hierarchy process (AHP), a decision making approach, incorporating qualitative and quantitative aspects of a problem is incorporated in the problem to prioritise the conflicting goals usually

1630 encountered when addressing the waste management problems of the petrochemical industry.

3.4 Environmental Synthesis and Design Brett et al (2000) believe that the incorporation of environmental sensitivity into process models has not been very satisfactory, mainly because of the difficulty in translating process information to environmental objectives. In their work they propose a methodology according to which the Life Cycle Analysis (LCA) assists in the development of environmental objectives in process design and they use a multiobjective formulation of the process that combines economic objectives with the LCA environmental objectives. A case study of a nitric acid plat has been undertaken to demonstrate their approach. The process is modelled in Hysys to obtain mass and energy information. Goal programming, a multiobjective optimisation technique, has been used to solve the problem. In conclusion, they believe that LCA linked to rigorous process analysis tools allow for explicit considerations to the design decisions. Linninger and Chakraborty (1999) proposed a hybrid methodology for the synthesis of waste treatment flowsheets through a search based superstructure generation step using a linear planning algorithm. Next, a rigorous plant specific policy optimisation is carried out, with a desired performance function, such as treatment cost, and a set of site specific environmental capacity and logistics constraints. 3.5 Facility location Rakas et al. (2004) have developed a model for determining locations of undesirable facilities. It is formulated as multiobjective model, since the problem of locating undesirable facilities faces many conflicting criteria. Mathematical models for the location of undesirable facilities are designed to address key questions, such as how many facilities should be located and how large each facility should be. In general, such problems are multiobjective. The objective functions of the optimisation model express the total cost minimisation and the minimisation of the population opposition to the construction of the landfill in their area. This paper also proposes another way to treat uncertainties in locating undesirable facilities, which is based on Fuzzy Mathematical Programming. Chang and Wei (2000) illustrate a new approach with a view to optimising siting and routing aspects using a fuzzy multiobjective nonlinear integer programming model as a means that is particularly solved by a genetic algorithm. The effective planning of solid waste recycling programs is a very important challenge in many solid waste management systems. One of such efforts is how to effectively allocate the recycling drop-off stations with appropriate size in the solid waste collection network to maximise the recycling achievement with minimum expense. 3.6 Supply chain with environmental considerations Hu et al (2002) present a cost-minimisation model for a multi-step, multi-type hazardous waste reverse logistics system. They develop a discrete-time linear analytical model that minimises total reverse logistics operating costs subject to constraints that take into account such internal and external factors as business operating strategies and environmental regulations. The model that is developed consists of four critical activities: collection, storage, treatment and distribution. The objective of the proposed

1631 model is to maximise the total reverse logistics cost for a given multi-step period, including total collection cost, total storage, treatment, transportation cost for reusing processed wastes and total transportation costs tbr disposing processed wastes. Turkay et al (2003) address the multicompany collaborative supply chain management problem. Fhe proposed approach consists of modelling process units using fundamentals of thermodynamics, conservation of mass and energy and process data, development of an MILP model for the supply chain integration of different process systems and comparative analysis of the results. The problem is solved using ILOG system.

3.7 Solid Waste Management Various deterministic mathematical programming models have been used for planning solid waste management systems. Nema and Gupta (1999) have dealt with the planning and design of a regional hazardous waste management system that involves the selection of treatment and disposal facilities, allocation of hazardous wastes and waste residues from generator to treatment and disposal sites and selection of the transportation routes. They present an improved formulation based upon multi-objective integer programming approach to arrive at the optimal configuration. The objectives addressed are the minimisation of the total cost, which includes treatment and disposal costs and transportation cost, minimisation of the total risk, which includes waste treatment and disposal risk as well as risk involved in waste transportation. The problem constraints are mass balances of wastes, allowable capacities for treatment and disposal technologies, waste-treatment technology compatibility constraints and waste-waste compatibility constraints. The resulting model is an MILP problem. Costi et. al (2003) have developed a Decision Support System (DSS) designed to help decision makers of a municipality in the development of incineration, disposal, treatment and recycling integrated programs. The main goal of the proposed DSS is to plan the MSW management, defining the refuse flows that have to be sent to recycling or to different treatment or disposal plants and suggesting the optimal number, the kinds and the localisation of the plants that have to be active. The DSS is based on a decision model that requires the solution of a constrained non-linear optimisation model where some variables are binary and other ones are continuous. The objective function takes into account all possible economic costs, whereas constraints arise from technical, normative and environmental issues. Huang et. al (2001) have applied an integrated solid waste management system based on inexact fuzzy stochastic mixed integer linear programming to the long term planning of waste management activities in the city of Regina. Their model can effectively reflect dynamic, interactive and uncertain characteristics of the solid waste management system in the city. Their approach is able to answer questions like the appropriate reduction goals, the waste flow allocation pattern, level of reliability and ways to handle rapid increase of waste generation.

4. Summary and conclusions The need for effective optimisation methods that incorporate concepts of efficient resource use and environmental concern is becoming more and more urgent as the

1632 environmental situation deteriorates. This paper offers a review on optimisation methods that have been used for the solution of environmental problems and reviews a number of papers in specific environmental problems. Depending on the characteristics of the treated problem, different optimization models and optimization algorithms are used. Critical success factors are the problem size and the reliability of various process models that are used. In any case, one of the most significant contributions of the optimization modeling is the identification of all the characteristics of the environmental problems and their integrated approach. References Alidi Abdulaziz S., 1996, A multiobjective optimization model for the waste management of the petrochemical industry, Appl. Math. Modelling, Vol. 20 Biegler, L. T., Grossmann, I. E., 2004, Retrospective on Optimisation, Computers and Chemical Engineering 28, 1169-1192 Brett A., Barton G., Petrie J., Romagnoli J., 2000, Process synthesis and optimisation tools for environmental design: methodology and structure, Comp. and Chemical Engng 24, 1195-1200 Chakraborty A., A.Malcolm, R. D. Colberg, A. Linninger, 2003, Optimal waste reduction and investment planning under uncertainty, Computers and Chemical Engineering 2003 Chang N-Bin, Y.L. Wei, 2000, Siting recycling drop-off stations in urban area by genetic algorithm-based fuzzy multiobjective nonlinear integer programming modelling, Fuzzy Sets and Systems 114, 133-149 Cheng S., C.W. Chan, G.H. Huang, 2003, An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management, Engineering Applications of Artificial Intelligence 16, 543-554 Cooper, W.W., Hemphill, H., Huang, S.L., Lelas, V., Sullivan D.W., 1997, Survey of Mathematical Programming models in air pollution management, 96, 1, 1-35. Costi P., Minciardi, R., Robba, M., Rovatti, M., Sacile R., 2003, An environmentally sustainable decision model for urban solid waste management, Waste Management 24, Issue 3,277-295 Grossmann, I. E., Biegler, L. T., 2004, Part II. Future Perspective on Optimisation, Computers and Chemical Engineering 28, 1193-1218 Hu Tung-Lai, Jiuh-Biing Sheu, Kuan-Hsiung Huang, 2002, A reverse logistics cost minimization model for the treatment of hazardous wastes, Transportation Research, Part E, 38 457-473 Huang G.H., N. Sae-Lim, Z. Chen and L. Liu, 2001, Long-term planning of waste management system in the City of Regina- An integrated inexact optimisation approach, Environmental Modelling and Assessment 6, 285-296 Ladhema R., Salminen P., Hokkanen J., 2000, Using Multicriteria Methods in Environmental Planning and Management, Environmental Management, 26, 595-605 Linninger A. A., Aninda Chakraborty, 1999, Synthesis and optimisation of waste treatment flowsheets, Computers and Chemical Engineering 23, 1415-1425 Nema Arvind K, S.K. Gupta, 1999, Optimization of regional hazardous waste management systems: an improved formulation, Waste Management 19, 441-451 Rakas J., Theodorovic D., Kim, T., 2004, Multi-objective modeling for determining location of undesirable facilities, Transportation Research Part D 9, 125-138 Shaban H. I., A. Elkamel, R. Gharbi, 1997, An optimization model for air pollution control decision making, Environmental Modeling & Software, Vol. 12, No. 1, pp. 51-58 TOrkay Metin, Cihan Orug, Kaoru Fujita, Tatsuyuki Asakura, 2003, Multi-company collaborative supply chain management with economical and environmental considerations, Comp. and Chemical Engineering Wu C.C., N.B. Chang, 2003, Global strategy for optimising textile dyeing manufacturing process via GA-based grey nonlinear integer programming, Comp.and Chemical Engng 27, 833-854

European Symposiumon ComputerAided Process Engineering- 15 I,. Puigjaner and A. Espufia (Editors) :CI:,2005 Elsevier B.V. All rights reserved.

1633

Models for integrated resource and operation scheduling Alain Ha~'ta*, Martin Tr~panier b and Pierre Baptiste b a Institut National Polytechnique de Toulouse, E N S I A C E T - LGC 118 route de Narbonne 31078 Toulouse cedex 4, France b Ecole Polytechnique de Montrdal C.P. 5079 Succ. Centre-Ville, Montrdal (Qudbec), Canada H3C3A7

Abstract This paper deals with energy and human resource constraints in scheduling models, it outlines the influence of these resources, and the necessity to account for them in scheduling models. A parallel view of these resources is presented, and their characteristics are illustrated in the case study of a tubing plant.

Keywords: scheduling, energy, human resources, integrated models.

1. Introduction As a part of production management, scheduling has been widely addressed in the process engineering literature (Pinto and Grossmann, 1998). According to Pinedo (Pinedo, 2002), "scheduling deals with the allocation of scarce resources to tasks over time. It is a decision-making process with the goal of optimizing one or more objectives." Most scheduling research deals with sequencing problems, assuming that processing times are constant and known. Many authors noticed that, unfortunately, those theoretical results are hardly applied in real situations. Sometimes processing times can be variable, due to the scheduling itself. This happens when a resource is shared between some processing stages: operator working simultaneously on several machines, limited power provided to several energyconsuming equipments, etc. Processing times then depend on the operator (availability, efficiency, priority choices), the energy provided, and so on. Consequently, processing times and scheduling decisions are embedded, due to "secondary" resources essential to know the processing behaviour. These resources, generally considered at a real-time control level, have a significant influence on the scheduling objective.

2. Scheduling with secondary resources Introducing secondary resources in scheduling models means that these resources have specific constraints (e.g. a limited capacity) and/or influence on the objective function (e.g. cost). In these cases, scheduling is not restricted to task sequencing.

Author/s to whom correspondence should be addressed: [email protected]

1634 The Resource Constrained Project Scheduling Problem (RCPSP) can be view as a general frame for these problems. A limited amount of renewable resources is shared between the operations. Each operation needs a fixed amount of each resource to be performed. Operation start and end times are then necessary to determine the cumulative resource needs at any time. Precedence constraints represent the sequence of operations. Solving approaches take advantage of problems specificities: few precedence constraints (project scheduling), disjunctive resources (job shop scheduling). However, the problem remains complex. Another solution is to separate operation and secondary resource scheduling in two steps (Boukas, Haurie and Soumis, 1990). When operations can be performed with a variable amount of resource, processing times are a function of this amount. Resource assignment decisions set the amount of resource for each operation at any time. Integrated scheduling must then solve simultaneously three problems: sequencing, start/end times determination and secondary resource assignment over time (Daniels and Mazzola, 1994).

3. Energy in scheduling models Energy may be an important part of production costs in the process industry. However, it has been often considered as an uncompressible cost, or hidden in a global bill without seeking for the origin of the consumption. Recently, some research in sustainable development addressed this problem, for strategic and tactic decisions: energy exchange between plants (korhonen, 2002), long-term maintenance scheduling for better energy utilization (Cheung and Hui, 2004). Some years earlier, Kondily et al. (Kondily, Shah and Pantelides, 1991) presented an algorithm for the planning of multiproduct energy intensive continuous operations. For short-term decision, Corominas et al. (Corominas, Espufia and Puigjaner, 1994) studied energy-saving by heat exchange between operations.

3.1 Processing time In scheduling problems, energy is treated as a renewable resource, shared by the process units. Capacity constraints represent the amount of energy available at any time (e.g. maximal power). Processing times may depend on the amount of resource provided. Continuous models (linear or not) describe processing time evolution, according to the equipment unit, the product and the operation. In (Corominas, Espufia and Puigjaner, 1994), the authors notice an energy-time trade off. Cycle time variations are due to decisions on operation start times, taken to optimize heat exchanges by operation synchronization. When processing time depends on the energy provided, another type of decision appears: assignment decisions.

3.2 Energy assignment Energy delivered to the units varies over time according to operation needs and assignment decisions. Scheduling aims at determining the assignment, along with operations start/end times and operation sequence, which give the best objective. Assignment models rely on the energy evolution: evolution on the time axis (when does the energy value change?) and on the values axis (how does it change?). For time evolution three policies are possible: • Free change: the energy provided to the units can change continuously;

1635 • Periodic change: energy delivery is re-evaluated at each period; • Event change: for example, the configuration changes after the end of an operation. These policies may be combined to fit with the process behavior, but this induces more complex models. A periodic approach with sufficiently small periods can be a satisfying way to represent in a same model the three policies. Energy value evolution also obeys to different constraints, according to equipment characteristics. For example, overall energy provided to the process may not increase too rapidly. Similarly, for a single unit, energy increase may be bounded, involving a continuous shape to the energy evolution curve.

4. H u m a n resources in s c h e d u l i n g m o d e l s Even though human resources (HR) are more important in manufacturing, they can have a significant action in the process industry. Due to variations of the demand, flexible organizations induce both more complex tasks and more important HR costs. Some research present scheduling approaches, integrating human resources, for parallel machines (Chen, 2004, Daniels, Hoopes and Mazzola, 1996), and flow shops (Daniels and Mazzola, 1994, Daniels Mazzola and Shi, 2004), where processing times vary according to the number of operators allocated to the tasks.

4.1 Processing time HR are renewable resources, but the capacity is not constant: operator availability varies with shifts, breaks and days-off. We identify three situations where processing times vary due to HR: • When an operator can run several machines. His work is shared between these machines and consequently productivity decreases on each machine. Various operating modes can be defined, to improve the productivity of one machine or another. • When work posts need several operators to run. The number of operators assigned to a work post determines the productivity of this post. • When productivity varies with skill or experience (or learning, etc.). Then individual assignment has an influence on processing time. Except for fatigue and learning, discrete models represent processing time variations, according to assignment and operating mode choices.

4.2 HR assignment In theory, the three change policies presented for energy are applicable. However, periodic change (at rest or lunch breaks) and event change (end of operation) are more realistic. These changes affect the number of operators at each work post, or the number of machines assigned to an operator (the workshop configuration), and the individual assignment, according to skill, experience, etc. Finally, they affect the operating modes.

4.3 Personnel scheduling HR are subject to legal constraints and specific agreements on the work duration, schedule, rest, etc. These constraints introduce interruptions, delays in some operations. Many research deals with this topic, but few approaches integrate it into scheduling

1636 (Mercier, Cordeau and Soumis, 2003). These approaches generally consider a discrete time horizon, and use column generation to deal with these problems.

5. Case study The case study is a tubing plant in the Montreal area. The plant is divided in three main departments: • Foundry: native and recycled metal is melted in induction melting furnace. Then, it is cast in individual billets and stored for further processing. • Drawing mill: billets are heated and drawn into bars. • Pipe-tubing: billets are heated and extruded to make pipes of different sizes, shapes and lengths. These melting and heating processes use a huge quantity of energy: electricity, natural gas and steam. Electricity expenses account for more than half the annual energy costs for the plant. Non regular power consumption peaks occur and cause high electricity bills. The subscription is 10 700 kW, while the average consumption power is about 65% of subscription. However, consumption along the day is highly irregular, leading to overspendings. Figure 1 shows the number of overspendings during the day. There are evident cuts at shift changes (7h00, 15h00 and 23h00) and break periods.

,4] 12

10 8 6 4 2 0

0 h O0

6 h O0

12 h O0

18 h O0

0 h O0

Figure 1. Number of overspendings (mean values between 01-01-2002 and 29-03-2003) Our goal is to limit these overspendings. A better synchronization of the furnaces would bring more regular electricity consumption and less power peaks, resulting in lower electricity costs. The following linear model minimises the electricity bill for the foundry. It is based on a formulation of the RCPSP (G61inas, 2004). There are m furnaces to perform n fusion operations. We assume that operation assignment to the furnaces and sequence on each furnace are known. Job j is composed of three consecutive operations: loading (duration aj), fusion (duration function of the power provided to the furnace) and unloading (duration bj). When fusion is completed, a minimal power Pwait is provided to the furnace until unloading. Loading and unloading are performed by an operator. The number of operators is limited to R. Energy consumption and overspendings are estimated by the supplier every 15 minutes. The horizon is divided in U periods of 15 min. Each period u is subdivided in N steps, so that the horizon is also divided in N. U steps. Period u starts at time t, = N . u .

1637 Nomenclature

Due date of job j Release date o f j o b j .

4

r/ X .t

.I

yj

t

Ai l!

e~

~f jl l

(l'c[l'n]).

= 1 if the loading operation of job j begins at time t or before.

ewi

=1 if the unloading operation of j o b j begins at time t or before. Set of jobs assigned to filmace i. Precedence links of Ii jobs. Ai = {(/l,j:) jl precedesje in i}. Energy necessary to complete operation j at time t,,. Energy necessary for job j.

ii

Pnlitl~

Pmax

Energy assigned to furnace i for the fusion of job j E li during period u. Energy spent in furnace i during period u, waiting for unloading job j. Mirdmax power in furnace i. Power in furnace i waiting for unloading. Energy consumption during period u. Overspending during period u.

Pwait

OVu

Power subscription

Constraints

Vt c [O ,'4- bj- @-2] v t ~ [,:;+~; • 4 - b,.-2] Vt _< t) -1 V t >- di--b/ . . - a; V t < t)+aj-1 . , Vt _> di-b/

(1)

x/+ / > - - x' ,]

(2)

.,V1/ + / > F/

(3) (4) (5) (6) (7)•

x.'1 = 0 r.'- 1 -.i y/- 0 .,v - ' = l xJ .('-"j) ->- .v.J

W, v t e [r/+a, • 4 - bj-/]

(8)

x / <_ )5./('-t'/)

Vt, Vi, V (l'l,j2)eAi

(9) (10) (11)

ei° - & e/'~ ¢ = e / ' - eft'

vj vj, Vu c [0; U-l] Vj, Vu c [0; U-1]

Vj, vj, Vj, Vj, Vj, Vj,

-

ef/' < ej" ,,

{~,~(,,+,,,

,

,,

Operation continuity. Loading operations time window. Unloading operations time window. Precedence constraints.

)

Amount of energy necessary at time t,, to complete operationj.

(13) e l "/ >- Prom ",._,,= (~-,,u,,,+,, N.,, , (X(/-"/) -- y~, ) -- e w /,, / p,,,~,,, )

Energy assigned to furnace i for fusion of job j ~ i;, during period 14.

(14) ew/,, > p.,,e,. ~,v("+"-' ,--,v.,, (xl,- / 4, - Y J) J / / Pmin ) , - ef"

Vj, Vu c [0; U-l]

(15)

Loading - unloading operator availability.

(12)

ef j

~

Plrlax

"v......d,

,.,".it

(x.(/ a/) _ .}]J ) __ e W j

/ Z/ ((x;• x"-':") + (y,'

- 3/

/ Pwait

))< R

-

Vt ~[0; N. U -1] (]6)

(17) (18) (19) (20) (21) (22) (23) (24)

or,, > sp,,-1,1.P or,, > 0 Xj.I e F. l

{0,1 } .~ E {0,1}

el'>_ 0

Vu e [O,U- 1] Vue[O,U-1] vj, v t ~ V; ; 4 - b / - , j - / ] vj, v t ~ [,~;+a; • 4 - bj-/]

e.ff'>_ 0 ew/'_> 0

vj, v u E [ 0 ; U-l] Vj, Vu c [ 0 ; U-l] Vj, Vu c [ 0 ; U-l]

sp,, >_ 0

Vue[O,U-1]

Energy consumption during period u. Overspending during period u. Binary variables Continuous variables.

1638

We wish to minimise the energy bill, function of subscription P, consumption overspendings or,,: min(f.P

sp, and

+ f2.~. sp. + f3.~-'~ ov.) II

It

This basic model can be modified: operator availability could vary with time (lunch, rest), subscription P could be variable so the model would choose the best subscription to minimise the bill, etc. A Constraint Programming formulation could be used for the cumulative constraints (15), replacing the numerous variables x/and y / b y the loading and unloading operation start times.

Conclusion This paper outlines the importance of secondary resources in scheduling. Energy and human resources are influent on processing times and production costs. Their assignment may change during processing, in order to provide the resources to the operating units. Accounting for these resources in scheduling is still a challenging problem. References Baptiste, P., M. Trepanier, S. Piraux, S. Quessy, 2004, Vers une int6gration de la gestion des ressources dans le pilotage des op6rations. Boukas, E.K., A. Haurie, F.Soumis 1990, Hierarchical approach to steel production scheduling under a global energy constraint, Annals of Operations Research, 26, 289-311. Chen, Z.-L., 2004, Simultaneous job scheduling and resource allocation on parallel machines, Annals of Operations Research, 129, 135-153. Cheung, K.-Y., and C.-W. Hui, 2004, Total-site scheduling for better energy utilization, Journal of Cleaner Production, 12, 171-184. Corominas, J., A. Espufia and L. Puigjaner, 1994, Method to incorporate energy integration considerations in multiproduct batch processes, Computers and Chemical Engineering, 18 (11/12), 1043-1055. Daniels, R.L., B.J. Hoopes and J.B. Mazzola, 1996, Scheduling parallel manufacturing cells with resource flexibility, Management science, 42 (9), 1260-1276. Daniels, R.L., and J.B. Mazzola, 1994, Flow shop scheduling with resource flexibility, Operations Research, 42 (3), 504-522. Daniels, R.L., J.B. Mazzola and D. Shi, 2004, Flow shop scheduling with partial resource flexibility, Management Science, 50 (5), 658-669. G61inas, S., 2004, Probl6mes d'ordonnancement, Ph.D. thesis, Ecole Polytechnique de Montr6al. Kondily, E., N. Shah and C.C. Pantelides, 1991, Production planning for the rational use of energy in multiproduct continuous plants, European Symposium on computer Aided Process Engineering, ESCAPE-2. Korhonen, J., 2002, A material and energy flow for co-production of heat and power, Journal of Cleaner Production, 10, 537-544. Mercier, A., J.-F. Cordeau and F. Soumis, 2003, A computational study of Benders decomposition for the integrated aircraft routing and crew scheduling problem, Tech. report G2003-48, Les cahiers du GERAD. Pinedo, M., 2002, Scheduling. Theory, algorithms and Systems, Prentice Hall. Pinto, J.M. and I.E. Grossmann, 1998, Assignment and sequencing models for the scheduling of process systems, Annals of Operations Research, 81,433-466.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.

1639

Automated Process Design Using Web-Service based Parameterised Constructors Timo Seuranen I *, Tommi Karhela 2, Markku Hurme 1 1Helsinki University of Technology Laboratory of Chemical Engineering and Plant Design P.O. Box 6100, FIN-02015 HUT, Finland 2VTT Industrial Systems P.O. Box 1301, FIN-02044 VTT

Abstract This paper introduces a web-service based approach in conceptual process design, parameterised constructors, which are able to construct process and initial data for control system configuration. Constructors use unit process or larger sub-process templates readily available in a plant model library. The templates consist of upper level process structures, control descriptions and detailed process structures. Thus, the preliminary process design can be defined in a more general level and as the design process proceeds, more accurate models ('e.g. PI and automation diagrams, simulation models) are composed and used. Definitions of a common data model are also discussed.

Keywords: Conceptual

process design, fiamework, plant model, process life-cycle

parameterised

constructor,

web-service

I. Introduction Open extensibility for value-added services is becoming an essential issue in information management during all phases of process life cycle, from process design to demolition. The progress in information technologies offers possibilities for new kind of integration of process design systems, simulation tools and different value-added services such as dimensioning tools and intelligent constructors. The new value-added services are implemented as web services. A common data model, manipulated through web service interfaces, links and reflects the different requirements of the process and automation design, delivery project and plant operation and maintenance. The objective of this paper is to introduce a value-added service applicable to construct a process and a control system configuration. In practice, the processes consists of almost alike structures. However, template based reuse does not solve the whole design problem because the modifications may be laborious. Thus more intelligent software components, parameterised constructors, are needed.

*Corresponding author: [email protected]

1640

2. Design support systems for conceptual process design In recent years, numerous approaches have been developed to support the activities in chemical process design. In this chapter, a few new methods are presented. Rodriguez-Martinez et al. (2004) have represented a proposal of a multi-model knowledge representation to be used within a retrofit methodology for chemical processes. The retrofit methodology consists of four steps: data extraction, analysis, modification and evaluation. The use of structural, behavioural, functional and teleological models of process equipment/devices allows the designer to work with a combination of detailed and abstract information depending on the retrofit step. Marquardt and Nagl (2004) have studied the early phases of the chemical process design lifecycle, the conceptual design and front-end engineering. The research issues were development of an integrated information model of the design process, a number of innovative functionalities to support collaborative design, and a-posterior integration of existing software tools to an integrated design support environment. Efficient networking emphasises the need to have a common data model. In different process design phases of the process life cycle, several interest groups interact and need to exchange information between each other. Global CAPE-OPEN is a project for standardising communication between components in process engineering, leading to the availability of software components offered by leading vendors, research institutes and specialised suppliers. This will enable the process industries to reach new quality and productivity levels in designing and operating their plants (CO-LaN, 2005). Open issues of information modelling are also discussed by Schneider and Marquardt (2002) and Bayer and Marquardt (2004). They have developed a conceptual model framework CliP, which holds solution approaches for the integrated representation of information and work processes, the description of documents as carriers of data, and the integration of existing data models. Clip can also serve as an integration basis for existing information models. Because design processes are highly creative, many design alternatives are explored, and both unexpected and planned feedback occurs frequently. Therefore, it is difficult to manage the workflows in design processes. One approach to manage design processes is the web-service framework, which also supports the progress of a new kind of design practice (Kondelin et. al., 2004).

3. Web-service framework In order to achieve tool integration for the whole process plant life cycle, a domain specific framework specification is needed. The specification takes into account the software architectural aspects and the variety of existing production related information systems that end users have. Compared to the use of separate systems, the proposed service framework provides • a common user interface and knowledge presentation • a common way to extend the existing systems with new value-added services The framework also enables discovering and binding of the services by service requestors. It thus makes it viable to construct, compose and consume software component based web services, which will add domain specific value.

1641 Life cycle information management is a common concern in research and development activities today. The issue is addressed from different viewpoints in several national and international projects. All these activities support the need of a generic framework for information management. The framework can be divided into core services, framework services and value added services. The interfaces of core services and framework services are defined in the framework specification while the interfaces of value added services are not fixed beforehand. Core services represent legacy systems in the architecture such as process design systems, simulators or control systems. The most important core service from the viewpoint of the case of this paper is the plant model core service. The plant model service contains information that is accumulated in design time, updated and specified in operational phase, and used by various services of the framework during various life cycle phases (Kondelin et. al., 2004). 3.1 Common data model of the web-service framework

A common data model (a plant model) offers possibility for transformations between different application software attached to the framework. For example different management, design and simulation tools are used at different stages of the process life cycle and many of them are incompatible. The plant model is actually a domain specific meta-model that describes how object types are defined. Object types are created by defining plant object types, property types, and relation types according to the meta-model. In addition, relation rules that restrict relations between objects and properties are defined. Object types describe the common taxonomy for plant object instances. In the framework, instances are represented and transferred as XML fragments that conform to the plant data model, which is defined by utilizing XML Schema type definitions (Kondelin et. al., 2004). In the case described in this paper, there are four different object types depicted in Figure 1. The Conceptual function type represents upper level functions of some kind, such as pressure change. The Constructional function type represents more specific functions analogous with objects in a PI-chart. Conceptual functions may contain several constructional functions. Base object type :

Represents:

I

Conceptual function

I

Broader requirement specifications i.e. requirements for pressure change

I

Constructional function

I

Design knowledge An object in a PI -chart i.e. requirements for pumping

Product

I

Product specific information i.e. pump model A from supplier B and its properties

I

Individual

Information related to individuals i.e. pump C in operation at plant D

Figure 1. Base object O~pes

1642 The Product type realizes the functionality of the Constructional function type i.e. an equipment type. The Individual type represent equipment individual (e.g. pump A in plant X).

3.2 Parameterised constructors Parameterised constructors can be applied to construct process and produce initial data for configuration. They use unit process templates and larger sub-process readily available in a plant model library. The templates consist of upper level process structures, control descriptions and detailed process structures. Parameterised constructors are used to: • Generate process structures and/or parts of the processes. • Intensify routine process design tasks. • Generate operational descriptions. Based on the loop type descriptions detailed initial data is generated for control engineers for design purposes, operation information for operators is also given. • Integrate operability and flexibility considerations into the process synthesis procedures. The benefit of using constructors is that the preliminary process design can be at first defined in a more general level. As the design proceeds, more accurate models (e.g. PI and automation diagrams, simulation models) are used. Unit processes and equipment models are defined to the plant model library and based on the user selections the plant model is dynamically created. The constructors also generate control scheme according to the user's selections and include it into the plant model. As a result, detailed operational descriptions are generated and are readily available to the control system supplier for configuration.

3.3 Process templates Similar process structures are often used in the design of processes. Existing design knowledge, like upper level process structures, automation diagrams and detailed process structures, is stored in the templates. They are defined to whole plant models, unit process models and equipment models, and stored in the plant model library. Different templates can be defined for the same process structure. Templates can also be differently equipped depending on the purpose of the design task. The templates in the plant |brary are updated when new design concepts, like new and better technical solutions or process improvements, are developed.

4. Case study: Fibre Refining Process The fibre refining process is a part of a stock preparation department in the paper plant. Typically, stock preparation consists of several refining lines, which produce different stock to the paper machine. Refining is one of the most important stages in raw material affecting the running of paper machine and especially the paper properties. Typically, there are two or three refiners in a series in a production line supplying one paper machine. Possible process design tasks are the following: 1. Utilize existing similar design concepts (old design documents) 2. Create new design concept 3. Equipment delivery

1643 4. Control system delivery 5. Define service and maintenance routines 4.1 Definition of plant object types

Before an engineering project, a set of object types is defined. In many cases, previous, well-established types can be re-used. The object types of the plant model are described in Section 3.1. The initial data and parameters for the conceptual model are derived from basis of design i.e. requirement specifications (raw materials, products, capacity, consistency, power demand, etc.). Conceptual models o f processes or sub-processes are also generalised in three sections: pre-treatment (raw material purification, initial feed), primary treatment (reaction, refining) and post treatment (product separation, recycle, discharge). Application-wide conceptual functions are derived from those generalized functions. An example of conceptual object type, Short Fibre Line, in which the essential properties (e.g. capacity, furnish, consistency) of the fibre line are defined, is presented in Table 1. The Short Fibre Line object type also includes information about unit processes it is composed of. The constructional, product and individual object types are defined in the similar way depending of accuracy of design. Fable 1. Short Fibre Line object type. i

Short Fibre Line property Raw materials (conceptual Products function Capacity type) Consistency Initial Feed Feed Refining Recycling Discharge

|

type enuln enum double double boolean boolean boolean boolean boolean

i

property set description design list of raw materials design list of products design admt/d, bdkg/min. design percentage of solids design feed from pulper design pre-processing design primary processing design post processing design feed blending chest

4.2 Use case: Design a new process concept

The fibre line design process begins with definition of functions in the conceptual level. First, the initial data of the refining process is defined. The initial data includes definition of stock to be produced, capacity of the refining line, specific refining energy, number of refiners, and connections of refiners (parallel/series). At this stage the upper level templates, from which the refining line is composed, are chosen. The upper level templates are e.g. Feed, Refining and Recycle. Depending on user's input and selections, the conceptual model is further composed by the constructor. The user can define what type of control loops (e.g. liquid level control, flow rate control)these functions are equipped with. When the conceptual plant model is sufficiently defined, the constructor begins to compose the constructional plant model based on user's selections. Constructional and control system hierarchies and their component type instances are dynamically composed and the suitable unit process templates are chosen from the plant model library. Unit process templates contain P I - a n d automation diagrams in SVG graphic-format. The constructional model can be disaggregated in very detailed level, e.g. every single pipeline component can be modelled.

1644 Operational description definitions i.e. loop type description of commonly used control systems are readily defined in the plant model library. The user selects and checks initial information for control system design, e.g. which kind of control structures is used. The constructor ensures that the operational description e.g. of liquid level control of the pulp tower is transformed to an automation schema, which is used by the automation system supplier. When the constructional plant model is defined, the user can transform the plant model to simulation service. Equipment selections and dimensioning, different operation value studies and mass and energy balance calculations are made in the simulator. After simulation the plant model is updated.

4.3 Hierarchies of the plant model During an engineering project, object types are instantiated and the plant model is constructed in different hierarchies. From web-service framework viewpoint, each hierarchy is a different view to the plant model. The constructors ensure that hierarchies, objects and their relations remain consistent. The fibre line upper level conceptual model hierarchy is formed based on the user selections when defining the requirement specifications for the process. After the conceptual modelling is finished, i.e. the process designer continues to the next design step, the constructional model hierarchy is derived by the constructor. The structure of the constructional hierarchy is based on the user's selections in the conceptual design phase. Product hierarchy is formed based on ~luipment models. Individual hierarchy consists of e.g. equipment operating in the plant. Conclusion In practice, processes are often designed based on previous solutions and using almost similar unit process structures. Routine process and control system design can be intensified using process templates readily defined in a plant model library and parameterised constructors. This approach also supports chance of design practice so that one designer will be responsible for all the design tasks of a certain sub-process. The web-service framework, which is able to manage all the information during process life cycle, and the common plant model give an opportunity for the integration of process and control system design, simulation, operation and maintenance and plant concept modelling. This means that any plant-modelling task is not a separate duty but an integrated part of information management in a plant delivery project.

References Bayer, B., W. Marquardt, 2004, Towards integrated information models for data and documents, Comp. Chem. Eng., 28, 1249. CO-LaN, 2005, The CAPE-OPEN laboratories network. Available online at http://www.colan.org/. Kondelin, K., T. Karhela, P. Laakso, 2004. Service Framework Specification for Process Plant Lifecycle, VTT Research Notes 2277. Marquardt, W., M. Nagl, 2004, Workflow and information centered support of design processes the IMPROVE perspective, Comp. Chem. Eng., 29, 65. Rodriguez-Martinez, A., I. Ldpez-Ar6valo, R. Bafiares-Alcfintara and A. Aldea, 2004, Multimodel knowledge representation in the retrofit of processes, Comp. Chem. Eng., 28, 781. Schneider, R., W. Marquardt, 2002, Information technology support in the chemical process design lifecycle. Chem. Eng. Sci., 57, 1763.

European Symposiumon ComputerAided Process Engineering- 15 L. PuiNanerand A. Espufia(Editors) ~')2005 Elsevier B.V. All rights reserved.

1645

Integrated Design of Optimal Processes and Molecules: A Framework for Solvent- Based Separation and ReactiveSeparation Systems Athanasios I. Papadopoulos and Patrick Linke* Centre for Process and Information Systems Engineering School of Engineering, University of Surrey GU2 7XH, Guildford, Surrey, U.K.

Abstract The presented work addresses the integrated design of solvent molecules with separation and reactive-separation process systems. The proposed design philosophy relies on extensive structural optimization both at the solvent and process synthesis stage and allows the identification of solvent molecules based on process performance criteria, it employs multi-objective optimization technology in order to capture the manifold trends and trade-offs characterizing the solvent design space, while avoiding the introduction of unnecessary biases or user defined assumptions. The obtained solvent design information is effectively incorporated into the process synthesis stage through the use of data mining techniques in the form of clustering. The process synthesis framework is sufficiently flexible to accommodate for separation or reactiveseparation superstructures of the most general type. The presented method is illustrated through examples on the design of solvents for liquid-liquid extraction, gas-absorption, extractive distillation and extractive fermentation processes.

Keywords" Solvent synthesis, Reaction- separation process synthesis, Multiobjective optimization, clustering

1. Introduction The design philosophy generally followed in computer aided molecular design (CAMD) solvent synthesis involves screening for solvent molecules based on pre-specified thermodynamic property objectives and constraints that are expected to have a positive impact in process performance (Marcoulaki and Kokossis, 2000a). Clearly, following this approach the synthesis drives involved in process synthesis are misrepresented and the results are prematurely biased towards presumably optimal options. In contrast, methods that facilitate the integrated CAMD solvent and process synthesis by accounting for process and solvent design interactions have also been proposed (Stefanis and Pistikopoulos, 1998; Hostrup et al., 1999). The design philosophy followed by these methods involves screening for solvent molecules based on prespecified property targets. The molecules meeting these targets are further screened with regards to their process performance either by participating in process simulation or Author to whom correspondence should be addressed: [email protected]

1646 process optimization, in these cases sub-systems of the overall system are targeted, thus the results are liable to assumptions regarding the size of the solvent-process design space. On the other hand, some methods (Marcoulaki and Kokossis, 2000b; Wang and Achenie, 2002; Linke and Kokossis, 2002) propose the simultaneous optimization of the formulated solvent-process superstructure which may involve separation and reactive separation processes. The enormous amount of solvent-process design options and the complexities caused by the non-convexities of the employed models introduce low confidence with regards to the optimality of the obtained results. This work addresses the previously presented limitations through a generic and systematic methodology that will robustly determine performance targets for integrated solvent and separation/reaction-separation process systems. Based on our previously presented work (Papadopoulos and Linke, 2004) multi-objective optimization is used at the solvent design stage in order to identify optimum solvent candidates without a priori excluding options that will potentially be useful at the process design stage. The obtained solvent design information is systematically introduced into the process synthesis stage through the efficient exploitation of this information using a data mining technique in the form of clustering. This work focuses on the development of an effective clustering strategy as well as on the exemplification of the proposed framework through extensive solvent-separation and solvent-reaction-separation synthesis cases.

2. Synthesis of solvent-separation processes

and solvent-reaction-separation

2.1 Multi-objective CAMD solvent synthesis-Overview In the proposed unified framework for solvent and process design CAMD solvent synthesis is performed using multiple objective optimization (M.O.O.) technology (Papadopoulos and Linke, 2004a). This formulation of the optimization problem allows unnecessarily premature assumptions about the process requirements to become redundant as each objective is treated independently, freed of artificial constraints. While the interactions among a variety of objectives are thoroughly explored, 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 will be utilized. This design philosophy allows all the underlying trends and trade-offs amongst the properties of the candidate optimal molecules, as well as the structure- property relations to be revealed. The design information included in the obtained solvent set can then be systematically exploited in the process synthesis stage so that the computational requirements remain largely unaffected.

2.2 Efficient exploitation of solvent design information in process synthesis The obtained solvent set from the M.O.O. CAMD solvent synthesis contains all the important solvent design information that must be incorporated into the process synthesis stage. We propose the formation of molecular clusters according to physical properties so that all the molecules in each cluster are similar to each other and as different as possible to the molecules in other clusters. The properties of the molecule

1647 that lies closest to the cluster centre can be considered to be approximately representative of the properties of the other molecules within the cluster and a representative molecule from each cluster can be introduced into the process synthesis. The result of the process pertFbrmance of each representative molecule ~br each cluster will reveal the cluster that includes the molecules that are ideally suited for the process, thus rejecting the molecules that belong to other clusters. An iterative application of this procedure will result into a tree-like representation tbr the optimization problem. In each iteration the various branches of the representation will focus the search on a decreased solvent solution space and the size of the problem will decrease without discarding important solvent infonnation. The appropriate directions for the development of the branches involved in the proposed representation are selected based on a set of decision criteria. In summary four major criteria have been identified: the number of clusters, the distances between the cluster centres and within each cluster, the number of data points in each cluster and the process performance of the molecule closest to the cluster centre. These criteria describe the clusters both in terms of statistical partitioning information and of cost of solvent/process configuration ~br each cluster. Each individual criterion provides a sense of quantity of what it describes, but, as the criteria operate independently from each other, they only identify the overall trends and directions of the clustering paths in a qualitative manner. A function is required in order to unite and quantify the proposed criteria under a single index. This function will suggest new clustering paths that are likely to lead to optimal clusters. We therefore define the chtstering heuristic probabiliO, as follows: P - exp[-(E,,cw

- Emm ) / ( a . T~j )]

a = 1- SSB/(SSB + SSW)

(1) (2)

Although the clustering heuristic probability P follows the Simulated Annealing (SA) probability function, the aim of this approach is to model the uncertainties involved in the clustering decisions and not to perform a SA search. This approach capitalizes on the knowledge regarding the physical characteristics of the clusters in order to identify clusters that are likely to include a molecule that can produce a solvent/process configuration with a cost lower than the best existing one. In this context the numerator of the probability fraction compares the cost of a cluster centre E,,e~,. with the best existing cost E,,,;,,. In the present case, the annealing temperature T can be appropriately reduced by a quantity a, that is a function of the available clustering information. The term a (Eq.4) is the R-Squared (RS) clustering index (Halkidi et al., 2002) ranging between 0 and 1 and represents a measure of between clusters difference (SSB) and within clusters homogeneity (SSW). For each cluster the annealing temperature is reset to an initial value (T~,/j) which is selected based on the discussion found in Aarts and van Laarhoven (1985). The advantage of using the clustering heuristic probability is that it allows the decision maker to quickly assess the problem and adjust the followed clustering policies. However, the understanding of the conditions of the overall problem at hand through the decision criteria previously discussed should always supplement the decisions made with the clustering probability.

1648

2.3 Process synthesis The process synthesis framework utilises stochastic optimization in combination with generic superstructures which have proved beneficial for the synthesis and optimization of separation (Papadopoulos and Linke, 2004b) and reaction/separation (Linke and Kokossis, 2003) processes. The process models incorporated in the superstructures represent reaction, reactive separation and separation options in generic reaction mass/exchange (RMX) units. An RMX unit can provide a conceptual or rigorous representation of all possible reaction or mass exchange phenomena taking place during process synthesis. Separation task units supplement the RMX units by offering a conceptual representation of separation options based on emerging separation paths, while leaving the rigorous representation of separation processes to RMX units 3. Illustrative e x a m p l e s 3.1 Design of solvents for separation processes The proposed method is illustrated with three applications on the integrated design of solvents and liquid-liquid extraction/recovery (P j), gas-absorption/recovery (P2) and extractive distillation (P3). The mixtures that are being separated are n-butanol-water for P1, air-acetone for P2 and cyclohexane-benzene for P3. An example of generation of new clustering paths based on the methodology analyzed in section 2 is shown in Figure 2 for P2. Each table shows the number of clusters (C1), the objective function value (OF), the number of points in each cluster (Nm) and the probability (P). Clusters 1 and 4 of iteration 1 present higher probabilities of including a molecule that benefits the process because of low OF values in combination with a large Nm. The information regarding OF and Nm as well as the rest of the decision criteria analyzed in section 2 are transparently represented by the reported probability values. On the other hand, the certainty that clusters 2 and 3 do not include beneficial molecules is high and this is also reflected in the probability values. Therefore, clusters 1 and 4 are further developed into the sub-clusters of iteration 2. Iteration 1

Iteration 2

(1) ~ C1 1 2 3 4

OF(k$/yr) 1971.7 3155.2

Nm 34 2

P 0.83 0.17

3190.1 1278.3

6 69

0.50 0.89

J

"•• (4)

C1 1 2 3 4

OF(kS/yr) 1712.3 1925.9 2030.9 2510.8

Nm 4 21 8 1

C1 1 2 3

OF(k$/yr) 1424.3 1640.9 1457.8

Nm 22 38 1

P 0.86 0.87

8

0.75

4

1383.0

0.41 0.56 0.46 -

0

Figure 1. Clustering decisions for (P2)

Following the presented clustering methodology it is possible to significantly reduce the computational time required for the identification of the cluster with the optimal solvent-process configuration. The number of molecules screened with regards to their

1649 process performance in cases P~, P2 and P3 are 18%, 15% and 25% of the initially obtained solvent set, respectively. These results represent a level of reduction from the initial solvent set that can be achieved following an approach that involves a low risk of missing the optimum molecule. Depending on the requirements of the problem, the method allows the user to set the threshold of the probability value below which clusters are rejected. Table 1 shows the optimum molecules identified for each case using the proposed methodology. For P~ the best molecule designed using M.O.O. is better in terms of process cost (OF) than the molecules designed using single objective optimization (S.O.O.). Furthermore, it is shown that by changing the objectives in the S.O.O. cases from solvent selectivity (S~) to solvent distribution coefficient (M) the process performance of the obtained molecules deteriorates. The same happens for case P2 as well when instead of using vapour pressure (Pvp) as the objective in S.O.O. we use solute solubility (Sb). Finally, in case P3 the process performance of the proposed molecule overcomes the process performance of industrial solvents or solvents reported in published literature. Table 1. Designed molecules and comparisons

Ca,~e P1

Method M.O.O. S.O.O. ( S ~ )

Malecllle CH~-CH~-CH(CH~)-CH~(C=O )-CH,-CN CH~-C(CH3)2-CH2(C=O)-CH2-CN

OF(k$/yr) 153.8 169.2 S.O.O. (M) CH2=CH-C(CH3)2-(CH2)2-(CH3)C(H(C=O))2 183.1 p-) M.O.O. CH~-O-CH(Br)CH(Br)C1 486.0 S.O.O.(Pvp) FCH20-C(Br)2-CH2C1 613.3 S.O.O.(Sb) CH2=C(-OCH3)-CH2-C1 657.7 M.O.O. FCH,-O-C-(HC=O)~ 317.2 P3 industrial a Aniline 711.8 Literature a n-meth~l-2-p~rrolidone 913.8 Results presented by van Dyk and Nieouwoudt (2000)

3.2 Design of solvents for reactive separation The second example involves the design of solvents for the extractive fermentation of ethanol. Details regarding the implementation of this example can be found in Linke and Kokossis (2002). Table 2. Molecules.fi)r the design of extractive fermentation processes

ID

Molecule

SI

CH3-O-CH2-C(CH=CH2)2 (OH)C(CH3)-CH=CH2 Dodecanol Large aromatic Octane Isopropyl-propionate

S~ $3 $4 $5

EF

S~:F(kg/hr )

EFN

S/zEFN(kg/hr)

1630.2

768

8100

400

6.46

1396

960 3135

2326 2000

13.91 15.77

1061 1321

A desired solvent-process superstructure must facilitate the complete conversion of glucose in the aqueous phase and the complete extraction of ethanol, whilst utilizing a minimum amount of solvent flow that dissolves as little glucose as possible. The

1650 employed objective function is a dimensionless equation incorporating these trends. The clustered solvent molecules are first screened with regards to their process performance in the synthesis of a well-mixed extractive fermentor (EF). Molecules with high process performance in EF synthesis are introduced in generic extraction fermentation network synthesis (EFN). Molecule S~ of Table 2 is designed using the presented method and molecule $2 has been proposed by Fournier (1986) as an ideal solvent. Molecule $3 has been proposed by Linke and Kokossis (2002) and is not shown for space economy. Finally, molecules $4 and $5 have been proposed by Wang and Achenie (2002). The results show that the already high performance of the EF structure can be significantly improved by EFN synthesis. The structure of the EFN allows the use of almost half of the solvent quantity

(S~rx) required in

EF (S~F). The proposed

molecule S~ performs better than all the molecules presented in literature and has lower toxicity than dodecanol, which is very important for extractive fermentation processes. Furthermore, molecules $3, $4 and $5 have been reported to be locally optimal, whereas following the proposed methodology we are confident that molecule $1 is a globally optimal solution.

4. Conclusions This presented work proposes a new technology for the integrated design of solvent and process synthesis. Molecules are designed for simultaneous optimality in a set of desired objectives using M.O.O. The obtained set of molecules is effectively introduced into the process synthesis through a clustering strategy that is especially designed to exploit the solvent design information, whilst reducing the amount of required computations. The methodology is exemplified through extensive examples in separation and reactive separation process synthesis. In all cases the obtained molecules outperform molecules designed using previously presented approaches. Overall, the proposed methodology demonstrates the systematic selection of solvents based on process performance criteria. This allows the introduction of confidence in the obtained solvent structures even in the most complex cases of the design of extractive fermentation networks.

References Fournier, R.L., 1986, Biotech. & Bioeng., 28, 1206 Halkidi, M., Batistakis, Y., Vazirgiannis, M., 2002, SIGMOD Record, 31 (3) Hostrup M, Harper P.M., Gani, R., 1999, Comp. & Chem. Eng., 23, 1395 Linke P., Kokossis, A.C, 2003, Comp. & Chem. Eng., 27(5), 733 Linke, P., Kokossis, A., 2002, In proceedings of ESCAPE-12, Elsevier Marcoulaki E.C., Kokossis, A.C., 2000a, Chem. Eng. Sci., 55(13), 2529 Marcoulaki, E.C., Kokossis, A.C, 2000b, Chem. Eng. Sci., 55(13), 2547 Papadopoulos A., Linke, P., 2004a, In proceedings of ESCAPE-14, Elsevier Papadopoulos A., Linke, P., 2004b, Comp. & Chem. Eng., 28, 2391 Stefanis, S.K., Pistikopou!os, E N., 1998, Comp. & Chem. Eng., 22(6), 717 Van Dyk, B, Nieuwoudt, I., 2000, Ind. Eng. Chem. Res., 39(5), 1423 Wang, Y., Achenie, L.E.K., 2002, Fluid Phase Equilibria, 201, 1

European Symposiumon Computer Aided Process Engineering- 15 I,. Puigjaner and A. Espufia(Editors) 4:, 2005 Elsevier B.V. All rights reserved.

1651

A computer-aided methodology for optimal solvent design for reactions with experimental verification Milica Folid, Claire S. Adjiman* and Efstratios. N. Pistikopoulos Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK

Abstract An extension of a hybrid experimental/computer-aided methodology for the design of solvents for reactions is presented. Previous work (Folid et al., 2004a,b) was based on the use of reaction rate measurements to build a reaction model, followed by the formulation and solution of an optimal computer-aided molecular design problem (CAMD). In this work~ feedback is introduced in the methodology to verify the suitability of the solvent candidates identified in the CAMD step via experimentation and to assess the reliability of the model used in the CAMD step. When the reliability of the model is found to be insufficient, experimental data for the candidate solvents are added to the original data set to create an updated reaction model which can be used to find new candidate solvents. This methodology is illustrated through application to a solvolysis reaction and to a Menschutkin reaction.

Keywords: solvent design, optimisation, solvatochromic equation, group contribution methods, reaction rate 1. Introduction Solvents are widely used as a reaction medium in the fine chemicals industry, where they serve to bring solid reactants together by dissolving them, to control temperature, and to enhance reaction rate. The effect of solvent choice on reaction rate can be dramatic. Reichardt (1988) reports that the solvolysis of 2-chloro-2-methylpropane is 335,000 times faster in water than in ethanol, while the reaction between trimethylamine and trymethylsulfonium ion is 119 times faster in nitromethane than in water. In spite of the importance of solvent choice on productivity, there has been little work on systematic approaches to the selection of solvents for reactions. Thus, industry currently relies mostly on experience and intuition to guide its choice during the development of new processes. This situation is in striking contrast with the selection of solvents for separation, where several computer-aided design approaches have been proposed in the last two decades. Several of these methods are described in Achenie el al. (2003). These have been successfully applied to a variety of solvent-based separation problems, allowing a much larger number of solvent molecules to be considered during separation system design

Author to whom correspondence should be adressed : [email protected]

1652 than is possible by experimentation alone. Based on these considerations, the goal of this work is develop a systematic approach to solvent design for reactions. The basic idea behind the methodology presented here is that, in the context of reactions, it is especially important to rely on a combination of experiments and computer-aided molecular design (CAMD). The computations serve as a guide to the experiments, focussing the search on promising solvents, and the experiments allow a verification of the models used. Furthermore, the methodology is developed with a view to plant-wide solvent selection, where it is important to focus on overall performance rather than the performance of single process units. This motivates the use of an optimisation-based approach to CAMD, where trade-offs between different aspects of the process can be accounted for explicitly. The methodology is described in section 2, and is applied to two reactions in section 3.

2. Methodology The overall methodology proposed in this work is illustrated in Figure 1. For a given reaction, eight initial solvents are chosen. These solvents should be selected to be

Choose 8 solvents

1

1

"1"1Obtain rate constant data I

1

I Build reaction model (

1

I Identify optimal solvent candidates I

1

I VerificatiOn, ]

YES

NO

Stop

)

Figure 1. Overview of the solvent design methodology diverse in terms of the types of interactions they can have with the species involved in the reaction. In general, the ETN solvent polarity scale (Reichardt and Harbusch-G0rnert, 1983). In addition, solvents with different functional groups are typically chosen. Wherever possible, literature data should be used at this stage to minimise experimental costs. Experimental reaction rate constants for these eight solvents are obtained. This information is then used to build a reaction model that predicts the reaction rate constant in other solvents based solely on their molecular structure. Next, a computer-aided solvent design problem (CAMD) is formulated and solved. Here, the objective is to find candidate solvents which give high values of the reaction rate constant. In the verification step, the predicted rate constants for the best candidate solvents identified are compared to experimental rate constants, to determine whether the reaction model needs improvement. If so, the experimental rate constants for the candidate solvents are

1653 added to set of initial solvents to build an updated reaction model. This procedure is repeated until the model reliability is sufficient. The computer-aided design step thus serves two purposes: it identifies promising solvents and it guides experiments. The model building and CAMD steps are briefly discussed in the next sections. 2.1 Building the reaction model The reaction model, as illustrated in Figure 2, consists of a set of property estimation methods which relate solvent molecular structure to solvent properties, and a solvatochromic equation (Abraham et al., 1987) which relates solvent properties to reaction rate constant for a given reaction.

Building

Group contribution techniques & correlations

t~b

Solvent properties

Solvatochromic

A, B, S, ~ ~1~

equation

Reaction rate constant k

blocks

Figure 2. Schematic of the reaction model

Atom groups such as CH2 and OH are used as building blocks. The solvent properties needed in the solvatochromic equation are the so-called solvatochromic parameters, A, B and S, a polarisability correction term, 6, and the cohesive energy density, which is the square of the Hildebrand solubility parameter, dH. The polarisability correction term can be calculated exactly based on molecular structure. The cohesive energy density is estimated through its relation with the molar volume, Vm, and the heat of vaporisation, Hv, as discussed in Sheldon et al. (2004). Vm and Hv are estimated using the first-order versions of the group contribution techniques of Constantinou and Gani (1994) and Marrero and Gani (2001) respectively. The group contribution techniques proposed in Sheldon et al. (2004) for the hydrogen-bond acidity A and the hydrogen-bond basicity B and the technique discussed in Folid et al. (2004a, b) for the dipolarity/polarisability S have been extended in this work. Group contribution coefficients are available for 43 groups, allowing a wider variety of solvent molecules to be represented. The regression has been based on a solvent database, which contains 350 solvents, giving increased confidence in the prediction techniques. The average absolute percentage error for each of the methods is reported in Table 1. Table 1. Average absolute percentage error (AAPE) for the proper~ estimation methods used to predict solvent properties.

Property AAPE

A

B

S

d,

0.017

0.043

0.065

1.13

The solvent properties are used in the solvatochromic equation: Iogk = Iogk. + s ( S + dd) + aA + bB + h d H I 100

(1)

where k is the reaction rate constant, and ko, s, el, a, b and h are reaction-specific parameters. The values of these reaction parameters are obtained via linear regression, based on measurements of the rate constant in a number of different solvents. Here,

1654 eight solvents are used to build the initial reaction model. Since the overall reaction model is based on predictions of the solvent properties, the predicted values of A, B, S and ~SHfor the eight solvents are used in the regression.

2.2 The computer-aided molecular design problem Once the reaction model has been developed, it is embedded within a CAMD optimisation problem. This is based on an MINLP formulation of the following form: max Iogk lt,y

s.t. logk =logk o +s(S+d6)+aA+bB+h6~ / I00 property estimation techniques for A, B, S, 6, Vm, H,,, Tm, t~4 melting point constraint molecular complexity constraints definition of n based on binary variables y

(2)

The constraint on the melting point 7,, ensures the solvent designed is liquid at room temperature. The group contribution technique of Constantinou and Gani (1994) is used to estimate E,,. The molecular complexity constraints consist of the octet rule (Odele and Macchietto, 1993), the bonding rule (as modified by Buxton et al., 1999), limits on the combinations of functional groups that may appear in the final molecule, and limits on the total number of groups in the molecule. Finally, the continuous variables n~ which define the number of groups of type i in the optimal molecule are related to binary variables to make sure that they only take on integer values. Nonlinearities arise in the above formulation from the estimation of the cohesive energy density. As a result, this problem is an MINLP which is linear in the binary variables. It can be solved locally with the outer-approximation algorithm (Viswanathan and Grossmann, 1990).

3. Case studies The case studies reported here are based on two reactions for which relatively large amounts of data are available in the literature. In such a case, it is desirable to complete the first iterations of the methodology using available data, in order to reduce process development time and cost. Such a procedure can then guide the choice of solvents in which to perform new measurements. 3.1 Soivolysis of t-butyl chloride Reaction rate constant data for the solvolysis of t-butyl chloride (CH3CCI --> (CH3)3C÷C1- --> (CH3)3C+ISolvlCI---~ Products) is available in 41 solvents (Abraham, 1972, Abraham et al., 1981, Abraham et al., 1987, Gon~alves et al., 1992, Dvorko et al., 2002). The reaction rate constants reported vary by 11 orders of magnitude and the best experimemal solvent is glycerol. The eight diverse solvents selected to build the reaction model are shown in Table 2 with their experimental ranking, where rank 1 denotes the solvent with the largest rate constant. A wide range of polarities and functional groups results in a set which contains both good and poor solvents. Good statistics are obtained for the solvatochromic equation regression: R 2 is 0.93 and the standard error is 1.9. The average absolute percentage error for all 41 solvents is 17%. A

1655 comparison of solvent rankings using experimental data and predictions (Table 3), shows good overall agreement. Table 2. Soh, ents /or the solvolysis case study, with experimental rank.

Solvent

Rank

Solvent

Rank

Solvent

Rank

Solvent

Rank

1,2ethanediol Dimethyl acetamide

2

2-methyl-2propanol Chlorobenzene

4

Diethylene glycol Benzene

6

Acetic acid Pentane

14

29

36

38

4l

Table 3- Comparison of solvenl rankings. experiments and predictions.

Solvent Glycerol Phenol Propane- 1,2-diol Butane-1,4-diol Butane- 1,2-diol

Exp

Pred

1 3 5 7 9

1 10 6 7 8

Solvent 1,2-ethanediol Propane- 1,3-diol Diethylene glycol Triethylene glycol Aniline

Exp

Pred

2 4 6 8 10

3 5 4 2 15

The CAMD MINLP identifies glycerol as the best solvent, with a reaction rate constant three times larger than that of 1.2-ethanediol, the best solvent used in the regression. Verification against literature data shows that the rate constant in glycerol has been measured and that it is the best solvent known to date. Given the consistency between the computational and experimental results, the search is stopped. 3.2 A Menschutkin reaction

In this case study, the Menschutkin reaction between methyl iodide and tripropylamine is considered: (n-CsHT)N + CH31 -+ (CH3)(n-C3H7)3N+-I -. Reaction rate constant measurements in 59 different solvents can be found in Lassau and Jungers (1968). The range of rate constants reported covers five orders of magnitude and the best ranked solvent is benzyl cyanide. A set of eight diverse solvents for which experimental data are available is chosen: it consists of a cyanide, an alkyltetrahalide, a nitrate, a halosubstituted aromatic, an aromatic, an alcohol, an oxide and an alkane. The solvatochromic reaction parameters are regressed based on these data, giving an R 2 value of 0.85 and a standard error of 1.2. When the predictions for all 59 solvents are compared with the experimental data, the average absolute percentage error is found to be only 19%. A comparison of the experimental and predicted solvent rankings shows that 7 out of the top 10 experimental solvent are predicted in the top 10 and that 17 out of the top 20 experimental solvents are predicted in the top 20. The CAMD MINLP identifies chiorobenzylcyanide as the best solvent. Integer cuts are added to find the second and third best solvents, chlorobenzylnitrate and 1,7-heptanediol. The verification step is then performed. Although no experimental data are available for any of the candidate solvents, data are available for benzylcyanide and chlorobenzene, which have functional groups and structures similar to the top two solvent candidates. Benzylcyanide is already included in the set of eight solvents used to build the reaction model, but the error between prediction and measurement is large, indicating that the

1656 model reliability could be improved. Since none of the eight initial solvents contains a chlorine group, the chlorobenzene data is added to the data set. A new reaction model is regressed based on these nine solvents. The overall statistics are similar to those obtained with eight solvents, but the qualitative ranking is slightly improved, with 8 of the top 10 experimental solvents predicted in the top 10. The CAMD MINLP is solved with the new reaction model and once again yields chlorobenzylcyanide as the top candidate. There is no further data in the data set which may be used to verify this prediction and the measurement of the rate of reaction in chlorobenzylcyanide is now needed.

4. Concluding remarks A methodology for the systematic design of solvents for reactions has been proposed. It is based on an iterative approach which alternates between experiments and computeraided molecular design. The reaction model at the core of the CAMD problem is based on the empirical solvatochromic equation, in which the solvent properties are obtained by group contribution techniques and the reaction parameters are regressed from experimental data. The CAMD results are verified against experimental data, and an improved reaction model is generated if needed. This is then used in an updated CAMD problem. The approach has been applied to a solvolysis reaction, in which only one reaction model was used, and to a Menschutkin reaction, in which two reaction models were used. Further verification of the results via experimentation is underway.

References Abraham, M.H., 1972, J. Chem. Soc.- Perkin Trans. 2, 1343. Abraham, M.H., R.W. Taft and M.J. Kamlet, 1981, J. Org. Chem. 46, 3053. Abraham M.H., R.M. Doherty, M.J. Kamlet., J.M. Harris and R.W. Taft, 1987, J. Chem. Soc., Perkin Trans. 2, 913. Achenie L.E.K., R. Gani and V. Venkatasubramanian, Eds., 2003, Computer Aided Molecular Design: Theory and Practice, Elsevier, Amsterdam. Buxton A., A.G. Livingston and E.N. Pistikopoulos, 1999, AIChE J. 45, 817. Constantinou L. and R. Gani, 1994, AIChE J. 40, 1697. Dvorko, G.F., V.V. Zaliznyi and N.E. Ponomarev, 2002, Russian J. General Chemistry 72, 1549. Foli6 M., C.S. Adjiman, E.N. Pistikopoulos, 2004a, Proceedings of ESCAPE-14, Elsevier. Foli6 M., C.S. Adjiman, E.N. Pistikopoulos, 2004b, Proceedings of FOCAPD, in press. Gon~:alves R.M.C., A.N.M. Sim6es, R.A.S.E Leitfio and L.M.P.C. Albuquerque, 1992, J. Chem. Research (S), 330. Lassau C. and J.C. Jungers, 1968, Bull. Soc. Chim. Fr. 7, 2678. Marrero J. and R. Gani, 2001, Fluid Phase Eq. 183-184, 183. Odele O. and S. Macchietto, 1993, Fluid Phase Eq. 82, 47. Reichardt C., 1988, Solvents and Solvent Effects in Organic Chemistry, VCM Publishers, UK. Reichardt C. and E. Harbusch-G6rnert, 1983, Liebigs. Ann. Chem., 721. Sheldon T., C.S. Adjiman and J.L. Cordiner, 2004, Fluid Phase Eq. accepted for publication. Viswanathan, J. and I.E. Grossmann, 1990, Computers chem. Engng. 14, 769.

Acknowledgements Financial support from the ORS scheme and CPSE is gratefully acknowledged.

European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espuna (Editors) g) 2005 Elsevier B.V. All rights reserved.

1657

Development of Information System for Extrusion Forming Process of Catalyst Pastes Andrey V. Jensa, Anatoliy A. Pohmin, Vyacheslav V. Kostutchenko, Igor A. Petropavlovskiy, Eleonora M. Koltsova Department of Cybernetics of Chemical Engineering, D. Mendeleev University of Chemical Technology of Russia 125047, Miusskaya pl. 9, Moscow, Russia, Tel. +7 (095) 978 65 89, E-mail: [email protected]

Abstract Evolution of theoretical basis of extrusion paste forming processes will raise the solution of several problems in the technology of catalysts, which are used in different branches of chemical, automobile (block ceramic overburning catalysts) and petrochemical industries. Taking into account the importance of this problem on the department of cybernetics of chemical technological processes we developed the information system which allow us to find initial concentrations of catalyst paste components for obtaining target product with predefined properties (mechanical strength and porosity). User of this system can specify desired values of target product specifications (such as mechanical strength, porosity of catalyst) or intermediate ones without dealing with experiments., i.e. specify the values of rheological parameters of catalyst pastes (viscosity, plastic strength, elasticity) on the catalysts preparation stage. As a result of interaction with this system end-user will receive a set of recipes (component mass compositions) for catalyst paste preparation and the ram extruder which can be used tbr production of catalyst with user defined properties.

Keywords: [extrusion, catalyst pastes, information system] 1. Introduction By means of extrusion forming it is possible to obtain various materials: catalysts with different form (from cylinder to figured grains and honeycomb blocks), ceramic materials, food materials (noodles, candies, etc.). Obtaining of materials, based on ot-Fe203 is considered in this work. Following stages are contained in the process of wide class materials obtaining (including new ones): synthesis, mixing, flowing through an extruder, drying and firing. The obtained materials should have a series of the given properties: appearance, durability, porosity, water absorption, etc. Extrusion is one of the processes, where the process of paste's particles agglomeration is unwelcome, as it leads to turn for the worse of the paste's properties. Therefore, this paper is devoted to investigation and mathematical simulation of catalyst pastes

1658 preparation with taking into account formation of solvate films, which prevent the agglomeration of particles. At this stage, the solid carrier (ot-Fe203) is being mixed with the water solutions of surfactants (in or case, these are solutions of PVA and MC). Addition of these substances makes the forming paste plastic. The substances keep the dispersed phase in a bounded condition, counteracting the factors, which disintegrate the structure. The most important problem at preparation of catalyst pastes is a problem of evaluation and prediction of their forming properties with help of their rheological properties, where the plastic strength and viscosity are two general ones. The properties of pastes start getting their properties at the preparation stage. According to representations of physical chemical mechanics, plastic forming pastes present themselves a system of rigid particles, surrounded by the solvate films. Cross-linking of such dispersed systems happens in the result of molecular coupling of dispersed phase particles by the most lyophobic areas of surface, which are the least protected by the solvate films of media. Thickness of solvate films significantly determines the system's technological parameters, including its formability.

2. Experimental A series o experiments were carried out, where the pastes with different composition were being prepared by varying the concentration of continuous phase (PVA and MC) and the content of a solid phase (table 1). Each paste was being prepared in a mixer for about 30 minutes, then it was being matured for 24 hours. Plastic strength was being determined after 30 minutes and after 24 hours by means of Rebinder's conic plastometer by the cone penetration method under action of a constant weight [1]. Viscosity was being determined after 24 hours by means of capillary viscosimeter at the shear strain, equal to 10 s-1. Table 1. Experimental values of rheological characteristics of catalyst pastes.

N exp. 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0,502 0,460 0,500 0,458 0,501 0,459 0,499 0,457 0,492 0,476 0,477 0,454 0,484 0,462

awhen jt =10s -1. b After 30 minutes. After 24 hours.

a

co

co

q

0,012 0,012 0,012 0,012 0,0012 0,0012 0,0012 0,0012 0,0075 0,0075 0,00375 0,00375 0,01125 0,01125

0,06 0,06 0,018 0,018 0,06 0,06 0,018 0,018 0,04 0,04 0,06 0,06 0,02 0,02

41,20 0,78 6,61 0,36 15,85 1,12 0,31 0,24 19,01 14,79 5,75 0,66 4,68 0,56

pmb

PITI c

2059 84 566 25 3031 74 173 32 727 507 496 105 289 63

3658 298 1304 82 3536 192 318 65 1755 1221 875 180 742 186

1659 Experimental values of plastic strength and viscosity are presented in the table 1. Behaviour plastic strength in time was observed for some experiments. The graph of plastic strength in time comes out to plateau (see figure 1), what means the system's stabilization. Only two limiting values of plastic strength are presented in table 1: after 30 minutes and after 24 hours. But even these two values are enough to get convinced in importance of taking into account the maturing stage. For 24 hours plastic strength doubles for almost all the experiments, and for the experiment 3 it even quadruples. Structurization of the system happens for this time, the paste becomes more dense and rigid. Pro,

kPa

1400 1200

1000 800 600 400

200 ,

0

2

4

6

8

:

10

12

14

16

18

20

22

24 t, hours

Figure 1. Experimental dependeno' of plastic strength fi'om time for the experiment 3.

3. Results 3.1 Obtaining of functional dependencies The mathematical model for the stage of catalyst paste mixing was built on a base of application of heterogeneous media mechanics apparatus and colloid chemistry. This model allows calculation of c~-Fe~O3 particle-size distribution density at any moment of time on solvate films thicknesses. Multicomponent two-phase system is considered at the stage of paste preparation in a mixing apparatus. First phase is continuous, the second one consists of solid ~-Fe203 particles. Components of continuous phase are: water, PVA and MC. We consider that in the process of mixing, particles of a-Fe203 get covered by the solvate film. Properties of this film depend on composition of continuous phase. The mathematical model of a catalyst pastes mixing stage is constructed on a base of application of heterogeneous media mechanics and methods of colloid chemistry. The model allows to calculate a distribution density of Fe203 particles number for any moment of time on solvate films thickness and includes the following equations:

1660 - b a l a n c e equation of ~-Fe203 particles number, predicting the number of particles in any moment of mixing and storing, having solvate film; predicting the medium size of solvate film:

-0f- + 0f~ =0; c~t

(1)

c~r

dependency for the solvate film growth rate:

-

dr _ 4zc/2 [K1C1C3 + K 2 C 2 C2+ K3C 3 ]; - -~-

(2)

mass change at the expense of solutions' components income of continuous

-particles

phase:

V - - dm ~ _ 47t/2 [Pl 1K1C1C3 + Pl2K2C2C~ + P13K3C3 ]; -

equation of liquid phase density changing: dPl dt

-

(3)

=-

Rm Ifaltdr; 0

(4)

equation of components concentrations changes for liquid phase: dC i

Pl ~

dt

Rm

Rm

= - fPliflai dr + Ci f f g tdr , 0

(5)

0

where la1 - 4zff2K1C1C3, ~t2 - 4FI2K2C2C~, ~t3 - 4~12K3C3 . Volume content of a solid phase is determined on a base of these equations (1-5): Rm

¢z2 - (xO + ~rfdr 0

(6)

Unknown kinetic constants of the mathematical model (1-6) are K1, 1£2, 1£3. For the definition of kinetic constants we took the data, represented in a paper of Yu. Mosin [2]. Following values of kinetic constants were found in the result of this search: K1 = 10,5.10 -1° (m s-l), 1£2 - 0,66.10 -1° (m s-l), 1£3 = 0,2.10 -1° (m s-l).

Following functional dependencies were obtained by comparing data, obtained with help of the mathematical model (for example, volume content of catalyst, taking into account the presence of a solvate film; average values of solvate films thicknesses) with the experimental data on plastic and rheological properties of pastes: - dependencies for the plastic strength: Pm - 103 exp(- 14,792 + 1,77.106h +8,1.1012h 2 + +15,207et 2 + 61,113(z 2 -2,547.10 7 h(x21 ; - dependencies for viscosity of catalyst paste:

(7)

1661

q 1 q°exp(98°t2 - - 36'8)(45'12"10-7h

-3,7

(8)

3.2 Informationsystems The Information System (IS) allows user to find paste composition for specified input parameters. Search results consist of a set of pastes, so user need to choose one of them. At the moment the IS applicable only to catalytic paste based on ferric oxide ~-Fe203 and consists of four modules. First module represents a database of theological, deformation properties of catalyst pastes and target product parameters. This database was built using the mathematical model of the mixing stage within the catalyst preparation process. This model takes into account formation and growth of adsorption solvate shells on solid phase particle. Rheological and deformation properties of catalyst pastes were generated by equations for plastic strength (7) and viscosity (8). Target product parameters were put into database from equations tbr mechanical durability and porosity of target product. This module allows one to choose automatically the composition of catalyst paste, which satisfy user demands (fig. 2). Second module is the database of ram extruder parameters, including unit geometry, manufacturer's name and address (at the moment the system contain information about ram extruder, but it is possible to put other types of extruders there). In the third module system calculates extruder load for chosen catalyst paste forming. Calculations are based on mathematical model for catalyst paste flow in extruder. Fourth module of information system allows us to choose ram extruder from industrial units database depending on calculated in the second module extruder load. By using the assurance factor when choosing the unit we can expand search range for the system. ' Resull o! Seleclio

,~Composition of Paste ................................................... Weicjht of iron oxide (g): 1667 Weight of sotution MC(g)(%wg):

157 (:3 :-',8I)

Weight of sotu~i:onPVA(g)(%wg):

183 (10.75)

Composition of Paste: 17

.......................................

Rheologicei property of Paste

Properly of Product .............................................

Plastic strength(kPet): ii :31-15.:377 Humidity(%):

aechetnice]

strength(MPet): ii..075

ti 5..',~6',_~ Porosity:

Vi sco s i~(Pe* s): ]:30 G4. !38

.................... Weightof

6

667

lweighto,so,

IPlestic

jHumidily(%)

I

Viscosity(Pet's)

Porosty

1 !',07.!--t42

15.868

8-1 r] n 75I

I :',FF,::177

1 ~ I~F,',:', :-1064.98 1 .L-17g . . . . . . . . . . . . .

n £2

8

11U '.i',-',:_:I . :!',:3)

1 2':~6..052

1 5..',3E,',:',

!',0 'E;.25'J

,

-

1..075

I

57 (14 92) , -

:!;063.76

IMechanice,

7 !~i67.................................... 157 i":-i-11-11 ......... =................................................ :. , ,

6G7

',-_-;:", (2!;5)

lweight ofsol.

11:J..5 .';"

11152

:!',069..28:-',

1..11175

0..52

9

800

11 0 11.78'~

57 (1 4.92)

1 0G4.:324

1 E;

:3659.2FI

1 lIE :i

0..519

1:0

813111

'8:?, (2..:35)

',-;:!',(10.75)

106:!1.879

16

:3659.425

1.0871

0.519

1t

8 I-II-I

57 1:I3.~J'l-',',l

11 Ill '~8 I :-I !i:3)

10E;1 !97

1 E;

:365'.:I.!322

1i 1383

0.51 II9

Figure 2. The results after we chosen the paste.

_...j

~

]

1662 Work sequence for this system include several stages: • Query definition for calculation of paste composition • Database preparation for rheological properties dependency on paste composition • Calculation of extrusion process parameters for ram extruder • Extrusion equipment vendor selection from database • Equipment selection from unit database basing on calculation results In order to determine paste composition in is necessary to specify following parameters: • catalyst powder nature, type and its dispersity • temporary technological linkage information (quantity and type of technological linkage used) • rheological and deformation properties of paste (plastic strength, humidity and viscosity) • target product parameters (mechanical strength and porosity) Data is input by ranges. For the plastic strength it is needed to specify more exact value. From the data obtained the program automatically choose appropriate catalyst paste compositions from database, from which user can select one item satisfying his demands. Then user chooses extruder type for this selected paste composition. Extrusion pressure calculations are performed using user specified ram extruder parameters. If extruder load does not suit user needs, it is possible to get back to previous stage and choose another paste composition. Then the same procedure executed for the new paste. As a result, user selects one of computer-proposed paste compositions, which satisfies not only demanded rheological and deformation properties, but also extruder load wanted. After this stage program look for suitable equipment for the selected paste in the database. In order to run this user should input geometry parameters of the unit and assurance factor. Additionally, you can use this module apart from others, but in that case you need to specify manually all unit parameters for database search. At the last stage you can print the report for all stages of calculation with this system. This report can be saved in a file or printed.

References M.S. Akutin, N.N. Tikhonov, Laboratory works on rheology of polymers, Mendeleyev University of Chemical Technology, 1983 (in Russian). Yu.M. Mosin, A.F. Krivoshepov, G.G. Shikhieva, A.V. Bulinko, Formation of interphase bound oxide-solution of high-molecular compound, Glass and Ceramics (1997), No 9, pp. 27-30 (in Russian).

Acknowledgements This work was supported by grants RFBR No 02-03-32215, ~o 03-01-00567, RFBRNSFC grant No 02-03-39003 and Ministration of Education Russian Federation T 0209.4-2936.

European Symposium on Computer Aided Process Engineering - 15 I,. Puigjaner and A. Espufia (Editors) (C: 2005 Elsevier B.V. All rights reserved.

1663

Integrating short-term budgeting into multi-site scheduling Gonzalo Guilldn, Mariana Badell, Antonio Espufia and Luis Puigjaner Universitat Politbcnica de Catalunya, Chemical Engineering Department, E.T.S.E.I.B., Diagonal 647, E-08028, Barcelona, Spain

Abstract In this work a novel approach is applied with the aim to improve the operation of supply chains with embedded multi-purpose batch chemical plants. The major contribution of this work with respect to previous approaches is that it includes a corporate financial planning model within the mathematical tbrmulation applied for optimizing scheduling/planning decisions variables regarding the supply chain management. Such model maximizes the change in equity of the company and provides the budgetary guidelines for the planned period. This consideration exhibits two main advantages compared to the existing methodologies. In first place, it allows to check the feasibility of the resulting planning decisions from the financial viewpoint thus ensuring that the production and distribution activities to be carried out through the different nodes of the network do not spend more cash than the available one. In second place, it leads to better overall economic performance than in previous methodologies since the model properly evaluates the impact of financial expenses and earnings derived from the SC operation thus integrating production and financial corporate decisions. Such integration also makes the difference when considering the opportunity of investing the idle cash.

Keywords" agents, multi-site scheduling, financial, uncertainty. 1. Introduction The concept of Supply Chain Management (SCM), which appeared in the early 90s, has recently raised a lot of interest since the opportunity of an integrated management of the SC can reduce the propagation of unexpected/undesirable events through the network and can influence decisively the profitability of all the members. A lot of attempts have been made to model and optimise the SC behaviour, currently existing a big amount of deterministic and stochastic derived approaches. Most of the works reported in the literature address the SCM problem from a strategic or tactical point of view. They identify the placement of production facilities or distribution centres, the flow of materials and the inventory levels optimizing a certain performance measure, commonly cost or profit. From an operational perspective, and due to the complexity associated to the interdependencies between the production and distribution tasks of the network, the detailed scheduling of the various processes of the SC has been left to be decided locally. In this sense, Applequist et al. (1993) highlight the importance of the coordination of the activities of the different entities and specifically at the enterprise level, which requires integration of the logistics and manufacturing aspects with strategic business and financial decisions. Grossmann

1664 (2004) highlights also that major challenges in enterprise and supply chain optimization include development of models for strategic and tactical planning for process networks which must be eventually integrated with scheduling models. The author suggests that while very significant progress has been made, these models still lack sufficient generality despite significant advances made in this area. A topical review of historical guidelines and approaches in integration of operative planning/scheduling and cash management modelling must take into account that budgeting models for financial control emerged earlier than operation schedules. The initial sequential approach, which focused on individual financing decisions, was later developed towards the simultaneous consideration of financial decisions. These included cash flow synchronization, financing distribution and the investment of the excess cash in marketable securities. On the operative side, a huge number of models, especially in the last 25 years, have been developed to perform short term scheduling and longer term planning. Most of these works address scheduling/planning activities by optimizing quality or cost-related performance measures. However, very limited works were reported on the joint financial and operative modelling. Shapiro et al. (2001) recognizes that optimization models offer an appealing framework for analyzing corporate financial decisions and constraints as well as for integrating them with supply chain decisions and constraints. Unfortunately, he also admits that relatively few corporate financial models of this type have been so far developed in the literature. If in practice the financial matters are not still integrated with operations management to support decision making, is mainly because until today scheduling/planning and budgeting modelling have been treated as separate problems and were implemented in independent environments.

2. Multi-site planning/scheduling In the chemical-processing context, production planning and scheduling refers to the routine of allocating resources and equipment over time in order to execute the processing tasks required for satisfying a specific product demand and quality while fulfilling some predefined optimization criteria. Production planning implies allocation decisions over longer time scales (months), while scheduling focuses on the shorter time scale allocation thus considering those sequencing decisions that satisfy the production requirements imposed by the former. When talking about a SC, it is important to extend the decision variables related to the plant activity to the whole network. This consideration gives rise to a muti-site scheduling/planning problem where it is necessary to decide not only the production rates of the plants and the flows of materials between sites but also the way in which such amounts of materials are manufactured (partial schedules), stored and transported through the nodes of the network.

3. Mathematical formulation The proposed model divides the planning and scheduling horizon H into intervals of length H1 where production is planned using known as well as estimated demands

1665 which are provided by a forecasting tool. Moreover, the first planning period is divided into intervals of lower length H2 where production is scheduled as depicted in Figure 1. The model is to be rerun every H1 period as forecasts become real orders. Therefore, the results of the planning horizon beyond the first period H1 will never reach execution. However, they are important to be considered when solving the scheduling horizon, because one could schedule in such period the production of materials needed in periods beyond it and keep them as inventory. At the financial side, the reschedule carried out each H1 period provides a reliable forward-looking scenario aiding the synchronized financial/operative decision making.

3.1 First stage" detailed scheduling In this first stage, production demands and raw materials and final product stocks are known. Here, the detailed schedules of the different sites of the SC as well as the transport decisions to be implemented through the nodes are computed. The first time period H1 is divided into t intervals of length H2. The scheduling constraints are based on the discrete STN formulation of Shah et al. (1993), although other either continuous or discrete time scheduling formulations could be easily applied. It should be also mentioned at this point, that it is necessary to slightly modify the mass balance constraints proposed by the author for properly modelling the transport of materials through the nodes of the SC. !

......~ ,i~,

:

ilil ~i2i!: ii~i~!iiiiii!i~i~ii~i~i~!~!!!~!~i~Jiiiii~iii~ii~!ii~iiiii~i~iiiiii~iii!i~Ji~Ji~ii!iiiiiii~i~i~iiii~iiiiiiiiiiiiiiiiiii~ii~iiiiiiiiiiiiii~i~Jii!Jiiiii~iiiiiii~iiiiii~i~iiiii~ii;iiiiiii!i~iiii~ii~i~i~iiiiiiiiiiiii~i~ii{~ii

i . . . . . . . .... . . . . . .IME . . . H o R , z o NI..............

4

...~ . . . < ,.~' ~' )i~ ...... •, ......~g~':: ~...-.-:

•

:) "~: ~~ ~

'

.

,, ...~

...............

~

!...2

Figure 1. Structure qf the model

Figure 2. Case Stud3,

3.2 Second stage: production planning Here, nor the exact sequence of batches produced neither the initial and finishing times of the involved tasks are computed within every period, apart from the first one, but estimated by means of an aggregated STN representation based on the work of Maravelias and Grossmann (2004). For each task i, it is defined a maximum number of copies, i.e. an upper bound on the number of batches of task i that can be carried out in any feasible solution. Constraint (1) is a relaxed assignment constraint which enforces that the sum of the durations of the tasks assigned to a unit does not exceed the length of each planning interval (H1). Here, !/ represents the set of tasks that can be assigned to unitj. In this case, it has been assumed constant processing times. The capacity limits for equipments are expressed by equation (2). ZZPti.Wi,<_H c'cC i ic1 i

Vt

(1)

1666

0 <_ Bci ' <_ BiMAx. Wci,

V c ~ C~,i,t

(2)

The amount of state s at the end of the time interval t is calculated through constraint (3) in which it is forced to be equal to the initial amount plus the amount produced and purchased and minus the amount consumed and sold during t. Therefore, only assignment (1), batch size (2) and mass balance constraints (3) are included.

Sst - Sst-I + Z Z Be°st + Z PblFChRM -- Z Z Blist- Salesst c~C icso,, e c~C i~SI,,

Vs, t

(3)

Concerning financial matters, it should be mentioned that the cash-management constraints applied in this work have been taken from Romero et al. (2003) and consider transactions of cash due to buys or sales of marketable securities, sales of final products, payment of liabilities, the use of short-term financing sources and pledging. Nevertheless, in our formulation the change in equity achieved by the enterprise (AEquity) for a given horizon of time, and not the cash withdrawn from the company as dividends, is pursued as objective aiming at the direct enhancement of the value of shareholder's interest (SHV) in the firm, which seems to be today's priority. This term can be computed as the net different between the change in assets, which include both, the current assets (CA) and the fixed ones (FA), and the change in liabilities, comprising the current liabilities (CL) and the long-term ones (L). To achieve the integration between operative and financial decisions, the production liabilities and exogenous cash at every period are calculated as a function of production planning variables. That is, the inflows of cash are determined from the sales of products assuming a known delay between the execution of the purchase and the corresponding payment, while the amount of raw materials and utilities purchased to the external suppliers are computed from the operative variables of the aggregated STN representation:

PuFCheTOTAL-- Z Z Z mcit'~ie'~-Bcit'flie'}c'c~.icUSupe t +

~ l

P ldr Cries "eM t Yse " g~,t

(4)

VS, t

s~RMSupe

4. Case study The proposed approach is applied to a case study (Figure 2), comprising two multipurpose batch plants, three warehouses and six markets. Twelve planning intervals with a length of one week each are considered. The scheduling formulation considers a time horizon of one week divided into 60 intervals of 2 hours each. The structure of the multipurpose batch plants has been taken from the case study proposed by Kondili et al. (1993). To highlight the advantages of our integrated approach, a two-step sequential scheduling-planning and budgeting approach is also applied. This situation corresponds to a typical nowadays optimized industrial routine where first operations are decided to then try to fit the finances. The implementation in GAMS of the planning model consists of 38203 equations, 38203 continuous variables, and 6839 discrete variables. It takes 544 CPU seconds to

1667 reach a solution with a 0 % optimality gap on a AMD Athlon 3000 computer using the MIP solver of CPLEX (7.0). Once the scheduling-planning model is solved, the budgeting model is optimized. This model has 448 equations and 664 continuous variables. The model is solved in 0.062 CPU seconds. On the other hand, the integrated model leads to 342485 equations, 38866 continuous variables, 6839 discrete variables and 1040 CPU seconds to reach a solution with a 0 % optimality gap on the same computer. 40,0

20 )3 1 ;5;,l-I 16,CI =. "- 14,0

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Figure 3. Total debt and amount pledged

As it can be observed in Figure 3, the solution achieved with the integrated model incurs in less debt and pledges less receivables than the sequential one. The change in equity achieved with the integrated approach is 30 % higher than the sequential one (3.576.209 m.u. tbr the integrated model and 2.488.312 m.u. for the sequential approach). It should be pointed out, that the case study presented here is a very specific situation where there is one product with a very high profitability in comparison with the others. Such item has a high price and consumes an expensive raw material. Given this data, the planning-scheduling model decides to fulfil the demand of this material as much as possible, what makes the budgeting model pledge receivables for purchasing the necessary raw materials. On the other hand, the integrated approach leads to lower production rates of this material, since it properly asses the financial impact derived from the operative decisions. 5. C o n c l u s i o n s This paper has addressed the importance of integrating planning and budgeting models. This work presents a more desired measure of the effectiveness of a production plan and schedule, based on an economic performance indicator (change in equity) as an alternative to the commonly used makespan or sum of tardiness objectives. By means of a comparison using a case study, it has been shown that significant improvements are possible as compared to the use of scheduling models followed by budgeting models. 6. N o m e n c l a t u r e aic cost fraction of i payable to e ,gic cost fraction of i payable to e Bc;, batch size of c of i in t B~.i,, amount ofs consumed by c of i in t

/.1-set ofj equipments available for task i j equipments pti processing time of i Pzn'chR~t~.,t amount ofs purchased to e in t

1668 B ~ x maximum batch size of/ B°cist amount of s produced by c of i in t c copies Ci set of copies of/ e external suppliers ~'se fraction of s purchased to e t planning periods g ~ price of s offered by e in t H planning period length i tasks

Purchr°rALet total purchases

payable to e

in t

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e

Wci~binary variable (1 if c of i is performed in t, 0 otherwise)

References Applequist, G.E., J. F. Pekny and G. V. Reklaitis, 2000, Risk and uncertainty in managing chemical manufacturing supply chains. Comput. Chem. Eng., 53 (24), 2211-2222. Grossmann, I. E., 2004, Challenges in the new millennium: product discovery and design, enterprise and supply chain optimization, global life cycle assessment. Comput. Chem. Eng., article in press. Kondili, E., C. C. Pantelides and R. Sargent, 1993, A General Algorithm for Short-Term Scheduling of Batch Operations I. MILP Formulation. Comput. Chem. Eng. 17 (2), 211. Maravelias, C. T, I. E. Grossmann, 2004, A hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants. Comput. Chem. Eng., 28, 1921-1949. Romero, J., M. Badell, M. Bagajewicz and L. Puigjaner, 2003, Integrating Budgeting Models into Scheduling and Planning Models for the Chemical Batch Industry. Ind. Eng. Chem. Res., 42, 6125-6134. Shah, N., C. C. Pantelides and R. Sargent, 1993, A General Algorithm for Short-Term Scheduling of Batch Operations-II. Computational Issues. Comput. Chem. Eng., 17, 229-244. Shapiro, J. F., 2001. Challenges of strategic supply chain planning and modelling framework. Comput. Chem. Eng., 28, 855-861.

Acknowledgements Financial support received from the Spanish "Ministerio de Educaci6n, Cultura y Deporte" (FPU programs) and from GICASA-D 00353) and OCCASION (DPI200200856) projects is gratefully acknowledged.

European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) ((')2005 Elsevier B.V. All rights reserved.

1669

An Integrated Modelling Framework for Asset-Wide Lifecycle Modelling Suresh Sundaram ~ and Kyle Loudermilk b aAspen Technology, Inc. Ten Canal Park, Cambridge, MA 02141 USA bAspen Technology, Inc. Ten Canal Park, Cambridge, MA 02141 USA Abstract This century is bringing new challenges to the engineering community, compelling it to undergo rapid change. The lines between traditional engineering disciplines are beginning to blur, requiring cross-functional knowledge and expertise across process, design, project management, environmental, mechanical, operations, maintenance, planning, scheduling, cost estimation, supply chain, process control, and other disciplines. This paper presents the Open Simulation Environment TM (OSE) that will meet the challenges presented by the changing industry and technology landscape. The Open Simulation Environment is a critical component by which the engineer of the 21st century will provide greater value-added, utilizing any of the technical modelling tools required to perform his/her job. Keywords: lifecycle modelling, asset-wide modelling, modelling framework

1. I n t r o d u c t i o n

The 2 l~t century is bringing new challenges to the engineering community, compelling it to undergo rapid change. The driving forces for this change include: • The traditional deployment of operational budgets (OPEX) and capital budgets (CAPEX) is changing. In Western Europe, the United States and Japan, CAPEX is employed primarily to increase the effectiveness of OPEX through de-bottlenecking projects and meeting environmental or other regulatory constraints. In developing economies, CAPEX is employed primarily on new construction of massive plants to meet the needs of bourgeoning regional wealth and a growing global economy. • Process simulation has changed from simply "automating design calculations" to being the center of "integrated engineering workflows" that support a variety of decision making tasks, from conceptual design to process design to plant troubleshooting. • Modeling technologies have established themselves as critical components of several specific tasks in plant operations, including model-based control technology in advanced process control (APC), first-principles simulation models in real-time optimization (RTO), and LP-based models in planning and supply-chain management.

1670

Information technology (IT) infrastructure has evolved so that most process companies are today able to access plant data on every desktop, across all disciplines in the organization. In this new environment, the lines between traditional engineering disciplines are beginning to blur, requiring cross-functional knowledge and expertise across process, design, project management, environmental, mechanical, operations, maintenance, planning, scheduling, cost estimation, supply chain, process control, and other disciplines. Meeting these challenges demands that engineers become more proficient in a broader range of disciplines. He/she must be able to model more complex processes across a wider array of assets and variables in order to perform their jobs professionally.

2. Value Creation Opportunities in Simulation and Modelling As we look forward and identify where the value creation opportunities are going to come from over the next decade, simulation and modelling will continue to be the critical elements that enable owner operators and engineering & construction companies to address the challenges they f a c e - and ultimately profit from them. We have identified three key areas of opportunity for customer value creation through the application of modelling and simulation technologies: • Accelerating the use of process simulation beyond engineering into plant operations • Performing simultaneous simulation and engineering design • Expanding the scope of simulation models from single-process to site-wide and business-wide analysis. The following sections describe each of these value creation opportunities in more detail.

2.1 Accelerating the Use of Process Simulation beyond Engineering into Plant Operations Customer value can be created by the following activities: • Using consistent models across the process lifecycle, from engineering to operations • Taking advantage of the knowledge embedded in first-principles, empirical, statistical and planning models -- deployed both off-line and o n - l i n e - to guide operational decision making and improve plant performance • Being able to use third-party and in-house models seamlessly with off-the-shelf simulation tools • Exploiting the knowledge within models by utilizing case management and case comparison capabilities for models • Using custom modelling capability for rapid development of new models that work inside the individual modelling tools, as well as in an integrated modelling environment. Creation of new custom models is also key for the innovation process. Lyondell (McGrath, 2004) has implemented a real-time operations decision support system for a propylene oxide/styrene monomer unit. The decision support system

1671 consists of an Aspen Plus plant model (adapted from an existing Aspen Plus design model), and online data connectivity using Aspen OnLine connected with the Aspen IP.21 plant information management database. The model runs with the Aspen Plus optimizer to reduce the combined cost of steam, solvent losses and propylene oxide product losses. Lyondell has reported that this real-time decision support system has resulted in savings in refining steam use of more than 8%.

2.2 Performing Simultaneous Simulation and Engineering Design Customer value can also be created in the engineering workflow through the open and flexible integration of commercial, third-party, and in-house models and engineering tools. Engineering analyses can be performed more productively and consistently, resulting in superior designs that consider technical and economic constraints. As the largest ethylene producer in Asia, YNCC (Lee, 2002) had a goal of increasing capacity at one of its major ethylene facilities. Original engineering proposals provided a 16% capacity increase at a 10 cents/lb capital investment. Working with AspenTech, YNCC adopted a new integrated engineering approach to identify the most costefficient revamp projects. The key aspect of the new approach was that simulation, process analysis and equipment modelling were executed in a simultaneous, integrated workflow, rather than in a sequential workflow. The new integrated engineering approach enabled capacity increase of 20% at 7 cents/lb, resulting in a 40% reduction in capital investment rate and at the same time 4% higher capacity than the original proposal. In addition, the new approach predicted $3.3.M/year in energy savings.

2.3 Expanding the Scope of Simulation Models from Single-Process to Site-Wide and Asset-Wide Analysis Customer value can be created by linking engineering with business decision making for capital investment and operations decisions by bringing together process, utility system and infrastructure simulation models into an integrated, site-wide environment, allowing producers to model and understand the economic and technical trade-offs required for site-wide optimization of a production facility. BP's Daily Optimizer (Stenhouse, 2000) predicts the offline operating conditions and available safety margins for the Harding Asset, from wellhead to tanker. The system displays the best selection of well production schedules and process facility parameters to the operations staff, thereby maximizing the profit for the given asset and economic constraints. The heart of the system is a full asset-wide model based on a combination of Aspen HYSYS process models and third-party models, coupled with in-house optimization technology that reconciles and optimizes the incoming plant data. The system uses a custom spreadsheet ffonl-end to provide an overview of the asset. BP has reported incremental oil production of 43MBPD due to the use of the daily optimizer, totalling approximately $30 M/year in benefits.

3. The O p e n S i m u l a t i o n E n v i r o n m e n t ( O S E ) The above value-creation opportunities can be made available to all companies by creating a more productized, configurable and scalable simulation and modelling

1672 environment that is based on open standards. The single open environment will also meet the challenges that engineers face in today's changing industry and technology landscape, by: • Bringing all of their disparate tools together and creates a common end-user experience • Enabling the seamless interoperability of multiple modelling applications, allowing disparate teams of engineers to work simultaneously on different parts of the same problem • Enabling the use of consistent models across the operations lifecycle, from engineering and innovation, to plant operations, to supply chain management. As the leader in providing engineering applications for Front End Engineering and Design (FEED), plant operations and supply chain management for the process industries, AspenTech is spearheading the effort to provide this open environment to the process industries.

3.1 Open Simulation Environment (OSE) OSE is AspenTech's initial step in delivering a common experience for traditional process simulation and modelling. OSE will enable expert applications to be easily applied in a plant operations environment, bringing the various engineering disciplines together over time so users can collaborate more effectively and leverage their expertise across engineering and operational disciplines into the plant. 3 . 1 . 1 0 S E Capabilities

OSE extends the value of models across the enterprise through the following five key capabilities as described below, and as shown pictorially in Figure 1:

Figure 2. The Open Simulation Environment

Model interoperability • Integration "plugs" for AspenTech, third-party, and in-house models • The Aspen Simulation Interface (ASI), an interface standard for integration • Support for CAPE-OPEN and other industry interface standards

1673 •

Model execution

• • • • • • •

Model-based

• • •

analysis

Layered engineering analysis tools, such as equipment design, sizing, and economic analysis Open interfaces to in-house and third-party engineering tools

Model management

• • • •

Combination of first-principles with empirical and/or statistical models Creation of integrated site-wide and asset-wide models representing entire business performance Common asset-wide representation interface Multiple modes of model execution, including sequential, simultaneous (equation-solving) and mixed-modes Updating (synchronizing) of one model type with another, such as planning model updated by simulation model Support for distributed computing

Model repository for accelerating model reuse and central deployment Case comparison utilities Support for model authoring tools

Model deployment

• • •

integration to plant information and automation systems for both off-line and online applications Layered utilities for data validation, steady-state detection, and data reconciliation Configurable end-user interfaces, via Excel or Role-Based Visualization from Aspen Operations Manager

OSE builds on the investments users have made in their existing models, and allows them to gain considerably greater value from these models by deploying them to address a wider range of business problems. As a long-term objective, OSE will incorporate planning and supply chain modelling to enable consistent decision making across the engineering, operations and business domains. The table below reflects the paradigm changes anticipated as a result of OSE. Table 1. Paradigm changes expected as a result o f OSE

From

To Models for operational decision Models tbr process design and support and asset-wide decision engineering making, a n d process design and engineering integrated models incorporating firstFirst-principles-only models principles, empirical, and statistical models Models of a single plant Integrated site-wide models

1674 Single point optimization

Scenario optimization over extended time periods

4. C o n c l u s i o n s

At the dawn of the 21st Century, the engineering community is undergoing rapid change. The lines between traditional engineering disciplines are blurring, requiring engineers to be proficient in a dozen or more technical computing applications to perform his/her job professionally across several of fields of expertise. The net result of is that the engineer is getting pulled deeper and deeper into the business of operations. The Open Simulation Environment is a critical component by which the engineer of the 21st century will provide greater value-added, utilizing any of the technical modelling tools required to perform his/her job, with potential impact on the business of: • More efficient deployment of capital by 15-20% • 10-15% reduction in energy and environment related expenses • 1-5% increase in operating margin • Double engineering productivity over the next decade: CAPEX and OPEX in the process industries are increasing at a much higher rate than the engineering workforce. Engineering productivity will thus need to double in the next decade when measured in CAPEX/OPEX dollars vs. engineering person-hours. OSE is the manifestation of model centricity for the process industries, enabling the interdisciplinary collaboration necessary for the engineering and operations community to effectively deploy CAPEX and OPEX investments in an optimal manner. References McGrath, P, 2004, Reaping Value from Offline Process Models in Plant Operations, AspenWorld 2004, Orlando, Florida. Lee, Y.G., 2002, Asset Optimization: A Better Approach for Energy Saving and Capacity Increase, AspenWorld 2002, Washington, DC. Stenhouse, B, 2000, The BP Harding Daily Optimizer, Hyprotech 2000, Amsterdam, The Netherlands. Acknowledgements The authors wish to acknowledge the help of Vikas Dhole, Michael Evans, Boyd Gochenour, Bill Mock and Robin Swanger in writing this manuscript.

1675

Author Index Abdelhady, A.F., Abildskov, J., Abonyi, J., Adhitya, A., Adjiman, C.S., Agachi, S., 1363, Agar, D.W., Aguado, R., Aguiar, H.C., Aguilar, O., Aguirre, P.A., Abroad, B.M., Ahmadpour, M., A'l'touche, A., Aittamaa, J., Ajah, A.N., AI-Arfaj, M.A., Alawi, A., Aldea, A., Alexopoulos, A.H.,

1609 217 667 985 1651 1435 673 613 CD 907 553 1279 451 1471 709 781 811 1459 1549 319, 433 Alfadala, H.E., 1279 Alhamad, B., 1495 Alhammadi, H.Y., CD Allg6wer, F., 1363 Alonso, A.A., 37, 121, 1105, 1333 Alsop, N.J., 1009 Alva, T., 109 Alvarez, S., 613 Alves, R. M.B., 211 Amaro, A. C.S., 1171 Androulakis, I.P., 235, 577 Antelo, L.T., 1105 Arbiza, M.J., 1381 Arellano-Garcia, H., 967 Arizmendi-Sfinchez, J. A., 901 Arora, S., 1255 Arruda, L. V.R., 1027 Arva, P., 667 Ashley, V.M., 175 Asprey, S.P., 307 Atasoy, I., 631 Attarakih, M.M., 163

Avramenko, Y., Azzaro-Pantel, C., Badell, M., Baeza, J., Bagajewicz, M.,

697 49 1663 475 I135, 1177 Bahri, P.A., 991, 1111, 1585 Baird, R.J., 1009 Bakogovfi, M., 1303 Balaguer, M.D., 1291 Baldea, M., 973 Balsa-Canto, E., 121, 1333 Bandoni, A., 1267 Bandyopadhyay, S., 751 Banerjee, I., 85,247 Banga, J.R., 37, 121, 1105, 1333 Bansal, M., 985 Bafiares-Alcantara, R., 787, 1345, 1549 Baptiste, P., 1633 Baquerizo, G., 33 7 Barbosa-P6voa, A. P., 1075, 1171, 1213 Barendregt, S., 241 Barkve, T., 169 Barnes, R., 679 Barolo, M., 1201 Bart, H.-J., 163 Barton, P.I., 133, 1093 Barz, T., 967 Basualdo, M., 1465 Batres, R., 1543 Baudet, P., 1081 Baudouin, O., 1081 Bedenik, N.I., 943 Beheshti, N., 139 Belaud, J.P., 607 Beliaev, S., 883 Belincanta, J., CD Bell, G., 733 Bellows, M.L., 115 Berber, R., 631 Bernardo, F.P., 1507 Bezzo, F., 1201

Biagiola, S.I., Biegler, L.T., Bieler, P., Bilbao, J., Bildea, C.S.,

1267 67 817 613 637, 769, 1525 Bindal, A., 193 Biscaia Jr., E.C., 151 Blanco, A.M., 1273 Bogle, I. D.L., 265 Bonet, J., 97 Bonfill, A., 1057, 1381 Bonvin, D., 1417 Bousquet, J., 319 Bouwmans, I., 997 Boyarinov, A. II., 385 Bozzano, G., 529 Brad, R.B., 229, 373 Braithwaite, M., 355 Brauner, N., 109,277 Bringas, g., 649 Broto, F., 799 Brown, D., 1153 BrOggemann, S., 757 Brusdal, K., 169 Bulatov, I., 295 Bumbac, G., 655 Butch, T.E., 1615 Burghofl; S., 103 Burluka, A.A., 139 Busch, J., 955 Caballero, J.A., 715 Cabassud, M., 1417 Cafaro, D.C., 1453 Cameron, I.T., 3,265, 481,535, 1111 Cano, J., 1399 Cfirdenas, J. C., 1483 Camero, M. C., 1447 Carrasco, E. F., 181 Carrera, J., 475 Casas, C., 475 Castellano, M., 1327 Castro, P. M., 1213 Cauikin, R., 367 Cerdfi, J., 1453

1676 Cesca, M.R., 1243 Cdzac, P., 799 Chachuat, B., 133, 1093 Chert, B.H., 1009 Chew, R., 1495 Chiu, M.-S., 1411 Cholakov, G., 277 Christina, T.S., 1357 Cifuentes, F., 1099 Ciornei, C., 655 Cisternas, L.A., 403 Cockerill, T., 295 Coimbra, M.C., 79 Colomer, J., 1291 Colprim, J., 1291 Conlin, A., 1597 Constantinidis, D., 1525 Cormos, C., 1435 Corominas, LI., 1291 Corvalfin, S.M., 853, 931 Costa, J., 97 Couenne, F., 625 Cruse, A., 955 Csendes, T., 661 Cummings, R.M., 1609 Cust6dio, A.F., 1441 Cutlip, M.B., 109 Czuczai, B., 889 Dai, W., 469 Dalaouti, N., 1525 d'Anterroches, L., 643 Daoutidis, P., 973 Davis, E., 193 Dente, M., 241,529 Deshmukh, B.F., 751 Dimian, A.C., 637 Disli-Uslu, I., 1423 Diwekar, U.M., 691 Domenech, S., 49 Dompazis, G., 427 Dua, P., 1015 Dua, V., 1015, 1249 Duefias Diez, M., 169 Duev, S.I., 385 Duque, D., 505 Durham, R.J., 493 Eberard, D., 625 Eden, M.R., 1609, 1615 Elgue, S., 1417 Eliceche, A.M., 853,931

Eljack, F.T., 1609 Emhamed, A.M., 877 Emmerich, M., 187 Engell, S., 187, 1033, 1255 English, P., 1597 Escott, R. E.A., 1141 Espasa, M.L., 1489 Espinosa, J., 757 Espufia, A., 1057, 1183, 1369, 1405, 1555, 1663 Evensen, G., 169 Faber, R., 415 Fairweather, M., 139, 229, 367,373,379 Faqir, N.M., 163 Farkas, T., 877, 889, 1069 Fell, B., 667 Feng, Z.P., 1009 Fernandes, J., 589 Fernandes, M.C., 685 Fernholz, G., 1525 Ferrer-Nadal, S., 961 Figueroa, J.L., 1267 Filho, R. M., 73, 199, 559, 565, 1441, CD Fischer, U., 817 Floquet, P., 211 Flores, X., 787 Flores-Tlacuahuac, A., 67, 745 Floudas, C.A., 1051 Folic, M., 1651 Fonyo, Z., 661,877, 889, 895, 1069 Fortunato, M. R.C., 1477 Fraga, E.S., 265 Franceschini, G., 349 Fraser, D.M., 877 Frausto-Hernfindez, S., 691 Frits, E.R., 661 Fuchino, T., 1237 Fuentes, M., 553 Furenes, B., 1339 Gabriel, D., 337 Gadalla, M., 805 Ghaeli, M., 991 Galan, M.I., 97 Gfilvez, E.D., 403

Gamisans, X., 337 Gangadwala, J., 847 Gani, R., 2 l, 439, 643, 733,841, 1519 Gao, Y., 1387 Garcia, M.G., 121 Garcia, M.R., 1333 Garea, A., 253 Garyulo, L., 1465 Georgiadis, M.C., 763, 1525 Gerbaud, V., 895, 1081 Gesthuisen, R., 1255 Ghafelebashi Zarand, S. M., CD Ghraizi, R.A., 1099 Gibert, F.B., 1489 Gimeno, L., 1225 Ginkel, M., 223 Ginsberg, T., 361 Glavi6, P., 343 Goel, V., 55 Gomes, V.G., 1495 Gomes Salema, M. I., 1075 G6mez, J.M., 925 Gdmez-Martinez, B., 457 Gonnet, S., 1231 Gonzfilez, A.H., 979 Gonzfilez, W., 1327 Goyal, V., 61 Gozfilvez-Zafrilla, J. M., 457 Graells, M., 949, 961 Gr6n, U., 511 Grievink, J., 769, 781, 1525 Griffiths, J.F., 229, 373 Grossmann, I.E., 55,649, 715,829 Grtinewald, M., 673 Guardiola Soler, J., 43 Gudi, R.D., 1621 Guhe, S.Y., 397 Guill6n, G., 1555, 1663 Guisasola, A., 475 Gut, J. A.W., 919 Hack, K., 361 H~ifele, M., 1423 HaYt, A., 1633

1677 Halim, I., 1513 Hangos, K.M., 535 Harper, P., 1525 Hass, V.C., 289 Haus, U.-U., 847 Heijnen, P., 997 Henning, G., 1231 Herder, P.M., 781 Herdes, C., 505 Hemfindez, J.L., 1447 Hernfindez, S., 1483 Hernfindez-Castro, S., 691 Heyen, G., 1153 Hiden, H., 1597 Hori, E.S., 1219 Hormozdi, Sh., CD Hostrup, M., 1525 Hourigan, J.A., 493 Hoyer, M., 1603 Huang, H., 229 Huepen, B., 1525 Hugo, A., 127 Hulle, S. Van, 1297 Hungerbfihler, K., 817 Hurme, M., 1639 Hum, J.P., 379 Ierapetritou, M. G., 61, 85, 193,247 Ingram, G.D., 481 Irabien, J.A., 253 Ivanov, B.B., 1183 Jain, A., 1561 Jallut, C., 625 Janak, S.L., 1051 Jansens, P.J., 805 Jara, J.A., 253 Jeffkins, P., 1393 Jensa, A.V., 1657 Jensen, J.B., 1429 Je2owski, J.M., 727 Jia, X., 367 Jiang, Y., 835 Jimdnez, F., 619 Jimdnez Esteller, L., 787, 1345, 1465, 1549 Jobson, M., 1525 Joensuu, I., 301 Joglekar, G., 1561 Johnston, J., 1615 Jones, I., 1069

Jorgensen, S.B.,

1147, 1351 Joulia, X., 211,895, 1081 Juuso, E., 301 Kafarov, V., 619 Kahrs, O., 595 Kalmukale, A.G., 1411 Kanellopoulos, V., 427 Kangas, M., 1531 Kapadi, M.D., 1621 Karhela, T., 1639 Karimi~ I.A., 985, 1165 Karpunina, M.I., 547 Kasiri, N., CD Katsanevakis, J., 1525 Kenig, E.Y., 103, 331, 1525 Kerasidis, C., 1525 Kheawhom, S., 145 Kienle, A., 223,847, 1423 Kikkinides, E.S., 763 Kim, J.-K., 907 Kind, M., 547 Kiparissides, C., 319,427, 433 Kipling, K., 1129 Kiss, A.A., 637 Kittisupakorn, P., 145 Klein, A., 721 Klemeg, J., 295, 1525 Knudsen, J., 1147 Kokossis, A., 679, 1345, 1387 Koltsova, E. M., 547, 601, 1657 Kondili, E., 1627 Kontoravdi, C., 307 Kostutchenko, V. V., 1657 Koulouris, A., 1045 Kova¢? Kralj, A., 343 Kovacs, T., 1069 Kraslawski, A., 697, 823, 883 Krasnyk, M., 223 Kravanja, Z., 91,943 Krishna, V.M., 1423 Krysiak, W., 697 Kubi~ek, M., 1207 Kuhnen, F., 289 Kumar, V., 391

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